Predicting the thermodynamic properties of an alloy requires sampling its configurations across many chemical conditions and recovering free energies on a common absolute scale. Markov chain Monte Carlo (MCMC) is the standard tool, but it requires separate simulations at different conditions, and auxiliary free-energy methods such as thermodynamic integration are used to place results on a common absolute scale. Modern discrete neural samplers typically use reverse KL divergence as the objective and can be mode-seeking or biased. We present Free energy Offering Generative Sampler (FrOGS), a hybrid discrete neural sampler that couples an autoregressive model to a continuous-time Markov chain (CTMC) to be trained jointly under a single shared loss. FrOGS draws i.i.d. configurations, returns an unbiased estimate of the partition function, and gives consistent estimates of thermodynamic observables. We train a single model across a wide range of chemical conditions to produce estimates on a common absolute free-energy scale. FrOGS matches exact finite-size results on the 2D Ising model and reference phase diagrams for AgPd and CuAu, without mode collapse. We additionally compare to SEGAL, a published autoregressive baseline, and find that only FrOGS recovers the stability range of the CuAu$_3$ phase.
Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.
While Neural Combinatorial Optimization (NCO) achieves strong performance, its interpretability remains an open question. In this paper, we introduce Evolving Programmatic Bottlenecks (EPB), the first post-hoc, surrogate-based interpretability method for NCO, which explains a black-box policy by distilling it into an interpretable behavior surrogate. A natural surrogate is a Concept Bottleneck Model (CBM), yet standard concepts are input attributes, whereas NCO is better explained by decision rules that are hard to predefine. EPB thus uses LLMs to evolve a bank of programmatic decision rules as concepts, each producing an action distribution, where a learned state-dependent router then mixes them to form the surrogate action. We optimize EPB through an iterative framework: Block I fixes the bank size and introduces the hybrid textual-numerical gradient descent to jointly optimize the textual programs and the numerical router; Block II adapts the bank size via failure-targeted expansion and redundancy pruning. Extensive experiments demonstrate that the EPB surrogate closely matches the teacher's behavior and solution quality. We then analyze the distilled rules, reveal several NCO decision patterns, and verify the rules' faithfulness to the surrogate's decisions. Moreover, the surrogate allows targeted program edits that improve its generalization beyond the teacher. Our work advances interpretable NCO and establishes EPB as a promising direction for interpreting complex learned decision-making policies.
When does training language models (LMs) to generate explanations of their predictions yield faithful introspection, rather than superficial imitation? We study LMs trained to explain which features of their inputs influenced their behavior, using models' counterfactual behavior on modified inputs as supervision. Surprisingly, we find that LMs trained on fixed counterfactual explanations derived from their earlier checkpoints, or even from behaviorally similar models in different families, frequently produce explanations more faithful to their own current behaviors than to those of their training targets. This "introspective" coupling between LM explanations and behaviors occurs when training explanations remain sufficiently correlated with current behaviors over the course of training, even as behaviors themselves shift. We also show that introspective coupling tracks behavior shifts: when explanation training is provided concurrently with other post-training objectives, explanations change to match without requiring updated supervision. This phenomenon appears in multiple tasks, including sycophancy and refusal, and is robust to label noise. Overall, our results show that even fixed datasets of counterfactual explanations can provide scalable and generalizable post-training signal for introspection.
When an AI algorithm makes decisions that affect more than one person, aligning it becomes a problem of social choice: how should people's divergent preferences about system behavior be reconciled and aggregated into a single coherent model? The standard approach to aligning frontier AI models - reinforcement learning from human feedback - largely sidesteps this question and has poor social choice guarantees. However, it remains unclear what alternative should replace it. We show that, when agent utilities can be expressed linearly in a fixed feature representation, the alignment problem can be reformulated as linear optimization over a convex impact space, which makes it amenable to the standard toolkit of welfare economics and mechanism design. This reformulation clarifies how alignment protocols translate into welfare consequences and, conversely, how a social planner's desired constraints on welfare consequences can be translated back into alignment protocols. We apply this transformation to show that voting-by-issues and random-dictatorship mechanisms are strategyproof and unanimous. Demonstrating the reverse direction, we also apply the impact representation to derive a family of alignment protocols that maximize utilitarian social welfare subject to various social desiderata, such as bounds on individual or group harm. We illustrate the welfare implications of these alignment protocols empirically using real human preferences over kidney allocation, charitable food distribution, LLM responses, and trolley problems.
