Daily Papers

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

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.

We propose a credit risk model for portfolios composed of green and brown loans, extending the ASRF framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, CDO pricing, and empirical analysis of green loan portfolios.

This work aims to implement Long Short-Term Memory mixture density networks (LSTM-MDNs) for Value-at-Risk forecasting and compare their performance with established models (historical simulation, CMM, and GARCH) using a defined backtesting procedure. The focus was on the neural network's ability to capture volatility clustering and its real-world applicability. Three architectures were tested: a 2-component mixture density network, a regularized 2-component model (Arimond et al., 2020), and a 3-component mixture model, the latter being tested for the first time in Value-at-Risk forecasting. Backtesting was performed on three stock indices (FTSE 100, S&P 500, EURO STOXX 50) over two distinct two-year periods (2017-2018 as a calm period, 2021-2022 as turbulent). Model performance was assessed through unconditional coverage and independence assumption tests. The neural network's ability to handle volatility clustering was validated via correlation analysis and graphical evaluation. Results show limited success for the neural network approach. LSTM-MDNs performed poorly for 2017/2018 but outperformed benchmark models in 2021/2022. The LSTM mechanism allowed the neural network to capture volatility clustering similarly to GARCH models. However, several issues were identified: the need for proper model initialization and reliance on large datasets for effective learning. The findings suggest that while LSTM-MDNs provide adequate risk forecasts, further research and adjustments are necessary for stable performance.

We develop and counterfactually evaluate a resolution-aware risk-design framework (PIRAP) for perpetual futures whose underlying tracks a single binary prediction-market probability through resolution. The framework specifies six components: an index estimator combining mid-price, depth-weighted mid, and time-decayed VWAP; jump-aware tiered margin sized against bounded-event terminal-collapse magnitude; leverage compression schedule contracting toward resolution; resolution-aware funding rule with boundary-aware correction; a multi-stage halt protocol; and an eligibility framework. Two formal non-portability propositions establish that standard basis-only funding paired with continuous-vol static margin fails on bounded-event underlyings. Empirical evaluation uses Polymarket's PMXT v2 archive for 2026-04-21 to 2026-04-27 (13,298-market analysis sample passing adequacy gates from 61,087 ingested; 13,115 resolved within the empirical window for E3). E1 evaluates two pre-registered stylized facts; E2 conducts counterfactual replay across three engine configurations; E3 isolates the resolution-zone protocol's contribution. Results are mixed. Five pre-registered floors: stylized-fact floors (boundary depth asymmetry, terminal-jump magnitude) PASS; welfare-side directional floors (final-hour liquidation -6%, drawdown -5.1% pooled, median PnL +14%) two FAIL one PASS; E3 mechanic floors (final-hour liquidation -80% by halt construction PASS; bad-debt frequency +2.4% FAIL). Three of five materiality floors fail: the framework as specified does not validate deployment, but the empirical record establishes a halt-versus-margin scope distinction (halt addresses execution-channel risk; terminal-jump bad-debt remains margin-side) and documents a pre-emption trade-off constraining the dynamic-margin component. The paper concludes with structural recommendations and explicit non-deployable status.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we propose a new formulation, Bayesian risk Markov Decision Process (BR-MDP), to address parameter uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distribution of the unknown parameters. The proposed formulation provides more flexible risk attitutes towards parameter uncertainty and takes into account the availability of data in future times stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. We demonstrate the empirical performance of the BR-MDP formulation and proposed algorithms on a gambler's betting problem and an inventory control problem.

Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.

Paper 1 of this research programme develops a resolution-aware risk-design framework for the simplest event-linked perpetual: a contract whose underlying tracks a single binary prediction-market probability through resolution. The instrument class is broader. Variants span conditional probabilities P(A|B), spreads p^A - p^B, weighted baskets sum w_i p^(i), derivatives on variance or entropy of the probability process, contracts on liquidity itself, perpetual-on-expiring-event roll structures, and funding-only derivatives with no settlement. Each variant inherits some framework components from the single-market binary case and requires its own design adaptations. This paper develops a formal taxonomy of seven pure-form canonical variants beyond the probability-index perpetual of Paper 1, organised along four orthogonal design axes: underlying geometry, temporal structure, settlement structure, and venue composition. The list is not exhaustive; combinations are not treated separately. For each variant we provide a precise payoff definition; an inheritance map identifying which Paper 1 components carry over, are modified, or fail; variant-specific design constraints; microstructure properties; empirical evaluability on the PMXT v2 archive; and limitations. Notable findings: the conditional variant admits a candidate non-portability proposition (denominator instability as the conditioning event becomes improbable); the spread variant requires a three-channel decomposition of resolution risk; the volatility/entropy variant avoids random binary terminal-collapse but introduces estimator-convention and entropy-decay issues; the basket variant requires multi-period jump-aware margin whose aggregation is correlation-dependent. The paper is theoretical primarily; it specifies how demonstrative time series can be constructed and provides evaluability criteria to guide future work.

This paper proposes a formal framework for reverse stress testing geopolitical risk in corporate credit portfolios. A joint macro-financial scenario vector, augmented with an explicit geopolitical risk factor, is mapped into stressed probabilities of default and losses given default. These stresses are then propagated to portfolio tail losses through a latent factor structure and translated into a stressed CET1 ratio, jointly accounting for capital depletion and risk-weighted asset dynamics. Reverse stress testing is formulated as a constrained maximum likelihood problem over the scenario space. This yields a geopolitical point reverse stress test, or design point, defined as the most probable scenario that breaches a prescribed capital adequacy constraint under a reference distribution. The framework further characterises neighbourhoods and near optimal sets of reverse stress scenarios, allowing for sensitivity analysis and governance oriented interpretation. The approach is compatible with internal rating based models and supports implementation at the exposure or sector level.

The rapid proliferation of Large Language Models (LLMs) and diverse specialized benchmarks necessitates a shift from fragmented, task-specific metrics to a holistic, competitive ranking system that effectively aggregates performance across multiple ability dimensions. Primarily using static scoring, current evaluation methods are fundamentally limited. They struggle to determine the proper mix ratio across diverse benchmarks, and critically, they fail to capture a model's dynamic competitive fitness or its vulnerability when confronted with sequential, high-stakes tasks. To address this, we introduce the novel Competitive Swiss-System Dynamics (CSD) framework. CSD simulates a multi-round, sequential contest where models are dynamically paired across a curated sequence of benchmarks based on their accumulated win-loss record. And Monte Carlo Simulation (N=100,000 iterations) is used to approximate the statistically robust Expected Win Score (E[S_m]), which eliminates the noise of random pairing and early-round luck. Furthermore, we implement a Failure Sensitivity Analysis by parameterizing the per-round elimination quantity (T_k), which allows us to profile models based on their risk appetite--distinguishing between robust generalists and aggressive specialists. We demonstrate that CSD provides a more nuanced and context-aware ranking than traditional aggregate scoring and static pairwise models, representing a vital step towards risk-informed, next-generation LLM evaluation.

Task robust adaptation is a long-standing pursuit in sequential decision-making. Some risk-averse strategies, e.g., the conditional value-at-risk principle, are incorporated in domain randomization or meta reinforcement learning to prioritize difficult tasks in optimization, which demand costly intensive evaluations. The efficiency issue prompts the development of robust active task sampling to train adaptive policies, where risk-predictive models are used to surrogate policy evaluation. This work characterizes the optimization pipeline of robust active task sampling as a Markov decision process, posits theoretical and practical insights, and constitutes robustness concepts in risk-averse scenarios. Importantly, we propose an easy-to-implement method, referred to as Posterior and Diversity Synergized Task Sampling (PDTS), to accommodate fast and robust sequential decision-making. Extensive experiments show that PDTS unlocks the potential of robust active task sampling, significantly improves the zero-shot and few-shot adaptation robustness in challenging tasks, and even accelerates the learning process under certain scenarios. Our project website is at https://thu-rllab.github.io/PDTS_project_page.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where rare but severe failures can result in irreversible harm. However, prevailing evaluation benchmarks often reduce complex social risk to mean-centered scalar scores, thereby obscuring distributional structure, cross-dimensional interactions, and worst-case behavior. This paper introduces Social Harm Analysis via Risk Profiles (SHARP), a framework for multidimensional, distribution-aware evaluation of social harm. SHARP models harm as a multivariate random variable and integrates explicit decomposition into bias, fairness, ethics, and epistemic reliability with a union-of-failures aggregation reparameterized as additive cumulative log-risk. The framework further employs risk-sensitive distributional statistics, with Conditional Value at Risk (CVaR95) as a primary metric, to characterize worst-case model behavior. Application of SHARP to eleven frontier LLMs, evaluated on a fixed corpus of n=901 socially sensitive prompts, reveals that models with similar average risk can exhibit more than twofold differences in tail exposure and volatility. Across models, dimension-wise marginal tail behavior varies systematically across harm dimensions, with bias exhibiting the strongest tail severities, epistemic and fairness risks occupying intermediate regimes, and ethical misalignment consistently lower; together, these patterns reveal heterogeneous, model-dependent failure structures that scalar benchmarks conflate. These findings indicate that responsible evaluation and governance of LLMs require moving beyond scalar averages toward multidimensional, tail-sensitive risk profiling.

Large language models (LLMs) achieve strong performance across benchmarks--from knowledge quizzes and math reasoning to web-agent tasks--but these tests occur in static settings, lacking real dynamics and uncertainty. Consequently, they evaluate isolated reasoning or problem-solving rather than decision-making under uncertainty. To address this, we introduce LiveTradeBench, a live trading environment for evaluating LLM agents in realistic and evolving markets. LiveTradeBench follows three design principles: (i) Live data streaming of market prices and news, eliminating dependence on offline backtesting and preventing information leakage while capturing real-time uncertainty; (ii) a portfolio-management abstraction that extends control from single-asset actions to multi-asset allocation, integrating risk management and cross-asset reasoning; and (iii) multi-market evaluation across structurally distinct environments--U.S. stocks and Polymarket prediction markets--differing in volatility, liquidity, and information flow. At each step, an agent observes prices, news, and its portfolio, then outputs percentage allocations that balance risk and return. Using LiveTradeBench, we run 50-day live evaluations of 21 LLMs across families. Results show that (1) high LMArena scores do not imply superior trading outcomes; (2) models display distinct portfolio styles reflecting risk appetite and reasoning dynamics; and (3) some LLMs effectively leverage live signals to adapt decisions. These findings expose a gap between static evaluation and real-world competence, motivating benchmarks that test sequential decision making and consistency under live uncertainty.

