Daily Papers

We propose a multicountry quantile factor augmeneted vector autoregression (QFAVAR) to model heterogeneities both across countries and across characteristics of the distributions of macroeconomic time series. The presence of quantile factors allows for summarizing these two heterogeneities in a parsimonious way. We develop two algorithms for posterior inference that feature varying level of trade-off between estimation precision and computational speed. Using monthly data for the euro area, we establish the good empirical properties of the QFAVAR as a tool for assessing the effects of global shocks on country-level macroeconomic risks. In particular, QFAVAR short-run tail forecasts are more accurate compared to a FAVAR with symmetric Gaussian errors, as well as univariate quantile autoregressions that ignore comovements among quantiles of macroeconomic variables. We also illustrate how quantile impulse response functions and quantile connectedness measures, resulting from the new model, can be used to implement joint risk scenario analysis.

In fully cooperative multi-agent reinforcement learning (MARL) settings, the environments are highly stochastic due to the partial observability of each agent and the continuously changing policies of the other agents. To address the above issues, we integrate distributional RL and value function factorization methods by proposing a Distributional Value Function Factorization (DFAC) framework to generalize expected value function factorization methods to their DFAC variants. DFAC extends the individual utility functions from deterministic variables to random variables, and models the quantile function of the total return as a quantile mixture. To validate DFAC, we demonstrate DFAC's ability to factorize a simple two-step matrix game with stochastic rewards and perform experiments on all Super Hard tasks of StarCraft Multi-Agent Challenge, showing that DFAC is able to outperform expected value function factorization baselines.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Policies with similar mean returns can differ sharply in rare failures, yet estimating lower-tail conditional value-at-risk (CVaR) accurately can require many costly rollouts. When different conditional components of a stochastic workflow can be queried separately, we ask how to allocate a fixed evaluation budget to estimate a fixed policy's CVaR most accurately. We derive a tail influence for each queryable conditional law that aggregates how its uncertainty affects CVaR across every Bellman reuse. Its variance yields the fixed-design efficiency bound and the oracle Neyman allocation. Tail-Influence Sampling (TIS) estimates these influence scales from a pilot model and reallocates fresh queries toward kernels that matter most for the tail; a visitation-anchored variant protects against pilot underallocation. Under fixed dimension and a positive quantile margin, TIS attains oracle asymptotic variance and first-order MSE including pilot cost, while the anchored variant is within a factor two of the oracle. We also characterize an exact-grid regime in which tail- and mean-optimal allocations coincide. On CliffWalking, TIS reduces MSE by 41% versus learned occupancy and 76% versus complete rollouts at the same charged transition budget. In frozen language-model review workflows, anchored TIS beats an equally regularized mean-influence blend in 23 of 24 MMLU-Pro settings and reaches 2.4-3.4times lower MSE than rollouts on six-call FinQA reviews.

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating C^s smooth functions with s >0 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests, for nonparametric quantile regression.

Accurately predicting watch time is crucial for optimizing recommendations and user experience in short video platforms. However, existing methods that estimate a single average watch time often fail to capture the inherent uncertainty in user engagement patterns. In this paper, we propose Conditional Quantile Estimation (CQE) to model the entire conditional distribution of watch time. Using quantile regression, CQE characterizes the complex watch-time distribution for each user-video pair, providing a flexible and comprehensive approach to understanding user behavior. We further design multiple strategies to combine the quantile estimates, adapting to different recommendation scenarios and user preferences. Extensive offline experiments and online A/B tests demonstrate the superiority of CQE in watch-time prediction and user engagement modeling. Specifically, deploying CQE online on a large-scale platform with hundreds of millions of daily active users has led to substantial gains in key evaluation metrics, including active days, engagement time, and video views. These results highlight the practical impact of our proposed approach in enhancing the user experience and overall performance of the short video recommendation system. The code will be released https://github.com/justopit/CQE.

