Daily Papers

Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textit{reasoning sparks}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of reasoning sparks is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a 60.17% average accuracy on five math benchmarks, an improvement of 2.66% over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

In spite of the outstanding performance, Neural Architecture Search (NAS) is criticized for massive computation. Recently, Zero-shot NAS has emerged as a promising approach by exploiting Zero-cost (ZC) proxies, which markedly reduce computational demands. Despite this, existing ZC proxies heavily rely on expert knowledge and incur significant trial-and-error costs. Particularly in NLP tasks, most existing ZC proxies fail to surpass the performance of the naive baseline. To address these challenges, we introduce a novel framework, LPZero, which is the first to automatically design ZC proxies for various tasks, achieving higher ranking consistency than human-designed proxies. Specifically, we model the ZC proxy as a symbolic equation and incorporate a unified proxy search space that encompasses existing ZC proxies, which are composed of a predefined set of mathematical symbols. To heuristically search for the best ZC proxy, LPZero incorporates genetic programming to find the optimal symbolic composition. We propose a Rule-based Pruning Strategy (RPS), which preemptively eliminates unpromising proxies, thereby mitigating the risk of proxy degradation. Extensive experiments on FlexiBERT, GPT-2, and LLaMA-7B demonstrate LPZero's superior ranking ability and performance on downstream tasks compared to current approaches.

Neural architecture search (NAS) is a hard computationally expensive optimization problem with a discrete, vast, and spiky search space. One of the key research efforts dedicated to this space focuses on accelerating NAS via certain proxy evaluations of neural architectures. Different from the prevalent predictor-based methods using surrogate models and differentiable architecture search via supernetworks, we propose an optimization proxy to streamline the NAS as an end-to-end optimization framework, named OptiProxy-NAS. In particular, using a proxy representation, the NAS space is reformulated to be continuous, differentiable, and smooth. Thereby, any differentiable optimization method can be applied to the gradient-based search of the relaxed architecture parameters. Our comprehensive experiments on 12 NAS tasks of 4 search spaces across three different domains including computer vision, natural language processing, and resource-constrained NAS fully demonstrate the superior search results and efficiency. Further experiments on low-fidelity scenarios verify the flexibility.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

Customer Lifetime Value (CLTV) prediction is a critical task in business applications. Accurately predicting CLTV is challenging in real-world business scenarios, as the distribution of CLTV is complex and mutable. Firstly, there is a large number of users without any consumption consisting of a long-tailed part that is too complex to fit. Secondly, the small set of high-value users spent orders of magnitude more than a typical user leading to a wide range of the CLTV distribution which is hard to capture in a single distribution. Existing approaches for CLTV estimation either assume a prior probability distribution and fit a single group of distribution-related parameters for all samples, or directly learn from the posterior distribution with manually predefined buckets in a heuristic manner. However, all these methods fail to handle complex and mutable distributions. In this paper, we propose a novel optimal distribution selection model OptDist for CLTV prediction, which utilizes an adaptive optimal sub-distribution selection mechanism to improve the accuracy of complex distribution modeling. Specifically, OptDist trains several candidate sub-distribution networks in the distribution learning module (DLM) for modeling the probability distribution of CLTV. Then, a distribution selection module (DSM) is proposed to select the sub-distribution for each sample, thus making the selection automatically and adaptively. Besides, we design an alignment mechanism that connects both modules, which effectively guides the optimization. We conduct extensive experiments on both two public and one private dataset to verify that OptDist outperforms state-of-the-art baselines. Furthermore, OptDist has been deployed on a large-scale financial platform for customer acquisition marketing campaigns and the online experiments also demonstrate the effectiveness of OptDist.

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are sample-centric: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a distribution-centric perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce HeurAgenix, a two-stage hyper-heuristic framework powered by large language models (LLMs) that first evolves heuristics and then selects among them automatically. In the heuristic evolution phase, HeurAgenix leverages an LLM to compare seed heuristic solutions with higher-quality solutions and extract reusable evolution strategies. During problem solving, it dynamically picks the most promising heuristic for each problem state, guided by the LLM's perception ability. For flexibility, this selector can be either a state-of-the-art LLM or a fine-tuned lightweight model with lower inference cost. To mitigate the scarcity of reliable supervision caused by CO complexity, we fine-tune the lightweight heuristic selector with a dual-reward mechanism that jointly exploits singals from selection preferences and state perception, enabling robust selection under noisy annotations. Extensive experiments on canonical benchmarks show that HeurAgenix not only outperforms existing LLM-based hyper-heuristics but also matches or exceeds specialized solvers. Code is available at https://github.com/microsoft/HeurAgenix.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

Deep learning has revolutionized computer vision, but it achieved its tremendous success using deep network architectures which are mostly hand-crafted and therefore likely suboptimal. Neural Architecture Search (NAS) aims to bridge this gap by following a well-defined optimization paradigm which systematically looks for the best architecture, given objective criterion such as maximal classification accuracy. The main limitation of NAS is however its astronomical computational cost, as it typically requires training each candidate network architecture from scratch. In this paper, we aim to alleviate this limitation by proposing a novel training-free proxy for image classification accuracy based on Fisher Information. The proposed proxy has a strong theoretical background in statistics and it allows estimating expected image classification accuracy of a given deep network without training the network, thus significantly reducing computational cost of standard NAS algorithms. Our training-free proxy achieves state-of-the-art results on three public datasets and in two search spaces, both when evaluated using previously proposed metrics, as well as using a new metric that we propose which we demonstrate is more informative for practical NAS applications. The source code is publicly available at http://www.github.com/ondratybl/VKDNW

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Because it is difficult to precisely specify complex objectives, reinforcement learning policies are often optimized using proxy reward functions that only approximate the true goal. However, optimizing proxy rewards frequently leads to reward hacking: the optimized reward function ceases to be a good proxy and the resulting policy performs poorly with respect to the unspecified true reward. Principled solutions to reward hacking have been impeded by the lack of a good definition for the problem. To address this gap, we introduce a definition of reward hacking based on the correlation between proxy and true rewards for states and actions seen by a "base policy" that breaks down under optimization. We show that this definition captures reward hacking behavior across several realistic settings, including in reinforcement learning from human feedback (RLHF). Using our formulation, we show theoretically that regularization to the base policy can effectively prevent reward hacking. While the current practice in RLHF applies a KL penalty between action distributions for this purpose, our theory suggests regularizing the chi^2 divergence between the policies' occupancy measures can be more effective. We intuitively show the benefits of this type of regularization and demonstrate that it better mitigates reward hacking in practice across four realistic settings, including RLHF. Our code is available at https://github.com/cassidylaidlaw/orpo.