The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. We propose a novel data-driven approach for simulating realistic, high-dimensional multi-asset scenarios, focusing on accurately representing tail risk for a class of static and dynamic trading strategies. We exploit the joint elicitability property of Value-at-Risk (VaR) and Expected Shortfall (ES) to design a Generative Adversarial Network (GAN) that learns to simulate price scenarios preserving these tail risk features. We demonstrate the performance of our algorithm on synthetic and market data sets through detailed numerical experiments. In contrast to previously proposed data-driven scenario generators, our proposed method correctly captures tail risk for a broad class of trading strategies and demonstrates strong generalization capabilities. In addition, combining our method with principal component analysis of the input data enhances its scalability to large-dimensional multi-asset time series, setting our framework apart from the univariate settings commonly considered in the literature.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific operational constraints. In this paper, we present a new machine learning approach to learn risk scores. We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm for non-convex settings to efficiently recover its optimal solution. We improve our algorithm with specialized techniques to generate feasible solutions, narrow the optimality gap, and reduce data-related computation. Our approach can fit risk scores in a way that scales linearly in the number of samples, provides a certificate of optimality, and obeys real-world constraints without parameter tuning or post-processing. We benchmark the performance benefits of this approach through an extensive set of numerical experiments, comparing to risk scores built using heuristic approaches. We also discuss its practical benefits through a real-world application where we build a customized risk score for ICU seizure prediction in collaboration with the Massachusetts General Hospital.

We present MixtureVitae, an open-access pretraining corpus built to minimize legal risk while providing strong model performance. MixtureVitae follows a risk-mitigated sourcing strategy that combines public-domain and permissively licensed text (e.g., CC-BY/Apache) with carefully justified low-risk additions (e.g., government works and EU TDM-eligible sources), alongside targeted instruction, reasoning and synthetic data with documented provenance. We detail a transparent, multi-stage pipeline for license-aware filtering, safety and quality screening, and domain-aware mixing, and we release the dataset and curation recipes to support reproducible research. In controlled experiments using the open-sci-ref training protocol (fixed architectures at 130M/400M/1.3B/1.7B parameters; training budgets of 50B and 300B tokens), models trained on MixtureVitae consistently outperform other permissive datasets across a suite of standard benchmarks, and at the 1.7B/300B setting they surpass FineWeb-Edu and approach DCLM in the later stages of training. Performance is particularly strong on math/code and competitive on QA tasks. These results demonstrate that permissive-first, risk-mitigated data provides a practical and legally mitigated foundation for training capable LLMs, reducing reliance on indiscriminate web scraping without sacrificing competitiveness. Code: https://github.com/ontocord/mixturevitae

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.

Delayed outcomes are ubiquitous in online experimentation: treatment can affect whether an outcome occurs, when it occurs, and its realized value. To accommodate staggered entry while remaining robust to environmental nonstationarity and unit-level heterogeneity, we adopt a design-based perspective and target the sample cumulative reward in each arm as a function of calendar time. Our confidence sequences allow practitioners to continuously monitor the counterfactual incremental reward, such as revenue, that would have been realized by calendar time t had all entered units been assigned to treatment rather than control. The main technical challenge is the choice of design-based filtration, complicated by the presence of asynchronous potential outcome times. We show that the IPW treatment-effect estimation error is not a martingale with respect to any filtration, while each arm-specific IPW estimation error is a martingale with respect to a carefully chosen arm-specific event-time filtration. We therefore construct a confidence sequence for the treatment effect by combining two arm-level confidence sequences with a union bound, and further demonstrate that this can outperform the traditional design-based variance upper bound. Finally, we characterize the class of augmentations for which the per-arm AIPW estimation error remains a martingale.

Identifying risky traders with high profits in financial markets is crucial for market makers, such as trading exchanges, to ensure effective risk management through real-time decisions on regulation compliance and hedging. However, capturing the complex and dynamic behaviours of individual traders poses significant challenges. Traditional classification and anomaly detection methods often establish a fixed risk boundary, failing to account for this complexity and dynamism. To tackle this issue, we propose a profit-aware risk ranker (PA-RiskRanker) that reframes the problem of identifying risky traders as a ranking task using Learning-to-Rank (LETOR) algorithms. Our approach features a Profit-Aware binary cross entropy (PA-BCE) loss function and a transformer-based ranker enhanced with a self-cross-trader attention pipeline. These components effectively integrate profit and loss (P&L) considerations into the training process while capturing intra- and inter-trader relationships. Our research critically examines the limitations of existing deep learning-based LETOR algorithms in trading risk management, which often overlook the importance of P&L in financial scenarios. By prioritising P&L, our method improves risky trader identification, achieving an 8.4% increase in F1 score compared to state-of-the-art (SOTA) ranking models like Rankformer. Additionally, it demonstrates a 10%-17% increase in average profit compared to all benchmark models.

The Internet of Value (IoV) is a heterogeneous, partially-trusted network in which the dominant marginal risk is composite (route, sentiment, liquidity, and the policy a system is willing to commit to) rather than a property of any single chain. We argue that a risk primitive adequate for this regime is a composition of five engines: a prediction engine over price, liquidity, volatility, and route health; a Bittensor verification subnet that decentralises and economically scores prediction outputs; a sentiment-fusion engine over text, on-chain flow, and grey-literature feeds; an agentic engine under constitutional, role-bound action constraints; and an API-risk and scenario engine that converts forecasts into pre-committed action programs in the sense of Monte-Carlo scenario generation. We anchor the architecture in two empirical artefacts: a 27-hour policy-constrained liquidity stress-response experiment on Solana, and a 168-hour prediction-router calibration arc reported with explicit class-imbalance honesty. The case study supports deployability; the validator-loss decomposition is stated formally and is falsifiable.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets' risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts.

Polymarket is a prediction market platform where users can speculate on future events by trading shares tied to specific outcomes, known as conditions. Each market is associated with a set of one or more such conditions. To ensure proper market resolution, the condition set must be exhaustive -- collectively accounting for all possible outcomes -- and mutually exclusive -- only one condition may resolve as true. Thus, the collective prices of all related outcomes should be \1, representing a combined probability of 1 of any outcome. Despite this design, Polymarket exhibits cases where dependent assets are mispriced, allowing for purchasing (or selling) a certain outcome for less than (or more than) 1, guaranteeing profit. This phenomenon, known as arbitrage, could enable sophisticated participants to exploit such inconsistencies. In this paper, we conduct an empirical arbitrage analysis on Polymarket data to answer three key questions: (Q1) What conditions give rise to arbitrage (Q2) Does arbitrage actually occur on Polymarket and (Q3) Has anyone exploited these opportunities. A major challenge in analyzing arbitrage between related markets lies in the scalability of comparisons across a large number of markets and conditions, with a naive analysis requiring O(2^{n+m}) comparisons. To overcome this, we employ a heuristic-driven reduction strategy based on timeliness, topical similarity, and combinatorial relationships, further validated by expert input. Our study reveals two distinct forms of arbitrage on Polymarket: Market Rebalancing Arbitrage, which occurs within a single market or condition, and Combinatorial Arbitrage, which spans across multiple markets. We use on-chain historical order book data to analyze when these types of arbitrage opportunities have existed, and when they have been executed by users. We find a realized estimate of 40 million USD of profit extracted.

Detecting AI risks becomes more challenging as stronger models emerge and find novel methods such as Alignment Faking to circumvent these detection attempts. Inspired by how risky behaviors in humans (i.e., illegal activities that may hurt others) are sometimes guided by strongly-held values, we believe that identifying values within AI models can be an early warning system for AI's risky behaviors. We create LitmusValues, an evaluation pipeline to reveal AI models' priorities on a range of AI value classes. Then, we collect AIRiskDilemmas, a diverse collection of dilemmas that pit values against one another in scenarios relevant to AI safety risks such as Power Seeking. By measuring an AI model's value prioritization using its aggregate choices, we obtain a self-consistent set of predicted value priorities that uncover potential risks. We show that values in LitmusValues (including seemingly innocuous ones like Care) can predict for both seen risky behaviors in AIRiskDilemmas and unseen risky behaviors in HarmBench.

This study develops and empirically validates a Mixture of Experts (MoE) framework for stock price prediction across heterogeneous volatility regimes using real market data. The proposed model combines a Recurrent Neural Network (RNN) optimized for high-volatility stocks with a linear regression model tailored to stable equities. A volatility-aware gating mechanism dynamically weights the contributions of each expert based on asset classification. Using a dataset of 30 publicly traded U.S. stocks spanning diverse sectors, the MoE approach consistently outperforms both standalone models. Specifically, it achieves up to 33% improvement in MSE for volatile assets and 28% for stable assets relative to their respective baselines. Stratified evaluation across volatility classes demonstrates the model's ability to adapt complexity to underlying market dynamics. These results confirm that no single model suffices across market regimes and highlight the advantage of adaptive architectures in financial prediction. Future work should explore real-time gate learning, dynamic volatility segmentation, and applications to portfolio optimization.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

We develop a rigorous walk-forward validation framework for algorithmic trading designed to mitigate overfitting and lookahead bias. Our methodology combines interpretable hypothesis-driven signal generation with reinforcement learning and strict out-of-sample testing. The framework enforces strict information set discipline, employs rolling window validation across 34 independent test periods, maintains complete interpretability through natural language hypothesis explanations, and incorporates realistic transaction costs and position constraints. Validating five market microstructure patterns across 100 US equities from 2015 to 2024, the system yields modest annualized returns (0.55%, Sharpe ratio 0.33) with exceptional downside protection (maximum drawdown -2.76%) and market-neutral characteristics (beta = 0.058). Performance exhibits strong regime dependence, generating positive returns during high-volatility periods (0.60% quarterly, 2020-2024) while underperforming in stable markets (-0.16%, 2015-2019). We report statistically insignificant aggregate results (p-value 0.34) to demonstrate a reproducible, honest validation protocol that prioritizes interpretability and extends naturally to advanced hypothesis generators, including large language models. The key empirical finding reveals that daily OHLCV-based microstructure signals require elevated information arrival and trading activity to function effectively. The framework provides complete mathematical specifications and open-source implementation, establishing a template for rigorous trading system evaluation that addresses the reproducibility crisis in quantitative finance research. For researchers, practitioners, and regulators, this work demonstrates that interpretable algorithmic trading strategies can be rigorously validated without sacrificing transparency or regulatory compliance.

When deploying machine learning models in high-stakes real-world environments such as health care, it is crucial to accurately assess the uncertainty concerning a model's prediction on abnormal inputs. However, there is a scarcity of literature analyzing this problem on medical data, especially on mixed-type tabular data such as Electronic Health Records. We close this gap by presenting a series of tests including a large variety of contemporary uncertainty estimation techniques, in order to determine whether they are able to identify out-of-distribution (OOD) patients. In contrast to previous work, we design tests on realistic and clinically relevant OOD groups, and run experiments on real-world medical data. We find that almost all techniques fail to achieve convincing results, partly disagreeing with earlier findings.

