Daily Papers

Transparent objects are common in daily life, and understanding their multi-layer depth information -- perceiving both the transparent surface and the objects behind it -- is crucial for real-world applications that interact with transparent materials. In this paper, we introduce LayeredDepth, the first dataset with multi-layer depth annotations, including a real-world benchmark and a synthetic data generator, to support the task of multi-layer depth estimation. Our real-world benchmark consists of 1,500 images from diverse scenes, and evaluating state-of-the-art depth estimation methods on it reveals that they struggle with transparent objects. The synthetic data generator is fully procedural and capable of providing training data for this task with an unlimited variety of objects and scene compositions. Using this generator, we create a synthetic dataset with 15,300 images. Baseline models training solely on this synthetic dataset produce good cross-domain multi-layer depth estimation. Fine-tuning state-of-the-art single-layer depth models on it substantially improves their performance on transparent objects, with quadruplet accuracy on our benchmark increased from 55.14% to 75.20%. All images and validation annotations are available under CC0 at https://layereddepth.cs.princeton.edu.

Sparse autoencoder (SAE) features are used to interpret and steer large language models, yet whether a feature's causal role is stable across SAE families remains untested. Single-token features that activate on one vocabulary item provide the diagnostic case where ground truth permits direct comparison. We analyze 3.9M features across six models and three SAE families using zero-ablation at full layer depth. Single-token features cluster 4.7x tighter in decoder space and concentrate in early layers (Layer 0 in GPT2-Small; L0-L4 in Gemma). Ablating them yields Benjamini-Hochberg-significant logit reductions in 178 of 208 full-layer conditions, with depth controlling whether damage cascades downstream or shapes the output directly. Cross-family causal differences exceed within-family scale effects: on the same base model, GemmaScope and BatchTopK features remain causally anchored, while LlamaScope features are locally redundant. The target token's rank recovers to within 2x baseline 96-98% of the time after the same ablation, and a controlled activation-function comparison reverses sign within the same model, leaving training recipe as the residual candidate. Cross-family interpretability claims are therefore sensitive to training methodology, not just activation function or scale.

Accurately modeling soft boundaries, e.g., hair and defocus blur, is a fundamental challenge in stereo conversion due to the ambiguous blending of foreground and background. Existing depth models primarily predict single-layer depth, leading to ambiguity in depth correspondence at soft boundaries. While matting techniques can capture opacity for layered modeling, they often struggle in complex scenes with multiple targets and usually require user intervention. This paper introduces αDepth, a layered representation that decomposes soft boundaries for high-fidelity stereo conversion. Specifically, we first resolve mixed color and depth ambiguity by estimating layered color and depth values at soft boundaries. Considering complex multi-target scenes, we design a Circular Alpha Representation (CAR) that shifts the paradigm from global target extraction to local boundary decomposition. Unlike prior matting methods restricted to a single foreground/background, CAR enables efficient scene-level inference without manual guidance. Extensive evaluations demonstrate that αDepth achieves state-of-the-art performance in stereo conversion, eliminating background bleeding and structural distortions at soft boundaries.

Fine-tuning pre-trained models has become the standard approach to endow them with specialized knowledge, but it poses fundamental challenges. In particular, (i) fine-tuning often leads to catastrophic forgetting, where improvements on a target domain degrade generalization on other tasks, and (ii) merging fine-tuned checkpoints from disparate tasks can lead to significant performance loss. To address these challenges, we introduce LiNeS, Layer-increasing Network Scaling, a post-training editing technique designed to preserve pre-trained generalization while enhancing fine-tuned task performance. LiNeS scales parameter updates linearly based on their layer depth within the network, maintaining shallow layers close to their pre-trained values to preserve general features while allowing deeper layers to retain task-specific representations. In multi-task model merging scenarios, layer-wise scaling of merged parameters reduces negative task interference. LiNeS demonstrates significant improvements in both single-task and multi-task settings across various benchmarks in vision and natural language processing. It mitigates forgetting, enhances out-of-distribution generalization, integrates seamlessly with existing multi-task model merging baselines improving their performance across benchmarks and model sizes, and can boost generalization when merging LLM policies aligned with different rewards via RLHF. Our method is simple to implement, computationally efficient and complementary to many existing techniques. Our source code is available at https://github.com/wang-kee/LiNeS

In this paper, we introduce the Curse of Depth, a concept that highlights, explains, and addresses the recent observation in modern Large Language Models(LLMs) where nearly half of the layers are less effective than expected. We first confirm the wide existence of this phenomenon across the most popular families of LLMs such as Llama, Mistral, DeepSeek, and Qwen. Our analysis, theoretically and empirically, identifies that the underlying reason for the ineffectiveness of deep layers in LLMs is the widespread usage of Pre-Layer Normalization (Pre-LN). While Pre-LN stabilizes the training of Transformer LLMs, its output variance exponentially grows with the model depth, which undesirably causes the derivative of the deep Transformer blocks to be an identity matrix, and therefore barely contributes to the training. To resolve this training pitfall, we propose LayerNorm Scaling, which scales the variance of output of the layer normalization inversely by the square root of its depth. This simple modification mitigates the output variance explosion of deeper Transformer layers, improving their contribution. Our experimental results, spanning model sizes from 130M to 1B, demonstrate that LayerNorm Scaling significantly enhances LLM pre-training performance compared to Pre-LN. Moreover, this improvement seamlessly carries over to supervised fine-tuning. All these gains can be attributed to the fact that LayerNorm Scaling enables deeper layers to contribute more effectively during training.

Recent feed-forward reconstruction models like VGGT and π^3 achieve impressive reconstruction quality but cannot process streaming videos due to quadratic memory complexity, limiting their practical deployment. While existing streaming methods address this through learned memory mechanisms or causal attention, they require extensive retraining and may not fully leverage the strong geometric priors of state-of-the-art offline models. We propose LASER, a training-free framework that converts an offline reconstruction model into a streaming system by aligning predictions across consecutive temporal windows. We observe that simple similarity transformation (Sim(3)) alignment fails due to layer depth misalignment: monocular scale ambiguity causes relative depth scales of different scene layers to vary inconsistently between windows. To address this, we introduce layer-wise scale alignment, which segments depth predictions into discrete layers, computes per-layer scale factors, and propagates them across both adjacent windows and timestamps. Extensive experiments show that LASER achieves state-of-the-art performance on camera pose estimation and point map reconstruction %quality with offline models while operating at 14 FPS with 6 GB peak memory on a RTX A6000 GPU, enabling practical deployment for kilometer-scale streaming videos. Project website: https://neu-vi.github.io/LASER/{https://neu-vi.github.io/LASER/}

Graph clustering discovers groups or communities within networks. Deep learning methods such as autoencoders (AE) extract effective clustering and downstream representations but cannot incorporate rich structural information. While Graph Neural Networks (GNN) have shown great success in encoding graph structure, typical GNNs based on convolution or attention variants suffer from over-smoothing, noise, heterophily, are computationally expensive and typically require the complete graph being present. Instead, we propose Self-Supervised Contrastive Graph Clustering (SCGC), which imposes graph-structure via contrastive loss signals to learn discriminative node representations and iteratively refined soft cluster labels. We also propose SCGC*, with a more effective, novel, Influence Augmented Contrastive (IAC) loss to fuse richer structural information, and half the original model parameters. SCGC(*) is faster with simple linear units, completely eliminate convolutions and attention of traditional GNNs, yet efficiently incorporates structure. It is impervious to layer depth and robust to over-smoothing, incorrect edges and heterophily. It is scalable by batching, a limitation in many prior GNN models, and trivially parallelizable. We obtain significant improvements over state-of-the-art on a wide range of benchmark graph datasets, including images, sensor data, text, and citation networks efficiently. Specifically, 20% on ARI and 18% on NMI for DBLP; overall 55% reduction in training time and overall, 81% reduction on inference time. Our code is available at : https://github.com/gayanku/SCGC

Understanding the internal mechanisms of large audio-language models (LALMs) is crucial for interpreting their behavior and improving performance. This work presents the first in-depth analysis of how LALMs internally perceive and recognize auditory attributes. By applying vocabulary projection on three state-of-the-art LALMs, we track how attribute information evolves across layers and token positions. We find that attribute information generally decreases with layer depth when recognition fails, and that resolving attributes at earlier layers correlates with better accuracy. Moreover, LALMs heavily rely on querying auditory inputs for predicting attributes instead of aggregating necessary information in hidden states at attribute-mentioning positions. Based on our findings, we demonstrate a method to enhance LALMs. Our results offer insights into auditory attribute processing, paving the way for future improvements.

Mechanistic interpretability reverse-engineers transformer circuits one input at a time, leaving observed mechanisms without guarantees over bounded input neighbourhoods. We address this gap with a framework based on constrained polynomial-zonotope (CPZ) propagation that lifts mechanistic-interpretability observations from a single input to certified statements over a bounded set of perturbations. Three internal-attention queries (top-k stability, evidence mass, and attention entropy) are formulated as tractable programs over the simplex of attention weights, and CPZ propagation through transformer blocks is shown to preserve the softmax simplex and the LayerNorm zero-mean identity exactly. A recursive Jacobian zonotope construction extends the same certificates across layer depth by linearising the block stack at the input and avoids per-layer generator growth. We instantiate the framework on transformer attention; the resulting certificates offer a way to sharpen mechanistic statements that single-input inspection cannot resolve on its own, and to inform downstream decisions in regimes where empirical heuristics may be misleading.

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

While Diffusion Transformers (DiTs) have achieved breakthroughs in video generation, this long sequence generation task remains constrained by the quadratic complexity of attention mechanisms, resulting in significant inference latency. Through detailed analysis of attention maps in Video Diffusion Transformer (vDiT), we identify three recurring sparsity patterns: diagonal, multi-diagonal, and vertical-stripe structures. And even 3-6\% attention heads can be skipped. Crucially, these patterns exhibit strong layer-depth and head-position correlations but show limited dependence on the input content. Leveraging these findings, we propose Sparse-vDiT, a sparsity acceleration framework for vDiT comprising: 1) Pattern-optimized sparse kernels that replace dense attention with computationally efficient implementations for each identified sparsity pattern. 2) An offline sparse diffusion search algorithm that selects the optimal sparse computation strategy per layer and head via hardware-aware cost modeling. After determining the optimal configuration, we fuse heads within the same layer that share the same attention strategy, enhancing inference efficiency. Integrated into state-of-the-art vDiT models (CogVideoX1.5, HunyuanVideo, and Wan2.1), Sparse-vDiT achieves 2.09times, 2.38times, and 1.67times theoretical FLOP reduction, and actual inference speedups of 1.76times, 1.85times, and 1.58times, respectively, while maintaining high visual fidelity, with PSNR values reaching 24.13, 27.09, and 22.59. Our work demonstrates that latent structural sparsity in vDiTs can be systematically exploited for long video synthesis.

Large language models (LLMs) are known to hallucinate, a phenomenon often linked to creativity. While previous research has primarily explored this connection through theoretical or qualitative lenses, our work takes a quantitative approach to systematically examine the relationship between hallucination and creativity in LLMs. Given the complex nature of creativity, we propose a narrow definition tailored to LLMs and introduce an evaluation framework, HCL, which quantifies Hallucination and Creativity across different Layers of LLMs during decoding. Our empirical analysis reveals a tradeoff between hallucination and creativity that is consistent across layer depth, model type, and model size. Notably, across different model architectures, we identify a specific layer at each model size that optimally balances this tradeoff. Additionally, the optimal layer tends to appear in the early layers of larger models, and the confidence of the model is also significantly higher at this layer. These findings provide a quantitative perspective that offers new insights into the interplay between LLM creativity and hallucination. The code and data for our experiments are available at https://github.com/ZicongHe2002/HCL-Spark.

Vision-language models are known to encode spatial information in their hidden states, yet often fail to use it when answering. However, it remains unclear when and where this encoded information reaches the answer. We address this with direction patching, a class-conditioned causal intervention applied across layers, token positions, and prompt formats. Using spatial-ID directions constructed following prior encoding evidence, we find that causal influence on answer logits emerges only at mid-to-deep depths. Text chain-of-thought suppresses immediate object-word argmax-level transport in most models, while visually grounded prompts keep it open. Positive target-logit gain can remain below the argmax threshold, and transport can re-emerge at the final prefix token or at the answer step in deeper layers. Across the ten VLMs we study, these local effects form descriptive transport patterns. Complementary experiments characterize how these patterns shift across datasets, attributes, and encoding amplitudes. Together, these results reframe the encoding-grounding gap as a problem of conditional transport in VLMs.

High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNNs evaluation. Experimental results show that SSL achieves on average 5.1x and 3.1x speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%, which is still slightly higher than that of original ResNet with 32 layers. For AlexNet, structure regularization by SSL also reduces the error by around ~1%. Open source code is in https://github.com/wenwei202/caffe/tree/scnn

We show that introducing a weighting factor to reduce the influence of identity shortcuts in residual networks significantly enhances semantic feature learning in generative representation learning frameworks, such as masked autoencoders (MAEs) and diffusion models. Our modification notably improves feature quality, raising ImageNet-1K K-Nearest Neighbor accuracy from 27.4% to 63.9% and linear probing accuracy from 67.8% to 72.7% for MAEs with a ViT-B/16 backbone, while also enhancing generation quality in diffusion models. This significant gap suggests that, while residual connection structure serves an essential role in facilitating gradient propagation, it may have a harmful side effect of reducing capacity for abstract learning by virtue of injecting an echo of shallower representations into deeper layers. We ameliorate this downside via a fixed formula for monotonically decreasing the contribution of identity connections as layer depth increases. Our design promotes the gradual development of feature abstractions, without impacting network trainability. Analyzing the representations learned by our modified residual networks, we find correlation between low effective feature rank and downstream task performance.

Training large foundation models from scratch for domain-specific applications is almost impossible due to data limits and long-tailed distributions -- taking remote sensing (RS) as an example. Fine-tuning natural image pre-trained models on RS images is a straightforward solution. To reduce computational costs and improve performance on tail classes, existing methods apply parameter-efficient fine-tuning (PEFT) techniques, such as LoRA and AdaptFormer. However, we observe that fixed hyperparameters -- such as intra-layer positions, layer depth, and scaling factors, can considerably hinder PEFT performance, as fine-tuning on RS images proves highly sensitive to these settings. To address this, we propose MetaPEFT, a method incorporating adaptive scalers that dynamically adjust module influence during fine-tuning. MetaPEFT dynamically adjusts three key factors of PEFT on RS images: module insertion, layer selection, and module-wise learning rates, which collectively control the influence of PEFT modules across the network. We conduct extensive experiments on three transfer-learning scenarios and five datasets in both RS and natural image domains. The results show that MetaPEFT achieves state-of-the-art performance in cross-spectral adaptation, requiring only a small amount of trainable parameters and improving tail-class accuracy significantly.