We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity. This allows propagating Gaussian and Cauchy input uncertainties through neural networks to quantify their output uncertainties. To demonstrate the utility of propagating distributions, we apply the proposed method to predicting calibrated confidence intervals and selective prediction on out-of-distribution data. The results demonstrate a broad applicability of propagating distributions and show the advantages of our method over other approaches such as moment matching.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

Recent advancements in reinforcement learning with verifiable rewards have pushed the boundaries of the visual reasoning capabilities in large vision-language models (LVLMs). However, training LVLMs with reinforcement fine-tuning (RFT) is computationally expensive, posing a significant challenge to scaling model size. In this work, we propose ProxyThinker, an inference-time technique that enables large models to inherit the visual reasoning capabilities from small, slow-thinking visual reasoners without any training. By subtracting the output distributions of base models from those of RFT reasoners, ProxyThinker modifies the decoding dynamics and successfully elicits the slow-thinking reasoning demonstrated by the emerged sophisticated behaviors such as self-verification and self-correction. ProxyThinker consistently boosts performance on challenging visual benchmarks on spatial, mathematical, and multi-disciplinary reasoning, enabling untuned base models to compete with the performance of their full-scale RFT counterparts. Furthermore, our implementation efficiently coordinates multiple language models with parallelism techniques and achieves up to 38 times faster inference compared to previous decoding-time methods, paving the way for the practical deployment of ProxyThinker. Code is available at https://github.com/MrZilinXiao/ProxyThinker.

We propose TAROT, a targeted data selection framework grounded in optimal transport theory. Previous targeted data selection methods primarily rely on influence-based greedy heuristics to enhance domain-specific performance. While effective on limited, unimodal data (i.e., data following a single pattern), these methods struggle as target data complexity increases. Specifically, in multimodal distributions, these heuristics fail to account for multiple inherent patterns, leading to suboptimal data selection. This work identifies two primary factors contributing to this limitation: (i) the disproportionate impact of dominant feature components in high-dimensional influence estimation, and (ii) the restrictive linear additive assumptions inherent in greedy selection strategies. To address these challenges, TAROT incorporates whitened feature distance to mitigate dominant feature bias, providing a more reliable measure of data influence. Building on this, TAROT uses whitened feature distance to quantify and minimize the optimal transport distance between the selected data and target domains. Notably, this minimization also facilitates the estimation of optimal selection ratios. We evaluate TAROT across multiple tasks, including semantic segmentation, motion prediction, and instruction tuning. Results consistently show that TAROT outperforms state-of-the-art methods, highlighting its versatility across various deep learning tasks. Code is available at https://github.com/vita-epfl/TAROT.

Diffusion-based large language models (dLLMs) are trained flexibly to model extreme dependence in the data distribution; however, how to best utilize this information at inference time remains an open problem. In this work, we uncover an interesting property of these models: dLLMs trained on textual data implicitly learn a mixture of semi-autoregressive experts, where different generation orders reveal different specialized behaviors. We show that committing to any single, fixed inference time schedule, a common practice, collapses performance by failing to leverage this latent ensemble. To address this, we introduce HEX (Hidden semiautoregressive EXperts for test-time scaling), a training-free inference method that ensembles across heterogeneous block schedules. By doing a majority vote over diverse block-sized generation paths, HEX robustly avoids failure modes associated with any single fixed schedule. On reasoning benchmarks such as GSM8K, it boosts accuracy by up to 3.56X (from 24.72% to 88.10%), outperforming top-K margin inference and specialized fine-tuned methods like GRPO, without additional training. HEX even yields significant gains on MATH benchmark from 16.40% to 40.00%, scientific reasoning on ARC-C from 54.18% to 87.80%, and TruthfulQA from 28.36% to 57.46%. Our results establish a new paradigm for test-time scaling in diffusion-based LLMs (dLLMs), revealing that the sequence in which masking is performed plays a critical role in determining performance during inference.

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual information of two subsets of variables, at a lower computation and estimation complexity. We describe the maximizers and their relations to the maximizers of the multi-information and the mutual information.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.

Evaluating fairness can be challenging in practice because the sensitive attributes of data are often inaccessible due to privacy constraints. The go-to approach that the industry frequently adopts is using off-the-shelf proxy models to predict the missing sensitive attributes, e.g. Meta [Alao et al., 2021] and Twitter [Belli et al., 2022]. Despite its popularity, there are three important questions unanswered: (1) Is directly using proxies efficacious in measuring fairness? (2) If not, is it possible to accurately evaluate fairness using proxies only? (3) Given the ethical controversy over inferring user private information, is it possible to only use weak (i.e. inaccurate) proxies in order to protect privacy? Our theoretical analyses show that directly using proxy models can give a false sense of (un)fairness. Second, we develop an algorithm that is able to measure fairness (provably) accurately with only three properly identified proxies. Third, we show that our algorithm allows the use of only weak proxies (e.g. with only 68.85%accuracy on COMPAS), adding an extra layer of protection on user privacy. Experiments validate our theoretical analyses and show our algorithm can effectively measure and mitigate bias. Our results imply a set of practical guidelines for practitioners on how to use proxies properly. Code is available at github.com/UCSC-REAL/fair-eval.

Explainability methods for NLP systems encounter a version of the fundamental problem of causal inference: for a given ground-truth input text, we never truly observe the counterfactual texts necessary for isolating the causal effects of model representations on outputs. In response, many explainability methods make no use of counterfactual texts, assuming they will be unavailable. In this paper, we show that robust causal explainability methods can be created using approximate counterfactuals, which can be written by humans to approximate a specific counterfactual or simply sampled using metadata-guided heuristics. The core of our proposal is the Causal Proxy Model (CPM). A CPM explains a black-box model N because it is trained to have the same actual input/output behavior as N while creating neural representations that can be intervened upon to simulate the counterfactual input/output behavior of N. Furthermore, we show that the best CPM for N performs comparably to N in making factual predictions, which means that the CPM can simply replace N, leading to more explainable deployed models. Our code is available at https://github.com/frankaging/Causal-Proxy-Model.

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of density ratio modeling, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show -- perhaps surprisingly -- that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as coverability (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2022) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

This paper proposes a novel admission and routing scheme which takes into account arbitrarily assigned priorities for network flows. The presented approach leverages the centralized Software Defined Networking (SDN) capabilities in order to do so. Exact and heuristic approaches to the stated Priority Flow Admission and Routing (PFAR) problem are provided. The exact approach which provides an optimal solution is based on Integer Linear Programming (ILP). Given the potentially long running time required to find an exact and optimal solution, a heuristic approach is proposed; this approach is based on Genetic Algorithms (GAs). In order to effectively estimate the performance of the proposed approaches, a simulator that is capable of generating semi-random network topologies and flows has been developed. Experimental results for large problem instances (up 50 network nodes and thousands of network flows), show that: i) an optimal solution can be often found in few seconds (even milliseconds), and ii) the heuristic approach yields close-to-optimal solutions (approximately 95\% of the optimal) in a fixed amount of time; these experimental results demonstrate the pertinence of the proposed approaches.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

Data quality and diversity are key to the construction of effective instruction-tuning datasets. % With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. % Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. % However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. % Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. % To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. % Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. % Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. % Notably, the model fine-tuned with 5\% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73\% on AlpacaEval and +6.89\% on Wildbench.