We study distributionally robust expected values under optimal transport distance with a quadratic cost function. In general the duality method, for this computation for the payoff function f, requires the computation of the λc-transform f^{λc}. We show that under the quadratic cost function there exists an intuitive and easily implementable representation of f^{λc}, if f is convex and piecewise linear. We apply this to the robust expected shortfall under the risk-neutral measure of an unhedged call option, from the point of view of the writer, as well as that of a portfolio mixing underlying shares with a call and a put option.

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations, enriched by human feedback. These new formulations provide a principled way to guarantee safety in each decision making step throughout the control process. Moreover, integrating human feedback into risk-sensitive RL framework bridges the gap between algorithmic decision-making and human participation, allowing us to also guarantee safety for human-in-the-loop systems. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis. Furthermore, we establish a matching lower bound to corroborate the optimality of our algorithms in a linear context.

This paper introduces a novel approach to financial risk analysis that does not rely on traditional price and market data, instead using market news to model assets as distributions over a metric space of risk factors. By representing asset returns as integrals over the scalar field of these risk factors, we derive the covariance structure between asset returns. Utilizing encoder-only language models to embed this news data, we explore the relationships between asset return distributions through the concept of Energy Distance, establishing connections between distributional differences and excess returns co-movements. This data-agnostic approach provides new insights into portfolio diversification, risk management, and the construction of hedging strategies. Our findings have significant implications for both theoretical finance and practical risk management, offering a more robust framework for modelling complex financial systems without depending on conventional market data.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

Assessing the capabilities and risks of frontier AI systems is a critical area of research, and recent work has shown that repeated sampling from models can dramatically increase both. For instance, repeated sampling has been shown to increase their capabilities, such as solving difficult math and coding problems, but it has also been shown to increase their potential for harm, such as being jailbroken. Such results raise a crucial question for both capability and safety forecasting: how can one accurately predict a model's behavior when scaled to a massive number of attempts, given a vastly smaller sampling budget? This question is directly relevant to model providers, who serve hundreds of millions of users daily, and to governmental regulators, who seek to prevent harms. To answer this questions, we make three contributions. First, we find that standard methods for fitting these laws suffer from statistical shortcomings that hinder predictive accuracy, especially in data-limited scenarios. Second, we remedy these shortcomings by introducing a robust estimation framework, which uses a beta-binomial distribution to generate more accurate predictions from limited data. Third, we propose a dynamic sampling strategy that allocates a greater budget to harder problems. Combined, these innovations enable more reliable prediction of rare risks and capabilities at a fraction of the computational cost.

We consider the classic supervised learning problem, where a continuous non-negative random label Y (i.e. a random duration) is to be predicted based upon observing a random vector X valued in R^d with dgeq 1 by means of a regression rule with minimum least square error. In various applications, ranging from industrial quality control to public health through credit risk analysis for instance, training observations can be right censored, meaning that, rather than on independent copies of (X,Y), statistical learning relies on a collection of ngeq 1 independent realizations of the triplet (X, ; min{Y,; C},; δ), where C is a nonnegative r.v. with unknown distribution, modeling censorship and δ=I{Yleq C} indicates whether the duration is right censored or not. As ignoring censorship in the risk computation may clearly lead to a severe underestimation of the target duration and jeopardize prediction, we propose to consider a plug-in estimate of the true risk based on a Kaplan-Meier estimator of the conditional survival function of the censorship C given X, referred to as Kaplan-Meier risk, in order to perform empirical risk minimization. It is established, under mild conditions, that the learning rate of minimizers of this biased/weighted empirical risk functional is of order O_{P}(log(n)/n) when ignoring model bias issues inherent to plug-in estimation, as can be attained in absence of censorship. Beyond theoretical results, numerical experiments are presented in order to illustrate the relevance of the approach developed.

Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring click-through rates for different demographic groups. The most standard approach is to report the plain average of each outcome. Despite simplicity, the estimates are noisy when the sample sizes or mean parameters are small. In contrast, the Empirical Bayes (EB) methods are able to boost the average accuracy by borrowing information across tasks. Nevertheless, the EB methods require a Bayesian model where the parameters are sampled from a prior distribution which, unlike the commonly-studied Gaussian case, is unidentified due to discreteness of binomial measurements. Even if the prior distribution is known, the computation is difficult when the sample sizes are heterogeneous as there is no simple joint conjugate prior for the sample size and mean parameter. In this paper, we consider the compound decision framework which treats the sample size and mean parameters as fixed quantities. We develop an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error given any class of estimators. For a class of machine learning-assisted linear shrinkage estimators, we establish asymptotic optimality, regret bounds, and valid inference. Unlike existing work, we work with the binomials directly without resorting to Gaussian approximations. This allows us to work with small sample sizes and/or mean parameters in both one-sample and two-sample settings. We demonstrate our approach using three datasets on firm discrimination, education outcomes, and innovation rates.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

In the post-pandemic world, manufacturing enterprises face increasing uncertainties, especially with vulnerabilities in global supply chains. Although supply chain management has been extensively studied, the critical influence of decision-makers (DMs) in these systems remains underexplored. This study studies the inventory management problem under risk using the newsvendor model by incorporating DMs risk preferences. By employing the Quantum Monte Carlo (QMC) combined with Quantum Amplitude Estimation (QAE) algorithm, the estimation of probabilities or expectation values can be done more efficiently. This offers near-quadratic speedup compared to classical Monte Carlo methods. Our findings illuminate the intricate relationship between risk-aware decision-making and inventory management, providing essential insights for enhancing supply chain resilience and adaptability in uncertain conditions

Algorithmic trading relies on machine learning models to make trading decisions. Despite strong in-sample performance, these models often degrade when confronted with evolving real-world market regimes, which can shift dramatically due to macroeconomic changes-e.g., monetary policy updates or unanticipated fluctuations in participant behavior. We identify two challenges that perpetuate this mismatch: (1) insufficient robustness in existing policy against uncertainties in high-level market fluctuations, and (2) the absence of a realistic and diverse simulation environment for training, leading to policy overfitting. To address these issues, we propose a Bayesian Robust Framework that systematically integrates a macro-conditioned generative model with robust policy learning. On the data side, to generate realistic and diverse data, we propose a macro-conditioned GAN-based generator that leverages macroeconomic indicators as primary control variables, synthesizing data with faithful temporal, cross-instrument, and macro correlations. On the policy side, to learn robust policy against market fluctuations, we cast the trading process as a two-player zero-sum Bayesian Markov game, wherein an adversarial agent simulates shifting regimes by perturbing macroeconomic indicators in the macro-conditioned generator, while the trading agent-guided by a quantile belief network-maintains and updates its belief over hidden market states. The trading agent seeks a Robust Perfect Bayesian Equilibrium via Bayesian neural fictitious self-play, stabilizing learning under adversarial market perturbations. Extensive experiments on 9 financial instruments demonstrate that our framework outperforms 9 state-of-the-art baselines. In extreme events like the COVID, our method shows improved profitability and risk management, offering a reliable solution for trading under uncertain and shifting market dynamics.

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.

For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence, the closest distribution is called the "information projection." The estimation risk of the maximum likelihood estimator (MLE) is defined as the expectation of K-L divergence between the information projection and the predictive distribution with plugged-in MLE. Here, the asymptotic expansion of the risk is derived up to n^{-2}-order, and the sufficient condition on the risk for the Bayes error rate between the true distribution and the information projection to be lower than a specified value is investigated. Combining these results, the "p-n criterion" is proposed, which determines whether the MLE is sufficiently close to the information projection for the given model and sample. In particular, the criterion for an exponential family model is relatively simple and can be used for a complex model with no explicit form of normalizing constant. This criterion can constitute a solution to the sample size or model acceptance problem. Use of the p-n criteria is demonstrated for two practical datasets. The relationship between the results and information criteria is also studied.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Recent works on large language models (LLMs) have successfully demonstrated the emergence of reasoning capabilities via reinforcement learning (RL). Although recent efforts leverage group relative policy optimization (GRPO) for MLLMs post-training, they constantly explore one specific aspect, such as grounding tasks, math problems, or chart analysis. There are no works that can leverage multi-source MLLM tasks for stable reinforcement learning. In this work, we present a unified perspective to solve this problem. We present Mixed-R1, a unified yet straightforward framework that contains a mixed reward function design (Mixed-Reward) and a mixed post-training dataset (Mixed-45K). We first design a data engine to select high-quality examples to build the Mixed-45K post-training dataset. Then, we present a Mixed-Reward design, which contains various reward functions for various MLLM tasks. In particular, it has four different reward functions: matching reward for binary answer or multiple-choice problems, chart reward for chart-aware datasets, IoU reward for grounding problems, and open-ended reward for long-form text responses such as caption datasets. To handle the various long-form text content, we propose a new open-ended reward named Bidirectional Max-Average Similarity (BMAS) by leveraging tokenizer embedding matching between the generated response and the ground truth. Extensive experiments show the effectiveness of our proposed method on various MLLMs, including Qwen2.5-VL and Intern-VL on various sizes. Our dataset and model are available at https://github.com/xushilin1/mixed-r1.

E-commerce risk management requires aggregating diverse, deeply embedded web data through multi-step, stateful interactions, which traditional scraping methods and most existing Graphical User Interface (GUI) agents cannot handle. These agents are typically limited to single-step tasks and lack the ability to manage dynamic, interactive content critical for effective risk assessment. To address this challenge, we introduce RISK, a novel framework designed to build and deploy GUI agents for this domain. RISK integrates three components: (1) RISK-Data, a dataset of 8,492 single-step and 2,386 multi-step interaction trajectories, collected through a high-fidelity browser framework and a meticulous data curation process; (2) RISK-Bench, a benchmark with 802 single-step and 320 multi-step trajectories across three difficulty levels for standardized evaluation; and (3) RISK-R1, a R1-style reinforcement fine-tuning framework considering four aspects: (i) Output Format Constraint, (ii) Single-step and (iii) Multi-step Level Reward, and (iv) Task Level Reweight. Experiments show that RISK-R1 achieves a 6.8% improvement in offline single-step and an 8.8% improvement in offline multi-step, using only 7.2% of the parameters of the SOTA baseline. Moreover, it attains a top task success rate of 70.5% in online evaluation. RISK provides a scalable, domain-specific solution for automating complex web interactions in e-commerce risk management. The code is available at https://github.com/RenqiChen/RISK-GUI.