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a much smaller, randomly projected problem. While standard subspace embeddings nearly preserve the regression cost, coordinate-wise accuracy is more delicate: rather than the objective value, we want the solution vector itself to be close to the optimum in $\ell_\infty$ norm. Specifically, we seek $x'\in\mathbb{R}^d$ with $\|x'-x^\star\|_\infty\leq\frac{\epsilon}{\sqrt d}\|Ax^\star-b\|_2\|A^\dagger\|_{\mathrm{op}}$, where $A\in\mathbb{R}^{n\times d}$ is the design matrix, $b\in\mathbb{R}^n$ the label vector, $x^\star$ the optimal solution and $A^\dagger$ the pseudo-inverse of $A$. Price, Song and Woodruff introduced this problem and claimed that the subsampled randomized Hadamard transform (SRHT) with $O(\epsilon^{-2}d^{1+\Theta(\sqrt{\log\log n/\log d})})$ rows achieves this guarantee; we point out a gap in the proof. Song, Ye, Yin and Zhang later claimed $O(\epsilon^{-2}d\log^3 n)$ rows, but their proof relies on an independence assumption that does not hold in general, and we exhibit an explicit instance on which it fails. To achieve a truly nearly-linear-in-$d$ row count, we introduce a new fast, dense randomized transform combining a randomized Hadamard flattening, a random permutation, and balanced, disjoint Gaussian pooling. Conditioned on the Hadamard-and-permutation stage, the sketched problem becomes an exact Gaussian regression whose noise is independent of the entire sketched design, exactly what Song, Ye, Yin and Zhang's argument was missing. Our sketch yields the $\ell_\infty$ guarantee with $m=O(\epsilon^{-2}d\log d)$ rows, using one Hadamard pass with padded internal dimension $N=\widetilde{O}(n+\epsilon^{-2}d^3)$. It is also efficient to apply: $(SA,Sb)$ can be computed in $O(Nd\log N)=\widetilde{O}(nd+\epsilon^{-2}d^4)$ time.
Adversarial team games (ATGs) with asymmetric information, such as adversarial path-finding, goal search, and reachability games on graphs, require strategies that are robust to hidden opponent types, such as a hidden goal flag, and to deception. Under asymmetric information, deception is seen as strategic shifts in the type distribution such that the omniscient opponent can collude with Nature and condition its play on the observed type. Existing risk-neutral solution concepts, such as Bayesian Nash equilibrium (BNE), are sensitive to distribution shifts, while distributionally robust approaches provide guarantees only within a prescribed ambiguity set. To address these limitations, we introduce Probabilistically Robust Minimax-Regret Equilibrium (PR-MRE), a novel equilibrium concept that combines the distribution-free robustness of minimax-regret reasoning with probabilistic information from a nominal type distribution. PR-MRE minimizes worst-case regret over a high-confidence subset of the type space, providing protection against strategic redistribution of probability mass while avoiding the conservatism of fully distribution-free approaches. We show that, for finite normal-form Bayesian games, approximate PR-MRE computation can be formulated as a robust bilinear program and derive a tractable semidefinite relaxation. We then adapt this relaxation into a novel meta-solver within a robust double-oracle framework, PRMRE-PSRO, enabling population-based learning of approximate PR-MRE strategies via deep reinforcement learning best responses. Experiments on graph-structured adversarial team games demonstrate that PR-MRE discovers strategies with substantially improved worst-case performance across hidden types compared to risk-neutral Bayesian Nash equilibrium solutions, resulting in more robust behavior under strategic distribution shifts.
Sampling from discrete, unnormalized distributions without access to data is a challenging problem. Neural samplers offer a promising approach by training generative models from density evaluations directly. However, existing discrete neural samplers are prone to mode collapse, come without convergence guarantees when trained via fixed-point iterations, and are often tied to a specific reference process such as masked or uniform diffusion. In this work, we introduce Discrete Gibbs Iterative Neural Sampler, a fixed-point neural sampler that addresses these limitations, enabling efficient, scalable learning, substantially reducing mode collapse in practice. Besides masked diffusion, the framework also extends to transport between arbitrary distributions. DIG-IN mitigates mode collapse on Ising and Potts models and scales to amortized sampling with up to 2,500 sites, recovers alloy phase diagrams, and learns to sample biomolecular Boltzmann distributions from energy alone. Its transport formulation accurately estimates solvation and conformational free energies. As a maximum-entropy RL policy, DIG-IN outperforms the Gaussian, diffusion, and flow policies we compare against across 20 continuous-control tasks.