We introduce a fairness-aware dataset for job recommendation in advertising, designed to foster research in algorithmic fairness within real-world scenarios. It was collected and prepared to comply with privacy standards and business confidentiality. An additional challenge is the lack of access to protected user attributes such as gender, for which we propose a solution to obtain a proxy estimate. Despite being anonymized and including a proxy for a sensitive attribute, our dataset preserves predictive power and maintains a realistic and challenging benchmark. This dataset addresses a significant gap in the availability of fairness-focused resources for high-impact domains like advertising -- the actual impact being having access or not to precious employment opportunities, where balancing fairness and utility is a common industrial challenge. We also explore various stages in the advertising process where unfairness can occur and introduce a method to compute a fair utility metric for the job recommendations in online systems case from a biased dataset. Experimental evaluations of bias mitigation techniques on the released dataset demonstrate potential improvements in fairness and the associated trade-offs with utility.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches on 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

Large-scale commercial platforms usually involve numerous business domains for diverse business strategies and expect their recommendation systems to provide click-through rate (CTR) predictions for multiple domains simultaneously. Existing promising and widely-used multi-domain models discover domain relationships by explicitly constructing domain-specific networks, but the computation and memory boost significantly with the increase of domains. To reduce computational complexity, manually grouping domains with particular business strategies is common in industrial applications. However, this pre-defined data partitioning way heavily relies on prior knowledge, and it may neglect the underlying data distribution of each domain, hence limiting the model's representation capability. Regarding the above issues, we propose an elegant and flexible multi-distribution modeling paradigm, named Adaptive Distribution Hierarchical Model (AdaptDHM), which is an end-to-end optimization hierarchical structure consisting of a clustering process and classification process. Specifically, we design a distribution adaptation module with a customized dynamic routing mechanism. Instead of introducing prior knowledge for pre-defined data allocation, this routing algorithm adaptively provides a distribution coefficient for each sample to determine which cluster it belongs to. Each cluster corresponds to a particular distribution so that the model can sufficiently capture the commonalities and distinctions between these distinct clusters. Extensive experiments on both public and large-scale Alibaba industrial datasets verify the effectiveness and efficiency of AdaptDHM: Our model achieves impressive prediction accuracy and its time cost during the training stage is more than 50% less than that of other models.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.

This paper presents a strategy to allocate services on a Cloud system without overloading nodes and maintaining the system stability with minimum cost. We specify an abstract model of cloud resources utilization, including multiple types of resources as well as considerations for the service migration costs. A prototype meta-heuristic load balancer is demonstrated and experimental results are presented and discussed. We also propose a novel genetic algorithm, where population is seeded with the outputs of other meta-heuristic algorithms.

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Fine-tuning diffusion models via online reinforcement learning (RL) has shown great potential for enhancing text-to-image alignment. However, since precisely specifying a ground-truth objective for visual tasks remains challenging, the models are often optimized using a proxy reward that only partially captures the true goal. This mismatch often leads to reward hacking, where proxy scores increase while real image quality deteriorates and generation diversity collapses. While common solutions add regularization against the reference policy to prevent reward hacking, they compromise sample efficiency and impede the exploration of novel, high-reward regions, as the reference policy is usually sub-optimal. To address the competing demands of sample efficiency, effective exploration, and mitigation of reward hacking, we propose Gated and Adaptive Regularization with Diversity-aware Optimization (GARDO), a versatile framework compatible with various RL algorithms. Our key insight is that regularization need not be applied universally; instead, it is highly effective to selectively penalize a subset of samples that exhibit high uncertainty. To address the exploration challenge, GARDO introduces an adaptive regularization mechanism wherein the reference model is periodically updated to match the capabilities of the online policy, ensuring a relevant regularization target. To address the mode collapse issue in RL, GARDO amplifies the rewards for high-quality samples that also exhibit high diversity, encouraging mode coverage without destabilizing the optimization process. Extensive experiments across diverse proxy rewards and hold-out unseen metrics consistently show that GARDO mitigates reward hacking and enhances generation diversity without sacrificing sample efficiency or exploration, highlighting its effectiveness and robustness.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an epsilon-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our epsilon-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a putative location. The initial target location is selected either in an exploitative fashion on the mean prediction, or -- with probability epsilon -- from elsewhere in the design space. This results in locations that are more densely sampled in regions where the function is changing rapidly and in locations predicted to be good (i.e close to predicted optima), with more scattered samples in regions where the function is flatter and/or of poorer quality. We empirically evaluate the epsilon-shotgun methods on a range of synthetic functions and two real-world problems, finding that they perform at least as well as state-of-the-art batch methods and in many cases exceed their performance.

While Large Language Models (LLMs) have demonstrated significant advancements in reasoning and agent-based problem-solving, current evaluation methodologies fail to adequately assess their capabilities: existing benchmarks either rely on closed-ended questions prone to saturation and memorization, or subjective comparisons that lack consistency and rigor. In this work, we introduce HeuriGym, an agentic framework designed for evaluating heuristic algorithms generated by LLMs for combinatorial optimization problems, characterized by clearly defined objectives and expansive solution spaces. HeuriGym empowers LLMs to propose heuristics, receive evaluative feedback via code execution, and iteratively refine their solutions. We evaluate nine state-of-the-art models on nine problems across domains such as computer systems, logistics, and biology, exposing persistent limitations in tool use, planning, and adaptive reasoning. To quantify performance, we propose the Quality-Yield Index (QYI), a metric that captures both solution pass rate and quality. Even top models like GPT-o4-mini-high and Gemini-2.5-Pro attain QYI scores of only 0.6, well below the expert baseline of 1. Our open-source benchmark aims to guide the development of LLMs toward more effective and realistic problem-solving in scientific and engineering domains.

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.

We consider non-clairvoyant scheduling with online precedence constraints, where an algorithm is oblivious to any job dependencies and learns about a job only if all of its predecessors have been completed. Given strong impossibility results in classical competitive analysis, we investigate the problem in a learning-augmented setting, where an algorithm has access to predictions without any quality guarantee. We discuss different prediction models: novel problem-specific models as well as general ones, which have been proposed in previous works. We present lower bounds and algorithmic upper bounds for different precedence topologies, and thereby give a structured overview on which and how additional (possibly erroneous) information helps for designing better algorithms. Along the way, we also improve bounds on traditional competitive ratios for existing algorithms.

Weight sharing promises to make neural architecture search (NAS) tractable even on commodity hardware. Existing methods in this space rely on a diverse set of heuristics to design and train the shared-weight backbone network, a.k.a. the super-net. Since heuristics and hyperparameters substantially vary across different methods, a fair comparison between them can only be achieved by systematically analyzing the influence of these factors. In this paper, we therefore provide a systematic evaluation of the heuristics and hyperparameters that are frequently employed by weight-sharing NAS algorithms. Our analysis uncovers that some commonly-used heuristics for super-net training negatively impact the correlation between super-net and stand-alone performance, and evidences the strong influence of certain hyperparameters and architectural choices. Our code and experiments set a strong and reproducible baseline that future works can build on.