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and f-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-k loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3times faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

Machine learning models frequently experience performance drops under distribution shifts. The underlying cause of such shifts may be multiple simultaneous factors such as changes in data quality, differences in specific covariate distributions, or changes in the relationship between label and features. When a model does fail during deployment, attributing performance change to these factors is critical for the model developer to identify the root cause and take mitigating actions. In this work, we introduce the problem of attributing performance differences between environments to distribution shifts in the underlying data generating mechanisms. We formulate the problem as a cooperative game where the players are distributions. We define the value of a set of distributions to be the change in model performance when only this set of distributions has changed between environments, and derive an importance weighting method for computing the value of an arbitrary set of distributions. The contribution of each distribution to the total performance change is then quantified as its Shapley value. We demonstrate the correctness and utility of our method on synthetic, semi-synthetic, and real-world case studies, showing its effectiveness in attributing performance changes to a wide range of distribution shifts.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

In quantitative finance, machine learning methods are essential for alpha generation. This study introduces a new approach that combines Hidden Markov Models (HMM) and neural networks, integrated with Black-Litterman portfolio optimization. During the COVID period (2019-2022), this dual-model approach achieved a 83% return with a Sharpe ratio of 0.77. It incorporates two risk models to enhance risk management, showing efficiency during volatile periods. The methodology was implemented on the QuantConnect platform, which was chosen for its robust framework and experimental reproducibility. The system, which predicts future price movements, includes a three-year warm-up to ensure proper algorithm function. It targets highly liquid, large-cap energy stocks to ensure stable and predictable performance while also considering broker payments. The dual-model alpha system utilizes log returns to select the optimal state based on the historical performance. It combines state predictions with neural network outputs, which are based on historical data, to generate trading signals. This study examined the architecture of the trading system, data pre-processing, training, and performance. The full code and backtesting data are available under the QuantConnect terms.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can carry greater risks than others in real-world long-tailed problems. For example, misclassifying patients (a tail class) as healthy individuals (a head class) entails far more serious consequences than the reverse scenario. To address this critical issue, we introduce Making Reliable and Flexible Decisions in Long-tailed Classification (RF-DLC), a novel framework aimed at reliable predictions in long-tailed problems. Leveraging Bayesian Decision Theory, we introduce an integrated gain to seamlessly combine long-tailed data distributions and the decision-making procedure. We further propose an efficient variational optimization strategy for the decision risk objective. Our method adapts readily to diverse utility matrices, which can be designed for specific tasks, ensuring its flexibility for different problem settings. In empirical evaluation, we design a new metric, False Head Rate, to quantify tail-sensitivity risk, along with comprehensive experiments on multiple real-world tasks, including large-scale image classification and uncertainty quantification, to demonstrate the reliability and flexibility of our method.

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strength and overcome the weaknesses of the two approaches by applying the doubly robust technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust approach uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice.

This paper investigates the application of Feature-Enriched Generative Adversarial Networks (FE-GAN) in financial risk management, with a focus on improving the estimation of Value at Risk (VaR) and Expected Shortfall (ES). FE-GAN enhances existing GANs architectures by incorporating an additional input sequence derived from preceding data to improve model performance. Two specialized GANs models, the Wasserstein Generative Adversarial Network (WGAN) and the Tail Generative Adversarial Network (Tail-GAN), were evaluated under the FE-GAN framework. The results demonstrate that FE-GAN significantly outperforms traditional architectures in both VaR and ES estimation. Tail-GAN, leveraging its task-specific loss function, consistently outperforms WGAN in ES estimation, while both models exhibit similar performance in VaR estimation. Despite these promising results, the study acknowledges limitations, including reliance on highly correlated temporal data and restricted applicability to other domains. Future research directions include exploring alternative input generation methods, dynamic forecasting models, and advanced neural network architectures to further enhance GANs-based financial risk estimation.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

The application scope of Large Language Models (LLMs) continues to expand, leading to increasing interest in personalized LLMs that align with human values. However, aligning these models with individual values raises significant safety concerns, as certain values may correlate with harmful information. In this paper, we identify specific safety risks associated with value-aligned LLMs and investigate the psychological principles behind these challenges. Our findings reveal two key insights. (1) Value-aligned LLMs are more prone to harmful behavior compared to non-fine-tuned models and exhibit slightly higher risks in traditional safety evaluations than other fine-tuned models. (2) These safety issues arise because value-aligned LLMs genuinely generate text according to the aligned values, which can amplify harmful outcomes. Using a dataset with detailed safety categories, we find significant correlations between value alignment and safety risks, supported by psychological hypotheses. This study offers insights into the "black box" of value alignment and proposes in-context alignment methods to enhance the safety of value-aligned LLMs.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight ξ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level λ> 0 at which the teacher ridge risk R(λ) is nonstationary (i.e., R'(λ) neq 0). We obtain a closed-form expression for the optimal mixing weight ξ^star(λ) for any value of λ and show that it obeys the sign rule: sign(ξ^star(λ))=-sign(R'(λ)). In particular, ξ^star(λ) can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes n and p both diverge but their aspect ratio p/n converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate ξ^star without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

Current question-answering benchmarks predominantly focus on accuracy in realizable prediction tasks. Conditioned on a question and answer-key, does the most likely token match the ground truth? Such benchmarks necessarily fail to evaluate LLMs' ability to quantify ground-truth outcome uncertainty. In this work, we focus on the use of LLMs as risk scores for unrealizable prediction tasks. We introduce folktexts, a software package to systematically generate risk scores using LLMs, and evaluate them against US Census data products. A flexible API enables the use of different prompting schemes, local or web-hosted models, and diverse census columns that can be used to compose custom prediction tasks. We evaluate 17 recent LLMs across five proposed benchmark tasks. We find that zero-shot risk scores produced by multiple-choice question-answering have high predictive signal but are widely miscalibrated. Base models consistently overestimate outcome uncertainty, while instruction-tuned models underestimate uncertainty and produce over-confident risk scores. In fact, instruction-tuning polarizes answer distribution regardless of true underlying data uncertainty. This reveals a general inability of instruction-tuned LLMs to express data uncertainty using multiple-choice answers. A separate experiment using verbalized chat-style risk queries yields substantially improved calibration across instruction-tuned models. These differences in ability to quantify data uncertainty cannot be revealed in realizable settings, and highlight a blind-spot in the current evaluation ecosystem that folktexts covers.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

In this paper, we focus on the task of conditional image generation, where an image is synthesized according to user instructions. The critical challenge underpinning this task is ensuring both the fidelity of the generated images and their semantic alignment with the provided conditions. To tackle this issue, previous studies have employed supervised perceptual losses derived from pre-trained models, i.e., reward models, to enforce alignment between the condition and the generated result. However, we observe one inherent shortcoming: considering the diversity of synthesized images, the reward model usually provides inaccurate feedback when encountering newly generated data, which can undermine the training process. To address this limitation, we propose an uncertainty-aware reward modeling, called Ctrl-U, including uncertainty estimation and uncertainty-aware regularization, designed to reduce the adverse effects of imprecise feedback from the reward model. Given the inherent cognitive uncertainty within reward models, even images generated under identical conditions often result in a relatively large discrepancy in reward loss. Inspired by the observation, we explicitly leverage such prediction variance as an uncertainty indicator. Based on the uncertainty estimation, we regularize the model training by adaptively rectifying the reward. In particular, rewards with lower uncertainty receive higher loss weights, while those with higher uncertainty are given reduced weights to allow for larger variability. The proposed uncertainty regularization facilitates reward fine-tuning through consistency construction. Extensive experiments validate the effectiveness of our methodology in improving the controllability and generation quality, as well as its scalability across diverse conditional scenarios. Code will soon be available at https://grenoble-zhang.github.io/Ctrl-U-Page/.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key component: (i) clean values, (ii) initial margin and Collateral Valuation Adjustment (ColVA), (iii) Credit/Debit Valuation Adjustments (CVA/DVA) together with Margin Valuation Adjustment (MVA), and (iv) Funding Valuation Adjustment (FVA). Because these layers depend on one another through collateral and default effects, a naive Monte Carlo approach would require deeply nested simulations, making the problem computationally intractable. To address this challenge, we use an iterative deep BSDE approach, handling each layer sequentially so that earlier outputs serve as inputs to the subsequent layers. Initial margin is computed via deep quantile regression to reflect margin requirements over the Margin Period of Risk. We also adopt a change-of-measure method that highlights rare but significant defaults of the bank or counterparty, ensuring that these events are accurately captured in the training process. We further extend Han and Long's (2020) a posteriori error analysis to BSDEs on bounded domains. Due to the random exit from the domain, we obtain an order of convergence of O(h^{1/4-epsilon}) rather than the usual O(h^{1/2}). Numerical experiments illustrate that this method drastically reduces computational demands and successfully scales to high-dimensional, non-symmetric portfolios. The results confirm its effectiveness and accuracy, offering a practical alternative to nested Monte Carlo simulations in multi-counterparty xVA analyses.

Fine-tuning foundation models often compromises their robustness to distribution shifts. To remedy this, most robust fine-tuning methods aim to preserve the pre-trained features. However, not all pre-trained features are robust and those methods are largely indifferent to which ones to preserve. We propose dual risk minimization (DRM), which combines empirical risk minimization with worst-case risk minimization, to better preserve the core features of downstream tasks. In particular, we utilize core-feature descriptions generated by LLMs to induce core-based zero-shot predictions which then serve as proxies to estimate the worst-case risk. DRM balances two crucial aspects of model robustness: expected performance and worst-case performance, establishing a new state of the art on various real-world benchmarks. DRM significantly improves the out-of-distribution performance of CLIP ViT-L/14@336 on ImageNet (75.9 to 77.1), WILDS-iWildCam (47.1 to 51.8), and WILDS-FMoW (50.7 to 53.1); opening up new avenues for robust fine-tuning. Our code is available at https://github.com/vaynexie/DRM .

Diffusion models have emerged as powerful generative tools across various domains, yet tailoring pre-trained models to exhibit specific desirable properties remains challenging. While reinforcement learning (RL) offers a promising solution,current methods struggle to simultaneously achieve stable, efficient fine-tuning and support non-differentiable rewards. Furthermore, their reliance on sparse rewards provides inadequate supervision during intermediate steps, often resulting in suboptimal generation quality. To address these limitations, dense and differentiable signals are required throughout the diffusion process. Hence, we propose VAlue-based Reinforced Diffusion (VARD): a novel approach that first learns a value function predicting expection of rewards from intermediate states, and subsequently uses this value function with KL regularization to provide dense supervision throughout the generation process. Our method maintains proximity to the pretrained model while enabling effective and stable training via backpropagation. Experimental results demonstrate that our approach facilitates better trajectory guidance, improves training efficiency and extends the applicability of RL to diffusion models optimized for complex, non-differentiable reward functions.

We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing the CVaR objective, we show that our stochastic prox-linear (SPL+) algorithm can better exploit the structure of the objective, while still providing a convenient closed form update. Our SPL+ method also adapts to the scaling of the loss function, which allows for easier tuning. We then specialize a general convergence theorem for SPL+ to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally.