This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution function (the quantile function) at specific points. For instance, this task is of key importance in private data generation. We present two different approaches. The first one consists in privately estimating the empirical quantiles of the samples and using this result as an estimator of the quantiles of the distribution. In particular, we study the statistical properties of the recently published algorithm introduced by Kaplan et al. 2022 that privately estimates the quantiles recursively. The second approach is to use techniques of density estimation in order to uniformly estimate the quantile function on an interval. In particular, we show that there is a tradeoff between the two methods. When we want to estimate many quantiles, it is better to estimate the density rather than estimating the quantile function at specific points.

The increasing availability of large and complex datasets across many scientific disciplines has led to widespread adoption of machine learning (ML) for prediction. However, most ML algorithms focus on point estimation and provide limited information about predictive uncertainty or the conditional distribution of the response, restricting their ability to characterize rare or extreme outcomes. We develop QXGB, a quantile-based gradient boosting framework, and introduce a convolution smoothed loss within it that estimates conditional quantiles for constructing dense cumulative distribution functions (CDFs), exceedance probabilities, and tail behaviour relevant to extreme outcomes. This approach preserves the computational efficiency of extreme gradient boosting while restoring the Hessian information XGBoost relies on for tree splitting, in turn providing interpretable measures of extreme value and exceedance probability predictions. We derive the gradients and Hessians needed to integrate convolution smoothed quantile loss with different kernel specifications into XGBoost, and with simulated data, benchmark this approach against alternative smoothed quantile regression losses, the native quantile objective in the XGBoost Python package, and independent versus multi-output tree estimation. The practical relevance is illustrated in an application predicting fine particulate matter (PM_{2.5}) in northern California, including periods where levels were elevated due to wildfire smoke. Our results show that convolution smoothed QXGB, particularly when paired with multi-output trees, delivers accurate predictions with near-zero quantile crossing, well-calibrated CDF and exceedance probability estimates, and useful tail characterization for extreme values. Interval estimation is also evaluated as a measure of data spread.

In traditional quantitative trading practice, navigating the complicated and dynamic financial market presents a persistent challenge. Fully capturing various market variables, including long-term information, as well as essential signals that may lead to profit remains a difficult task for learning algorithms. In order to tackle this challenge, this paper introduces quantformer, an enhanced neural network architecture based on transformers, to build investment factors. By transfer learning from sentiment analysis, quantformer not only exploits its original inherent advantages in capturing long-range dependencies and modeling complex data relationships, but is also able to solve tasks with numerical inputs and accurately forecast future returns over a given period. This work collects more than 5,000,000 rolling data of 4,601 stocks in the Chinese capital market from 2010 to 2019. The results of this study demonstrated the model's superior performance in predicting stock trends compared with other 100 factor-based quantitative strategies. Notably, the model's innovative use of transformer-liked model to establish factors, in conjunction with market sentiment information, has been shown to enhance the accuracy of trading signals significantly, thereby offering promising implications for the future of quantitative trading strategies.

Quantile forecasts summarize uncertainty at each future time step, while diffusion forecasters represent it through sampled future trajectories. We study how predicted quantiles can serve as distributional controls for diffusion forecasting. Specifically, we investigate how the mechanism of quantile integration affects its effectiveness in guiding a pretrained diffusion forecaster. We find that residual control throughout the denoising network yields the most consistent improvements. We instantiate this approach as Control-TS, which learns a quantile-control pathway while keeping the pretrained backbone frozen. Across eight benchmarks, Control-TS consistently improves the backbone's CRPS, achieves competitive performance against state-of-the-art forecasting models, and retains its gains in capacity-matched comparisons. Further analyses examine how these gains depend on quantile granularity, predictor choice, and forecast quality. Finally, we introduce the Conditional Linear Predictive Score (CLPS), which complements distributional metrics by evaluating the downstream forecasting utility of generated futures. Together, these findings support predicted quantiles as an effective interface between explicit uncertainty estimates and diffusion-based trajectory generation.