We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.
Stochastic nonconvex optimization is central to training deep networks and LLMs in modern machine learning. We give a black-box reduction from stochastic nonconvex optimization to ordinary static regret minimization in online convex optimization (OCO), addressing the open problem posed by Chen and Hazan (2024). Our reduction maintains a predictable gradient tracker, while a black-box online learner $\mathcal A$ selects a preconditioner that transforms this tracker into the update direction. Given a $\beta$-smooth function with initial gap at most $M$ and an unbiased gradient oracle with variance bounded by $\sigma^2$, we bound the expected average squared gradient norm by $O(\sigma\sqrt{M\beta/T}+\sqrt{M\beta}\mathrm{Reg}_T(\mathcal A)/T+\frac{M\beta}{T})$, where $\mathrm{Reg}_T(\mathcal A)$ is the static regret of $\mathcal A$ against the identity preconditioner. Thus, any OCO oracle with $O(\sqrt T)$ regret recovers the classical $O(T^{-1/2})$ convergence rate. We also prove that the additive variance term cannot be removed: every conversion making a constant number of stochastic-oracle queries per round, whose guarantee is stated through static regret against a comparator that the online learner can play, must contain an additive term of order $\sigma\sqrt{M\beta/T}$ for sufficiently large $T$. Moreover, for every online learner, our conversion bound is tight up to universal constants. We also extend the framework to nonsmooth nonconvex optimization, still relying only on ordinary static regret, and attain the optimal convergence rate for Goldstein-type stationarity. Finally, we conduct numerical experiments on nonconvex objectives to illustrate how the reduction exploits online-selected preconditioners while using the same stochastic-oracle budget as stochastic gradient descent.
We study online optimization with nested shrinking feasible regions in two settings: convex optimization with nested evolving feasible sets (CONES) and adversarial constrained online convex optimization (COCO). Our algorithms separate loss control from geometric movement: constrained minimizers and cumulative-loss tests preserve regret guarantees, while a deterministic resettable nested convex-body chaser limits movement. For CONES with a $G$-Lipschitz, $\mu$-strongly convex objective on a diameter-$D$ domain, we chase intersections of the current feasible set with adaptive objective sublevel sets. Using the Euclidean chasing ratio $O(\sqrt{d\log(1+d)})$, we obtain nonpositive regret at every prefix and movement $O(\sqrt{d\log(1+d)\,GD\log(eT)/\mu})$. The bound adapts to the increase in the constrained optimum value. In dimension two, with all other parameters fixed, every randomized algorithm with terminal expected regret $O(T^\beta)$, $\beta<1$, suffers $\Omega(\sqrt{\log T})$ expected movement on some deterministic nested sequence, proving optimal horizon dependence. Under linear growth away from the constrained minimizer set, Steiner-point tracking yields movement independent of $T$. For general convex COCO, one-step-delayed chasing with regularized-leader resets gives regret $O(G_fD\sqrt{d\log(1+d)T})$ and cumulative constraint violation $O(G_gD\sqrt{d\log(1+d)T})$. For strongly convex losses, both are $O(d\log(1+d)\log(eT))$ when other parameters are fixed. These reductions replace the $O(d^{d/2})$ projection-path factor in prior analyses by the polynomial dimension dependence of Euclidean nested convex-body chasing.