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

Evaluating the safety of LLM-based agents is increasingly important because risks in realistic deployments often emerge over multi-step interactions rather than isolated prompts or final responses. Existing trajectory-level benchmarks remain limited by insufficient interaction diversity, coarse observability of safety failures, and weak long-horizon realism. We introduce ATBench, a trajectory-level benchmark for structured, diverse, and realistic evaluation of agent safety. ATBench organizes agentic risk along three dimensions: risk source, failure mode, and real-world harm. Based on this taxonomy, we construct trajectories with heterogeneous tool pools and a long-context delayed-trigger protocol that captures realistic risk emergence across multiple stages. The benchmark contains 1,000 trajectories (503 safe and 497 unsafe), averaging 9.01 turns and 3.95k tokens, with 1,954 invoked tools drawn from pools spanning 2,084 available tools. Data quality is supported by rule-based and LLM-based filtering plus full human audit. Experiments on frontier LLMs, open-source models, and specialized guard systems show that ATBench is challenging even for strong evaluators, while enabling taxonomy-stratified analysis, cross-benchmark comparison, and diagnosis of long-horizon failure patterns.

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

Systematic Investment Plans (SIPs) are a primary vehicle for retail equity participation in India, yet the impact of their intra-month timing remains underexplored. This study offers a 22-year (2003--2024) comparative analysis of SIP performance in the Nifty 50 index, contrasting the conventional first-trading-day (FTD-SIP) strategy with an alternative aligned to monthly Futures and Options expiry days (EXP-SIP). Using a multi-layered statistical framework -- including non-parametric tests, effect size metrics, and stochastic dominance -- we uncover two key findings. First, EXP-SIPs outperform FTD-SIPs by 0.5--2.5\% annually over short-to-medium-term horizons (1--5 years), with Second-Order Stochastic Dominance (SSD) confirming the EXP-SIP as the preferred choice for all risk-averse investors. Second, we establish boundary conditions for this advantage, showing it decays and becomes economically negligible over longer horizons (10--20 years), where compounding and participation dominate. Additionally, the study challenges the prevalent ``12\% return'' narrative in Indian equity markets, finding that the 20-year pre-tax CAGR for Nifty 50 SIPs is closer to 6.7\%. These findings carry significant implications for investor welfare, financial product design, and transparency in return reporting.

Quantitative tools are increasingly appealing for decision support in healthcare, driven by the growing capabilities of advanced AI systems. However, understanding the predictive uncertainties surrounding a tool's output is crucial for decision-makers to ensure reliable and transparent decisions. In this paper, we present a case study on pulmonary nodule detection for lung cancer screening, enhancing an advanced detection model with an uncertainty quantification technique called conformal risk control (CRC). We demonstrate that prediction sets with conformal guarantees are attractive measures of predictive uncertainty in the safety-critical healthcare domain, allowing end-users to achieve arbitrary validity by trading off false positives and providing formal statistical guarantees on model performance. Among ground-truth nodules annotated by at least three radiologists, our model achieves a sensitivity that is competitive with that generally achieved by individual radiologists, with a slight increase in false positives. Furthermore, we illustrate the risks of using off-the-shelve prediction models when faced with ontological uncertainty, such as when radiologists disagree on what constitutes the ground truth on pulmonary nodules.

Foundation models are powerful technologies: how they are released publicly directly shapes their societal impact. In this position paper, we focus on open foundation models, defined here as those with broadly available model weights (e.g. Llama 2, Stable Diffusion XL). We identify five distinctive properties (e.g. greater customizability, poor monitoring) of open foundation models that lead to both their benefits and risks. Open foundation models present significant benefits, with some caveats, that span innovation, competition, the distribution of decision-making power, and transparency. To understand their risks of misuse, we design a risk assessment framework for analyzing their marginal risk. Across several misuse vectors (e.g. cyberattacks, bioweapons), we find that current research is insufficient to effectively characterize the marginal risk of open foundation models relative to pre-existing technologies. The framework helps explain why the marginal risk is low in some cases, clarifies disagreements about misuse risks by revealing that past work has focused on different subsets of the framework with different assumptions, and articulates a way forward for more constructive debate. Overall, our work helps support a more grounded assessment of the societal impact of open foundation models by outlining what research is needed to empirically validate their theoretical benefits and risks.

Uncertainty estimation is critical for cost-sensitive deep-learning applications (i.e. disease diagnosis). It is very challenging partly due to the inaccessibility of uncertainty groundtruth in most datasets. Previous works proposed to estimate the uncertainty from softmax calibration, Monte Carlo sampling, subjective logic and so on. However, these existing methods tend to be over-confident about their predictions with unreasonably low overall uncertainty, which originates from the imbalance between positive (correct classifications) and negative (incorrect classifications) samples. For this issue, we firstly propose the distributional imbalance to model the imbalance in uncertainty estimation as two kinds of distribution biases, and secondly propose Balanced True Class Probability (BTCP) framework, which learns an uncertainty estimator with a novel Distributional Focal Loss (DFL) objective. Finally, we evaluate the BTCP in terms of failure prediction and out-of-distribution (OOD) detection on multiple datasets. The experimental results show that BTCP outperforms other uncertainty estimation methods especially in identifying incorrect classifications.

This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data.

Large Language Models (LLMs) can produce surprisingly sophisticated estimates of their own uncertainty. However, it remains unclear to what extent this expressed confidence is tied to the reasoning, knowledge, or decision making of the model. To test this, we introduce RiskEval: a framework designed to evaluate whether models adjust their abstention policies in response to varying error penalties. Our evaluation of several frontier models reveals a critical dissociation: models are neither cost-aware when articulating their verbal confidence, nor strategically responsive when deciding whether to engage or abstain under high-penalty conditions. Even when extreme penalties render frequent abstention the mathematically optimal strategy, models almost never abstain, resulting in utility collapse. This indicates that calibrated verbal confidence scores may not be sufficient to create trustworthy and interpretable AI systems, as current models lack the strategic agency to convert uncertainty signals into optimal and risk-sensitive decisions.

The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Advisors (CTAs) which -- when adequately measured -- turns out to be much stronger than anticipated. We also highlight interesting connections with so-called Risk Parity portfolios. Finally, we propose a new portfolio of strangle options that provides a pure exposure to the long-term variance of the underlying, offering yet another viewpoint on the link between trend and volatility.

Recent advances in Large Language Models (LLMs) have sparked concerns over their potential to acquire and misuse dangerous or high-risk capabilities, posing frontier risks. Current safety evaluations primarily test for what a model can do - its capabilities - without assessing what it would do if endowed with high-risk capabilities. This leaves a critical blind spot: models may strategically conceal capabilities or rapidly acquire them, while harboring latent inclinations toward misuse. We argue that propensity - the likelihood of a model to pursue harmful actions if empowered - is a critical, yet underexplored, axis of safety evaluation. We present PropensityBench, a novel benchmark framework that assesses the proclivity of models to engage in risky behaviors when equipped with simulated dangerous capabilities using proxy tools. Our framework includes 5,874 scenarios with 6,648 tools spanning four high-risk domains: cybersecurity, self-proliferation, biosecurity, and chemical security. We simulate access to powerful capabilities via a controlled agentic environment and evaluate the models' choices under varying operational pressures that reflect real-world constraints or incentives models may encounter, such as resource scarcity or gaining more autonomy. Across open-source and proprietary frontier models, we uncover 9 alarming signs of propensity: models frequently choose high-risk tools when under pressure, despite lacking the capability to execute such actions unaided. These findings call for a shift from static capability audits toward dynamic propensity assessments as a prerequisite for deploying frontier AI systems safely. Our code is available at https://github.com/scaleapi/propensity-evaluation.

This paper presents a novel risk-sensitive trading agent combining reinforcement learning and large language models (LLMs). We extend the Conditional Value-at-Risk Proximal Policy Optimization (CPPO) algorithm, by adding risk assessment and trading recommendation signals generated by a LLM from financial news. Our approach is backtested on the Nasdaq-100 index benchmark, using financial news data from the FNSPID dataset and the DeepSeek V3, Qwen 2.5 and Llama 3.3 language models. The code, data, and trading agents are available at: https://github.com/benstaf/FinRL_DeepSeek

Many deployments must compare candidate language models for safety before a labeled benchmark exists for the relevant language, sector, or regulatory regime. We formalize this setting as benchmarkless comparative safety scoring and specify the contract under which a scenario-based audit can be interpreted as deployment evidence. Scores are valid only under a fixed scenario pack, rubric, auditor, judge, sampling configuration, and rerun budget. Because no labels are available, we replace ground-truth agreement with an instrumental-validity chain: responsiveness to a controlled safe-versus-abliterated contrast, dominance of target-driven variance over auditor and judge artifacts, and stability across reruns. We instantiate the chain in SimpleAudit, a local-first scoring instrument, and validate it on a Norwegian safety pack. Safe and abliterated targets separate with AUROC values between 0.89 and 1.00, target identity is the dominant variance component (η^2 approx 0.52), and severity profiles stabilize by ten reruns. Applying the same chain to Petri shows that it admits both tools. The substantial differences arise upstream of the chain, in claim-contract enforcement and deployment fit. A Norwegian public-sector procurement case comparing Borealis and Gemma 3 demonstrates the resulting evidence in practice: the safer model depends on scenario category and risk measure. Consequently, scores, matched deltas, critical rates, uncertainty, and the auditor and judge used must be reported together rather than collapsed into a single ranking.

Large language models (LLMs) are increasingly applied to structured clinical data, yet whether they can recognize the limits of their own knowledge on such tasks remains unexplored. We study this question through the lens of cross-model attribution divergence with the goal of reducing epistemic uncertainty for structured tasks, comparing Qwen 2.5 7B and XGBoost on a prediction task via attribution divergence analysis. We report four findings. First, LLM verbalized confidence is epistemically vacuous, it outputs a near-constant (0.856-0.937) regardless of whether accuracy is 49% or 75.3%, tracking prompt format rather than prediction quality. Second, the LLM exhibits an inverse difficulty effect: accuracy drops to 64.8% when XGBoost is 99% correct, but matches XGBoost (73.8% vs. 73.1%) when it is moderately uncertain. Third, few-shot examples and SHAP-derived feature evidence are orthogonal, super-additive interventions: they reduce the Attribution Disagreement Score (ADS) from 1.54 to 0.38 and improve accuracy from 49% to 75.3% without training. Fourth, a cross-model calibrator that determined LLM reliability using attribution divergence signals reduces expected calibration error from 0.254 to 0.080, replacing uninformative verbalized confidence with patient-specific reliability estimates, without accessing model internals or requiring repeated inference. We frame these findings as a cold start problem for LLMs on structured data and outline a path toward genuine epistemic self-awareness.