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Large language models (LLMs) demonstrate proficiency across numerous computational tasks, yet their inner workings remain unclear. In theory, the combination of causal self-attention and multilayer perceptron layers allows every token to access and compute information based on all preceding tokens. In practice, to what extent are such operations present? In this paper, on mental math tasks (i.e., direct math calculation via next-token prediction without explicit reasoning), we investigate this question in three steps: inhibiting input-specific token computations in the initial layers, restricting the routes of information transfer across token positions in the next few layers, and forcing all computation to happen at the last token in the remaining layers. With two proposed techniques, Context-Aware Mean Ablation (CAMA) and Attention-Based Peeking (ABP), we identify an All-for-One subgraph (AF1) with high accuracy on a wide variety of mental math tasks, where meaningful computation occurs very late (in terms of layer depth) and only at the last token, which receives information of other tokens in few specific middle layers. Experiments on a variety of models and arithmetic expressions show that this subgraph is sufficient and necessary for high model performance, transfers across different models, and works on a variety of input styles. Ablations on different CAMA and ABP alternatives reveal their unique advantages over other methods, which may be of independent interest.

Ensembles of neural network weight matrices are studied through the training process for the MNIST classification problem, testing the efficacy of matrix models for representing their distributions, under assumptions of Gaussianity and permutation-symmetry. The general 13-parameter permutation invariant Gaussian matrix models are found to be effective models for the correlated Gaussianity in the weight matrices, beyond the range of applicability of the simple Gaussian with independent identically distributed matrix variables, and notably well beyond the initialisation step. The representation theoretic model parameters, and the graph-theoretic characterisation of the permutation invariant matrix observables give an interpretable framework for the best-fit model and for small departures from Gaussianity. Additionally, the Wasserstein distance is calculated for this class of models and used to quantify the movement of the distributions over training. Throughout the work, the effects of varied initialisation regimes, regularisation, layer depth, and layer width are tested for this formalism, identifying limits where particular departures from Gaussianity are enhanced and how more general, yet still highly-interpretable, models can be developed.

The subpolar gyre is at risk of crossing a tipping point under future climate change associated with the collapse of deep convection. As such tipping can have significant climate impacts, it is important to understand the mechanisms at play and how they are represented in modern climate models. In this study we use causal inference to investigate the representation of several proposed mechanisms of subpolar gyre variability in CMIP6 models. As expected, an increase in sea surface salinity or a decrease in sea surface temperature leads to an increase in mixed layer depth in nearly all CMIP6 models due to an intensification of deep convection. However, the effect of convection to modify sea surface temperature due to re-stratification is less clear. In most models the deepening of the mixed layer caused by an increase of sea surface salinity, does result in a cooling of the water at intermediate depths. The feedback from the subsurface temperature through density to the strength of the subpolar gyre circulation is more ambiguous, with fewer models indicating a significant link. Those that do show a significant link, do not agree on its sign. The CMIP6 models that have the expected sign for the links from density to the subpolar gyre strength and on to sea surface salinity, are also the models in which abrupt shifts in the subpolar gyre region have been found in climate change scenario runs. One model (CESM2) contains all proposed mechanisms, with both a negative and delayed positive feedback loop being significant.

The extensive need for computational resources poses a significant obstacle to deploying large-scale Deep Neural Networks (DNN) on devices with constrained resources. At the same time, studies have demonstrated that a significant number of these DNN parameters are redundant and extraneous. In this paper, we introduce a novel approach for learning structured sparse neural networks, aimed at bridging the DNN hardware deployment challenges. We develop a novel regularization technique, termed Weighted Group Sparse Envelope Function (WGSEF), generalizing the Sparse Envelop Function (SEF), to select (or nullify) neuron groups, thereby reducing redundancy and enhancing computational efficiency. The method speeds up inference time and aims to reduce memory demand and power consumption, thanks to its adaptability which lets any hardware specify group definitions, such as filters, channels, filter shapes, layer depths, a single parameter (unstructured), etc. The properties of the WGSEF enable the pre-definition of a desired sparsity level to be achieved at the training convergence. In the case of redundant parameters, this approach maintains negligible network accuracy degradation or can even lead to improvements in accuracy. Our method efficiently computes the WGSEF regularizer and its proximal operator, in a worst-case linear complexity relative to the number of group variables. Employing a proximal-gradient-based optimization technique, to train the model, it tackles the non-convex minimization problem incorporating the neural network loss and the WGSEF. Finally, we experiment and illustrate the efficiency of our proposed method in terms of the compression ratio, accuracy, and inference latency.

Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the orthonormalization with the Newton--Schulz (NS) iteration. Since NS is only approximate, directions with small singular values fail to be orthonormalized. In Muon, NS is applied to the momentum matrix at every step, yet little is known about how the singular value spectrum of these momentum matrices behaves during training, or how that behavior changes with model size. We present the first systematic study of this question. Tracking singular value quantiles of the momentum buffer across layers in models ranging from 77M to 2.8B parameters, we observe a consistent picture: after a short burn-in, the quantiles stabilize at a value determined by the layer type and model size. These stabilization values follow remarkably clean power laws in model size, with layer-dependent exponents. Layers up to mid-late depth scale very mildly with model size M (around M^{-0.25}), so the standard 5-step NS configuration used at academic scale will continue to orthonormalize them at much larger scales. Some of the late layers, however, scale much more aggressively (up to M^{-0.96}) and will fall into the NS failure regime at frontier scale unless one uses more NS iterations or better-tuned coefficients. NS iterations are computationally expensive at scale; our laws give practitioners a principled, layer-aware recipe for choosing the minimum NS configuration that still orthonormalizes the directions that matter -- avoiding unnecessary computation without sacrificing update quality.

Multilingual language models can solve the same mathematical problem in different languages, but it remains unclear whether they rely on shared features or on language-specific computations that only produce similar outputs. We study this question in five models from four families using the Multilingual Grade School Math (MGSM) dataset, with problems solved in English, German, French, Spanish, Russian, and Chinese, retaining problems with valid reasoning traces in all six languages and replaying those traces through the model to record representations at multiple layers. For each model, we first use Centered Kernel Alignment (CKA) to identify layers with cross-language alignment. At each selected layer, we train two sparse autoencoders (SAE): a baseline reconstruction-only model and a contrastive variant introduced in this work, the Geometry-Invariant SAE (GI-SAE). GI-SAE supplements the reconstruction loss with an Information Noise-Contrastive Estimation (InfoNCE) loss that trains the encoder to produce similar activations for traces of the same problem, regardless of language or token position. We then test whether the resulting shared features are functionally interchangeable by swapping their values between languages during the model's forward pass and measuring the resulting change in output, quantified by Kullback-Leibler (KL) divergence per feature. Although GI-SAE yields higher CKA and Jaccard similarity at nearly every layer, higher geometric similarity does not consistently imply greater functional interchangeability. We find that cross-language feature sharing is model- and architecture-dependent in this sample and appears at different depths in different models. GI-SAE primarily amplifies cross-language structure already present: the pattern is model-specific, with strengthening in Qwen, no functional benefit in Gemma, and mixed layer-dependent effects in Llama and Phi.

Reinforcement Learning from Verifiable Rewards (RLVR) has become the dominant approach for improving mathematical reasoning in large language models, yet current methods reduce each correct rollout to a single reward bit, ignoring the geometric structure shared among their hidden states. Investigating this structure, we find that at the anchor token (the position immediately before the answer marker), correct rollouts converge naturally because they must produce the same answer (cosine similarity ~0.84), yet each retains residual variance from its unique reasoning path. Encouraging full alignment at this point pushes the model to extract a unified "correct decision" representation, reducing sensitivity to which reasoning path was taken. Based on this observation, we propose Hidden-Align, an auxiliary loss function that aligns the last-layer hidden states of correct rollouts at the anchor token during RL training, with zero overhead in both training and inference. On eight mathematical reasoning benchmarks, Hidden-Align improves average pass@1 over the DAPO baseline by 3.8, 6.2, and 5.4 percentage points on Qwen3-1.7B, 4B, and 14B respectively, with consistent pass@k gains across all three scales, supported by ablations on loss type, anchor position, layer depth, and loss weight.

Transformer architectures have proven to learn useful representations for protein classification and generation tasks. However, these representations present challenges in interpretability. In this work, we demonstrate a set of methods for analyzing protein Transformer models through the lens of attention. We show that attention: (1) captures the folding structure of proteins, connecting amino acids that are far apart in the underlying sequence, but spatially close in the three-dimensional structure, (2) targets binding sites, a key functional component of proteins, and (3) focuses on progressively more complex biophysical properties with increasing layer depth. We find this behavior to be consistent across three Transformer architectures (BERT, ALBERT, XLNet) and two distinct protein datasets. We also present a three-dimensional visualization of the interaction between attention and protein structure. Code for visualization and analysis is available at https://github.com/salesforce/provis.

Currently, many theoretical as well as practically relevant questions towards the transferability and robustness of Convolutional Neural Networks (CNNs) remain unsolved. While ongoing research efforts are engaging these problems from various angles, in most computer vision related cases these approaches can be generalized to investigations of the effects of distribution shifts in image data. In this context, we propose to study the shifts in the learned weights of trained CNN models. Here we focus on the properties of the distributions of dominantly used 3x3 convolution filter kernels. We collected and publicly provide a dataset with over 1.4 billion filters from hundreds of trained CNNs, using a wide range of datasets, architectures, and vision tasks. In a first use case of the proposed dataset, we can show highly relevant properties of many publicly available pre-trained models for practical applications: I) We analyze distribution shifts (or the lack thereof) between trained filters along different axes of meta-parameters, like visual category of the dataset, task, architecture, or layer depth. Based on these results, we conclude that model pre-training can succeed on arbitrary datasets if they meet size and variance conditions. II) We show that many pre-trained models contain degenerated filters which make them less robust and less suitable for fine-tuning on target applications. Data & Project website: https://github.com/paulgavrikov/cnn-filter-db

Long-context reasoning is a critical capability of large language models (LLMs), enabling applications such as long-document understanding, summarization, and code generation. However, efficient autoregressive inference relies on the key-value (KV) cache, whose memory footprint grows linearly with sequence length, leading to a major memory bottleneck. To mitigate this overhead, KV cache pruning methods discard cached tokens with low attention scores during inference. Most existing methods apply a uniform pruning ratio across layers, implicitly assuming that all layers contribute equally to overall model performance. We show that this assumption is suboptimal, as layers differ significantly in their sensitivity to pruning. We propose DepthKV, a layer-dependent pruning framework that allocates a fixed global KV budget across layers based on their sensitivity, rather than using a uniform allocation. Across multiple models and tasks, DepthKV consistently outperforms uniform pruning at the same global pruning ratio, demonstrating more effective utilization of the KV cache budget through layer-dependent allocation.

Machine learning-based computer-generated holography (ML-CGH) has advanced rapidly in recent years, yet progress is constrained by the limited availability of high-quality, large-scale hologram datasets. To address this, we present KOREATECH-CGH, a publicly available dataset comprising 6,000 pairs of RGB-D images and complex holograms across resolutions ranging from 256*256 to 2048*2048, with depth ranges extending to the theoretical limits of the angular spectrum method for wide 3D scene coverage. To improve hologram quality at large depth ranges, we introduce amplitude projection, a post-processing technique that replaces amplitude components of hologram wavefields at each depth layer while preserving phase. This approach enhances reconstruction fidelity, achieving 27.01 dB PSNR and 0.87 SSIM, surpassing a recent optimized silhouette-masking layer-based method by 2.03 dB and 0.04 SSIM, respectively. We further validate the utility of KOREATECH-CGH through experiments on hologram generation and super-resolution using state-of-the-art ML models, confirming its applicability for training and evaluating next-generation ML-CGH systems.

A faithful 3D world representation should account for layered geometry, where a single camera ray may contain multiple visible and geometrically valid surfaces. Monocular depth estimation, however, reduces this structure to one scalar depth per pixel. Transparent scenes make this ambiguity measurable: the same ray can pass through foreground glass and observe the background, turning the supervised target into a convention of annotation, data, and training rather than a scene-intrinsic truth. A learned predictor exposes this convention as its depth-layer preference. We introduce MultiDepth-3k (MD-3k), a sparse two-layer ordinal benchmark for measuring depth-layer preference and multi-layer spatial relationship accuracy (ML-SRA). On MD-3k, leading depth foundation models exhibit diverse layer preferences under standard RGB input, showing that the same layered geometry can be resolved differently across models. We further find that Laplacian Visual Prompting (LVP), a training-free spectral input transformation, can substantially change the reported layer for certain frozen models. The strongest RGB/LVP pair, DAv2-L, reaches 75.5% ML-SRA. These results suggest that depth foundation models may express complementary geometric hypotheses that standard RGB inference leaves unexpressed. We invite the community to rethink depth supervision and evaluation through an ambiguity-aware lens, where multiple valid 3D interpretations are treated as geometric structure to be measured, preserved, and expressed.

Scaling depth is a key driver for large language models (LLMs). Yet, as LLMs become deeper, they often suffer from signal degradation: informative features formed in shallow layers are gradually diluted by repeated residual updates, making them harder to recover in deeper layers. We introduce mixture-of-depths attention (MoDA), a mechanism that allows each attention head to attend to sequence KV pairs at the current layer and depth KV pairs from preceding layers. We further describe a hardware-efficient algorithm for MoDA that resolves non-contiguous memory-access patterns, achieving 97.3% of FlashAttention-2's efficiency at a sequence length of 64K. Experiments on 1.5B-parameter models demonstrate that MoDA consistently outperforms strong baselines. Notably, it improves average perplexity by 0.2 across 10 validation benchmarks and increases average performance by 2.11% on 10 downstream tasks, with a negligible 3.7% FLOPs computational overhead. We also find that combining MoDA with post-norm yields better performance than using it with pre-norm. These results suggest that MoDA is a promising primitive for depth scaling. Code is released at https://github.com/hustvl/MoDA .