Dynamic hand gestures play a pivotal role in assistive human-robot interaction (HRI), facilitating intuitive, non-verbal communication, particularly for individuals with mobility constraints or those operating robots remotely. Current gesture recognition methods are mostly limited to short-range interactions, reducing their utility in scenarios demanding robust assistive communication from afar. In this paper, we introduce a novel approach designed specifically for assistive robotics, enabling dynamic gesture recognition at extended distances of up to 30 meters, thereby significantly improving accessibility and quality of life. Our proposed Distance-aware Gesture Network (DiG-Net) effectively combines Depth-Conditioned Deformable Alignment (DADA) blocks with Spatio-Temporal Graph modules, enabling robust processing and classification of gesture sequences captured under challenging conditions, including significant physical attenuation, reduced resolution, and dynamic gesture variations commonly experienced in real-world assistive environments. We further introduce the Radiometric Spatio-Temporal Depth Attenuation Loss (RSTDAL), shown to enhance learning and strengthen model robustness across varying distances. Our model demonstrates significant performance improvement over state-of-the-art gesture recognition frameworks, achieving a recognition accuracy of 97.3% on a diverse dataset with challenging hyper-range gestures. By effectively interpreting gestures from considerable distances, DiG-Net significantly enhances the usability of assistive robots in home healthcare, industrial safety, and remote assistance scenarios, enabling seamless and intuitive interactions for users regardless of physical limitations
The majority of parameters in neural networks are naturally represented as matrices. However, most commonly used optimizers treat these matrix parameters as flattened vectors during optimization, potentially overlooking their inherent structural properties. Recently, an optimizer called Muon has been proposed, specifically designed to optimize matrix-structured parameters. Extensive empirical evidence shows that Muon can significantly outperform traditional optimizers when training neural networks. Nonetheless, the theoretical understanding of Muon's convergence behavior and the reasons behind its superior performance remain limited. In this work, we present a comprehensive convergence rate analysis of Muon and its comparison with Gradient Descent (GD). We further characterize the conditions under which Muon can outperform GD. Our theoretical results reveal that Muon can benefit from the low-rank and approximate blockwise diagonal structure of Hessian matrices -- phenomena widely observed in practical neural network training. Our experimental results support and corroborate the theoretical findings.
AI developers are releasing large language models (LLMs) under a variety of different licenses. Many of these licenses restrict the ways in which the models or their outputs may be used. This raises the question how license violations may be recognized. In particular, how can we identify that an API or product uses (an adapted version of) a particular LLM? We present a new method that enable model developers to perform such identification via fingerprints: statistical patterns that are unique to the developer's model and robust to common alterations of that model. Our method permits model identification in a black-box setting using a limited number of queries, enabling identification of models that can only be accessed via an API or product. The fingerprints are non-invasive: our method does not require any changes to the model during training, hence by design, it does not impact model quality. Empirically, we find our method provides a high degree of robustness to common changes in the model or inference settings. In our experiments, it substantially outperforms prior art, including invasive methods that explicitly train watermarks into the model.
Solving (Stampacchia) variational inequalities (SVIs) is a foundational problem at the heart of optimization, with a host of critical applications ranging from engineering to economics. However, this expressivity comes at the cost of computational hardness. As a result, most research has focused on carving out specific subclasses that elude those intractability barriers. A classical property that goes back to the 1960s is the Minty condition, which postulates that the Minty VI (MVI) problem -- the weak dual of the SVI problem -- admits a solution. In this paper, we establish the first polynomial-time algorithm -- that is, with complexity growing polynomially in the dimension $d$ and $\log(1/\epsilon)$ -- for solving $\epsilon$-SVIs for Lipschitz continuous mappings under the Minty condition. Prior approaches either incurred an exponentially worse dependence on $1/\epsilon$ (and other natural parameters of the problem) or made overly restrictive assumptions -- such as strong monotonicity. To do so, we introduce a new variant of the ellipsoid algorithm wherein separating hyperplanes are obtained after taking a gradient descent step from the center of the ellipsoid. It succeeds even though the set of SVIs can be nonconvex and not fully dimensional. Moreover, when our algorithm is applied to an instance with no MVI solution and fails to identify an SVI solution, it produces a succinct certificate of MVI infeasibility. We also show that deciding whether the Minty condition holds is $\mathsf{coNP}$-complete. We provide several extensions and new applications of our main results. Specifically, we obtain the first polynomial-time algorithms for i) solving monotone VIs, ii) globally minimizing a (potentially nonsmooth) quasar-convex function, and iii) computing Nash equilibria in multi-player harmonic games.
In the past decade, motivated by the putative failure of naive self-play deep reinforcement learning (DRL) in adversarial imperfect-information games, researchers have developed numerous DRL algorithms based on fictitious play (FP), double oracle (DO), and counterfactual regret minimization (CFR). In light of recent results of the magnetic mirror descent algorithm, we hypothesize that simpler generic policy gradient methods like PPO are competitive with or superior to these FP, DO, and CFR-based DRL approaches. To facilitate the resolution of this hypothesis, we implement and release the first broadly accessible exact exploitability computations for four large games. Using these games, we conduct the largest-ever exploitability comparison of DRL algorithms for imperfect-information games. Over 5600 training runs, FP, DO, and CFR-based approaches fail to outperform generic policy gradient methods. Code is available at https://github.com/nathanlct/IIG-RL-Benchmark and https://github.com/gabrfarina/exp-a-spiel .