Backtests of cryptocurrency perpetual futures are fragile when they ignore microstructure frictions and reuse evaluation windows during parameter search. We study four liquid perpetuals (BTC/USDT, ETH/USDT, SOL/USDT, AVAX/USDT) and quantify how execution delay, funding, fees, and slippage can inflate reported performance. We introduce AutoQuant, an execution-centric, alpha-agnostic framework for auditable strategy configuration selection. AutoQuant encodes strict T+1 execution semantics and no-look-ahead funding alignment, runs Bayesian optimization under realistic costs, and applies a two-stage double-screening protocol across held-out rolling windows and a cost-sensitivity grid. We show that fee-only and zero-cost backtests can materially overestimate annualized returns relative to a fully costed configuration, and that double screening tends to reduce drawdowns under the same strict semantics even when returns are not higher. A CSCV/PBO diagnostic indicates substantial residual overfitting risk, motivating AutoQuant as validation and governance infrastructure rather than a claim of persistent alpha. Returns are reported for small-account simulations with linear trading costs and without market impact or capacity modeling.

Robust planning in interactive scenarios requires predicting the uncertain future to make risk-aware decisions. Unfortunately, due to long-tail safety-critical events, the risk is often under-estimated by finite-sampling approximations of probabilistic motion forecasts. This can lead to overconfident and unsafe robot behavior, even with robust planners. Instead of assuming full prediction coverage that robust planners require, we propose to make prediction itself risk-aware. We introduce a new prediction objective to learn a risk-biased distribution over trajectories, so that risk evaluation simplifies to an expected cost estimation under this biased distribution. This reduces the sample complexity of the risk estimation during online planning, which is needed for safe real-time performance. Evaluation results in a didactic simulation environment and on a real-world dataset demonstrate the effectiveness of our approach. The code and a demo are available.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Large language models (LLMs) have recently demonstrated strong capabilities as autonomous agents, showing promise in reasoning, tool use, and sequential decision-making. While prior benchmarks have evaluated LLM agents in domains such as software engineering and scientific discovery, the finance domain remains underexplored, despite its direct relevance to economic value and high-stakes decision-making. Existing financial benchmarks primarily test static knowledge through question answering, but they fall short of capturing the dynamic and iterative nature of trading. To address this gap, we introduce StockBench, a contamination-free benchmark designed to evaluate LLM agents in realistic, multi-month stock trading environments. Agents receive daily market signals -- including prices, fundamentals, and news -- and must make sequential buy, sell, or hold decisions. Performance is assessed using financial metrics such as cumulative return, maximum drawdown, and the Sortino ratio. Our evaluation of state-of-the-art proprietary (e.g., GPT-5, Claude-4) and open-weight (e.g., Qwen3, Kimi-K2, GLM-4.5) models shows that while most LLM agents struggle to outperform the simple buy-and-hold baseline, several models demonstrate the potential to deliver higher returns and manage risk more effectively. These findings highlight both the challenges and opportunities in developing LLM-powered financial agents, showing that excelling at static financial knowledge tasks does not necessarily translate into successful trading strategies. We release StockBench as an open-source resource to support reproducibility and advance future research in this domain.

Adversarial robustness often comes at the cost of degraded accuracy, impeding the real-life application of robust classification models. Training-based solutions for better trade-offs are limited by incompatibilities with already-trained high-performance large models, necessitating the exploration of training-free ensemble approaches. Observing that robust models are more confident in correct predictions than in incorrect ones on clean and adversarial data alike, we speculate amplifying this "benign confidence property" can reconcile accuracy and robustness in an ensemble setting. To achieve so, we propose "MixedNUTS", a training-free method where the output logits of a robust classifier and a standard non-robust classifier are processed by nonlinear transformations with only three parameters, which are optimized through an efficient algorithm. MixedNUTS then converts the transformed logits into probabilities and mixes them as the overall output. On CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points, sacrificing merely 0.87 points in robust accuracy.

This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs have exponentially distributed sojourn times (waiting times between jumps). We explicitly derive the probabilities of all possible jump sizes at the first jump and obtain the Laplace transform of the joint distribution of the first jump time and its corresponding jump size. In ruin theory, the classical Cramér-Lundberg model assumes that claims arrive independently according to a Poisson process. In contrast, our model employs an MIPP to allow for clustered arrivals, reflecting real-world scenarios, such as catastrophic events. Under this new framework, we derive the corresponding scale function in closed form, facilitating accurate calculations of the probability of ruin in the presence of clustered claims. These results improve the modeling of extreme risks and have practical implications for insurance solvency assessments, reinsurance pricing, and capital reserve estimation.

Clinical LLMs are often scaled by increasing model size, context length, retrieval complexity, or inference-time compute, with the implicit expectation that higher accuracy implies safer behavior. This assumption is incomplete in medicine, where a few confident, high-risk, or evidence-contradicting errors can matter more than average benchmark performance. We introduce SaFE-Scale, a framework for measuring how clinical LLM safety changes across model scale, evidence quality, retrieval strategy, context exposure, and inference-time compute. To instantiate this framework, we introduce RadSaFE-200, a Radiology Safety-Focused Evaluation benchmark of 200 multiple-choice questions with clinician-defined clean evidence, conflict evidence, and option-level labels for high-risk error, unsafe answer, and evidence contradiction. We evaluated 34 locally deployed LLMs across six deployment conditions: closed-book prompting (zero-shot), clean evidence, conflict evidence, standard RAG, agentic RAG, and max-context prompting. Clean evidence produced the strongest improvement, increasing mean accuracy from 73.5% to 94.1%, while reducing high-risk error from 12.0% to 2.6%, contradiction from 12.7% to 2.3%, and dangerous overconfidence from 8.0% to 1.6%. Standard RAG and agentic RAG did not reproduce this safety profile: agentic RAG improved accuracy over standard RAG and reduced contradiction, but high-risk error and dangerous overconfidence remained elevated. Max-context prompting increased latency without closing the safety gap, and additional inference-time compute produced only limited gains. Worst-case analysis showed that clinically consequential errors concentrated in a small subset of questions. Clinical LLM safety is therefore not a passive consequence of scaling, but a deployment property shaped by evidence quality, retrieval design, context construction, and collective failure behavior.

Recent deployments of large language models (LLMs) as autonomous trading agents raise questions about whether financial decision-making competence generalizes beyond specific market patterns and how it should be trained and evaluated in noisy markets lacking ground truth. We propose a structured framework for training and evaluating such models. Central to our approach is a curated, multiple-choice question (MCQ) dataset derived from classic textbooks and historical markets, verified by an AI committee, enriched with structured reasoning traces, and augmented to reduce shortcut learning. To evaluate whether performance on isolated MCQs generalizes to real-world trading, we introduce a two-stage protocol combining test-set evaluation with an MCQ-based chronological trading simulation. Extensive evaluations across market regimes provide statistically robust evidence that open models trained with our framework exhibit competitive, risk-aware behavior over time, outperform open-source baselines, and approach frontier-model performance at smaller scale. We release the dataset and evaluation framework to support further research.

Evaluating conditional coverage remains one of the most persistent challenges in assessing the reliability of predictive systems. Although conformal methods can give guarantees on marginal coverage, no method can guarantee to produce sets with correct conditional coverage, leaving practitioners without a clear way to interpret local deviations. To overcome sample-inefficiency and overfitting issues of existing metrics, we cast conditional coverage estimation as a classification problem. Conditional coverage is violated if and only if some classifier can achieve lower risk than the target coverage. Through the choice of a (proper) loss function, the resulting risk difference gives a conservative estimate of natural miscoverage measures such as L1 and L2 distance, and can even separate the effects of over- and under-coverage, and non-constant target coverages. We call the resulting family of metrics excess risk of the target coverage (ERT). We show experimentally that the use of modern classifiers provides much higher statistical power than simple classifiers underlying established metrics like CovGap. Additionally, we use our metric to benchmark different conformal prediction methods. Finally, we release an open-source package for ERT as well as previous conditional coverage metrics. Together, these contributions provide a new lens for understanding, diagnosing, and improving the conditional reliability of predictive systems.

People use language models for practical questions whose answers are difficult to verify. We show that models exhibit covert value leakage: the information they provide is influenced by their own values, without this influence being disclosed to the user. In one of our evaluations, the user is considering investing in an AI company and wants to know how likely the AI bubble is to pop. Claude Opus 4.8 gives a lower probability when the company under consideration is Anthropic rather than OpenAI. Yet Claude mostly fails to disclose this influence to the user. Covert value leakage is a form of misalignment because it goes against the user's preferences and is likely to mislead them. To investigate this phenomenon, we introduce a suite of evaluations to quantify value leakage and whether models disclose it. We find that models are influenced by different types of values, including preferences for morally good outcomes, for the company that developed them, and for some human leisure activities over others. We often observe large differences among frontier models on the same evaluation. For example, on a Fermi-estimation task, Claude models falsely claim to give unbiased answers in their chain-of-thought, while Qwen models explain how their values bias their answers. Value leakage is a failure mode distinct from sycophancy and reward hacking, and current alignment training and evaluations do not adequately address it.

Portfolio optimization has been an area that has attracted considerable attention from the financial research community. Designing a profitable portfolio is a challenging task involving precise forecasting of future stock returns and risks. This chapter presents a comparative study of three portfolio design approaches, the mean-variance portfolio (MVP), hierarchical risk parity (HRP)-based portfolio, and autoencoder-based portfolio. These three approaches to portfolio design are applied to the historical prices of stocks chosen from ten thematic sectors listed on the National Stock Exchange (NSE) of India. The portfolios are designed using the stock price data from January 1, 2018, to December 31, 2021, and their performances are tested on the out-of-sample data from January 1, 2022, to December 31, 2022. Extensive results are analyzed on the performance of the portfolios. It is observed that the performance of the MVP portfolio is the best on the out-of-sample data for the risk-adjusted returns. However, the autoencoder portfolios outperformed their counterparts on annual returns.

Risk management in finance involves recognizing, evaluating, and addressing financial risks to maintain stability and ensure regulatory compliance. Extracting relevant insights from extensive regulatory documents is a complex challenge requiring advanced retrieval and language models. This paper introduces RiskData, a dataset specifically curated for finetuning embedding models in risk management, and RiskEmbed, a finetuned embedding model designed to improve retrieval accuracy in financial question-answering systems. The dataset is derived from 94 regulatory guidelines published by the Office of the Superintendent of Financial Institutions (OSFI) from 1991 to 2024. We finetune a state-of-the-art sentence BERT embedding model to enhance domain-specific retrieval performance typically for Retrieval-Augmented Generation (RAG) systems. Experimental results demonstrate that RiskEmbed significantly outperforms general-purpose and financial embedding models, achieving substantial improvements in ranking metrics. By open-sourcing both the dataset and the model, we provide a valuable resource for financial institutions and researchers aiming to develop more accurate and efficient risk management AI solutions.