Self-attention gives LLMs fine-grained, query-dependent access to context, but dense token interactions incur quadratic prefill cost and a key--value cache growing with context length. Research thus spans explicit-memory compression, sparse access, recurrent state construction, structured state dynamics, and heterogeneous mechanism composition. This survey analyzes these developments as model-internal contextual memory. We introduce a five-dimensional lens---Memory Representation, Memory Update, Access, Readout, and Integration---describing what is represented, how it changes, what is query-eligible, how it is read, and how readouts form outputs. This lens compares overlapping research lines without imposing one computational model. We reconstruct mechanism-level developments and architectural adoption using 59 release-level records from 14 major model lineages and 11 high-performing open-weight endpoints. First, explicit-memory and recurrent-state methods retain distinct interfaces but increasingly control overlapping memory functions. Second, heterogeneous architectures increasingly coordinate across network depth: layer-wise composition distributes complementary memory processing across representational stages, while cross-layer reuse carries selected memory and routing artifacts forward. Depth thus becomes a dimension along which contextual memory is constructed and managed. Third, these developments motivate a stateful multidimensional memory-routing hypothesis: persistent memory is organized across temporal scope, network depth, substrate type, and representation granularity, while coordinated Sparse Write and Sparse Read determine what is maintained and what contributes to each query. Overall, efficient sequence architecture design increasingly concerns the organization, lifecycle, and selective use of contextual memory rather than an isolated Attention operator.

Transfer learning on edge is challenging due to on-device limited resources. Existing work addresses this issue by training a subset of parameters or adding model patches. Developed with inference in mind, Inverted Residual Blocks (IRBs) split a convolutional layer into depthwise and pointwise convolutions, leading to more stacking layers, e.g., convolution, normalization, and activation layers. Though they are efficient for inference, IRBs require that additional activation maps are stored in memory for training weights for convolution layers and scales for normalization layers. As a result, their high memory cost prohibits training IRBs on resource-limited edge devices, and making them unsuitable in the context of transfer learning. To address this issue, we present MobileTL, a memory and computationally efficient on-device transfer learning method for models built with IRBs. MobileTL trains the shifts for internal normalization layers to avoid storing activation maps for the backward pass. Also, MobileTL approximates the backward computation of the activation layer (e.g., Hard-Swish and ReLU6) as a signed function which enables storing a binary mask instead of activation maps for the backward pass. MobileTL fine-tunes a few top blocks (close to output) rather than propagating the gradient through the whole network to reduce the computation cost. Our method reduces memory usage by 46% and 53% for MobileNetV2 and V3 IRBs, respectively. For MobileNetV3, we observe a 36% reduction in floating-point operations (FLOPs) when fine-tuning 5 blocks, while only incurring a 0.6% accuracy reduction on CIFAR10. Extensive experiments on multiple datasets demonstrate that our method is Pareto-optimal (best accuracy under given hardware constraints) compared to prior work in transfer learning for edge devices.

Large vision-language models (LVLMs) achieve impressive performance, yet their internal decision-making processes remain opaque, making it difficult to determine if the success stems from true multimodal fusion or from reliance on unimodal priors. To address this attribution gap, we introduce a novel framework using partial information decomposition (PID) to quantitatively measure the "information spectrum" of LVLMs -- decomposing a model's decision-relevant information into redundant, unique, and synergistic components. By adapting a scalable estimator to modern LVLM outputs, our model-agnostic pipeline profiles 26 LVLMs on four datasets across three dimensions -- breadth (cross-model & cross-task), depth (layer-wise information dynamics), and time (learning dynamics across training). Our analysis reveals two key results: (i) two task regimes (synergy-driven vs. knowledge-driven) and (ii) two stable, contrasting family-level strategies (fusion-centric vs. language-centric). We also uncover a consistent three-phase pattern in layer-wise processing and identify visual instruction tuning as the key stage where fusion is learned. Together, these contributions provide a quantitative lens beyond accuracy-only evaluation and offer insights for analyzing and designing the next generation of LVLMs. Code and data are available at https://github.com/RiiShin/pid-lvlm-analysis .

Accurate estimation of pasture biomass from agricultural imagery is critical for sustainable livestock management, yet existing methods are limited by the small, imbalanced, and sparsely annotated datasets typical of real world monitoring. In this study, adaptation of vision foundation models to agricultural regression is systematically evaluated on the CSIRO Pasture Biomass benchmark, a 357 image dual view dataset with laboratory validated, component wise ground truth for five biomass targets, through 17 configurations spanning four backbones (EfficientNet-B3 to DINOv3-ViT-L), five cross view fusion mechanisms, and a 4x2 metadata factorial. A counterintuitive principle, termed "fusion complexity inversion", is uncovered: on scarce agricultural data, a two layer gated depthwise convolution (R^2 = 0.903) outperforms cross view attention transformers (0.833), bidirectional SSMs (0.819), and full Mamba (0.793, below the no fusion baseline). Backbone pretraining scale is found to monotonically dominate all architectural choices, with the DINOv2 -> DINOv3 upgrade alone yielding +5.0 R^2 points. Training only metadata (species, state, and NDVI) is shown to create a universal ceiling at R^2 ~ 0.829, collapsing an 8.4 point fusion spread to 0.1 points. Actionable guidelines for sparse agricultural benchmarks are established: backbone quality should be prioritized over fusion complexity, local modules preferred over global alternatives, and features unavailable at inference excluded.

We introduce Illustrator's Depth, a novel definition of depth that addresses a key challenge in digital content creation: decomposing flat images into editable, ordered layers. Inspired by an artist's compositional process, illustrator's depth infers a layer index to each pixel, forming an interpretable image decomposition through a discrete, globally consistent ordering of elements optimized for editability. We also propose and train a neural network using a curated dataset of layered vector graphics to predict layering directly from raster inputs. Our layer index inference unlocks a range of powerful downstream applications. In particular, it significantly outperforms state-of-the-art baselines for image vectorization while also enabling high-fidelity text-to-vector-graphics generation, automatic 3D relief generation from 2D images, and intuitive depth-aware editing. By reframing depth from a physical quantity to a creative abstraction, illustrator's depth prediction offers a new foundation for editable image decomposition.

Depth completion (DC) aims to predict a dense depth map from an RGB image and sparse depth observations. Existing methods for DC generalize poorly on new datasets or unseen sparse depth patterns, limiting their practical applications. We propose OMNI-DC, a highly robust DC model that generalizes well across various scenarios. Our method incorporates a novel multi-resolution depth integration layer and a probability-based loss, enabling it to deal with sparse depth maps of varying densities. Moreover, we train OMNI-DC on a mixture of synthetic datasets with a scale normalization technique. To evaluate our model, we establish a new evaluation protocol named Robust-DC for zero-shot testing under various sparse depth patterns. Experimental results on Robust-DC and conventional benchmarks show that OMNI-DC significantly outperforms the previous state of the art. The checkpoints, training code, and evaluations are available at https://github.com/princeton-vl/OMNI-DC.

We revisit a universally accepted but under-examined design choice in every modern LLM: a token index is looked up once at the input embedding layer and then permanently discarded. This single-injection assumption induces two structural failures: (i) the Rare Token Problem, where a Zipf-type distribution of vocabulary causes rare-token embeddings are chronically under-trained due to receiving a fraction of the cumulative gradient signal compared to common tokens; and (ii) the Contextual Collapse Problem, where limited parameters models map distributionally similar tokens to indistinguishable hidden states. As an attempt to address both, we propose TIDE, which augments the standard transformer with EmbeddingMemory: an ensemble of K independent MemoryBlocks that map token indices to context-free semantic vectors, computed once and injected into every layer through a depth-conditioned softmax router with a learnable null bank. We theoretically and empirically establish the benefits of TIDE in addressing the issues associated with single-token identity injection as well as improve performance across multiple language modeling and downstream tasks.

Autoregressive large language models (LLMs) are bottlenecked by sequential decoding, where each new token typically requires executing all transformer layers. Existing dynamic-depth and layer-skipping methods reduce this cost, but often rely on auxiliary routing mechanisms or incur accuracy degradation when bypassed layers are left uncompensated. We present LoRA-Drop, a plug-and-play inference framework that accelerates decoding by applying a temporal compute schedule to a fixed subset of intermediate layers: on most decoding steps, selected layers reuse the previous-token hidden state and apply a low-rank LoRA correction, while periodic refresh steps execute the full model to prevent drift. LoRA-Drop requires no routing network, is compatible with standard KV caching, and can reduce KV-cache footprint by skipping KV updates in droppable layers during LoRA steps and refreshing periodically. Across LLaMA2-7B, LLaMA3-8B, Qwen2.5-7B, and Qwen2.5-14B, LoRA-Drop achieves up to 2.6times faster decoding and 45--55\% KV-cache reduction while staying within 0.5 percentage points (pp) of baseline accuracy. Evaluations on reasoning (GSM8K, MATH, BBH), code generation (HumanEval, MBPP), and long-context/multilingual benchmarks (LongBench, XNLI, XCOPA) identify a consistent safe zone of scheduling configurations that preserves quality while delivering substantial efficiency gains, providing a simple path toward adaptive-capacity inference in LLMs. Codes are available at https://github.com/hosseinbv/LoRA-Drop.git.

Convolutional neural networks (CNNs) have made resounding success in many computer vision tasks such as image classification and object detection. However, their performance degrades rapidly on tougher tasks where images are of low resolution or objects are small. In this paper, we point out that this roots in a defective yet common design in existing CNN architectures, namely the use of strided convolution and/or pooling layers, which results in a loss of fine-grained information and learning of less effective feature representations. To this end, we propose a new CNN building block called SPD-Conv in place of each strided convolution layer and each pooling layer (thus eliminates them altogether). SPD-Conv is comprised of a space-to-depth (SPD) layer followed by a non-strided convolution (Conv) layer, and can be applied in most if not all CNN architectures. We explain this new design under two most representative computer vision tasks: object detection and image classification. We then create new CNN architectures by applying SPD-Conv to YOLOv5 and ResNet, and empirically show that our approach significantly outperforms state-of-the-art deep learning models, especially on tougher tasks with low-resolution images and small objects. We have open-sourced our code at https://github.com/LabSAINT/SPD-Conv.

Quantization-aware training (QAT) leverages lower-precision arithmetic to reduce the cost of LLM deployment, but aggressive quantization degrades final model performance. A common remedy is mixed-precision training, in which high precision is assigned to some of the layers to maintain performance while keeping the cost constrained. This approach then requires precision assignments for model layers during training. We provide a new approach, called Q-PACE, consisting of a second-order sensitivity model that predicts the loss increase as a sum of quantization noise MSE weighted by per-layer curvature coefficients. During training, we periodically re-compute these coefficients using perturbations across layers, and re-assign precision. Pretraining and supervised fine-tuning experiments on LLMs of up to 4B parameters show that Q-PACE consistently improves over existing mixed-precision training recipes, and achieves comparable loss at substantially lower total memory budgets. We further find that quantization sensitivity is highly predictable by depth and layer type, and its stability during training allows for infrequent, cheap recalibration.

The rapidly increasing computational cost of pretraining Large Language Models necessitates more efficient approaches. Numerous computational costs have been invested in existing well-trained checkpoints, but many of them remain underutilized due to engineering constraints or limited model capacity. To efficiently reuse this "sunk" cost, we propose to recycle pretrained checkpoints by expanding their parameter counts and continuing training. We propose orthogonal growth method well-suited for converged Mixture-of-Experts model: interpositional layer copying for depth growth and expert duplication with injected noise for width growth. To determine the optimal timing for such growth across checkpoints sequences, we perform comprehensive scaling experiments revealing that the final accuracy has a strong positive correlation with the amount of sunk cost, indicating that greater prior investment leads to better performance. We scale our approach to models with 70B parameters and over 1T training tokens, achieving 10.66% accuracy gain over training from scratch under the same additional compute budget. Our checkpoint recycling approach establishes a foundation for economically efficient large language model pretraining.

We present adversarial flow models, a class of generative models that unifies adversarial models and flow models. Our method supports native one-step or multi-step generation and is trained using the adversarial objective. Unlike traditional GANs, where the generator learns an arbitrary transport plan between the noise and the data distributions, our generator learns a deterministic noise-to-data mapping, which is the same optimal transport as in flow-matching models. This significantly stabilizes adversarial training. Also, unlike consistency-based methods, our model directly learns one-step or few-step generation without needing to learn the intermediate timesteps of the probability flow for propagation. This saves model capacity, reduces training iterations, and avoids error accumulation. Under the same 1NFE setting on ImageNet-256px, our B/2 model approaches the performance of consistency-based XL/2 models, while our XL/2 model creates a new best FID of 2.38. We additionally show the possibility of end-to-end training of 56-layer and 112-layer models through depth repetition without any intermediate supervision, and achieve FIDs of 2.08 and 1.94 using a single forward pass, surpassing their 2NFE and 4NFE counterparts.

Large Transformer models have been central to recent advances in natural language processing. The training and inference costs of these models, however, have grown rapidly and become prohibitively expensive. Here we aim to reduce the costs of Transformers by searching for a more efficient variant. Compared to previous approaches, our search is performed at a lower level, over the primitives that define a Transformer TensorFlow program. We identify an architecture, named Primer, that has a smaller training cost than the original Transformer and other variants for auto-regressive language modeling. Primer's improvements can be mostly attributed to two simple modifications: squaring ReLU activations and adding a depthwise convolution layer after each Q, K, and V projection in self-attention. Experiments show Primer's gains over Transformer increase as compute scale grows and follow a power law with respect to quality at optimal model sizes. We also verify empirically that Primer can be dropped into different codebases to significantly speed up training without additional tuning. For example, at a 500M parameter size, Primer improves the original T5 architecture on C4 auto-regressive language modeling, reducing the training cost by 4X. Furthermore, the reduced training cost means Primer needs much less compute to reach a target one-shot performance. For instance, in a 1.9B parameter configuration similar to GPT-3 XL, Primer uses 1/3 of the training compute to achieve the same one-shot performance as Transformer. We open source our models and several comparisons in T5 to help with reproducibility.

This paper introduces ConvShareViT, a novel deep learning architecture that adapts Vision Transformers (ViTs) to the 4f free-space optical system. ConvShareViT replaces linear layers in multi-head self-attention (MHSA) and Multilayer Perceptrons (MLPs) with a depthwise convolutional layer with shared weights across input channels. Through the development of ConvShareViT, the behaviour of convolutions within MHSA and their effectiveness in learning the attention mechanism were analysed systematically. Experimental results demonstrate that certain configurations, particularly those using valid-padded shared convolutions, can successfully learn attention, achieving comparable attention scores to those obtained with standard ViTs. However, other configurations, such as those using same-padded convolutions, show limitations in attention learning and operate like regular CNNs rather than transformer models. ConvShareViT architectures are specifically optimised for the 4f optical system, which takes advantage of the parallelism and high-resolution capabilities of optical systems. Results demonstrate that ConvShareViT can theoretically achieve up to 3.04 times faster inference than GPU-based systems. This potential acceleration makes ConvShareViT an attractive candidate for future optical deep learning applications and proves that our ViT (ConvShareViT) can be employed using only the convolution operation, via the necessary optimisation of the ViT to balance performance and complexity.