Handcrafting heuristics for solving complex planning tasks (e.g., NP-hard combinatorial optimization (CO) problems) is a common practice but requires extensive domain knowledge. Recently, Large Language Model (LLM)-based automatic heuristics design (AHD) methods have shown promise in generating high-quality heuristics without manual intervention. Existing LLM-based AHD methods employ a population to maintain a fixed number of top-performing LLM-generated heuristics and introduce evolutionary computation (EC) to enhance the population iteratively. However, the population-based procedure brings greedy properties, often resulting in convergence to local optima. Instead, to more comprehensively explore the space of heuristics, we propose using Monte Carlo Tree Search (MCTS) for LLM-based heuristic evolution while preserving all LLM-generated heuristics in a tree structure. With a novel thought-alignment process and an exploration-decay technique, the proposed MCTS-AHD method delivers significantly higher-quality heuristics on various complex tasks. Our code is available at https://github.com/zz1358m/MCTS-AHD-master.

Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size k, our goal is to sample k out of n items with probability proportional to the determinant of the kernel matrix induced by the subset (a.k.a. k-DPP). Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets. A naïve heuristic addressing this problem is to uniformly subsample a fraction of the data and perform k-DPP sampling only on those items, however this method offers no guarantee that the produced sample will even approximately resemble the target distribution over the original dataset. In this paper, we develop an algorithm which adaptively builds a sufficiently large uniform sample of data that is then used to efficiently generate a smaller set of k items, while ensuring that this set is drawn exactly from the target distribution defined on all n items. We show empirically that our algorithm produces a k-DPP sample after observing only a small fraction of all elements, leading to several orders of magnitude faster performance compared to the state-of-the-art.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Finite symmetric groups S_n are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over S_n poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce SymmetricDiffusers, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over S_n by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performances on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at https://github.com/DSL-Lab/SymmetricDiffusers.

This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA), and the other one based on neural network (NN). Empirical results on three classic CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA- and NN-based solvers. In particular, our SA algorithm reduces the runtime of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems. Our code is available at https://github.com/Shengyu-Feng/RLD4CO.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

Guidance is a crucial technique for extracting the best performance out of image-generating diffusion models. Traditionally, a constant guidance weight has been applied throughout the sampling chain of an image. We show that guidance is clearly harmful toward the beginning of the chain (high noise levels), largely unnecessary toward the end (low noise levels), and only beneficial in the middle. We thus restrict it to a specific range of noise levels, improving both the inference speed and result quality. This limited guidance interval improves the record FID in ImageNet-512 significantly, from 1.81 to 1.40. We show that it is quantitatively and qualitatively beneficial across different sampler parameters, network architectures, and datasets, including the large-scale setting of Stable Diffusion XL. We thus suggest exposing the guidance interval as a hyperparameter in all diffusion models that use guidance.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Learning from active human involvement enables the human subject to actively intervene and demonstrate to the AI agent during training. The interaction and corrective feedback from human brings safety and AI alignment to the learning process. In this work, we propose a new reward-free active human involvement method called Proxy Value Propagation for policy optimization. Our key insight is that a proxy value function can be designed to express human intents, wherein state-action pairs in the human demonstration are labeled with high values, while those agents' actions that are intervened receive low values. Through the TD-learning framework, labeled values of demonstrated state-action pairs are further propagated to other unlabeled data generated from agents' exploration. The proxy value function thus induces a policy that faithfully emulates human behaviors. Human-in-the-loop experiments show the generality and efficiency of our method. With minimal modification to existing reinforcement learning algorithms, our method can learn to solve continuous and discrete control tasks with various human control devices, including the challenging task of driving in Grand Theft Auto V. Demo video and code are available at: https://metadriverse.github.io/pvp

Intervention-based model steering offers a lightweight and interpretable alternative to prompting and fine-tuning. However, by adapting strong optimization objectives from fine-tuning, current methods are susceptible to overfitting and often underperform, sometimes generating unnatural outputs. We hypothesize that this is because effective steering requires the faithful identification of internal model mechanisms, not the enforcement of external preferences. To this end, we build on the principles of distributed alignment search (DAS), the standard for causal variable localization, to propose a new steering method: Concept DAS (CDAS). While we adopt the core mechanism of DAS, distributed interchange intervention (DII), we introduce a novel distribution matching objective tailored for the steering task by aligning intervened output distributions with counterfactual distributions. CDAS differs from prior work in two main ways: first, it learns interventions via weak-supervised distribution matching rather than probability maximization; second, it uses DIIs that naturally enable bi-directional steering and allow steering factors to be derived from data, reducing the effort required for hyperparameter tuning and resulting in more faithful and stable control. On AxBench, a large-scale model steering benchmark, we show that CDAS does not always outperform preference-optimization methods but may benefit more from increased model scale. In two safety-related case studies, overriding refusal behaviors of safety-aligned models and neutralizing a chain-of-thought backdoor, CDAS achieves systematic steering while maintaining general model utility. These results indicate that CDAS is complementary to preference-optimization approaches and conditionally constitutes a robust approach to intervention-based model steering. Our code is available at https://github.com/colored-dye/concept_das.

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of this approach, there is a lack of a common repository that provides distributions of similar MILP instances across different domains, at different hardness levels, with standardized test sets. In this paper, we introduce Distributional MIPLIB, a multi-domain library of problem distributions for advancing ML-guided MILP methods. We curate MILP distributions from existing work in this area as well as real-world problems that have not been used, and classify them into different hardness levels. It will facilitate research in this area by enabling comprehensive evaluation on diverse and realistic domains. We empirically illustrate the benefits of using Distributional MIPLIB as a research vehicle in two ways. We evaluate the performance of ML-guided variable branching on previously unused distributions to identify potential areas for improvement. Moreover, we propose to learn branching policies from a mix of distributions, demonstrating that mixed distributions achieve better performance compared to homogeneous distributions when there is limited data and generalize well to larger instances. The dataset is publicly available at https://sites.google.com/usc.edu/distributional-miplib/home.

We propose Heuristic Blending (HUBL), a simple performance-improving technique for a broad class of offline RL algorithms based on value bootstrapping. HUBL modifies the Bellman operators used in these algorithms, partially replacing the bootstrapped values with heuristic ones that are estimated with Monte-Carlo returns. For trajectories with higher returns, HUBL relies more on the heuristic values and less on bootstrapping; otherwise, it leans more heavily on bootstrapping. HUBL is very easy to combine with many existing offline RL implementations by relabeling the offline datasets with adjusted rewards and discount factors. We derive a theory that explains HUBL's effect on offline RL as reducing offline RL's complexity and thus increasing its finite-sample performance. Furthermore, we empirically demonstrate that HUBL consistently improves the policy quality of four state-of-the-art bootstrapping-based offline RL algorithms (ATAC, CQL, TD3+BC, and IQL), by 9% on average over 27 datasets of the D4RL and Meta-World benchmarks.