Recent works explore deep learning's success by examining functions or data with hierarchical structure. To study the learning complexity of functions with hierarchical structure, we study the noise stability of functions with tree hierarchical structure on independent inputs. We show that if each function in the hierarchy is $\varepsilon$-far from linear, the noise stability is exponentially small in the depth of the hierarchy. Our results have immediate applications for learning. In the Boolean setting using the results of Dachman-Soled, Feldman, Tan, Wan and Wimmer (2014) our results provide Statistical Query super-polynomial lower bounds for learning classes that are based on hierarchical functions. Similarly, using the results of Diakonikolas, Kane, Pittas and Zarifis (2021) our results provide super-polynomial lower bounds for SQ learning under the Gaussian measure. Using the results of Abbe, Bengio, Cornacchiam, Kleinberg, Lotfi, Raghu and Zhang (2022) our results imply sample complexity lower bounds for learning hierarchical functions with gradient descent on fully connected neural networks.
Economists often estimate treatment effects in experiments using remotely sensed variables (RSVs), e.g. satellite images or mobile phone activity, in place of directly measured economic outcomes. A common practice is to use an observational sample to train a predictor of the economic outcome from the RSV, and then to use its predictions as the outcomes in the experiment. We show that this method is biased whenever the RSV is post-outcome, i.e. if variation in the economic outcome causes variation in the RSV. In program evaluation, changes in poverty or environmental quality cause changes in satellite images, but not vice versa. As our main result, we nonparametrically identify the treatment effect by formalizing the intuition that underlies common practice: the conditional distribution of the RSV given the outcome and treatment is stable across the samples.Based on our identifying formula, we find that the efficient representation of RSVs for causal inference requires three predictions rather than one. Valid inference does not require any rate conditions on RSV predictions, justifying the use of complex deep learning algorithms with unknown statistical properties. We re-analyze the effect of an anti-poverty program in India using satellite images.
High-speed video (HSV) phase detection (PD) segmentation is crucial for monitoring vapor, liquid, and microlayer phases in industrial processes. While CNN-based models like U-Net have shown success in simplified shadowgraphy-based two-phase flow (TPF) analysis, their application to complex HSV PD tasks remains unexplored, and vision foundation models (VFMs) have yet to address the complexities of either shadowgraphy-based or PD TPF video segmentation. Existing uncertainty quantification (UQ) methods lack pixel-level reliability for critical metrics like contact line density and dry area fraction, and the absence of large-scale, multimodal experimental datasets tailored to PD segmentation further impedes progress. To address these gaps, we propose MSEG-VCUQ. This hybrid framework integrates U-Net CNNs with the transformer-based Segment Anything Model (SAM) to achieve enhanced segmentation accuracy and cross-modality generalization. Our approach incorporates systematic UQ for robust error assessment and introduces the first open-source multimodal HSV PD datasets. Empirical results demonstrate that MSEG-VCUQ outperforms baseline CNNs and VFMs, enabling scalable and reliable PD segmentation for real-world boiling dynamics.
Highly performant large-scale pre-trained models promise to also provide a valuable foundation for learning specialized tasks, by fine-tuning the model to the desired task. By starting from a good general-purpose model, the goal is to achieve both specialization in the target task and maintain robustness. To assess the robustness of models to out-of-distribution samples after fine-tuning on downstream datasets, we introduce a new robust fine-tuning benchmark, ImageNet-RIB (Robustness Inheritance Benchmark). The benchmark consists of a set of related but distinct specialized (downstream) tasks; pre-trained models are fine-tuned on one task in the set and their robustness is assessed on the rest, iterating across all tasks for fine-tuning and assessment. We find that the continual learning methods, EWC and LwF maintain robustness after fine-tuning though fine-tuning generally does reduce performance on generalization to related downstream tasks across models. Not surprisingly, models pre-trained on large and rich datasets exhibit higher initial robustness across datasets and suffer more pronounced degradation during fine-tuning. The distance between the pre-training and downstream datasets, measured by optimal transport, predicts this performance degradation on the pre-training dataset. However, counterintuitively, model robustness after fine-tuning on related downstream tasks is the worst when the pre-training dataset is the richest and the most diverse. This suggests that starting with the strongest foundation model is not necessarily the best approach for performance on specialist tasks. The benchmark thus offers key insights for developing more resilient fine-tuning strategies and building robust machine learning models. https://jd730.github.io/projects/ImageNet-RIB