We present t_0, a family of open-weights foundation models for forecasting with multivariate context. We release its first two members: t0-alpha and t0-beta, respectively 102M and 256M parameters. Both condition their forecasts on target history, past covariates, and known-future covariates, without task-specific retraining. Their transformer layers alternate attention along time and across variates. They produce probabilistic forecasts through quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain covariate-to-target dependencies. On GIFT-Eval, t0-alpha reaches an aggregate CRPS of 0.4941, and t0-beta a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze t0-alpha in depth. Known-future covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand benchmark, t0-beta is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.

In this work, we build on recent advances in distributional reinforcement learning to give a generally applicable, flexible, and state-of-the-art distributional variant of DQN. We achieve this by using quantile regression to approximate the full quantile function for the state-action return distribution. By reparameterizing a distribution over the sample space, this yields an implicitly defined return distribution and gives rise to a large class of risk-sensitive policies. We demonstrate improved performance on the 57 Atari 2600 games in the ALE, and use our algorithm's implicitly defined distributions to study the effects of risk-sensitive policies in Atari games.

Quantile-based reinforcement learning provides an interpretable approach to risk-sensitive decision-making by optimizing a prescribed quantile of the cumulative-return distribution. Despite this appeal, learning under a point quantile objective is challenging: quantiles can change abruptly under small perturbations of the return distribution, and exact quantile-sensitive planning requires computationally demanding distributional optimization. Lower-buffered quantiles alleviate the former difficulty by averaging neighboring quantiles immediately below the target level, providing a smoother surrogate while preserving the underlying point-quantile objective. Existing methods based on this principle, however, remain model-based and rely on explicit return-law planning, limiting their applicability beyond small tabular problems. We develop Deep-BQRL, a model-free distributional reinforcement-learning framework that extends buffered-quantile learning to neural function approximation. The method learns conditional return quantiles directly from sampled transitions, constructs buffered action scores from the relevant region of the learned quantile function, and uses ensemble disagreement to guide exploration. An augmented input representation allows the learned policy to respond to trajectory information without explicitly reproducing the quantile-state recursion required by exact planning. Experiments on an asset-selling optimal-stopping problem and slippery FrozenLake compare Deep-BQRL with model-based UCB-BQRL and tabular PPO and TRPO implementations. In asset selling, Deep-BQRL attains smaller mean cumulative point-quantile policy gaps than PPO and TRPO at the reported target levels, while UCB-BQRL retains the smallest gaps. The learned stopping decisions also vary with the target quantile, providing an interpretable illustration of the method's risk-sensitive behavior.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

With an increasing number of replication studies performed in psychological science, the question of how to evaluate the outcome of a replication attempt deserves careful consideration. Bayesian approaches allow to incorporate uncertainty and prior information into the analysis of the replication attempt by their design. The Replication Bayes Factor, introduced by Verhagen & Wagenmakers (2014), provides quantitative, relative evidence in favor or against a successful replication. In previous work by Verhagen & Wagenmakers (2014) it was limited to the case of t-tests. In this paper, the Replication Bayes Factor is extended to F-tests in multi-group, fixed-effect ANOVA designs. Simulations and examples are presented to facilitate the understanding and to demonstrate the usefulness of this approach. Finally, the Replication Bayes Factor is compared to other Bayesian and frequentist approaches and discussed in the context of replication attempts. R code to calculate Replication Bayes factors and to reproduce the examples in the paper is available at https://osf.io/jv39h/.

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.