Diffusion (Large) Language Models (dLLMs) now match the downstream performance of their autoregressive counterparts on many tasks, while holding the promise of being more efficient during inference. One particularly successful variant is masked discrete diffusion, in which a buffer filled with special mask tokens is progressively replaced with tokens sampled from the model's vocabulary. Efficiency can be gained by unmasking several tokens in parallel, but doing too many at once risks degrading the generation quality. Thus, one critical design aspect of dLLMs is the sampling procedure that selects, at each step of the diffusion process, which tokens to replace. Indeed, recent work has found that heuristic strategies such as confidence thresholding lead to both higher quality and token throughput compared to random unmasking. However, such heuristics have downsides: they require manual tuning, and we observe that their performance degrades with larger buffer sizes. In this work, we instead propose to train sampling procedures using reinforcement learning. Specifically, we formalize masked diffusion sampling as a Markov decision process in which the dLLM serves as the environment, and propose a lightweight policy architecture based on a single-layer transformer that maps dLLM token confidences to unmasking decisions. Our experiments show that these trained policies match the performance of state-of-the-art heuristics when combined with semi-autoregressive generation, while outperforming them in the full diffusion setting. We also examine the transferability of these policies, finding that they can generalize to new underlying dLLMs and longer sequence lengths. However, we also observe that their performance degrades when applied to out-of-domain data, and that fine-grained tuning of the accuracy-efficiency trade-off can be challenging with our approach.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

Diffusion models have emerged as a pivotal advancement in generative models, setting new standards to the quality of the generated instances. In the current paper we aim to underscore a discrepancy between conventional training methods and the desired conditional sampling behavior of these models. While the prevalent classifier-free guidance technique works well, it's not without flaws. At higher values for the guidance scale parameter w, we often get out of distribution samples and mode collapse, whereas at lower values for w we may not get the desired specificity. To address these challenges, we introduce an updated loss function that better aligns training objectives with sampling behaviors. Experimental validation with FID scores on CIFAR-10 elucidates our method's ability to produce higher quality samples with fewer sampling timesteps, and be more robust to the choice of guidance scale w. We also experiment with fine-tuning Stable Diffusion on the proposed loss, to provide early evidence that large diffusion models may also benefit from this refined loss function.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

Existing long-tailed recognition methods, aiming to train class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution. However, practical test class distributions often violate this assumption (e.g., being either long-tailed or even inversely long-tailed), which may lead existing methods to fail in real applications. In this paper, we study a more practical yet challenging task, called test-agnostic long-tailed recognition, where the training class distribution is long-tailed while the test class distribution is agnostic and not necessarily uniform. In addition to the issue of class imbalance, this task poses another challenge: the class distribution shift between the training and test data is unknown. To tackle this task, we propose a novel approach, called Self-supervised Aggregation of Diverse Experts, which consists of two strategies: (i) a new skill-diverse expert learning strategy that trains multiple experts from a single and stationary long-tailed dataset to separately handle different class distributions; (ii) a novel test-time expert aggregation strategy that leverages self-supervision to aggregate the learned multiple experts for handling unknown test class distributions. We theoretically show that our self-supervised strategy has a provable ability to simulate test-agnostic class distributions. Promising empirical results demonstrate the effectiveness of our method on both vanilla and test-agnostic long-tailed recognition. Code is available at https://github.com/Vanint/SADE-AgnosticLT.

Out-of-distribution (OOD) prediction is often approached by restricting models to causal or invariant covariates, avoiding non-causal spurious associations that may be unstable across environments. Despite its theoretical appeal, this strategy frequently underperforms empirical risk minimization (ERM) in practice. We investigate the source of this gap and show that such failures naturally arise when only a subset of the true causes of the outcome is observed. In these settings, non-causal spurious covariates can serve as informative proxies for unobserved causes and substantially improve prediction, except under distribution shifts that break these proxy relationships. Consequently, the optimal set of predictive covariates is neither universal nor necessarily exhibits invariant relationships with the outcome across all environments, but instead depends on the specific type of shift encountered. Crucially, we observe that different covariate shifts induce distinct, observable signatures in the covariate distribution itself. Moreover, these signatures can be extracted from unlabeled data in the target OOD environment and used to assess when proxy covariates remain reliable and when they fail. Building on this observation, we propose an environment-adaptive covariate selection (EACS) algorithm that maps environment-level covariate summaries to environment-specific covariate sets, while allowing the incorporation of prior causal knowledge as constraints. Across simulations and applied datasets, EACS consistently outperforms static causal, invariant, and ERM-based predictors under diverse distribution shifts.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require ``differentiable'' proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation. The code is available at https://github.com/masa-ue/SVDD{https://github.com/masa-ue/SVDD}.

In reinforcement learning from human feedback, it is common to optimize against a reward model trained to predict human preferences. Because the reward model is an imperfect proxy, optimizing its value too much can hinder ground truth performance, in accordance with Goodhart's law. This effect has been frequently observed, but not carefully measured due to the expense of collecting human preference data. In this work, we use a synthetic setup in which a fixed "gold-standard" reward model plays the role of humans, providing labels used to train a proxy reward model. We study how the gold reward model score changes as we optimize against the proxy reward model using either reinforcement learning or best-of-n sampling. We find that this relationship follows a different functional form depending on the method of optimization, and that in both cases its coefficients scale smoothly with the number of reward model parameters. We also study the effect on this relationship of the size of the reward model dataset, the number of reward model and policy parameters, and the coefficient of the KL penalty added to the reward in the reinforcement learning setup. We explore the implications of these empirical results for theoretical considerations in AI alignment.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity 1 / log(1/sparsity). This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

Recent progress in Large Language Model (LLM) reasoning is increasingly driven by the refinement of post-training loss functions and alignment strategies. However, standard Reinforcement Learning (RL) paradigms like Group Relative Policy Optimization (GRPO) remain constrained by static uniformity: uniform prompt sampling and a fixed number of rollouts per prompt. For heterogeneous, heavy-tailed reasoning data, this creates structural inefficiencies that waste compute on already-solved patterns while under-training the long tail of hard problems. To address this, we propose Multi-Adversary Group Distributionally Robust Optimization (GDRO), an optimization-first framework that moves beyond uniform reasoning models by dynamically adapting the training distribution. We introduce an Online Difficulty Classifier that partitions prompts into dynamic pass@k difficulty groups. We then propose two independent GDRO games for post-training: (1) Prompt-GDRO, which employs an EMA-debiased multiplicative-weights bandit sampler to target the intensive difficulty margin and upweight persistently hard groups without frequency bias; and (2) Rollout-GDRO, which uses a shadow-price controller to reallocate rollouts across groups, maximizing gradient variance reduction on hard tasks under a fixed mean budget (compute-neutral). We provide no-regret guarantees for both controllers and additionally a variance-proxy analysis motivating a square-root optimal rollout allocation for Rollout-GDRO. We validate our framework on the DAPO 14.1k dataset using Qwen3-Base models. Prompt-GDRO and Rollout-GDRO achieve average relative gains of +10.6% and +10.1%, respectively, in pass@8 accuracy across 1.7B, 4B, and 8B scales compared to the GRPO baseline. Qualitative analysis shows an emergent curriculum: the adversaries shift resources to the evolving reasoning frontier, enhancing the reasoning model's performance.