We propose a relighting method for outdoor images. Our method mainly focuses on predicting cast shadows in arbitrary novel lighting directions from a single image while also accounting for shading and global effects such the sun light color and clouds. Previous solutions for this problem rely on reconstructing occluder geometry, e.g. using multi-view stereo, which requires many images of the scene. Instead, in this work we make use of a noisy off-the-shelf single-image depth map estimation as a source of geometry. Whilst this can be a good guide for some lighting effects, the resulting depth map quality is insufficient for directly ray-tracing the shadows. Addressing this, we propose a learned image space ray-marching layer that converts the approximate depth map into a deep 3D representation that is fused into occlusion queries using a learned traversal. Our proposed method achieves, for the first time, state-of-the-art relighting results, with only a single image as input. For supplementary material visit our project page at: https://dgriffiths.uk/outcast.

Techniques for automatically designing deep neural network architectures such as reinforcement learning based approaches have recently shown promising results. However, their success is based on vast computational resources (e.g. hundreds of GPUs), making them difficult to be widely used. A noticeable limitation is that they still design and train each network from scratch during the exploration of the architecture space, which is highly inefficient. In this paper, we propose a new framework toward efficient architecture search by exploring the architecture space based on the current network and reusing its weights. We employ a reinforcement learning agent as the meta-controller, whose action is to grow the network depth or layer width with function-preserving transformations. As such, the previously validated networks can be reused for further exploration, thus saves a large amount of computational cost. We apply our method to explore the architecture space of the plain convolutional neural networks (no skip-connections, branching etc.) on image benchmark datasets (CIFAR-10, SVHN) with restricted computational resources (5 GPUs). Our method can design highly competitive networks that outperform existing networks using the same design scheme. On CIFAR-10, our model without skip-connections achieves 4.23\% test error rate, exceeding a vast majority of modern architectures and approaching DenseNet. Furthermore, by applying our method to explore the DenseNet architecture space, we are able to achieve more accurate networks with fewer parameters.

The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks. We first present a complete characterization of inputs indistinguishable by models derived by a given architecture. From this results, we derive how separability is influenced by hyperparameters and architectural choices-such as activation functions, depth, hidden layer width, and representation types. Notably, all non-polynomial activations, including ReLU and sigmoid, are equivalent in expressivity and reach maximum separation power. Depth improves separation power up to a threshold, after which further increases have no effect. Adding invariant features to hidden representations does not impact separation power. Finally, block decomposition of hidden representations affects separability, with minimal components forming a hierarchy in separation power that provides a straightforward method for comparing the separation power of models.

Scaling up self-supervised learning has driven breakthroughs in language and vision, yet comparable progress has remained elusive in reinforcement learning (RL). In this paper, we study building blocks for self-supervised RL that unlock substantial improvements in scalability, with network depth serving as a critical factor. Whereas most RL papers in recent years have relied on shallow architectures (around 2 - 5 layers), we demonstrate that increasing the depth up to 1024 layers can significantly boost performance. Our experiments are conducted in an unsupervised goal-conditioned setting, where no demonstrations or rewards are provided, so an agent must explore (from scratch) and learn how to maximize the likelihood of reaching commanded goals. Evaluated on simulated locomotion and manipulation tasks, our approach increases performance on the self-supervised contrastive RL algorithm by 2times - 50times, outperforming other goal-conditioned baselines. Increasing the model depth not only increases success rates but also qualitatively changes the behaviors learned. The project webpage and code can be found here: https://wang-kevin3290.github.io/scaling-crl/.

Self-attention selects information freely across the sequence, but across depth, Transformers merely add each layer's output to the residual stream, so later layers cannot selectively reuse earlier-layer representations. Recent cross-layer methods improve this flow but operate on hidden states outside attention, adding state beyond the key-value cache at inference--a cost that becomes increasingly salient as modern LLMs compress the cache with grouped-query and multi-head latent attention. We introduce Depth-Attention, which performs this selection inside the attention module itself: before a layer attends over the sequence, its query attends over the keys of earlier layers at the same token position and mixes their values into the value that self-attention then reads. Because Depth-Attention reuses the standard attention queries, keys, and value-cache slots, storing depth-mixed values in place of the original values, it adds no parameters and introduces no persistent inference state beyond the standard key-value cache--the same cache size as a vanilla decoder and less than hidden-state-based cross-layer methods. On Qwen3-style decoders at 1.5B and 3B parameters, Depth-Attention attains the lowest perplexity and the highest average downstream accuracy, improving over the vanilla Transformer by up to 2.3 accuracy points and surpassing strong cross-layer baselines in perplexity and average accuracy, while adding under 0.01% extra arithmetic FLOPs and no additional persistent inference state. The gains hold from 360M to 3B parameters and extend to looped Transformers.

Depth pruning improves the inference efficiency of large language models by removing Transformer blocks. Prior work typically treats layer redundancy as an inherent structural property of pretrained networks, emphasizing importance criteria and search algorithms to identify removable layers. In this study, we empirically investigate depth pruning from a functional perspective. Evaluating representative LLM families across diverse calibration configurations and multiple search algorithms, we show that different configurations produce different pruning patterns. Furthermore, under a fixed calibration configuration, complex search algorithms yield marginal performance improvements over simple one-shot methods, converging to similar pruned subsets. Overall, our results suggest that the calibration configuration plays a substantially larger role than the choice of search algorithm in shaping pruning patterns and calibration perplexity, while contributing comparably to variance in downstream reasoning accuracy. This indicates that future pruning efforts may benefit from prioritizing the calibration configuration over search complexity.

Recent works show that reducing the number of layers in a convolutional neural network can enhance efficiency while maintaining the performance of the network. Existing depth compression methods remove redundant non-linear activation functions and merge the consecutive convolution layers into a single layer. However, these methods suffer from a critical drawback; the kernel size of the merged layers becomes larger, significantly undermining the latency reduction gained from reducing the depth of the network. We show that this problem can be addressed by jointly pruning convolution layers and activation functions. To this end, we propose LayerMerge, a novel depth compression method that selects which activation layers and convolution layers to remove, to achieve a desired inference speed-up while minimizing performance loss. Since the corresponding selection problem involves an exponential search space, we formulate a novel surrogate optimization problem and efficiently solve it via dynamic programming. Empirical results demonstrate that our method consistently outperforms existing depth compression and layer pruning methods on various network architectures, both on image classification and generation tasks. We release the code at https://github.com/snu-mllab/LayerMerge.

Recent works have indicated redundancy across transformer blocks, prompting the research of depth compression to prune less crucial blocks. However, current ways of entire-block pruning suffer from risks of discarding meaningful cues learned in those blocks, leading to substantial performance degradation. As another line of model compression, channel pruning can better preserve performance, while it cannot reduce model depth and is challenged by inconsistent pruning ratios for individual layers. To pursue better model compression and acceleration, this paper proposes FlattenGPT, a novel way to detect and reduce depth-wise redundancies. By flatting two adjacent blocks into one, it compresses the network depth, meanwhile enables more effective parameter redundancy detection and removal. FlattenGPT allows to preserve the knowledge learned in all blocks, and remains consistent with the original transformer architecture. Extensive experiments demonstrate that FlattenGPT enhances model efficiency with a decent trade-off to performance. It outperforms existing pruning methods in both zero-shot accuracies and WikiText-2 perplexity across various model types and parameter sizes. On LLaMA-2/3 and Qwen-1.5 models, FlattenGPT retains 90-96\% of zero-shot performance with a compression ratio of 20\%. It also outperforms other pruning methods in accelerating LLM inference, making it promising for enhancing the efficiency of transformers.

Can a pretrained neural network adapt its architecture to different inputs without any finetuning? Do we need all layers for simple tasks, and are they adequate for challenging tasks? We found that the layers of a pretrained large language model (LLM) can be manipulated as separate modules to build a better and even shallower model customized for each test sample. In particular, each layer from the pretrained model can be skipped/pruned or repeated multiple times as recurrent neural networks (RNN), and stacked with others in arbitrary orders, yielding a chain-of-layers (CoLa) per sample. This compositional space greatly expands the scope of existing works on looped/recurrent pretrained modules, layer pruning, or early-exit networks. We develop a Monte Carlo Tree Search (MCTS) protocol to explore and identify the optimal CoLa for each sample from math and commonsense reasoning benchmarks. Compared to a static model of a fixed depth, CoLa allows shortcut paths (fast thinking), recurrence of the same layer(s) (slow thinking), and combining both, offering more flexible, dynamic architectures for different inputs. We conduct an extensive analysis of the MCTS-optimized CoLa, which leads to two key findings: (1) For >75% of samples with correct predictions by the original LLM, we can find shorter CoLa, suggesting a large space for improving inference efficiency; (2) For >60% of samples with originally incorrect predictions, we can identify CoLa achieving correct predictions, suggesting a large space of performance enhancement. Our results highlight the shortcomings of using a fixed architecture of pre-trained LLMs for inference on different samples and pave the way to unlock the generalization power of test-time depth adaptation.

Residual connections are central to modern deep neural networks, enabling stable optimization and efficient information flow across depth. In this work, we propose SCORE (Skip-Connection ODE Recurrent Embedding), a discrete recurrent alternative to classical layer stacking. Instead of composing multiple independent layers, SCORE iteratively applies a single shared neural block using an ODE (Ordinary Differential Equation)-inspired contractive update: ht+1 = (1 - dt) * ht + dt * F(ht) This formulation can be interpreted as a depth-by-iteration refinement process, where the step size dt explicitly controls stability and update magnitude. Unlike continuous Neural ODE approaches, SCORE uses a fixed number of discrete iterations and standard backpropagation without requiring ODE solvers or adjoint methods. We evaluate SCORE across graph neural networks (ESOL molecular solubility), multilayer perceptrons, and Transformer-based language models (nanoGPT). Across architectures, SCORE generally improves convergence speed and often accelerates training. SCORE is reducing parameter count through shared weights. In practice, simple Euler integration provides the best trade-off between computational cost and performance, while higher-order integrators yield marginal gains at increased compute. These results suggest that controlled recurrent depth with contractive residual updates offers a lightweight and effective alternative to classical stacking in deep neural networks.

Tool-augmented LLM agents introduce security risks that extend beyond user-input filtering, including indirect prompt injection through fetched content, unsafe tool execution, credential leakage, and tampering with local control files. We present OpenClaw PRISM, a zero-fork runtime security layer for OpenClaw-based agent gateways. PRISM combines an in-process plugin with optional sidecar services and distributes enforcement across ten lifecycle hooks spanning message ingress, prompt construction, tool execution, tool-result persistence, outbound messaging, sub-agent spawning, and gateway startup. Rather than introducing a novel detection model, PRISM integrates a hybrid heuristic-plus-LLM scanning pipeline, conversation- and session-scoped risk accumulation with TTL-based decay, policy-enforced controls over tools, paths, private networks, domain tiers, and outbound secret patterns, and a tamper-evident audit and operations plane with integrity verification and hot-reloadable policy management. We outline an evaluation methodology and benchmark pipeline for measuring security effectiveness, false positives, layer contribution, runtime overhead, and operational recoverability in an agent-runtime setting, and we report current preliminary benchmark results on curated same-slice experiments and operational microbenchmarks. The system targets deployable runtime defense for real agent gateways rather than benchmark-only detection.

Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are impossible in shallow models, or do they merely spread the same kinds of computation out over more layers? To address these questions, we analyze the residual stream of the Llama 3.1 and Qwen 3 family of models. We find: First, comparing the output of the sublayers to the residual stream reveals that layers in the second half contribute much less than those in the first half, with a clear phase transition between the two halves. Second, skipping layers in the second half has a much smaller effect on future computations and output predictions. Third, for multihop tasks, we are unable to find evidence that models are using increased depth to compose subresults in examples involving many hops. Fourth, we seek to directly address whether deeper models are using their additional layers to perform new kinds of computation. To do this, we train linear maps from the residual stream of a shallow model to a deeper one. We find that layers with the same relative depth map best to each other, suggesting that the larger model simply spreads the same computations out over its many layers. All this evidence suggests that deeper models are not using their depth to learn new kinds of computation, but only using the greater depth to perform more fine-grained adjustments to the residual. This may help explain why increasing scale leads to diminishing returns for stacked Transformer architectures.

Layer interventions are widely used to probe the internal organization of language models, yet most analyses examine a single training checkpoint even though model representations and computations evolve throughout pretraining. This leaves open which depth-dependent intervention responses reflect persistent organization and which are transient consequences of training. We study this question using single-block identity bypass on fixed teacher-forced contexts across five released trajectories and 11 model-domain combinations. We find that block-bypass responses retain recognizable depth ordering while their magnitudes redistribute: nearby checkpoints preserve stronger rank correspondence than distant ones, and large changes concentrate at positions that recur across text samples and transfer across evaluation domains. Controlled experiments further show that changes in the natural bypass effect cannot be reduced to a single downstream sensitivity: in replicated Pythia runs, local missing-update magnitude grows while the pooled matched downstream response decreases, whereas OLMo-2 7B exhibits a different balance. These matched responses also depend on perturbation strength and direction, without identifying targeted compensation. Together, our results show that longitudinal layer sensitivity is structured but not static, and that single-checkpoint intervention responses should be interpreted in the context of how the underlying perturbation pathway evolves during training.

Large Language Models (LLMs) process every token through all layers of a transformer stack, causing wasted computation on simple queries and insufficient flexibility for harder ones that need deeper reasoning. Adaptive-depth methods can improve efficiency, but prior approaches rely on costly inference-time search, architectural changes, or large-scale retraining, and in practice often degrade accuracy despite efficiency gains. We introduce Dr.LLM, Dynamic routing of Layers for LLMs, a retrofittable framework that equips pretrained models with lightweight per-layer routers deciding to skip, execute, or repeat a block. Routers are trained with explicit supervision: using Monte Carlo Tree Search (MCTS), we derive high-quality layer configurations that preserve or improve accuracy under a compute budget. Our design, windowed pooling for stable routing, focal loss with class balancing, and bottleneck MLP routers, ensures robustness under class imbalance and long sequences. On ARC (logic) and DART (math), Dr.LLM improves accuracy by up to +3.4%p while saving 5 layers per example on average. Routers generalize to out-of-domain tasks (MMLU, GSM8k, AIME, TruthfulQA, SQuADv2, GPQA, PIQA, AGIEval) with only 0.85% accuracy drop while retaining efficiency, and outperform prior routing methods by up to +7.7%p. Overall, Dr.LLM shows that explicitly supervised routers retrofit frozen LLMs for budget-aware, accuracy-driven inference without altering base weights.