Time series foundation models are becoming increasingly popular for general-purpose forecasting. However, most leading models predict marginal quantiles, leaving the dependence structure of future trajectories unspecified. This distinction matters for trajectory-dependent quantities such as cumulative demand, peak load, and event timing, yet point and marginal scores do not reveal it. To model this dependence, we introduce PathFM, a trajectory-based forecasting model that uses flow matching to generate complete future paths. We further distill the model to one or two steps and share history attention cache across draws. Together, these enable PathFM to generate multiple paths for a single series in roughly the time needed for one query to a quantile model. The distilled sampler also makes it practical to optimize a calibration loss directly. PathFM achieves competitive marginal accuracy on the established forecasting benchmarks fev-bench and TIME. To complement these evaluations, we introduce Forecast Path Score Bench (fps-bench), which augments fev-bench tasks with energy and variogram scores and downstream metrics. PathFM achieves a higher aggregate path score on fps-bench than all evaluated external baselines. Experiments on chaotic systems further show that our flow model sustains long-run variability, while strong baselines rapidly collapse. PathFM makes generative time series forecasting both competitive and practical, enabling diverse downstream applications.

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre training compute budget, what downstream accuracy is attainable with contemporary post training practice, and how stable is that mapping as the field evolves? Using large scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries, high conditional quantiles of benchmark scores as a function of log pre training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task dependent saturation and to probe contamination related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near full data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus 2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries shift across time.

Financial markets are noisy and non-stationary, making alpha mining highly sensitive to noise in backtesting results and sudden market regime shifts. While recent agentic frameworks improve alpha mining automation, they often lack controllable multi-round search and reliable reuse of validated experience. To address these challenges, we propose QuantaAlpha, an evolutionary alpha mining framework that treats each end-to-end mining run as a trajectory and improves factors through trajectory-level mutation and crossover operations. QuantaAlpha localizes suboptimal steps in each trajectory for targeted revision and recombines complementary high-reward segments to reuse effective patterns, enabling structured exploration and refinement across mining iterations. During factor generation, QuantaAlpha enforces semantic consistency across the hypothesis, factor expression, and executable code, while constraining the complexity and redundancy of the generated factor to mitigate crowding. Extensive experiments on the China Securities Index 300 (CSI 300) demonstrate consistent gains over strong baseline models and prior agentic systems. When utilizing GPT-5.2, QuantaAlpha achieves an Information Coefficient (IC) of 0.1501, with an Annualized Rate of Return (ARR) of 27.75% and a Maximum Drawdown (MDD) of 7.98%. Moreover, factors mined on CSI 300 transfer effectively to the China Securities Index 500 (CSI 500) and the Standard & Poor's 500 Index (S&P 500), delivering 160% and 137% cumulative excess return over four years, respectively, which indicates strong robustness of QuantaAlpha under market distribution shifts.

In a recent paper Juodis and Reese (2022) (JR) show that the application of the CD test proposed by Pesaran (2004) to residuals from panels with latent factors results in over-rejection. They propose a randomized test statistic to correct for over-rejection, and add a screening component to achieve power. This paper considers the same problem but from a different perspective, and shows that the standard CD test remains valid if the latent factors are weak in the sense the strength is less than half. In the case where latent factors are strong, we propose a bias-corrected version, CD*, which is shown to be asymptotically standard normal under the null of error cross-sectional independence and have power against network type alternatives. This result is shown to hold for pure latent factor models as well as for panel regression models with latent factors. The case where the errors are serially correlated is also considered. Small sample properties of the CD* test are investigated by Monte Carlo experiments and are shown to have the correct size for strong and weak factors as well as for Gaussian and non-Gaussian errors. In contrast, it is found that JR's test tends to over-reject in the case of panels with non-Gaussian errors, and has low power against spatial network alternatives. In an empirical application, using the CD* test, it is shown that there remains spatial error dependence in a panel data model for real house price changes across 377 Metropolitan Statistical Areas in the U.S., even after the effects of latent factors are filtered out.