When the performance of a machine learning model varies over groups defined by sensitive attributes (e.g., gender or ethnicity), the performance disparity can be expressed in terms of the probability distributions of the input and output variables over each group. In this paper, we exploit this fact to reduce the disparate impact of a fixed classification model over a population of interest. Given a black-box classifier, we aim to eliminate the performance gap by perturbing the distribution of input variables for the disadvantaged group. We refer to the perturbed distribution as a counterfactual distribution, and characterize its properties for common fairness criteria. We introduce a descent algorithm to learn a counterfactual distribution from data. We then discuss how the estimated distribution can be used to build a data preprocessor that can reduce disparate impact without training a new model. We validate our approach through experiments on real-world datasets, showing that it can repair different forms of disparity without a significant drop in accuracy.

Instruction tuning is a standard paradigm for adapting large language models (LLMs), but modern instruction datasets are large, noisy, and redundant, making full-data fine-tuning costly and often unnecessary. Existing data selection methods either build expensive gradient datastores or assign static scores from a weak proxy, largely ignoring evolving uncertainty, and thus missing a key source of LLM interpretability. We propose GRADFILTERING, an objective-agnostic, uncertainty-aware data selection framework that utilizes a small GPT-2 proxy with a LoRA ensemble and aggregates per-example gradients into a Gradient Signal-to-Noise Ratio (G-SNR) utility. Our method matches or surpasses random subsets and strong baselines in most LLM-as-a-judge evaluations as well as in human assessment. Moreover, GRADFILTERING-selected subsets converge faster than competitive filters under the same compute budget, reflecting the benefit of uncertainty-aware scoring.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

Large language models are typically aligned with human preferences by optimizing reward models (RMs) fitted to human feedback. However, human preferences are multi-faceted, and it is increasingly common to derive reward from a composition of simpler reward models which each capture a different aspect of language quality. This itself presents a challenge, as it is difficult to appropriately weight these component RMs when combining them. Compounding this difficulty, because any RM is only a proxy for human evaluation, this process is vulnerable to overoptimization, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform, to our knowledge, the first study on overoptimization in composite RMs, showing that correlation between component RMs has a significant effect on the locations of these points. We then introduce an approach to solve this issue using constrained reinforcement learning as a means of preventing the agent from exceeding each RM's threshold of usefulness. Our method addresses the problem of weighting component RMs by learning dynamic weights, naturally expressed by Lagrange multipliers. As a result, each RM stays within the range at which it is an effective proxy, improving evaluation performance. Finally, we introduce an adaptive method using gradient-free optimization to identify and optimize towards these points during a single run.

A popular approach for sequential decision-making is to perform simulator-based search guided with Machine Learning (ML) methods like policy learning. On the other hand, model-relaxation heuristics can guide the search effectively if a full declarative model is available. In this work, we consider how a practitioner can improve ML-based black-box planning on settings where a complete symbolic model is not available. We show that specifying an incomplete STRIPS model that describes only part of the problem enables the use of relaxation heuristics. Our findings on several planning domains suggest that this is an effective way to improve ML-based black-box planning beyond collecting more data or tuning ML architectures.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

We study the problem of multi-task learning under user-level differential privacy, in which n users contribute data to m tasks, each involving a subset of users. One important aspect of the problem, that can significantly impact quality, is the distribution skew among tasks. Certain tasks may have much fewer data samples than others, making them more susceptible to the noise added for privacy. It is natural to ask whether algorithms can adapt to this skew to improve the overall utility. We give a systematic analysis of the problem, by studying how to optimally allocate a user's privacy budget among tasks. We propose a generic algorithm, based on an adaptive reweighting of the empirical loss, and show that when there is task distribution skew, this gives a quantifiable improvement of excess empirical risk. Experimental studies on recommendation problems that exhibit a long tail of small tasks, demonstrate that our methods significantly improve utility, achieving the state of the art on two standard benchmarks.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

In pruning, the Lottery Ticket Hypothesis posits that large networks contain sparse subnetworks, or winning tickets, that can be trained in isolation to match the performance of their dense counterparts. However, most existing approaches assume a single universal winning ticket shared across all inputs, ignoring the inherent heterogeneity of real-world data. In this work, we propose Routing the Lottery (RTL), an adaptive pruning framework that discovers multiple specialized subnetworks, called adaptive tickets, each tailored to a class, semantic cluster, or environmental condition. Across diverse datasets and tasks, RTL consistently outperforms single- and multi-model baselines in balanced accuracy and recall, while using up to 10 times fewer parameters than independent models and exhibiting semantically aligned. Furthermore, we identify subnetwork collapse, a performance drop under aggressive pruning, and introduce a subnetwork similarity score that enables label-free diagnosis of oversparsification. Overall, our results recast pruning as a mechanism for aligning model structure with data heterogeneity, paving the way toward more modular and context-aware deep learning.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is applicable to a wide range of use cases that have worst-case performance requirements. After defining the DMMV problem mathematically, we explore its properties to establish a foundational understanding. To tackle DMMV instance sizes of practical relevance, we develop a GPU-accelerated heuristic that takes advantage of the mathematical properties of DMMV for speeding up the solution process. We demonstrate the versatile applicability of our heuristic by solving three optimization problems as use cases: (1) post-training quantization of language models, (2) discrete tomography, and (3) Finite Impulse Response (FIR) filter design. In quantization without outlier separation, our heuristic achieves 14% improvement on average over existing methods. In discrete tomography, it reduces reconstruction error by 16% under uniform noise and accelerates computations by a factor of 6 on GPU. For FIR filter design, it nearly achieves 50% ripple reduction compared to using the commercial integer optimization solver, Gurobi. Our comparative results point to the benefits of studying DMMV as a context-free optimization problem and the advantages that our proposed heuristic offers on three distinct problems. Our GPU-accelerated heuristic will be made open-source to further stimulate research on DMMV and its other applications. The code is available at https://anonymous.4open.science/r/AMVM-5F3E/

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose in-neighbors have already been examined. In this paper, we address a learning setting where we allow the agent to stop before having found the object and restart searching on a new independent instance of the same problem. Our goal is to maximize the total number of hidden objects found given a time budget. The agent can thus skip an instance after realizing that it would spend too much time on it. Our contributions are both to the search theory and multi-armed bandits. If the distribution is known, we provide a quasi-optimal and efficient stationary strategy. If the distribution is unknown, we additionally show how to sequentially approximate it and, at the same time, act near-optimally in order to collect as many hidden objects as possible.