Clinical early warning systems built on electronic health records, in which clinical observations are recorded as irregularly sampled medical time series (ISMTS), must deliver both calibrated risk scores for patient triage and interpretable rationales that clinicians can verify. Large Language Models (LLMs) have been explored for this task, yet they collapse graded clinical risk into overconfident binary predictions. This risk polarization undermines both calibration and cross-patient comparability. To address this, we propose TRIAGE, a framework that trains an LLM to generate dialectical reasoning over competing clinical outcomes by eliciting outcome-specific rationales. This dialectical formulation mitigates risk polarization, enabling a single LLM to yield continuous risk scores grounded in explicit clinical reasoning. Evaluated on three ISMTS benchmarks, TRIAGE achieves an average AUPRC improvement of 3.3% and reduces calibration error by 81% compared to the competitive baselines. An LLM-as-a-judge assessment further shows that our rationales surpass post-hoc explanations from the baseline by 20% in clinical reasoning quality. The source code is available at https://github.com/HyeongWon-Jang/TRIAGE .

Whether pairing people with AI helps or hurts is usually reported as a single average effect. Using a real-money prediction market (Polymarket) as an objective, externally resolved benchmark, this pilot shows that the value of human-AI collaboration depends on a specific, measurable form of human capital. Analyzed at the level of the individual forecaster, hybrid performance is trimodal: most people either deferred to the model (matching it) or used it to rubber-stamp a prior guess (performing worse than the model alone), while a minority engaged in genuine complementary reasoning and reached accuracy matching or even exceeding (i.e., lower error than) the market itself. Collaborative traits (perspective-taking, intellectual humility, and curiosity) rather than raw cognitive ability or model benchmarks, distinguished who reached that mode. The results are preliminary but statistically robust, and motivate a pre-registered replication now in preparation.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation problems and especially neural machine translation, in both human and automatic evaluations. However, the standard sampling-based algorithm for MBR is substantially more computationally expensive than beam search, requiring a large number of samples as well as a quadratic number of calls to the utility function, limiting its applicability. We describe an algorithm for MBR which gradually grows the number of samples used to estimate the utility while pruning hypotheses that are unlikely to have the highest utility according to confidence estimates obtained with bootstrap sampling. Our method requires fewer samples and drastically reduces the number of calls to the utility function compared to standard MBR while being statistically indistinguishable in terms of accuracy. We demonstrate the effectiveness of our approach in experiments on three language pairs, using chrF++ and COMET as utility/evaluation metrics.

We develop a portfolio allocation framework that leverages deep learning techniques to address challenges arising from high-dimensional, non-stationary, and low-signal-to-noise market information. Our approach includes a dynamic embedding method that reduces the non-stationary, high-dimensional state space into a lower-dimensional representation. We design a reinforcement learning (RL) framework that integrates generative autoencoders and online meta-learning to dynamically embed market information, enabling the RL agent to focus on the most impactful parts of the state space for portfolio allocation decisions. Empirical analysis based on the top 500 U.S. stocks demonstrates that our framework outperforms common portfolio benchmarks and the predict-then-optimize (PTO) approach using machine learning, particularly during periods of market stress. Traditional factor models do not fully explain this superior performance. The framework's ability to time volatility reduces its market exposure during turbulent times. Ablation studies confirm the robustness of this performance across various reinforcement learning algorithms. Additionally, the embedding and meta-learning techniques effectively manage the complexities of high-dimensional, noisy, and non-stationary financial data, enhancing both portfolio performance and risk management.

Large language models (LLMs) are increasingly used as judges to replace costly human preference labels in pairwise evaluation. Despite their practicality, LLM judges remain prone to miscalibration and systematic biases. This paper proposes SCOPE (Selective Conformal Optimized Pairwise Evaluation), a framework for selective pairwise judging with finite-sample statistical guarantees. Under exchangeability, SCOPE calibrates an acceptance threshold such that the error rate among non-abstained judgments is at most a user-specified level α. To provide SCOPE with a bias-neutral uncertainty signal, we introduce Bidirectional Preference Entropy (BPE), which queries the judge under both response positions, aggregates the implied preference probabilities to enforce invariance to response order, and converts the aggregated probability into an entropy-based uncertainty score. Across MT-Bench, RewardBench, and Chatbot Arena, BPE improves uncertainty quality over standard confidence proxies, providing a stronger selection signal that enables SCOPE to consistently meet the target risk level while retaining good coverage across judge scales. In particular, at α= 0.10, SCOPE consistently satisfies the risk bound across all benchmarks and judge scales (empirical risk approx 0.097 to 0.099), while retaining substantial coverage, reaching 0.89 on RewardBench with Qwen-14B and 0.98 on RewardBench with Qwen-32B. Compared to naïve baselines, SCOPE accepts up to 2.4times more judgments on MT-Bench with Qwen-7B under the same target risk constraint, demonstrating that BPE enables reliable and high-coverage LLM-based evaluation.

We study permissionless spot--perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot inventory and derivative margin under on-chain liquidity and execution frictions. The paper delivers three results. First, it solves a static control problem for the collateral share and shows that the risk-constrained formulation provides a more robust operating benchmark relative to the economic optimum. In comparative calibration, the required collateral rises monotonically under volatility stress. The collateral is the lowest for BTC and increases significantly for long tail assets such as LINK and DOGE. Second, the paper derives an asymmetric dynamic extension in which the lower boundary of intervention is solvency driven, and the upper boundary is determined by a trade-off between carry-loss and the cost of rebalancing. Monte Carlo simulation shows that the lower boundary remains structurally relevant, whereas meaningful interior upper triggers survive mainly in the regimes with high carry and low costs. Third, the paper validates an execution-aware implementation with live routed execution and historical backtests. The execution layer shows that the realized wedges are significant, but become worse in the case of selling the basis. This justifies a minimum effective rebalancing size and a positive execution buffer. The historical validation shows that in the case of a fixed control rule the realized performance is predominantly explained by the funding environment.

Autonomous language-model agents increasingly rely on installable skills and tools to complete user tasks. Static skill auditing can expose capability surface before deployment, but it cannot determine whether a particular invocation is unsafe under the current user request and runtime context. We therefore study skill invocation auditing as a continuous-risk estimation problem: given a user request, candidate skill, and runtime context, predict a score that supports ranking and triage before a hard intervention is applied. We introduce STARS, which combines a static capability prior, a request-conditioned invocation risk model, and a calibrated risk-fusion policy. To evaluate this setting, we construct SIA-Bench, a benchmark of 3,000 invocation records with group-safe splits, lineage metadata, runtime context, canonical action labels, and derived continuous-risk targets. On a held-out split of indirect prompt injection attacks, calibrated fusion reaches 0.439 high-risk AUPRC, improving over 0.405 for the contextual scorer and 0.380 for the strongest static baseline, while the contextual scorer remains better calibrated with 0.289 expected calibration error. On the locked in-distribution test split, gains are smaller and static priors remain useful. The resulting claim is therefore narrower: request-conditioned auditing is most valuable as an invocation-time risk-scoring and triage layer rather than as a replacement for static screening. Code is available at https://github.com/123zgj123/STARS.

Financial time-series forecasting is a high-stakes problem where regime shifts and shocks make point-accurate yet overconfident models dangerous. We propose Uncertainty-Gated Generative Modeling (UGGM), which treats uncertainty as an internal control signal that gates (i) representation via gated reparameterization, (ii) propagation via similarity and confidence routing, and (iii) generation via uncertainty-controlled predictive distributions, together with uncertainty-driven regularization and calibration to curb miscalibration. Instantiated on Weak Innovation AutoEncoder (WIAE-GPF), our UG-WIAE-GPF significantly improves risk-sensitive forecasting, delivering a 63.5\% MSE reduction on NYISO (0.3508 rightarrow 0.1281), with improved robustness under shock intervals (mSE: 0.2739 rightarrow 0.1748).

Throughout the different phases of a drug development program, randomized trials are used to establish the tolerability, safety, and efficacy of a candidate drug. At each stage one aims to optimize the design of future studies by extrapolation from the available evidence at the time. This includes collected trial data and relevant external data. However, relevant external data are typically available as averages only, for example from trials on alternative treatments reported in the literature. Here we report on such an example from a drug development for wet age-related macular degeneration. This disease is the leading cause of severe vision loss in the elderly. While current treatment options are efficacious, they are also a substantial burden for the patient. Hence, new treatments are under development which need to be compared against existing treatments. The general statistical problem this leads to is meta-analysis, which addresses the question of how we can combine datasets collected under different conditions. Bayesian methods have long been used to achieve partial pooling. Here we consider the challenge when the model of interest is complex (hierarchical and nonlinear) and one dataset is given as raw data while the second dataset is given as averages only. In such a situation, common meta-analytic methods can only be applied when the model is sufficiently simple for analytic approaches. When the model is too complex, for example nonlinear, an analytic approach is not possible. We provide a Bayesian solution by using simulation to approximately reconstruct the likelihood of the external summary and allowing the parameters in the model to vary under the different conditions. We first evaluate our approach using fake-data simulations and then report results for the drug development program that motivated this research.

Introduction: The paper addresses the challenging problem of predicting the short-term realized volatility of the Bitcoin price using order flow information. The inherent stochastic nature and anti-persistence of price pose difficulties in accurate prediction. Methods: To address this, we propose a method that transforms order flow data over a fixed time interval (snapshots) into images. The order flow includes trade sizes, trade directions, and limit order book, and is mapped into image colour channels. These images are then used to train both a simple 3-layer Convolutional Neural Network (CNN) and more advanced ResNet-18 and ConvMixer, with additionally supplementing them with hand-crafted features. The models are evaluated against classical GARCH, Multilayer Perceptron trained on raw data, and a naive guess method that considers current volatility as a prediction. Results: The experiments are conducted using price data from January 2021 and evaluate model performance in terms of root mean square error (RMSPE). The results show that our order flow representation with a CNN as a predictive model achieves the best performance, with an RMSPE of 0.85+/-1.1 for the model with aggregated features and 1.0+/-1.4 for the model without feature supplementation. ConvMixer with feature supplementation follows closely. In comparison, the RMSPE for the naive guess method was 1.4+/-3.0.

Generative models trained using self-supervision of tokenized electronic health record (EHR) timelines show promise for clinical outcome prediction. This is typically done using Monte Carlo simulation for future patient trajectories. However, existing approaches suffer from three key limitations: sparse estimate distributions that poorly differentiate patient risk levels, extreme computational costs, and high sampling variance. We propose two new estimators: the Sum of Conditional Outcome Probability Estimator (SCOPE) and Risk Estimation from Anticipated Conditional Hazards (REACH), that leverage next-token probability distributions discarded by standard Monte Carlo. We prove both estimators are unbiased and that REACH guarantees variance reduction over Monte Carlo sampling for any model and outcome. Empirically, on hospital mortality prediction in MIMIC-IV using the ETHOS-ARES framework, SCOPE and REACH match 100-sample Monte Carlo performance using only 10-11 samples (95% CI: [9,11]), representing a ~10x reduction in inference cost without degrading calibration. For ICU admission prediction, efficiency gains are more modest (~1.2x), which we attribute to the outcome's lower "spontaneity," a property we characterize theoretically and empirically. These methods substantially improve the feasibility of deploying generative EHR models in resource-constrained clinical settings.