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the known lower bounds for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the recently proposed min-max regression procedure, thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p in (2, infty). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

This research presents a framework for quantitative risk management in volatile markets, specifically focusing on expectile-based methodologies applied to the FTSE 100 index. Traditional risk measures such as Value-at-Risk (VaR) have demonstrated significant limitations during periods of market stress, as evidenced during the 2008 financial crisis and subsequent volatile periods. This study develops an advanced expectile-based framework that addresses the shortcomings of conventional quantile-based approaches by providing greater sensitivity to tail losses and improved stability in extreme market conditions. The research employs a dataset spanning two decades of FTSE 100 returns, incorporating periods of high volatility, market crashes, and recovery phases. Our methodology introduces novel mathematical formulations for expectile regression models, enhanced threshold determination techniques using time series analysis, and robust backtesting procedures. The empirical results demonstrate that expectile-based Value-at-Risk (EVaR) consistently outperforms traditional VaR measures across various confidence levels and market conditions. The framework exhibits superior performance during volatile periods, with reduced model risk and enhanced predictive accuracy. Furthermore, the study establishes practical implementation guidelines for financial institutions and provides evidence-based recommendations for regulatory compliance and portfolio management. The findings contribute significantly to the literature on financial risk management and offer practical tools for practitioners dealing with volatile market environments.

Quantitative research is an iterative loop: a researcher proposes a market hypothesis, implements it as an executable signal, tests it on historical data, and decides what to keep. Existing benchmarks score formulas, code, or individual trading decisions, leaving open whether large language models (LLMs) can complete this loop and produce strategies that work beyond the research period. We introduce Quant-Arena, a benchmark and public leaderboard for end-to-end quantitative research on real A-share market data. A model constructs features and stock-scoring code, receives feedback only on 2022--2023, and freezes one strategy for assessment on the sealed year 2024. A cash-account evaluator applies trading constraints and costs, including market impact estimated from a simulated order book. Scores are dominated by realized excess return and complemented by signal quality and the diversity of features used by the strategy. We evaluate nine frontier models, among which GPT-6 Astra scores highest; yet no model beats the equal-weight market in 2024. Quant-Arena is open to submissions from any model or agent harness.

Reinforcement learning from human feedback (RLHF) has become a key method for aligning large language models (LLMs) with human preferences through the use of reward models. However, traditional reward models typically generate point estimates, which oversimplify the diversity and complexity of human values and preferences. In this paper, we introduce Quantile Reward Models (QRMs), a novel approach to reward modeling that learns a distribution over rewards instead of a single scalar value. Our method uses quantile regression to estimate a full, potentially multimodal distribution over preferences, providing a more powerful and nuanced representation of preferences. This distributional approach can better capture the diversity of human values, addresses label noise, and accommodates conflicting preferences by modeling them as distinct modes in the distribution. Our experimental results show that QRM outperforms comparable traditional point-estimate models on RewardBench. Furthermore, we demonstrate that the additional information provided by the distributional estimates can be utilized in downstream applications, such as risk-aware reinforcement learning, resulting in LLM policies that generate fewer extremely negative responses. Our code and model are released at https://github.com/Nicolinho/QRM.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Time series foundation models (TSFMs) enable cross-domain forecasting, but their development as general-purpose forecasters remains constrained by underexplored training potential and limited architectural versatility. To address these challenges, we introduce Aurora-X, a billion-scale TSFM with a progressive curriculum and a unified architecture. We first use channel-independent pretraining to learn temporal patterns, then introduce cross-variable dependencies, varied context and horizon lengths, and future covariates if available during midtraining. Variable-resolution post-training further enables an adjustable temporal span per token at inference. With fixed model weights, this supports longer histories under a fixed token budget or fewer tokens for the same history, enabling test-time scaling. With a versatile architecture, Aurora-X supports cross-variable modeling, covariate conditioning, and parallel decoding of future patches for probabilistic forecasting. These are supported by a novel pattern-guided mixture-of-experts that expands model capacity through sparse activation and uses shallow patch similarities to constrain deep-layer routing, guiding expert specialization across heterogeneous time series. Furthermore, we propose an implicit quantile network head that predicts arbitrary quantiles to characterize predictive distributions, enhancing probabilistic forecasting flexibility. Comprehensive experiments on GIFT-Eval, TIME, FEV-Bench, TFB, and DAG-Bench demonstrate state-of-the-art forecasting performance against pretrained TSFMs and task-specific supervised models.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the input space. In this paper we propose a new method that is fully adaptive to heteroscedasticity. It combines conformal prediction with classical quantile regression, inheriting the advantages of both. We establish a theoretical guarantee of valid coverage, supplemented by extensive experiments on popular regression datasets. We compare the efficiency of conformalized quantile regression to other conformal methods, showing that our method tends to produce shorter intervals.