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs). This paper introduces Language Hyper-Heuristics (LHHs), an emerging variant of Hyper-Heuristics that leverages LLMs for heuristic generation, featuring minimal manual intervention and open-ended heuristic spaces. To empower LHHs, we present Reflective Evolution (ReEvo), a novel integration of evolutionary search for efficiently exploring the heuristic space, and LLM reflections to provide verbal gradients within the space. Across five heterogeneous algorithmic types, six different COPs, and both white-box and black-box views of COPs, ReEvo yields state-of-the-art and competitive meta-heuristics, evolutionary algorithms, heuristics, and neural solvers, while being more sample-efficient than prior LHHs.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

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

In domains ranging from computer vision to natural language processing, machine learning models have been shown to exhibit stark disparities, often performing worse for members of traditionally underserved groups. One factor contributing to these performance gaps is a lack of representation in the data the models are trained on. It is often unclear, however, how to operationalize representativeness in specific applications. Here we formalize the problem of creating equitable training datasets, and propose a statistical framework for addressing this problem. We consider a setting where a model builder must decide how to allocate a fixed data collection budget to gather training data from different subgroups. We then frame dataset creation as a constrained optimization problem, in which one maximizes a function of group-specific performance metrics based on (estimated) group-specific learning rates and costs per sample. This flexible approach incorporates preferences of model-builders and other stakeholders, as well as the statistical properties of the learning task. When data collection decisions are made sequentially, we show that under certain conditions this optimization problem can be efficiently solved even without prior knowledge of the learning rates. To illustrate our approach, we conduct a simulation study of polygenic risk scores on synthetic genomic data -- an application domain that often suffers from non-representative data collection. We find that our adaptive sampling strategy outperforms several common data collection heuristics, including equal and proportional sampling, demonstrating the value of strategic dataset design for building equitable models.

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems - generalising to significantly larger problems than the ones seen during training - while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

Although large language models (LLMs) have shown great potential in recommender systems, the prohibitive computational costs for fine-tuning LLMs on entire datasets hinder their successful deployment in real-world scenarios. To develop affordable and effective LLM-based recommender systems, we focus on the task of coreset selection which identifies a small subset of fine-tuning data to optimize the test loss, thereby facilitating efficient LLMs' fine-tuning. Although there exist some intuitive solutions of subset selection, including distribution-based and importance-based approaches, they often lead to suboptimal performance due to the misalignment with downstream fine-tuning objectives or weak generalization ability caused by individual-level sample selection. To overcome these challenges, we propose GORACS, which is a novel Group-level Optimal tRAnsport-guided Coreset Selection framework for LLM-based recommender systems. GORACS is designed based on two key principles for coreset selection: 1) selecting the subsets that minimize the test loss to align with fine-tuning objectives, and 2) enhancing model generalization through group-level data selection. Corresponding to these two principles, GORACS has two key components: 1) a Proxy Optimization Objective (POO) leveraging optimal transport and gradient information to bound the intractable test loss, thus reducing computational costs by avoiding repeated LLM retraining, and 2) a two-stage Initialization-Then-Refinement Algorithm (ITRA) for efficient group-level selection. Our extensive experiments across diverse recommendation datasets and tasks validate that GORACS significantly reduces fine-tuning costs of LLMs while achieving superior performance over the state-of-the-art baselines and full data training. The source code of GORACS are available at https://github.com/Mithas-114/GORACS.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

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

For general users, training a neural network from scratch is usually challenging and labor-intensive. Fortunately, neural network zoos enable them to find a well-performing model for directly use or fine-tuning it in their local environments. Although current model retrieval solutions attempt to convert neural network models into vectors to avoid complex multiple inference processes required for model selection, it is still difficult to choose a suitable model due to inaccurate vectorization and biased correlation alignment between the query dataset and models. From the perspective of knowledge consistency, i.e., whether the knowledge possessed by the model can meet the needs of query tasks, we propose a model retrieval scheme, named Know2Vec, that acts as a black-box retrieval proxy for model zoo. Know2Vec first accesses to models via a black-box interface in advance, capturing vital decision knowledge from models while ensuring their privacy. Next, it employs an effective encoding technique to transform the knowledge into precise model vectors. Secondly, it maps the user's query task to a knowledge vector by probing the semantic relationships within query samples. Furthermore, the proxy ensures the knowledge-consistency between query vector and model vectors within their alignment space, which is optimized through the supervised learning with diverse loss functions, and finally it can identify the most suitable model for a given task during the inference stage. Extensive experiments show that our Know2Vec achieves superior retrieval accuracy against the state-of-the-art methods in diverse neural network retrieval tasks.

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

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is often neglected: preferences vary across individuals and should be represented with more granularity. To address this, we propose SmPO-Diffusion, a novel method for modeling preference distributions to improve the DPO objective, along with a numerical upper bound estimation for the diffusion optimization objective. First, we introduce a smoothed preference distribution to replace the original binary distribution. We employ a reward model to simulate human preferences and apply preference likelihood averaging to improve the DPO loss, such that the loss function approaches zero when preferences are similar. Furthermore, we utilize an inversion technique to simulate the trajectory preference distribution of the diffusion model, enabling more accurate alignment with the optimization objective. Our approach effectively mitigates issues of excessive optimization and objective misalignment present in existing methods through straightforward modifications. Our SmPO-Diffusion achieves state-of-the-art performance in preference evaluation, outperforming baselines across metrics with lower training costs. The project page is https://jaydenlyh.github.io/SmPO-project-page/.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter beta is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying beta. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

Despite increasing progress in development of methods for generating visual counterfactual explanations, especially with the recent rise of Denoising Diffusion Probabilistic Models, previous works consider them as an entirely local technique. In this work, we take the first step at globalizing them. Specifically, we discover that the latent space of Diffusion Autoencoders encodes the inference process of a given classifier in the form of global directions. We propose a novel proxy-based approach that discovers two types of these directions with the use of only single image in an entirely black-box manner. Precisely, g-directions allow for flipping the decision of a given classifier on an entire dataset of images, while h-directions further increase the diversity of explanations. We refer to them in general as Global Counterfactual Directions (GCDs). Moreover, we show that GCDs can be naturally combined with Latent Integrated Gradients resulting in a new black-box attribution method, while simultaneously enhancing the understanding of counterfactual explanations. We validate our approach on existing benchmarks and show that it generalizes to real-world use-cases.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