Binary options trading is often marketed as a field where predictive models can generate consistent profits. However, the inherent randomness and stochastic nature of binary options make price movements highly unpredictable, posing significant challenges for any forecasting approach. This study demonstrates that machine learning algorithms struggle to outperform a simple baseline in predicting binary options movements. Using a dataset of EUR/USD currency pairs from 2021 to 2023, we tested multiple models, including Random Forest, Logistic Regression, Gradient Boosting, and k-Nearest Neighbors (kNN), both before and after hyperparameter optimization. Furthermore, several neural network architectures, including Multi-Layer Perceptrons (MLP) and a Long Short-Term Memory (LSTM) network, were evaluated under different training conditions. Despite these exhaustive efforts, none of the models surpassed the ZeroR baseline accuracy, highlighting the inherent randomness of binary options. These findings reinforce the notion that binary options lack predictable patterns, making them unsuitable for machine learning-based forecasting.

Data attribution seeks to trace model outputs back to training data. With the recent development of diffusion models, data attribution has become a desired module to properly assign valuations for high-quality or copyrighted training samples, ensuring that data contributors are fairly compensated or credited. Several theoretically motivated methods have been proposed to implement data attribution, in an effort to improve the trade-off between computational scalability and effectiveness. In this work, we conduct extensive experiments and ablation studies on attributing diffusion models, specifically focusing on DDPMs trained on CIFAR-10 and CelebA, as well as a Stable Diffusion model LoRA-finetuned on ArtBench. Intriguingly, we report counter-intuitive observations that theoretically unjustified design choices for attribution empirically outperform previous baselines by a large margin, in terms of both linear datamodeling score and counterfactual evaluation. Our work presents a significantly more efficient approach for attributing diffusion models, while the unexpected findings suggest that at least in non-convex settings, constructions guided by theoretical assumptions may lead to inferior attribution performance. The code is available at https://github.com/sail-sg/D-TRAK.

Recent incidents involving LLMs used for mental-health support reveal a critical evaluation gap: surface-level safety scores do not capture how models behave across realistic, emotionally sensitive interactions over time. Existing benchmarks measure knowledge, safety, or static response quality, but miss whether LLM interactions help users keep reflecting, coping, and making decisions themselves. We formalize this missing dimension as COGNITIVE ATROPHY, a process-level behavioural measure in AI-mediated mental-health support distinct from safety and helpfulness. To measure it, we introduce COGNITIVE ATROPHY BENCH, a clinically grounded benchmark built from 1,576 fully human-generated counseling conversations, 15,680 turns, and 42,230 responses from five LLMs. Three clinical and neuropsychology experts developed a 20-attribute schema spanning user context, response behaviour, and global risk flags; six trained clinical reviewers applied it with span-grounded evidence, producing 5,324 reviewer judgments. We further introduce the User-Input Risk Index (UIRI), the Cognitive Atrophy Risk Index (ARI), and trajectory summaries. Across five LLMs, models show a consistent moderate-to-high level of atrophy-aligned behaviour across single and multi-turn settings. While models generally respond to overt safety cues, they adapt less reliably when users seek solutions or decisions. The dominant recurring patterns are directive advice, problem-solving, recommendation responses, topic shifts, and forms of validation that may reinforce dependence rather than reflection. Our work makes COGNITIVE ATROPHY measurable and provides a foundation for auditing model behaviour in sensitive LLM conversations.

Accurate prediction of major adverse cardiovascular events recurrence risk in acute myocardial infarction patients based on postoperative cardiac MRI and associated clinical notes is crucial for precision treatment and personalized intervention. Existing methods primarily focus on risk stratification capability while overlooking the need for intermediate robust reasoning and model interpretability in clinical practice. Moreover, end-to-end risk prediction using LLM/VLM faces significant challenges due to data limitations and modeling complexity. To bridge this gap, we propose CardioCoT, a novel two-stage hierarchical reasoning-enhanced survival analysis framework designed to enhance both model interpretability and predictive performance. In the first stage, we employ an evidence-augmented self-refinement mechanism to guide LLM/VLMs in generating robust hierarchical reasoning trajectories based on associated radiological findings. In the second stage, we integrate the reasoning trajectories with imaging data for risk model training and prediction. CardioCoT demonstrates superior performance in MACE recurrence risk prediction while providing interpretable reasoning processes, offering valuable insights for clinical decision-making.

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.

We seek to identify the most relevant benefits offered by Medicare Advantage Health Plans that drive membership and market share. As an example, we explore plans operating in a single county in New Jersey between 2018 and 2023. A dataset of benefits from publicly available data sources was created and the variance inflation factor was applied to identify the correlation between the extracted features, to avoid multicollinearity and overparameterization problems. We categorized the variable Market Share and used it as a multinomial response variable with three categories: less than 0.3\%, 0.3\% to 1.5\%, and over 1.5\%. Categories were chosen to achieve approximately uniform distribution of plans (47, 60, and 65 respectively). We built a multinomial Lasso model using 5-fold cross-validation to tune the penalty parameter. Lasso forced some features to be dropped from the model, which reduces the risk of overfitting and increases the interpretability of the results. For each category, important variables are different. Certain brands drive market share, as do PPO plans and prescription drug coverage. Benefits, particularly ancillary benefits that are not part of CMS's required benefits, appear to have little influence, while financial terms such as deductibles, copays, and out-of-pocket limits are associated with higher market share. Finally, we evaluated the predictive accuracy of the Lasso model with the test set. The accuracy is 0.76.

Conventional wisdom suggests that neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. Our work reassesses this assumption for neural networks with high-dimensional inputs. Rather than extrapolating in arbitrary ways, we observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. Moreover, we find that this value often closely approximates the optimal constant solution (OCS), i.e., the prediction that minimizes the average loss over the training data without observing the input. We present results showing this phenomenon across 8 datasets with different distributional shifts (including CIFAR10-C and ImageNet-R, S), different loss functions (cross entropy, MSE, and Gaussian NLL), and different architectures (CNNs and transformers). Furthermore, we present an explanation for this behavior, which we first validate empirically and then study theoretically in a simplified setting involving deep homogeneous networks with ReLU activations. Finally, we show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.

Black-box risk scoring models permeate our lives, yet are typically proprietary or opaque. We propose Distill-and-Compare, a model distillation and comparison approach to audit such models. To gain insight into black-box models, we treat them as teachers, training transparent student models to mimic the risk scores assigned by black-box models. We compare the student model trained with distillation to a second un-distilled transparent model trained on ground-truth outcomes, and use differences between the two models to gain insight into the black-box model. Our approach can be applied in a realistic setting, without probing the black-box model API. We demonstrate the approach on four public data sets: COMPAS, Stop-and-Frisk, Chicago Police, and Lending Club. We also propose a statistical test to determine if a data set is missing key features used to train the black-box model. Our test finds that the ProPublica data is likely missing key feature(s) used in COMPAS.

This paper proposes a reinforcement learning framework that employs Proximal Policy Optimization (PPO) to dynamically optimize the weights of multiple large language model (LLM)-generated formulaic alphas for stock trading strategies. Formulaic alphas are mathematically defined trading signals derived from price, volume, sentiment, and other data. Although recent studies have shown that LLMs can generate diverse and effective alphas, a critical challenge lies in how to adaptively integrate them under varying market conditions. To address this gap, we leverage the deepseek-r1-distill-llama-70b model to generate fifty alphas for five major stocks: Apple, HSBC, Pepsi, Toyota, and Tencent, and then use PPO to adjust their weights in real time. Experimental results demonstrate that the PPO-optimized strategy achieves strong returns and high Sharpe ratios across most stocks, outperforming both an equal-weighted alpha portfolio and traditional benchmarks such as the Nikkei 225, S&P 500, and Hang Seng Index. The findings highlight the importance of reinforcement learning in the allocation of alpha weights and show the potential of combining LLM-generated signals with adaptive optimization for robust financial forecasting and trading.

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.

Purpose. Patients with advanced cancer may undergo multiple lines of treatment, switching therapies as their disease progresses. Motivated by a study of metastatic prostate cancer, we develop a microsimulation framework to study therapy sequence. Methods. We propose a discrete-time state transition model to study two lines of anti-cancer therapy. Based on digitized published progression-free survival (PFS) and overall survival (OS) curves, we infer event types (progression or death), and estimate transition probabilities using cumulative incidence functions with competing risks. Our model incorporates within-patient dependence over time, such that response to first-line therapy informs subsequent event probabilities. Parameters governing the degree of within-patient dependence can be used to calibrate the model-based results to those of a target trial. We demonstrate these methods in a study of two therapy sequences for metastatic prostate cancer, where Docetaxel (DCT) and Abiraterone Acetate (AA) are both appropriate for use in either first or second line treatment. We assess costs, Quality-Adjusted Life Years (QALYs) and Incremental Cost Effectiveness Ratio (ICER) for two treatment strategies: DCT then AA vs AA then DCT. Results. Using digitized survival curves from relevant clinical trials, we identified 8.6-13.9% of PFS times that should be categorized as deaths, allowing for estimation of cumulative incidence functions. Models assuming within-patient independence overestimated OS time, corrected with our calibration approach. Correction resulted in meaningful changes in the difference in QALYs between treatment strategies (0.07 vs 0.15) and the ICER (-\76,836/QALY vs -21,030/QALY). Conclusions. Microsimulation models can be successfully used to study cost-effectiveness of therapy sequences, taking care to account correctly for within-patient dependence.

We investigate imbalanced regression with tabular data that have an imbalance ratio larger than 1,000 ("highly imbalanced"). Accurately estimating the target values of rare instances is important in applications such as forecasting the intensity of rare harmful Solar Energetic Particle (SEP) events. For regression, the MSE loss does not consider the correlation between predicted and actual values. Typical inverse importance functions allow only convex functions. Uniform sampling might yield mini-batches that do not have rare instances. We propose CISIR that incorporates correlation, Monotonically Decreasing Involution (MDI) importance, and stratified sampling. Based on five datasets, our experimental results indicate that CISIR can achieve lower error and higher correlation than some recent methods. Also, adding our correlation component to other recent methods can improve their performance. Lastly, MDI importance can outperform other importance functions. Our code can be found in https://github.com/Machine-Earning/CISIR.

In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called "transfer risk", within the optimization framework of transfer learning. A series of numerical experiments are conducted from three categories: cross-continent transfer, cross-sector transfer, and cross-frequency transfer. In particular, 1. a strong correlation between the transfer risk and the overall performance of transfer learning methods is established, underscoring the significance of transfer risk as a viable indicator of "transferability"; 2. transfer risk is shown to provide a computationally efficient way to identify appropriate source tasks in transfer learning, enhancing the efficiency and effectiveness of the transfer learning approach; 3. additionally, the numerical experiments offer valuable new insights for portfolio management across these different settings.