Vision transformers (ViTs) have garnered significant attention for their performance in vision tasks, but the high computational cost and significant latency issues have hindered widespread adoption. Post-training quantization (PTQ), a promising method for model compression, still faces accuracy degradation challenges with ViTs. There are two reasons for this: the existing quantization paradigm does not fit the power-law distribution of post-Softmax activations well, and accuracy inevitably decreases after reparameterizing post-LayerNorm activations. We propose a Distribution-Friendly and Outlier-Aware Post-training Quantization method for Vision Transformers, named DopQ-ViT. DopQ-ViT analyzes the inefficiencies of current quantizers and introduces a distribution-friendly Tan Quantizer called TanQ. TanQ focuses more on values near 1, more accurately preserving the power-law distribution of post-Softmax activations, and achieves favorable results. Besides, during the reparameterization of post-LayerNorm activations from channel-wise to layer-wise quantization, the accuracy degradation is mainly due to the significant impact of outliers in the scaling factors. Therefore, DopQ-ViT proposes a method to select Median as the Optimal Scaling Factor, denoted as MOSF, which compensates for the influence of outliers and preserves the performance of the quantization model. DopQ-ViT has been extensively validated and significantly improves the performance of quantization models, especially in low-bit settings.

For fair academic recruitment at universities and research institutions, determination of the right measure based on globally accepted academic quality features is a highly delicate, challenging, but quite important problem to be addressed. In a series of two papers, we consider the modeling part for academic quality quantification in the first paper, in this paper, and the case studies part in the second paper. For academic quality quantification modeling, we develop two computational frameworks which can be used to construct a decision-support tool: (i) an optimization-based framework and (ii) a Siamese network (a type of artificial neural network)-based framework. The output of both models is a single index called Academic Quality Index (AQI) which is a measure of the overall academic quality. The data of academics from first-class and average-class world universities, based on Times Higher Education World University Rankings and QS World University Rankings, are assumed as the reference data for tuning model parameters.

Financial markets pose fundamental challenges for asset return prediction due to their high dimensionality, non-stationarity, and persistent volatility. Despite advances in large language models and multi-agent systems, current quantitative research pipelines suffer from limited automation, weak interpretability, and fragmented coordination across key components such as factor mining and model innovation. In this paper, we propose R&D-Agent for Quantitative Finance, in short RD-Agent(Q), the first data-centric multi-agent framework designed to automate the full-stack research and development of quantitative strategies via coordinated factor-model co-optimization. RD-Agent(Q) decomposes the quant process into two iterative stages: a Research stage that dynamically sets goal-aligned prompts, formulates hypotheses based on domain priors, and maps them to concrete tasks, and a Development stage that employs a code-generation agent, Co-STEER, to implement task-specific code, which is then executed in real-market backtests. The two stages are connected through a feedback stage that thoroughly evaluates experimental outcomes and informs subsequent iterations, with a multi-armed bandit scheduler for adaptive direction selection. Empirically, RD-Agent(Q) achieves up to 2X higher annualized returns than classical factor libraries using 70% fewer factors, and outperforms state-of-the-art deep time-series models on real markets. Its joint factor-model optimization delivers a strong balance between predictive accuracy and strategy robustness. Our code is available at: https://github.com/microsoft/RD-Agent.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-level distribution-valued characteristics can instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed from Qwen3-Embedding-8B news representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reported frozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.