Depth is a natural way to increase the computational capacity in Transformers, yet the contribution of deeper layers can diminish as depth grows larger. Recent approaches enhance normalization (e.g., LayerNorm Scaling) or residual connections (e.g., mHC, AttnRes) to enable better information flow and depth utilization. However, it remains unclear whether they truly translate increased architectural depth into effective computational depth, and whether their reported gains stem from better access to information across depth, or unaccounted-for confounding factors. In this paper, we introduce DepthBench, a controlled benchmark for studying computational depth across various architectures. We systematically vary the width--depth aspect ratio (d_{model}/n_{layer}) from shallow--wide to deep--narrow shapes, while keeping the model size and pre-training recipe fixed. Across 10 representative architectures, we find that the benefit of allocating more capacity to depth is strongly architecture-dependent. Standard Pre-LN and most of its norm- and scaling-based variants provide little benefit and can even degrade performance as models become deeper and narrower, whereas HC and Full AttnRes improve consistently even at extreme deep shapes. These gains extend beyond pre-training loss and consistently translate into improved domain-specific performance and effective computation. Controlled layer-level analyses further show that the gains of HC and Full AttnRes are associated with more effective utilization of additional layers, revealing distinct mechanisms of computational depth across architectures. Overall, our results identify residual connection design as a key determinant of whether depth can serve as a meaningful scaling axis by enabling additional architectural depth to translate into effective computation.

Vision-language-action (VLA) policies emphasize semantic understanding, whereas world-action models (WAMs) learn predictive representations of environment dynamics. Systems that expose a policy to both sources often still concentrate action computation on a single expert. We present EWAM, an action-centric unified embodied model whose asymmetric joint attention lets action tokens read semantic, current-visual, predicted-future, and action information at every layer while the perceptual experts retain their distinct roles. Without layer-wise supervision, EWAM develops an emergent depth-wise specialization: action queries attend mainly to vision-language features in shallow layers, to predicted future frames in intermediate layers, and to action tokens themselves in deep layers. This handoff replicates across tasks and is stable across denoising steps. Checkpoint tracking and causal interventions show that it is learned and that action generation depends on it. EWAM is pretrained in two separate regimes, one on cross-embodiment robot trajectories and one on human egocentric video. In simulation and real-robot experiments, it surpasses existing VLA, WAM, and hybrid baselines. Human egocentric data improve both cross-embodiment transfer and real-robot robustness, and subtask-phase supervision improves long-horizon completion. Together, these results suggest that unified embodied learning can induce an ordered internal progression from semantic understanding, through visual foresight, to action formation.

Recurrent Transformers increase computational depth through temporal recurrence, feeding each token's high-level hidden state into the computation of the next. This raises a natural question: is additional computation better spent on more temporal steps or greater physical depth? We investigate this question using Latent Recurrent Transformers (LRTs), which retain one backbone forward pass per vocabulary token during decoding and provide a controlled setting for comparing these two ways of adding computation. Specifically, we insert a latent thought token between consecutive vocabulary tokens. Each thought token passes through the same L layers as a vocabulary token, sharing the backbone parameters and providing an additional stage of hidden-state refinement before predicting the next token. We compare this L-layer LRT against a 2L-layer LRT without thought tokens. Both execute 2L Transformer blocks per vocabulary token during decoding, but the thought-token model uses fewer parameters. On 16- and 20-layer mixture-of-experts NanoChat backbones, one thought token brings the shallower model within 0.006 and 0.004 bits per byte of its double-depth counterpart, recovering 67% and 81% of the improvement with approximately 48% fewer total parameters. These results suggest that temporal thinking offers a parameter-efficient alternative to increasing physical depth in recurrent Transformers.

Visual recognition requires rich representations that span levels from low to high, scales from small to large, and resolutions from fine to coarse. Even with the depth of features in a convolutional network, a layer in isolation is not enough: compounding and aggregating these representations improves inference of what and where. Architectural efforts are exploring many dimensions for network backbones, designing deeper or wider architectures, but how to best aggregate layers and blocks across a network deserves further attention. Although skip connections have been incorporated to combine layers, these connections have been "shallow" themselves, and only fuse by simple, one-step operations. We augment standard architectures with deeper aggregation to better fuse information across layers. Our deep layer aggregation structures iteratively and hierarchically merge the feature hierarchy to make networks with better accuracy and fewer parameters. Experiments across architectures and tasks show that deep layer aggregation improves recognition and resolution compared to existing branching and merging schemes. The code is at https://github.com/ucbdrive/dla.

Designing Transformer architectures with the optimal layer normalization (LN) strategy that ensures large-scale training stability and expedite convergence has remained elusive, even in this era of large language models (LLMs). To this end, we present a comprehensive analytical foundation for understanding how different LN strategies influence training dynamics in large-scale Transformer training. Until recently, Pre-LN and Post-LN have long dominated standard practices despite their limitations in large-scale training. However, several open-source large-scale models have recently begun silently adopting a third strategy without much explanation. This strategy places layer normalization (LN) peripherally around sublayers, a design we term Peri-LN. While Peri-LN has demonstrated promising empirical performance, its precise mechanisms and benefits remain almost unexplored. Our in-depth analysis shows that Peri-LN strikes an ideal balance in variance growth -- unlike Pre-LN and Post-LN, which are prone to vanishing gradients and ``massive activations.'' To validate our theoretical insight, we conduct large-scale experiments on Transformers up to 3.2B parameters, showing that Peri-LN consistently achieves more balanced variance growth, steadier gradient flow, and convergence stability. Our results suggest that Peri-LN warrants broader consideration for large-scale Transformer architectures, providing renewed insights into the optimal placement and application of LN.

Due to the large number of parameters, the inference phase of Large Language Models (LLMs) is resource-intensive. Unlike traditional model compression, which needs retraining, recent dynamic computation methods show that not all components are required for inference, enabling a training-free pipeline. In this paper, we focus on the dynamic depth of LLM generation. A token-position aware layer skipping framework is proposed to save 1.5x times operations efficiently while maintaining performance. We first observed that tokens predicted later have lower perplexity and thus require less computation. Then, we propose a training-free algorithm called Position-Aware Depth Decay Decoding (D^3), which leverages a power-law decay function, leftlfloor L times (alpha^i) rightrfloor, to determine the number of layers to retain when generating token T_i. Remarkably, without any retraining, the D^3 achieves success across a wide range of generation tasks for the first time. Experiments on large language models (\ie the Llama) with 7 sim 70 billion parameters show that D^3 can achieve an average 1.5x speedup compared with the full-inference pipeline while maintaining comparable performance with nearly no performance drop (<1%) on the GSM8K and BBH benchmarks.

Recent DiT-based text-to-image models increasingly adopt LLMs as text encoders, yet text conditioning remains largely static and often utilizes only a single LLM layer, despite pronounced semantic hierarchy across LLM layers and non-stationary denoising dynamics over both diffusion time and network depth. To better match the dynamic process of DiT generation and thereby enhance the diffusion model's generative capability, we introduce a unified normalized convex fusion framework equipped with lightweight gates to systematically organize multi-layer LLM hidden states via time-wise, depth-wise, and joint fusion. Experiments establish Depth-wise Semantic Routing as the superior conditioning strategy, consistently improving text-image alignment and compositional generation (e.g., +9.97 on the GenAI-Bench Counting task). Conversely, we find that purely time-wise fusion can paradoxically degrade visual generation fidelity. We attribute this to a train-inference trajectory mismatch: under classifier-free guidance, nominal timesteps fail to track the effective SNR, causing semantically mistimed feature injection during inference. Overall, our results position depth-wise routing as a strong and effective baseline and highlight the critical need for trajectory-aware signals to enable robust time-dependent conditioning.

Deep neural networks with repeated architectural blocks, such as transformers, often exhibit structured relationships across layers that emerge during training. Motivated by this observation, we introduce Depth-wise Gradient Augmentation, a general optimization paradigm in which the update applied to each layer is obtained by transforming the collection of block-wise optimizer updates along the depth dimension. Within this framework, we study Gradient Smoothing, a family of depth-wise smoothing methods, and instantiate it with a simple local Window Smoothing operator. The resulting method operates directly on block-wise updates produced by arbitrary base optimizers (e.g., SGD, Adam, Muon), incurs minimal computational overhead, and is compatible with existing optimization pipelines. We evaluate Gradient Smoothing across a diverse set of architectures and training regimes, including language model pretraining, RL post-training of LLMs for reasoning, diffusion modeling, and image classification with Vision Transformers. Across these settings, Gradient Smoothing consistently improves optimization and generalization performance without modifying model architectures or training objectives. We further show that it promotes more structured representation evolution across depth, consistent with its interpretation as a structured depth-wise preconditioning method. Together, these results establish Depth-wise Gradient Augmentation as a promising framework for exploiting cross-depth structure in optimization and demonstrate Gradient Smoothing as a simple and broadly applicable instantiation.

Large language models (LLMs) have shown remarkable performances across a wide range of tasks. However, the mechanisms by which these models encode tasks of varying complexities remain poorly understood. In this paper, we explore the hypothesis that LLMs process concepts of varying complexities in different layers, introducing the idea of "Concept Depth" to suggest that more complex concepts are typically acquired in deeper layers. Specifically, we categorize concepts based on their level of abstraction, defining them in the order of increasing complexity within factual, emotional, and inferential tasks. We conduct extensive probing experiments using layer-wise representations across various LLM families (Gemma, LLaMA, QWen) on various datasets spanning the three domains of tasks. Our findings reveal that models could efficiently conduct probing for simpler tasks in shallow layers, and more complex tasks typically necessitate deeper layers for accurate understanding. Additionally, we examine how external factors, such as adding noise to the input and quantizing the model weights, might affect layer-wise representations. Our findings suggest that these factors can impede the development of a conceptual understanding of LLMs until deeper layers are explored. We hope that our proposed concept and experimental insights will enhance the understanding of the mechanisms underlying LLMs. Our codes are available at https://github.com/Luckfort/CD.

In this paper, we propose Transformer Layer Injection (TLI), a novel method for efficiently upscaling large language models (LLMs) while minimizing computational costs and maintaining model performance. Model scale is a key factor in enhancing the quality of machine learning models, and TLI addresses the challenge of scaling by reducing initial loss, minimizing fine-tuning requirements, and preserving model complexity. Our approach improves upon the conventional Depth Up-Scaling (DUS) technique by injecting new layers into every set of K layers, enabling hidden representations to pass through transformer blocks with minimal disruption. We compare TLI with existing approaches, including Mixture of Experts (MoE) and DUS, and validate its efficiency through experiments on small LLMs (LLama3 1B, 3B, and 8B). Results show that TLI achieves better initialization, requires fewer training steps, and delivers superior accuracy on tasks such as KoBEST and KMCQA, with models performing effectively even without additional training. TLI is demonstrated to be both data-efficient and cost-effective, significantly outperforming existing methods. Its scalability and simplicity make it a promising solution for upscaling transformer-based models, with potential applications in scaling models from 10B to 405B parameters.

Specializing large language models (LLMs) for local deployment in domain-specific use cases is necessary for strong performance while meeting latency and privacy constraints. However, conventional task-specific adaptation approaches do not show simultaneous memory saving and inference speedup at deployment time. Practical compression techniques like quantization and pruning require dedicated hardware or kernel support to achieve measured inference speedup. We develop TrimLLM based on the layer-wise specialization phenomenon we empirically observed and verified on contemporary LLMs. TrimLLM reduces the depth of LLMs via progressive layer dropping. We show it retains LLMs' capacity in specific domains and achieves inference speedup irrespective of hardware and deep learning frameworks. We evaluated TrimLLM on LLMs of various sizes for inference; models adapted on medical, legal, and financial datasets all demonstrate 2.1-5.7times inference speedup on consumer GPUs and up to 3.1times speedup on A100 when compared to state-of-the-art model compression algorithms, with no loss in accuracy at 50sim60\% model compression ratio.

As 360{\deg} cameras become prevalent in many autonomous systems (e.g., self-driving cars and drones), efficient 360{\deg} perception becomes more and more important. We propose a novel self-supervised learning approach for predicting the omnidirectional depth and camera motion from a 360{\deg} video. In particular, starting from the SfMLearner, which is designed for cameras with normal field-of-view, we introduce three key features to process 360{\deg} images efficiently. Firstly, we convert each image from equirectangular projection to cubic projection in order to avoid image distortion. In each network layer, we use Cube Padding (CP), which pads intermediate features from adjacent faces, to avoid image boundaries. Secondly, we propose a novel "spherical" photometric consistency constraint on the whole viewing sphere. In this way, no pixel will be projected outside the image boundary which typically happens in images with normal field-of-view. Finally, rather than naively estimating six independent camera motions (i.e., naively applying SfM-Learner to each face on a cube), we propose a novel camera pose consistency loss to ensure the estimated camera motions reaching consensus. To train and evaluate our approach, we collect a new PanoSUNCG dataset containing a large amount of 360{\deg} videos with groundtruth depth and camera motion. Our approach achieves state-of-the-art depth prediction and camera motion estimation on PanoSUNCG with faster inference speed comparing to equirectangular. In real-world indoor videos, our approach can also achieve qualitatively reasonable depth prediction by acquiring model pre-trained on PanoSUNCG.

Integrating Automatic Speech Recognition (ASR) into Speech Emotion Recognition (SER) enhances modeling by providing linguistic context. However, conventional feature fusion faces performance bottlenecks, and multi-task learning often suffers from optimization conflicts. While task vectors and model merging have addressed such conflicts in NLP and CV, their potential in speech tasks remains largely unexplored. In this work, we propose an Adaptive Layer-wise Task Vector Merging (AdaLTM) framework based on WavLM-Large. Instead of joint optimization, we extract task vectors from in-domain ASR and SER models fine-tuned on emotion datasets. These vectors are integrated into a frozen base model using layer-wise learnable coefficients. This strategy enables depth-aware balancing of linguistic and paralinguistic knowledge across transformer layers without gradient interference. Experiments on the MSP-Podcast demonstrate that the proposed approach effectively mitigates conflicts between ASR and SER.