A commonly used heuristic in RL is experience replay (e.g.~lin1993reinforcement, mnih2015human), in which a learner stores and re-uses past trajectories as if they were sampled online. In this work, we initiate a rigorous study of this heuristic in the setting of tabular Q-learning. We provide a convergence rate guarantee, and discuss how it compares to the convergence of Q-learning depending on important parameters such as the frequency and number of replay iterations. We also provide theoretical evidence showing when we might expect this heuristic to strictly improve performance, by introducing and analyzing a simple class of MDPs. Finally, we provide some experiments to support our theoretical findings.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

A central challenge in large language model inference is the trade-off between generation speed and output quality. Autoregressive models produce high-quality text but generate tokens sequentially. Diffusion models can generate tokens in parallel but often need many iterations to match the same quality. We propose planned diffusion, a hybrid method that combines the strengths of both paradigms. Planned diffusion works in two stages: first, the model creates a short autoregressive plan that breaks the output into smaller, independent spans. Second, the model generates these spans simultaneously using diffusion. This approach expands the speed-quality Pareto frontier and provides a practical path to faster, high-quality text generation. On AlpacaEval, a suite of 805 instruction-following prompts, planned diffusion achieves Pareto-optimal trade-off between quality and latency, achieving 1.27x to 1.81x speedup over autoregressive generation with only 0.87\% to 5.4\% drop in win rate, respectively. Our sensitivity analysis shows that the planning mechanism of planned diffusion is minimal and reliable, and simple runtime knobs exist to provide flexible control of the quality-latency trade-off.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

In this report, we introduce DASD-4B-Thinking, a lightweight yet highly capable, fully open-source reasoning model. It achieves SOTA performance among open-source models of comparable scale across challenging benchmarks in mathematics, scientific reasoning, and code generation -- even outperforming several larger models. We begin by critically reexamining a widely adopted distillation paradigm in the community: SFT on teacher-generated responses, also known as sequence-level distillation. Although a series of recent works following this scheme have demonstrated remarkable efficiency and strong empirical performance, they are primarily grounded in the SFT perspective. Consequently, these approaches focus predominantly on designing heuristic rules for SFT data filtering, while largely overlooking the core principle of distillation itself -- enabling the student model to learn the teacher's full output distribution so as to inherit its generalization capability. Specifically, we identify three critical limitations in current practice: i) Inadequate representation of the teacher's sequence-level distribution; ii) Misalignment between the teacher's output distribution and the student's learning capacity; and iii) Exposure bias arising from teacher-forced training versus autoregressive inference. In summary, these shortcomings reflect a systemic absence of explicit teacher-student interaction throughout the distillation process, leaving the essence of distillation underexploited. To address these issues, we propose several methodological innovations that collectively form an enhanced sequence-level distillation training pipeline. Remarkably, DASD-4B-Thinking obtains competitive results using only 448K training samples -- an order of magnitude fewer than those employed by most existing open-source efforts. To support community research, we publicly release our models and the training dataset.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

The Lottery Ticket Hypothesis asserts the existence of highly sparse, trainable subnetworks ('winning tickets') within dense, randomly initialized neural networks. However, state-of-the-art methods of drawing these tickets, like Lottery Ticket Rewinding (LTR), are computationally prohibitive, while more efficient saliency-based Pruning-at-Initialization (PaI) techniques suffer from a significant accuracy-sparsity trade-off and fail basic sanity checks. In this work, we argue that PaI's reliance on first-order saliency metrics, which ignore inter-weight dependencies, contributes substantially to this performance gap, especially in the sparse regime. To address this, we introduce Concrete Ticket Search (CTS), an algorithm that frames subnetwork discovery as a holistic combinatorial optimization problem. By leveraging a Concrete relaxation of the discrete search space and a novel gradient balancing scheme (GRADBALANCE) to control sparsity, CTS efficiently identifies high-performing subnetworks near initialization without requiring sensitive hyperparameter tuning. Motivated by recent works on lottery ticket training dynamics, we further propose a knowledge distillation-inspired family of pruning objectives, finding that minimizing the reverse Kullback-Leibler divergence between sparse and dense network outputs (CTS-KL) is particularly effective. Experiments on varying image classification tasks show that CTS produces subnetworks that robustly pass sanity checks and achieve accuracy comparable to or exceeding LTR, while requiring only a small fraction of the computation. For example, on ResNet-20 on CIFAR10, it reaches 99.3% sparsity with 74.0% accuracy in 7.9 minutes, while LTR attains the same sparsity with 68.3% accuracy in 95.2 minutes. CTS's subnetworks outperform saliency-based methods across all sparsities, but its advantage over LTR is most pronounced in the highly sparse regime.

Reinforcement learning (RL) allows an agent interacting sequentially with an environment to maximize its long-term expected return. In the distributional RL (DistrRL) paradigm, the agent goes beyond the limit of the expected value, to capture the underlying probability distribution of the return across all time steps. The set of DistrRL algorithms has led to improved empirical performance. Nevertheless, the theory of DistrRL is still not fully understood, especially in the control case. In this paper, we present the simpler one-step distributional reinforcement learning (OS-DistrRL) framework encompassing only the randomness induced by the one-step dynamics of the environment. Contrary to DistrRL, we show that our approach comes with a unified theory for both policy evaluation and control. Indeed, we propose two OS-DistrRL algorithms for which we provide an almost sure convergence analysis. The proposed approach compares favorably with categorical DistrRL on various environments.

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.

Subset selection-based methods are widely used to explain deep vision models: they attribute predictions by highlighting the most influential image regions and support object-level explanations. While these methods perform well in in-distribution (ID) settings, their behavior under out-of-distribution (OOD) conditions remains poorly understood. Through extensive experiments across multiple ID-OOD sets, we find that reliability of the existing subset based methods degrades markedly, yielding redundant, unstable, and uncertainty-sensitive explanations. To address these shortcomings, we introduce a framework that combines submodular subset selection with layer-wise, gradient-based uncertainty estimation to improve robustness and fidelity without requiring additional training or auxiliary models. Our approach estimates uncertainty via adaptive weight perturbations and uses these estimates to guide submodular optimization, ensuring diverse and informative subset selection. Empirical evaluations show that, beyond mitigating the weaknesses of existing methods under OOD scenarios, our framework also yields improvements in ID settings. These findings highlight limitations of current subset-based approaches and demonstrate how uncertainty-driven optimization can enhance attribution and object-level interpretability, paving the way for more transparent and trustworthy AI in real-world vision applications.

We propose and evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Such cost to serve analysis has application both strategically and operationally in transportation. The problem is formally given by the traveling salesperson game (TSG), a cooperative total utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The cost to serve a location is an allocated portion of the cost of an optimal tour. The Shapley value is one of the most important normative division schemes in cooperative games, giving a principled and fair allocation both for the TSG and more generally. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and present the first proof that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we then develop six proxies for that value which are relatively easy to compute. We perform an experimental evaluation using Synthetic Euclidean games as well as games derived from real-world tours calculated for fast-moving consumer goods scenarios. Our experiments show that several computationally tractable allocation techniques correspond to good proxies for the Shapley value.

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.

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.