In this paper, we introduce a conformal prediction method to construct prediction sets in a oneshot federated learning setting. More specifically, we define a quantile-of-quantiles estimator and prove that for any distribution, it is possible to output prediction sets with desired coverage in only one round of communication. To mitigate privacy issues, we also describe a locally differentially private version of our estimator. Finally, over a wide range of experiments, we show that our method returns prediction sets with coverage and length very similar to those obtained in a centralized setting. Overall, these results demonstrate that our method is particularly well-suited to perform conformal predictions in a one-shot federated learning setting.

We study the problem of temporal-difference-based policy evaluation in reinforcement learning. In particular, we analyse the use of a distributional reinforcement learning algorithm, quantile temporal-difference learning (QTD), for this task. We reach the surprising conclusion that even if a practitioner has no interest in the return distribution beyond the mean, QTD (which learns predictions about the full distribution of returns) may offer performance superior to approaches such as classical TD learning, which predict only the mean return, even in the tabular setting.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Many studies on scaling laws consider basic factors such as model size, model shape, dataset size, and compute power. These factors are easily tunable and represent the fundamental elements of any machine learning setup. But researchers have also employed more complex factors to estimate the test error and generalization performance with high predictability. These factors are generally specific to the domain or application. For example, feature diversity was primarily used for promoting syn-to-real transfer by Chen et al. (2021). With numerous scaling factors defined in previous works, it would be interesting to investigate how these factors may affect overall generalization performance in the context of self-supervised learning with CNN models. How do individual factors promote generalization, which includes varying depth, width, or the number of training epochs with early stopping? For example, does higher feature diversity result in higher accuracy held in complex settings other than a syn-to-real transfer? How do these factors depend on each other? We found that the last layer is the most diversified throughout the training. However, while the model's test error decreases with increasing epochs, its diversity drops. We also discovered that diversity is directly related to model width.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are limited to learning from preference pairs or relative signals. To bridge this gap, we introduce Quantile Reward Policy Optimization (QRPO), which learns from pointwise absolute rewards while preserving the simplicity and offline applicability of DPO-like methods. QRPO uses quantile rewards to enable regression to the closed-form solution of the KL-regularized RL objective. This reward yields an analytically tractable partition function, removing the need for relative signals to cancel this term. Moreover, QRPO scales with increased compute to estimate quantile rewards, opening a new dimension for pre-computation scaling. Empirically, QRPO consistently achieves top performance on chat and coding evaluations--reward model scores, AlpacaEval 2, and LeetCode--compared to DPO, REBEL, and SimPO across diverse datasets and 8B-scale models. Finally, we find that training with robust rewards instead of converting them to preferences induces less length bias.

Quantitative trading is moving from isolated predictive models toward agentic workflows that combine reasoning, tool use, memory, and feedback. This survey reviews agentic quantitative trading across five stages: factor mining, signal discovery, portfolio construction, order execution, and risk management. We further examine agentic quant trading systems through architecture, coordination, and adaptation, while comparing benchmarks across strategy construction, offline trading, live market evaluation, and reliability assessment. Our review finds that current systems remain concentrated on signal discovery, while complete integration with portfolio construction, execution, and risk control is still uncommon. Multi-agent systems also rely heavily on aggregation despite increasingly diverse workflow structures. Benchmark evidence further shows that strong model or forecasting capability does not reliably translate into trading performance under live market conditions and reliability controls. We conclude with future directions for more complete trading workflows, stronger coordination, and evaluation matched to the capability being assessed.

Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).

We introduce Moirai 2.0, a decoder-only time-series foundation model trained on a new corpus of 36M series. The model adopts quantile forecasting and multi-token prediction, improving both probabilistic accuracy and inference efficiency. On the Gift-Eval benchmark, it ranks among the top pretrained models while achieving a strong trade-off between accuracy, speed, and model size. Compared to Moirai 1.0, Moirai 2.0 replaces masked-encoder training, multi-patch inputs, and mixture-distribution outputs with a simpler decoder-only architecture, single patch, and quantile loss. Ablation studies isolate these changes -- showing that the decoder-only backbone along with recursive multi-quantile decoding contribute most to the gains. Additional experiments show that Moirai 2.0 outperforms larger models from the same family and exhibits robust domain-level results. In terms of efficiency and model size, Moirai 2.0 is twice as fast and thirty times smaller than its prior best version, Moirai 1.0-Large, while also performing better. Model performance plateaus with increasing parameter count and declines at longer horizons, motivating future work on data scaling and long-horizon modeling. We release code and evaluation details to support further research.

Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

Document manipulation localization models achieve strong performance on public benchmarks yet fail to generalize to operational document workflows. We identify a critical and overlooked source of this gap: the mismatch between the narrow distribution of JPEG quantization tables used during training -restricted to standard libjpeg quality factors -and the heterogeneous compression profiles encountered in real-world insurance document pipelines. To isolate this factor, we conduct a controlled factorial study comparing two architectures with contrasting levels of quantization table awareness -FFDN [2] and Mesorch [20] -each trained under either standard quality factor augmentation (Standard-QT ) or operationally calibrated quantization tables sampled from DocQT, a quantization-table bank derived from a MAIF operational image corpus (Real-QT ), and evaluated under three recompression conditions. Training under Real-QT yields substantial localization gains on DocTamper [15] and significantly reduces the pixel-level false positive rate on authentic operational documents, but only for architectures that explicitly ingest the quantization table as input. The released DocQT quantization-table dataset and compression-reproduction material are directly available at https://github.com/Kyliroco/Improving-Document-Forgery-Localization-Robustness-via-Diverse-JPEG-Quantization-Tables. These results demonstrate that standard quality factor augmentation does not adequately proxy operational compression diversity, and that architectural choices explicitly conditioning on the quantization table provide a meaningful robustness advantage for real-world deployment.

Almost every large language model that reaches a broad audience is quantized: trained in full precision, then compressed for efficiency. This step is assumed harmless and its safety is rarely re-checked. We find its principal side effect is increased bias that standard safety evaluation misses. Holding the model, its training, and the prompts fixed, a quantized model still refuses harmful requests, still avoids over-refusing benign prompts, and still selects the unbiased multiple-choice answer. Yet asked an open-ended question, the same model volunteers stereotypes in all eight languages we probe, in roughly one in four open-ended answers under an independent judge (~24% to ~27% across the compression ladder): it passes every standard check and still reaches users measurably more biased. The selective gap is a robust finding; whether open-ended bias further increases with compression is less certain, sensitive to the judge that scores it. We address both with QuantiBias, a benchmark that pairs a generative, multilingual stereotype probe with the refusal and multiple-choice controls that isolate open-ended generation, contrasts each build with and without reasoning, and rates the content severity of what it generates. Across two backbone models (Qwen and Gemma), a five-family screen, and eight benchmarks, quantizers allocate their extra precision by capability data that carries no bias-prevention signal, and reasoning before answering roughly halves the effect on some families while doing nothing on others. A quantized build must be re-evaluated for open-ended bias, not only on the short-form safeguards it already passes.

Open-ended search combined with foundation models has produced advances such as faster algorithms, new results on open mathematical problems, and self-improving agents. We extend this paradigm to recommendation for decision-making, focusing on decisions where the set of possible choices is fixed but the reasons for choosing them are not. In high-stakes decisions, e.g., which company to acquire or which customer to target, comparing diverse, well-reasoned options can be more useful than a single ranked list. We formalize open-ended recommendation as building a diverse, high-quality set of recommendations, each an item together with a hypothesis, a natural-language reason why the item fits the needs of a decision maker. We propose QD-Rec, a quality--diversity method that selects items with a contextual bandit and generates hypotheses with a foundation model from earlier ones kept in an archive as stepping stones. A new recommendation enters the archive if it is novel or better than its nearest neighbor. Across M&A, customer targeting, and paper and book recommendation, QD-Rec gives the highest mean quality and builds the largest archive in most settings.