Depth from Defocus (DfD) is the task of estimating a dense metric depth map from a focus stack. Unlike previous works overfitting to a certain dataset, this paper focuses on the challenging and practical setting of zero-shot generalization. We first propose a new real-world DfD benchmark ZEDD, which contains 8.3x more scenes and significantly higher quality images and ground-truth depth maps compared to previous benchmarks. We also design a novel network architecture named FOSSA. FOSSA is a Transformer-based architecture with novel designs tailored to the DfD task. The key contribution is a stack attention layer with a focus distance embedding, allowing efficient information exchange across the focus stack. Finally, we develop a new training data pipeline allowing us to utilize existing large-scale RGBD datasets to generate synthetic focus stacks. Experiment results on ZEDD and other benchmarks show a significant improvement over the baselines, reducing errors by up to 55.7%. The ZEDD benchmark is released at https://zedd.cs.princeton.edu. The code and checkpoints are released at https://github.com/princeton-vl/FOSSA.

Recent work has demonstrated that machine unlearning in Large Language Models (LLMs) fails to generalize across languages: knowledge erased in one language frequently remains accessible through others. However, the underlying cause of this failure and a principled solution remain open. In this work, we identify intervention depth as the key factor determining multilingual generalization. Through systematic layer-wise experiments, we characterize two distinct failure modes: shallow-layer interventions achieve erasure but collapse multilingual capabilities in held-out languages, while deep-layer interventions preserve utility but fail to erase target knowledge even in source languages. These findings reveal that the choice of intervention layer is not a free parameter; it fundamentally determines whether multilingual unlearning succeeds. We propose MUTE (Multilingual Unlearning via Targeted Erasure), a framework that uses Centered Kernel Alignment (CKA) and Linguistic Regions Development Score (LRDS) to identify intermediate, language-agnostic layers where cross-lingual representations converge. By restricting unlearning updates to these layers, MUTE achieves robust multilingual knowledge erasure while optimizing on only a small set of source languages. Extensive experiments across three LLM architectures and three unlearning algorithms validate our approach, with mechanistic analysis via Logit Lens probing confirming genuine knowledge removal rather than output-level suppression.

Representation autoencoders that reuse frozen pretrained vision encoders as visual tokenizers have achieved strong reconstruction and generation quality. However, existing methods universally extract features from only the last encoder layer, discarding the rich hierarchical information distributed across intermediate layers. We show that low-level visual details survive in the last layer merely as attenuated residuals after multiple layers of semantic abstraction, and that explicitly fusing multi-layer features can substantially recover this lost information. We propose DRoRAE (Depth-Routed Representation AutoEncoder), a lightweight fusion module that adaptively aggregates all encoder layers via energy-constrained routing and incremental correction, producing an enriched latent compatible with a frozen pretrained decoder. A three-phase decoupled training strategy first learns the fusion under the implicit distributional constraint of the frozen decoder, then fine-tunes the decoder to fully exploit the enriched representation. On ImageNet-256, DRoRAE reduces rFID from 0.57 to 0.29 and improves generation FID from 1.74 to 1.65 (with AutoGuidance), with gains also transferring to text-to-image synthesis. Furthermore, we uncover a log-linear scaling law (R^2{=}0.86) between fusion capacity and reconstruction quality, identifying representation richness as a new, predictably scalable dimension for visual tokenizers analogous to vocabulary size in NLP.

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM's latent reasoning capacity.

Standard transformer architectures apply the same number of layers to every token regardless of contextual difficulty. We present Token-Selective Attention (TSA), a learned per-token gate on residual updates between consecutive transformer blocks. Each gate is a lightweight two-layer multi-layer perceptron (MLP) that produces a continuous halting probability, making the mechanism end-to-end differentiable with 1.7% parameter overhead and no changes to the base architecture. Notably, TSA learns difficulty-proportional routing without any explicit depth pressure: even at λ=0 (no depth regularisation), the task-loss gradient alone drives the router to skip 20% of token-layer operations. On character-level language modeling, TSA saved 14-23% of token-layer operations (TLOps) across Tiny-Shakespeare and enwik8 at <0.5% quality loss. At matched efficiency, TSA achieved 0.7% lower validation loss than early exit, and the learned routing transfers directly to inference-time sparse execution for real wall-clock speedup.

Vision-language-action (VLA) models route driving decisions through a deep language model, but it is unclear how much of that depth the action itself requires. We study a representative driving VLA whose entire plan is carried by a single planning token that a generative planner decodes into a trajectory. Borrowing the planner as a trajectory-space logit lens, we decode the planning token from every one of the 32 decoder layers and measure two signals: the linear decodability of the navigation command and trajectory compatibility with the frozen native planner. Our diagnostic shows that semantic intent is linearly decodable early: command-probe accuracy reaches 97.7\% after the first decoder layer, compared with 16.7\% chance. In contrast, compatibility with the frozen native planner improves gradually across depth, with open-loop Avg-L2 reaching its minimum of 2.11\,m only at the final layer. Learned readouts from the first layer recover much of this gap, indicating that planning information is already present early but is not yet represented in the format expected by the deployed planner. Ranking decoder layers by the angular deviation they induce in the planning token permits removal of 8 of 32 layers within an approximately 5\% relative open-loop error increase and yields a measured 1.33times decoder speedup. At the evaluated sample size, no family-specific degradation is statistically resolved. These findings are limited to the evaluated ORION checkpoint and Bench2Drive setup.

Large language models (LLMs) are expensive to deploy. Parameter sharing offers a possible path towards reducing their size and cost, but its effectiveness in modern LLMs remains fairly limited. In this work, we revisit "layer tying" as form of parameter sharing in Transformers, and introduce novel methods for converting existing LLMs into smaller "Recursive Transformers" that share parameters across layers, with minimal loss of performance. Here, our Recursive Transformers are efficiently initialized from standard pretrained Transformers, but only use a single block of unique layers that is then repeated multiple times in a loop. We further improve performance by introducing Relaxed Recursive Transformers that add flexibility to the layer tying constraint via depth-wise low-rank adaptation (LoRA) modules, yet still preserve the compactness of the overall model. We show that our recursive models (e.g., recursive Gemma 1B) outperform both similar-sized vanilla pretrained models (such as TinyLlama 1.1B and Pythia 1B) and knowledge distillation baselines -- and can even recover most of the performance of the original "full-size" model (e.g., Gemma 2B with no shared parameters). Finally, we propose Continuous Depth-wise Batching, a promising new inference paradigm enabled by the Recursive Transformer when paired with early exiting. In a theoretical analysis, we show that this has the potential to lead to significant (2-3x) gains in inference throughput.

Pre-Layer Normalization (Pre-LN) is the de facto choice for large language models (LLMs) and is crucial for stable pretraining and effective transfer learning. However, Pre-LN is inefficient due to repeated statistical calculations and suffers from the curse of depth. As layers grow, the magnitude and variance of the hidden state escalate, destabilizing training. Efficiency-oriented normalization-free methods such as Dynamic Tanh (DyT) improve speed but remain fragile at depth. To jointly address stability and efficiency, we propose Bounded Hyperbolic Tanh (BHyT), a drop-in replacement for Pre-LN. BHyT couples a tanh nonlinearity with explicit, data-driven input bounding to keep activations within a non-saturating range. It prevents depth-wise growth in activation magnitude and variance and comes with a theoretical stability guarantee. For efficiency, BHyT computes exact statistics once per block and replaces a second normalization with a lightweight variance approximation, enhancing efficiency. Empirically, BHyT demonstrates improved stability and efficiency during pretraining, achieving an average of 15.8% faster training and an average of 4.2% higher token generation throughput compared to RMSNorm., while matching or surpassing its inference performance and robustness across language understanding and reasoning benchmarks. Our code is available at: https://anonymous.4open.science/r/BHyT

Neural scaling laws describe how language model loss decreases with parameters and data, but treat architecture as interchangeable--a billion parameters could arise from a shallow-wide model (10 layers & 8,192 hidden dimension) or a deep-narrow one (80 layers & 2,048 hidden dimension). We propose architecture-conditioned scaling laws decomposing this dependence, finding that optimal depth scales as D* ~ C^0.12 while optimal width scales as W* ~ C^0.34, meaning width should grow 2.8x faster than depth. We discover a critical depth phenomenon: beyond D_crit ~ W^0.44 (sublinear in W), adding layers increases loss despite adding parameters--the Depth Delusion. Empirically, we validate these findings across 30 transformer architectures spanning 17M to 7B parameters, each trained on representative high-compute samples, achieving R^2 = 0.922. Our central finding: at 7B scale, a 64-layer model (6.38B params) underperforms a 32-layer model (6.86B params) by 0.12 nats, despite being significantly deeper. This demonstrates that optimal depth-width tradeoffs persist at the production scale.

Multimodal large language models (MLLMs) commonly inherit the deep, symmetric Transformer backbone designed for unimodal text modeling, and apply the same computation uniformly to image and language tokens. This design overlooks a key modality asymmetry: image and text tokens differ substantially in information density, redundancy, and required reasoning depth. Through a layer-wise analysis of LLaVA-1.5, we observe that vision tokens tend to saturate in the middle layers. Specifically, text-to-image attention decreases from 0.68 at layer 0 to 0.07 by layer 4, and stabilizes near 0.04 after layer 18, whereas text tokens continue to benefit from deep semantic processing. These findings suggest a mismatch between architectural symmetry and depth-asynchronous modality evolution, resulting in redundant visual computation and possible drift in perceptual representations during deep task-specific adaptation. Motivated by this, we propose Dual-Path Vision Token Routing (DPVR), a modality-asymmetric routing framework for efficient MLLMs. Its core instantiation, DPVR-LF (Late-Layer Fusion), routes vision tokens at the saturation point into a one-layer trainable side branch, runs a thirteen-layer text-only forward that skips image positions in the deep stack, and re-fuses the visual and textual streams only at the final layer. With approximately 3% trainable parameters, DPVR-LF preserves competitive multimodal performance on standard benchmarks while reducing visual computation in the deep Transformer stack. The results challenge the conventional assumption that vision tokens must traverse all deep language-model layers, and indicate that a single late fusion layer can be sufficient for maintaining strong perceptual competence in LLaVA-style MLLMs.

Large language models are known to contain representational redundancy across network depth, making depth pruning an effective approach for improving inference efficiency. Existing one-shot pruning methods rely on local layer importance or fixed redundancy assumptions across architectures. We propose Locality-Aware Redundancy Pruning (LoRP), a training-free one-shot depth pruning framework guided by representation locality. We show that inter-layer redundancy can be either localized or globally distributed depending on the LLM architecture. To characterize this phenomenon, we introduce Representation Locality Score (RLS), derived from global inter-layer hidden-state similarity. Using a small calibration set, LoRP computes pairwise layer similarity, clusters layers by representational similarity, and allocates pruning according to residual intra-cluster redundancy. Experiments across diverse LLM families show improvements in both perplexity and downstream task accuracy. Official github repository: https://github.com/daniel-eai/LoRP-Locality-Aware-Redundancy-Pruning/

Transformer depth is not used uniformly: lower and middle layers build semantic representations, while upper layers increasingly specialize them for prediction. We turn this division of labor into CoMem (Comprehension Memory), which writes each context chunk only through an intermediate layer, retrieves a fixed number of cached residual states, and recomputes the query-conditioned upper layers over the resulting pack. For a fixed retrieval budget, model-side read compute and memory are independent of stored-context length. We evaluate a continued-trained Qwen3-8B base LM under a unified chat-template-free protocol. The backbone is frozen; the flagship trains only a rank-32 self-distillation LoRA on plain PG19, and we report an adapter-free arm separately. CoMem reaches 97.05 on RULER and 38.27 on LoCoMo versus 34.59 for full-context KV-Direct; the dialogue-memory advantage survives conversation-cluster resampling and an independent judge. Results on additional long-context and long-document tasks expose both the benefits of bounded retrieval and its in-window compression tax. Controlled depth sweeps show that deeper caching lowers per-query recomputation but incurs a fidelity loss that self-distillation substantially repairs. In a separate adapter-free efficiency control on an NVIDIA H20 at 128k, CoMem uses 18.26 GB rather than 89.36 GB and achieves a 7.83x prefill speedup. These results show that long-context memory can be organized along the layer axis, not only the token axis.

Layer dropout (a.k.a. stochastic depth) has been shown to enable faster training, higher accuracy, and robustness to zero-shot layer pruning in both language and vision transformers. However, as models and datasets have scaled, dropout - particularly layer dropout - has largely disappeared from large language models (LLMs) pre-training recipes. While some prior work has reported that dropout can degrade accuracy, no comprehensive study has quantified, let alone mitigated, this effect. In this study, we show that layer dropout should be used in state-of-the-art LLM training, establishing best practices and scaling analysis for both training and post-training benefits. Concretely, with optimal layer distribution, time schedule, and optimizer hyperparameters, we observe that at the same training FLOPs layer dropout leads to lower loss. For a given number of training steps, LLMs can achieve lower or similar validation loss while saving upto 25% of training FLOPs. Moreover, layer dropout enables significant post-training optimizations, such as early exit, intermediate-layer skipping, and self-speculative decoding, yielding up to 1.5x inference speedup with negligible accuracy loss. Across more than 2400 training experiments, spanning models from 271M to 8.2B parameters and datasets up to 160B tokens, we demonstrate that these findings extend reliably to large-scale training regimes. All pre-training experiments were run on Cerebras CS-3 systems.

Deep networks often suffer from vanishing or exploding gradients due to inefficient signal propagation, leading to long training times or convergence difficulties. Various architecture designs, sophisticated residual-style networks, and initialization schemes have been shown to improve deep signal propagation. Recently, Pennington et al. used free probability theory to show that dynamical isometry plays an integral role in efficient deep learning. We show that the simplest architecture change of gating each residual connection using a single zero-initialized parameter satisfies initial dynamical isometry and outperforms more complex approaches. Although much simpler than its predecessors, this gate enables training thousands of fully connected layers with fast convergence and better test performance for ResNets trained on CIFAR-10. We apply this technique to language modeling and find that we can easily train 120-layer Transformers. When applied to 12 layer Transformers, it converges 56% faster on enwiki8.

We propose a method for converting a single RGB-D input image into a 3D photo - a multi-layer representation for novel view synthesis that contains hallucinated color and depth structures in regions occluded in the original view. We use a Layered Depth Image with explicit pixel connectivity as underlying representation, and present a learning-based inpainting model that synthesizes new local color-and-depth content into the occluded region in a spatial context-aware manner. The resulting 3D photos can be efficiently rendered with motion parallax using standard graphics engines. We validate the effectiveness of our method on a wide range of challenging everyday scenes and show fewer artifacts compared with the state of the arts.

In practice, deeper networks tend to be more powerful than shallow ones, but this has not been understood theoretically. In this paper, we find the analytical solution of a three-layer network with a matrix exponential activation function, i.e., $ f(X)=W_3exp(W_2exp(W_1X)), Xin C^{dtimes d} have analytical solutions for the equations Y_1=f(X_1),Y_2=f(X_2) for X_1,X_2,Y_1,Y_2 with only invertible assumptions. Our proof shows the power of depth and the use of a non-linear activation function, since one layer network can only solve one equation,i.e.,Y=WX$.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks and comparisons across model architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features. These findings challenge the standard focus on final-layer embeddings and open new directions for model analysis and optimization, including strategic use of mid-layer representations for more robust and accurate AI systems.

The integration of Rotary Position Embedding (RoPE) in Multimodal Diffusion Transformer (MMDiT) has significantly enhanced text-to-image generation quality. However, the fundamental reliance of self-attention layers on positional embedding versus query-key similarity during generation remains an intriguing question. We present the first mechanistic analysis of RoPE-based MMDiT models (e.g., FLUX), introducing an automated probing strategy that disentangles positional information versus content dependencies by strategically manipulating RoPE during generation. Our analysis reveals distinct dependency patterns that do not straightforwardly correlate with depth, offering new insights into the layer-specific roles in RoPE-based MMDiT. Based on these findings, we propose a training-free, task-specific image editing framework that categorizes editing tasks into three types: position-dependent editing (e.g., object addition), content similarity-dependent editing (e.g., non-rigid editing), and region-preserved editing (e.g., background replacement). For each type, we design tailored key-value injection strategies based on the characteristics of the editing task. Extensive qualitative and quantitative evaluations demonstrate that our method outperforms state-of-the-art approaches, particularly in preserving original semantic content and achieving seamless modifications.

Single Image Reflection Separation (SIRS) disentangles mixed images into transmission and reflection layers. Existing methods suffer from transmission-reflection confusion under nonlinear mixing, particularly in deep decoder layers, due to implicit fusion mechanisms and inadequate multi-scale coordination. We propose ReflexSplit, a dual-stream framework with three key innovations. (1) Cross-scale Gated Fusion (CrGF) adaptively aggregates semantic priors, texture details, and decoder context across hierarchical depths, stabilizing gradient flow and maintaining feature consistency. (2) Layer Fusion-Separation Blocks (LFSB) alternate between fusion for shared structure extraction and differential separation for layer-specific disentanglement. Inspired by Differential Transformer, we extend attention cancellation to dual-stream separation via cross-stream subtraction. (3) Curriculum training progressively strengthens differential separation through depth-dependent initialization and epoch-wise warmup. Extensive experiments on synthetic and real-world benchmarks demonstrate state-of-the-art performance with superior perceptual quality and robust generalization. Our code is available at https://github.com/wuw2135/ReflexSplit.

Layering information spaces is a promising strategy to design intuitive and engaging interactive experiences. Although multi-layer displays enable promising interaction techniques through limited depth perception - achieved via slight separation between layers - it remains unclear how to fully design experiences that leverage the unique affordances of layered information. To address this, we introduce Proscenium, a dual-layer, large transparent display workspace setup with an adjustable separation between the layers. We demonstrate our preliminary design space focusing on how rendered information can be transitioned and linked across displays, and showcase 14 speculative experience prototypes across six categories.

Serving transformer language models with high throughput requires caching Key-Values (KVs) to avoid redundant computation during autoregressive generation. The memory footprint of KV caching is significant and heavily impacts serving costs. This work proposes to lessen these memory requirements. While recent work has largely addressed KV cache reduction via compression and eviction along the temporal axis, we argue that the depth dimension offers an orthogonal and robust avenue for optimization. Although prior research suggests that a full cache for every layer is redundant, implementing cross-layer cache sharing remains a practical challenge; existing methods typically suffer from reduced throughput or increased time-to-first-token. In this paper, we demonstrate that dropping a layer's cache offers efficient optimization without information loss. We propose a simple training approach: random cross-layer attention. During training, layers randomly choose to attend either to their own KV states or those of a preceding layer. This stochastic process adapts the model to be robust to various depth-wise cache sharing strategies, ensuring flexibility for unknown hardware constraints at deployment time. Our evaluations show that applying this scheme during pre-training or fine-tuning enables depth-wise cache sharing for various model families. Furthermore, for larger models in data-constrained settings, this approach is suggestive of a regularization-like effect, frequently preserving or improving performance while significantly reducing the cache's memory footprint.

Large language models run every token through every layer, regardless of difficulty. We present TIDE, a post-training system that attaches tiny learned routers at periodic checkpoint layers and, at inference time, selects the earliest layer whose hidden state has converged for each token. TIDE requires no model retraining, works with any HuggingFace causal LM, auto-detects GPU architecture, and supports float32, float16, and bfloat16 through fused CUDA kernels. On an NVIDIA A100 with DeepSeek R1 Distill 8B, TIDE achieves 100% prefill exit rate (5% of tokens exit at layer 11, the remaining at layer 31), reduces prefill latency by 7.2%, and increases single-batch throughput by 6.6%. During autoregressive decoding, 98-99% of tokens exit early while the model correctly solves a multi-step math problem with 95 unique output tokens. On Qwen3 8B (36 layers), throughput improves by 8.1% at batch size 8. Calibration on 2,000 WikiText samples takes under 3 minutes and produces a ~4 MB router checkpoint. The system comprises 1,308 lines of Python and 1,081 lines of CUDA/C++ with 74 passing tests. Code: https://github.com/RightNow-AI/TIDE

Long-context inference in decoder-only language models is costly because long prompts are processed during Prefill, cached at every layer, and repeatedly attended to during autoregressive Decode. We introduce Shallow Prefill, dEEp Decode (SPEED), a phase-asymmetric KV-visibility policy that materializes non-anchor prompt-token KV states only in lower layers while keeping Decode-phase tokens full-depth. Unlike previous approaches that make upper-layer prompt KV states cheaper to store or construct, SPEED removes prefill tokens from the upper-layer Decode visibility set altogether. With a minimal BoS anchor, this simple change preserves broad benchmark quality while reducing long-context cost. In a controlled Llama-3.1-8B instruction-tuning study, SPEED using only 75\% of layers for prefill tokens reaches 51.2 average score on OLMES-style benchmarks, compared with 51.4 for the full-depth baseline, while improving TTFT by 33\%, TPOT by 22\%, and reducing active KV memory by 25.0\% at 128K context. Layer-wise diagnostics suggest that this cutoff retains the main prompt-selection and representation-stabilization regions of the full-depth model. These results show that long-context prompt tokens need not always persist as full-depth KV-cache objects when Decode-phase tokens remain full-depth.

Large language model (LLM) unlearning has emerged as a crucial post-hoc mechanism for privacy protection and AI safety, yet auditing whether target knowledge is truly erased remains challenging. Existing output-level metrics fail to detect when this knowledge remains recoverable from internal representations. Recent white-box studies reveal such residual knowledge but often rely on auxiliary training or dataset-specific adaptations, leaving no generalizable metric. To address these limitations, we propose the Unlearning Depth Score (UDS), a metric that quantifies the mechanistic depth of unlearning via activation patching. UDS first identifies layers that encode the target knowledge using a retain model baseline, then measures how much of it is erased in the unlearned model on a 0-1 scale. In a meta-evaluation across 20 metrics on 150 unlearned models spanning 8 methods, UDS achieves the highest faithfulness and robustness, confirming our causal approach as the most reliable for unlearning evaluation. Case studies further reveal that white-box metrics can disagree at the layer level and that erasure depth varies across examples. We provide guidelines for integrating UDS into existing benchmarking frameworks and streamlining the evaluation pipeline. Code and data are available at https://github.com/gnueaj/unlearning-depth-score

Universal multimodal embedding (UME) maps heterogeneous multimodal inputs into a shared embedding space. Existing UME models either form embeddings through single forward encoding or add computation through explicit rationale tokens and latent autoregressive states. Although token expansion can improve complex matching, serial generation increases retrieval latency and makes the final embedding depend on generated intermediate states. This raises a different question: can useful computation be expanded along model depth while keeping the token workspace fixed? We analyze positive-negative similarity separation at every layer of independently trained UME models and observe a shared progression: early layers contextualize multimodal inputs, a contiguous middle-to-late stage forms retrieval-discriminative features, and the final layers map them into the embedding space. Based on this finding, we propose ReLoop-UME, which executes the early layers once, recurrently reuses a parameter-shared retrieval-forming block, and applies the final mapping layers after the last loop. Learnable Retrieval Registers provide persistent retrieval-specific states that accumulate and exchange evidence across loops, with the final register serving as the embedding readout. On MMEB-V2 and MRMR, ReLoop-UME consistently improves retrieval across different backbones while running 44.9x faster than UME-R1 and 1.5x faster than PLUME.

When generating text, a Transformer produces representations of past tokens at every layer, but each layer can normally use only representations from the same depth. This restriction prevents the model from fully reusing information it has already computed. We introduce WhiteMatter, which allows every layer to draw on past-token representations from any depth. A learned mixer selects the most useful depths for the current context and combines their representations into shared key-value (KV) cache channels. Sharing these channels across layers can reduce the cache size. Given the same number of training tokens, WhiteMatter with a full-size cache performs comparably to a standard Transformer with 50% more layers. With half the KV cache, WhiteMatter outperforms matched standard Transformers at two model scales, up to 1.3B parameters. Cross-layer connections, however, introduce dependencies that slow training and prompt processing. We address this problem with cyclic iteration, which updates interleaved groups of tokens in turn while processing the tokens within each group in parallel. On a reference model trained with exact autoregressive execution, cyclic iteration converges 12.5x faster than standard Jacobi iteration.

The transformer architecture by Vaswani et al. (2017) is now ubiquitous across application domains, from natural language processing to speech processing and image understanding. We propose DenseFormer, a simple modification to the standard architecture that improves the perplexity of the model without increasing its size -- adding a few thousand parameters for large-scale models in the 100B parameters range. Our approach relies on an additional averaging step after each transformer block, which computes a weighted average of current and past representations -- we refer to this operation as Depth-Weighted-Average (DWA). The learned DWA weights exhibit coherent patterns of information flow, revealing the strong and structured reuse of activations from distant layers. Experiments demonstrate that DenseFormer is more data efficient, reaching the same perplexity of much deeper transformer models, and that for the same perplexity, these new models outperform transformer baselines in terms of memory efficiency and inference time.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

Predominant techniques on talking head generation largely depend on 2D information, including facial appearances and motions from input face images. Nevertheless, dense 3D facial geometry, such as pixel-wise depth, plays a critical role in constructing accurate 3D facial structures and suppressing complex background noises for generation. However, dense 3D annotations for facial videos is prohibitively costly to obtain. In this work, firstly, we present a novel self-supervised method for learning dense 3D facial geometry (ie, depth) from face videos, without requiring camera parameters and 3D geometry annotations in training. We further propose a strategy to learn pixel-level uncertainties to perceive more reliable rigid-motion pixels for geometry learning. Secondly, we design an effective geometry-guided facial keypoint estimation module, providing accurate keypoints for generating motion fields. Lastly, we develop a 3D-aware cross-modal (ie, appearance and depth) attention mechanism, which can be applied to each generation layer, to capture facial geometries in a coarse-to-fine manner. Extensive experiments are conducted on three challenging benchmarks (ie, VoxCeleb1, VoxCeleb2, and HDTF). The results demonstrate that our proposed framework can generate highly realistic-looking reenacted talking videos, with new state-of-the-art performances established on these benchmarks. The codes and trained models are publicly available on the GitHub project page at https://github.com/harlanhong/CVPR2022-DaGAN

Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters. This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient κ_R. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from 1/4 to 1/2 as loop count grows at fixed physical depth. The resulting method, DeepLoop, keeps the Post-LN DeepNorm architecture and sets α=(2N)^{1/2} and β=(8N)^{-1/2} for unrolled depth N. On GPT-style looped language models at GPT-2 small and GPT-2 medium scale, DeepLoop is neutral when no physical block is revisited and improves validation loss and downstream accuracy once recurrent depth is activated. These results show that stable recurrent depth requires residual scaling rules that account for parameter visits, not only nominal layer count.

Scaling transformer language models creates an inherent tension between expressivity and memory efficiency. While unique weights across layers preserve functional specialization---from input-grounding to abstract refinement---they incur a substantial memory footprint. Conversely, standard depth-sharing enforces uniform transformations that collapse representational diversity and degrade modeling quality. We introduce Gated Recurrent Transformer, a recurrent depth transformer where fixed-depth prelude and coda blocks bracket a single shared core iterated R times. Inspired by gated recurrent neural networks, we employ a lightweight projection and an elementwise update gate---conditioned on the hidden state, the fixed prelude output, and noise resampled at every step---to modulate the recurrent update. This allows the model to specialize the input to the same few layers across recurrences, rather than requiring many unique layers to achieve functional diversity. Under an isoFLOPS constraint, a 3-layer Gated Recurrent Transformer matches the accuracy of a 12-layer GPT-2 Small baseline with similar training and inference FLOPs, and leads MoR and heavy-tail depth sampling in all nine scale-by-budget cells; at medium and large scale it approaches dense quality at the standard token budget and overtakes it at medium scale once that budget is doubled. Under an isoPARAMS constraint, deeper recurrence achieves a 2.76 validation loss versus 2.84 for a non-recurrent counterpart at matched parameter and data budget. Our results demonstrate that adaptive depth reuse is a principled strategy for trading parameters for quality: at large scale, 63% fewer parameters and 59% less peak decoding memory for a 10% increase in compiled generation latency.

Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta^n, which keeps the meta-operation fixed and recurses on its input instead. That operation, Ω, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because Ω never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and an evolutionary archive searches over layer chains. Across two backbones, Meta^n outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n

We identify Harmfulness Propagation Dynamics (HPD): for harmful prompts, the projection of the last-token hidden state onto a learned harm direction rises monotonically with transformer depth, whereas benign prompts remain flat or oscillatory. This cross-layer signature reflects harmful intent as a progressively resolved semantic property: surface form appears early, while pragmatic intent consolidates later, making the trajectory shape more informative than any single-layer snapshot. Moreover, LDA-based harm directions, learned per layer, remain stable across random splits (pairwise cosine similarity >0.97), supporting the projection sequence as a reproducible structured signal. Building on HPD, we introduce \herald{} (Harmful Encoding Recognition via Activation Layer Dynamics). This lightweight input moderator extracts a seven-dimensional feature record, slope, curvature, monotonicity, onset layer, and related statistics from the cross-layer projection sequence and classifies it with a 288-parameter MLP. stores one d-dimensional direction per layer (262\,KB for a 32-layer, d{=}4096 model), requires no gradient computation during training, and adds only 2.6{times}10^{-6} prefill FLOPs at inference. Across eight prompt-harmfulness benchmarks and four model families, achieves an average F1 of 89.3 on OLMo2-7B, surpassing all tested guard models on adversarial jailbreak detection (98.4 vs.\ 96.9 F1) and outperforming prior latent-based methods by 2.3-4.1 F1 points on every backbone. Per-instance trajectories provide machine-readable audit records that reveal when and how harmfulness emerges, offering an interpretability advantage over single-layer approaches.

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

Transformer-based end-to-end speech recognition has achieved great success. However, the large footprint and computational overhead make it difficult to deploy these models in some real-world applications. Model compression techniques can reduce the model size and speed up inference, but the compressed model has a fixed architecture which might be suboptimal. We propose a novel Transformer encoder with Input-Dependent Dynamic Depth (I3D) to achieve strong performance-efficiency trade-offs. With a similar number of layers at inference time, I3D-based models outperform the vanilla Transformer and the static pruned model via iterative layer pruning. We also present interesting analysis on the gate probabilities and the input-dependency, which helps us better understand deep encoders.

In this paper, we propose TitaNet, a novel neural network architecture for extracting speaker representations. We employ 1D depth-wise separable convolutions with Squeeze-and-Excitation (SE) layers with global context followed by channel attention based statistics pooling layer to map variable-length utterances to a fixed-length embedding (t-vector). TitaNet is a scalable architecture and achieves state-of-the-art performance on speaker verification task with an equal error rate (EER) of 0.68% on the VoxCeleb1 trial file and also on speaker diarization tasks with diarization error rate (DER) of 1.73% on AMI-MixHeadset, 1.99% on AMI-Lapel and 1.11% on CH109. Furthermore, we investigate various sizes of TitaNet and present a light TitaNet-S model with only 6M parameters that achieve near state-of-the-art results in diarization tasks.

Self-supervised monocular depth estimation has garnered considerable attention for its applications in autonomous driving and robotics. While recent methods have made strides in leveraging techniques like the Self Query Layer (SQL) to infer depth from motion, they often overlook the potential of strengthening pose information. In this paper, we introduce SPIdepth, a novel approach that prioritizes enhancing the pose network for improved depth estimation. Building upon the foundation laid by SQL, SPIdepth emphasizes the importance of pose information in capturing fine-grained scene structures. By enhancing the pose network's capabilities, SPIdepth achieves remarkable advancements in scene understanding and depth estimation. Experimental results on benchmark datasets such as KITTI, Cityscapes, and Make3D showcase SPIdepth's state-of-the-art performance, surpassing previous methods by significant margins. Specifically, SPIdepth tops the self-supervised KITTI benchmark. Additionally, SPIdepth achieves the lowest AbsRel (0.029), SqRel (0.069), and RMSE (1.394) on KITTI, establishing new state-of-the-art results. On Cityscapes, SPIdepth shows improvements over SQLdepth of 21.7% in AbsRel, 36.8% in SqRel, and 16.5% in RMSE, even without using motion masks. On Make3D, SPIdepth in zero-shot outperforms all other models. Remarkably, SPIdepth achieves these results using only a single image for inference, surpassing even methods that utilize video sequences for inference, thus demonstrating its efficacy and efficiency in real-world applications. Our approach represents a significant leap forward in self-supervised monocular depth estimation, underscoring the importance of strengthening pose information for advancing scene understanding in real-world applications. The code and pre-trained models are publicly available at https://github.com/Lavreniuk/SPIdepth.

Despite the significant progress in multimodal large language models (MLLMs), their high computational cost remains a barrier to real-world deployment. Inspired by the mixture of depths (MoDs) in natural language processing, we aim to address this limitation from the perspective of ``activated tokens''. Our key insight is that if most tokens are redundant for the layer computation, then can be skipped directly via the MoD layer. However, directly converting the dense layers of MLLMs to MoD layers leads to substantial performance degradation. To address this issue, we propose an innovative MoD adaptation strategy for existing MLLMs called gamma-MoD. In gamma-MoD, a novel metric is proposed to guide the deployment of MoDs in the MLLM, namely rank of attention maps (ARank). Through ARank, we can effectively identify which layer is redundant and should be replaced with the MoD layer. Based on ARank, we further propose two novel designs to maximize the computational sparsity of MLLM while maintaining its performance, namely shared vision-language router and masked routing learning. With these designs, more than 90% dense layers of the MLLM can be effectively converted to the MoD ones. To validate our method, we apply it to three popular MLLMs, and conduct extensive experiments on 9 benchmark datasets. Experimental results not only validate the significant efficiency benefit of gamma-MoD to existing MLLMs but also confirm its generalization ability on various MLLMs. For example, with a minor performance drop, i.e., -1.5%, gamma-MoD can reduce the training and inference time of LLaVA-HR by 31.0% and 53.2%, respectively.

Transformer models have established new benchmarks in natural language processing; however, their increasing depth results in substantial growth in parameter counts. While existing recurrent transformer methods address this issue by reprocessing layers multiple times, they often apply recurrence indiscriminately across entire blocks of layers. In this work, we investigate Intra-Layer Recurrence (ILR), a more targeted approach that applies recurrence selectively to individual layers within a single forward pass. Our experiments show that allocating more iterations to earlier layers yields optimal results. These findings suggest that ILR offers a promising direction for optimizing recurrent structures in transformer architectures.

For any positive integer k, there exist neural networks with Θ(k^3) layers, Θ(1) nodes per layer, and Θ(1) distinct parameters which can not be approximated by networks with O(k) layers unless they are exponentially large --- they must possess Ω(2^k) nodes. This result is proved here for a class of nodes termed "semi-algebraic gates" which includes the common choices of ReLU, maximum, indicator, and piecewise polynomial functions, therefore establishing benefits of depth against not just standard networks with ReLU gates, but also convolutional networks with ReLU and maximization gates, sum-product networks, and boosted decision trees (in this last case with a stronger separation: Ω(2^{k^3}) total tree nodes are required).

Diffusion Transformers (DiTs) have shown exceptional performance in image generation, yet their large parameter counts incur high computational costs, impeding deployment in resource-constrained settings. To address this, we propose Pluggable Pruning with Contiguous Layer Distillation (PPCL), a flexible structured pruning framework specifically designed for DiT architectures. First, we identify redundant layer intervals through a linear probing mechanism combined with the first-order differential trend analysis of similarity metrics. Subsequently, we propose a plug-and-play teacher-student alternating distillation scheme tailored to integrate depth-wise and width-wise pruning within a single training phase. This distillation framework enables flexible knowledge transfer across diverse pruning ratios, eliminating the need for per-configuration retraining. Extensive experiments on multiple Multi-Modal Diffusion Transformer architecture models demonstrate that PPCL achieves a 50\% reduction in parameter count compared to the full model, with less than 3\% degradation in key objective metrics. Notably, our method maintains high-quality image generation capabilities while achieving higher compression ratios, rendering it well-suited for resource-constrained environments. The open-source code, checkpoints for PPCL can be found at the following link: https://github.com/OPPO-Mente-Lab/Qwen-Image-Pruning.

Using solar-cycle long helioseismic measurements of meridional and zonal flows in the near-surface shear layer (NSSL) of the Sun, we study their spatio-temporal variations and connections to active regions. We find that near-surface inflows towards active latitudes are part of a local circulation with an outflow away from them at depths around 0.97 R, which is also the location where the deviations in the radial gradient of rotation change sign. These results, together with opposite-signed changes over latitude and depth in the above quantities observed during the solar minimum period, point to the action of the Coriolis force on large-scale flows as the primary cause of changes in the rotation gradient within the NSSL. We also find that such Coriolis force-mediated changes in near-surface flows towards active latitudes only marginally change the amplitude of zonal flow and hence are not likely to be its driving force. Our measurements typically achieve a high signal-to-noise ratio (>5σ) for near-surface flows but can drop to 3σ near the base (0.95 R) of the NSSL. Close agreements between the depth profiles of changes in rotation gradient and in meridional flows measured from quite different global and local helioseismic techniques, respectively, show that the results are not dependent on the analysis techniques.

We introduce a framework that automates the transformation of static anime illustrations into manipulatable 2.5D models. Current professional workflows require tedious manual segmentation and the artistic ``hallucination'' of occluded regions to enable motion. Our approach overcomes this by decomposing a single image into fully inpainted, semantically distinct layers with inferred drawing orders. To address the scarcity of training data, we introduce a scalable engine that bootstraps high-quality supervision from commercial Live2D models, capturing pixel-perfect semantics and hidden geometry. Our methodology couples a diffusion-based Body Part Consistency Module, which enforces global geometric coherence, with a pixel-level pseudo-depth inference mechanism. This combination resolves the intricate stratification of anime characters, e.g., interleaving hair strands, allowing for dynamic layer reconstruction. We demonstrate that our approach yields high-fidelity, manipulatable models suitable for professional, real-time animation applications.

Mixture-of-Experts (MoE) decouples model capacity from per-token computation, yet their scalability remains limited by the physical dimensions of depth and width. To overcome this, we propose Mixture of Universal Experts (MOUE),a MoE generalization introducing a novel scaling dimension: Virtual Width. In general, MoUE aims to reuse a universal layer-agnostic expert pool across layers, converting depth into virtual width under a fixed per-token activation budget. However, two challenges remain: a routing path explosion from recursive expert reuse, and a mismatch between the exposure induced by reuse and the conventional load-balancing objectives. We address these with three core components: a Staggered Rotational Topology for structured expert sharing, a Universal Expert Load Balance for depth-aware exposure correction, and a Universal Router with lightweight trajectory state for coherent multi-step routing. Empirically, MoUE consistently outperforms matched MoE baselines by up to 1.3% across scaling regimes, enables progressive conversion of existing MoE checkpoints with up to 4.2% gains, and reveals a new scaling dimension for MoE architectures.

Recent work has demonstrated the curse of depth in large language models (LLMs), where later layers contribute less to learning and representation than earlier layers. Such under-utilization is linked to the accumulated growth of variance in Pre-Layer Normalization, which can push deep blocks toward near-identity behavior. In this paper, we demonstrate that, sparsity, beyond enabling efficiency, acts as a regulator of variance propagation and thereby improves depth utilization. Our investigation covers two sources of sparsity: (i) implicit sparsity, which emerges from training and data conditions, including weight sparsity induced by weight decay and attention sparsity induced by long context inputs; and (ii) explicit sparsity, which is enforced by architectural design, including key/value-sharing sparsity in Grouped-Query Attention and expert-activation sparsity in Mixtureof-Experts. Our claim is thoroughly supported by controlled depth-scaling experiments and targeted layer effectiveness interventions. Across settings, we observe a consistent relationship: sparsity improves layer utilization by reducing output variance and promoting functional differentiation. We eventually distill our findings into a practical rule-of-thumb recipe for training deptheffective LLMs, yielding a notable 4.6% accuracy improvement on downstream tasks. Our results reveal sparsity, arising naturally from standard design choices, as a key yet previously overlooked mechanism for effective depth scaling in LLMs. Code is available at https://github.com/pUmpKin-Co/SparsityAndCoD.

Depth-recurrence facilitates latent reasoning by sharing parameters across depths. However, prior work lacks combined FLOP-, parameter-, and memory-matched baselines, underutilizes depth-recurrence due to partially fixed layer stacks, and ignores the bottleneck of constant hidden-sizes that restricts many-step latent reasoning. To address this, we introduce a modular framework of depth-recurrent attention mixtures (Dreamer), combining sequence attention, depth attention, and sparse expert attention. It alleviates the hidden-size bottleneck through attention along depth, decouples scaling dimensions, and allows depth-recurrent models to scale efficiently and effectively. Across language reasoning benchmarks, our models require 2 to 8x fewer training tokens for the same accuracy as FLOP-, parameter-, and memory-matched SOTA, and outperform ca. 2x larger SOTA models with the same training tokens. We further present insights into knowledge usage across depths, e.g., showing 2 to 11x larger expert selection diversity than SOTA MoEs.

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and attention speedup. This leaves an underexplored research question: can we reduce the number of stacked transformer layers while maintaining comparable representational capacity? To answer this, we propose a branch-based structural reparameterization technique that operates during the training phase. Our approach leverages parallel branches within transformer blocks that can be systematically consolidated into streamlined single-path models suitable for inference deployment. The consolidation mechanism works by gradually merging branches at the entry points of nonlinear components, enabling both feed-forward networks (FFN) and multi-head self-attention (MHSA) modules to undergo exact mathematical reparameterization without inducing approximation errors at test time. When applied to ViT-Tiny, the framework successfully reduces the original 12-layer architecture to 6, 4, or as few as 3 layers while maintaining classification accuracy on ImageNet-1K. The resulting compressed models achieve inference speedups of up to 37% on mobile CPU platforms. Our findings suggest that the conventional wisdom favoring extremely deep transformer stacks may be unnecessarily restrictive, and point toward new opportunities for constructing efficient vision transformers.

Transformers process tokens in parallel but are temporally shallow: at position t, each layer attends to key-value pairs computed based on the previous layer, yielding a depth capped by the number of layers. Recurrent models offer unbounded temporal depth but suffer from optimization instability and historically underutilize modern accelerators. We introduce the Recurrent Transformer, a simple architectural change where each layer attends to key-value pairs computed off its own activations, yielding layerwise recurrent memory while preserving standard autoregressive decoding cost. We show that the architecture can emulate both (i) a conventional Transformer and (ii) token-to-token recurrent updates under mild assumptions, while avoiding optimization instability. Naively, prefill/training appears bandwidth-bound with effective arithmetic intensity near 1 because keys and values are revealed sequentially; we give an exact tiling-based algorithm that preserves the mathematical computation while reducing HBM traffic from Θ(N^2) to Θ(Nlog N), increasing effective arithmetic intensity to Θ(N/log N) for sequence length N. On 150M and 300M parameter C4 pretraining, Recurrent Transformers improve cross-entropy over a parameter-matched Transformer baseline and achieve the improvement with fewer layers (fixed parameters), suggesting that recurrence can trade depth for width, thus reducing KV cache memory footprint and inference latency.

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight γ: with depth, γ grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise γ vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and <0.02% change in FLOPs. Across a model ladder scaled up to 100B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with 3.4times less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by 3-10times, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.