Chess is a canonical example of a task that requires rigorous reasoning and long-term planning. Modern decision Transformers - trained similarly to LLMs - are able to learn competent gameplay, but it is unclear to what extent they truly capture the rules of chess. To investigate this, we train a 270M parameter chess Transformer and test it on out-of-distribution scenarios, designed to reveal failures of systematic generalization. Our analysis shows that Transformers exhibit compositional generalization, as evidenced by strong rule extrapolation: they adhere to fundamental syntactic rules of the game by consistently choosing valid moves even in situations very different from the training data. Moreover, they also generate high-quality moves for OOD puzzles. In a more challenging test, we evaluate the models on variants including Chess960 (Fischer Random Chess) - a variant of chess where starting positions of pieces are randomized. We found that while the model exhibits basic strategy adaptation, they are inferior to symbolic AI algorithms that perform explicit search, but gap is smaller when playing against users on Lichess. Moreover, the training dynamics revealed that the model initially learns to move only its own pieces, suggesting an emergent compositional understanding of the game.

The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same cluster. To tackle this NP-hard problem in practice, local search heuristics have been proposed and studied in the context of applications. Here, we establish partial optimality conditions for cubic correlation clustering, i.e., for the special case of at most 3-cliques. We define and implement algorithms for deciding these conditions and examine their effectiveness numerically, on two data sets.

While chain-of-thought prompting with Best-of-N (BoN) selection has become popular for mathematical reasoning in large language models (LLMs), its linear structure fails to capture the branching and exploratory nature of complex problem-solving. In this work, we propose an adaptive algorithm to maximize process reward model (PRM) scores over the intractable action space, and investigate whether PRM-guided tree search can improve mathematical reasoning by exploring multiple partial solution paths. Across $23$ diverse mathematical problems using Qwen2.5-Math-7B-Instruct with its associated PRM as a case study, we find that: (1) PRM-guided tree search shows no statistically significant improvements over BoN despite higher costs, (2) Monte Carlo tree search and beam search outperform other PRM-guided tree search methods, (3) PRMs poorly approximate state values and their reliability degrades with reasoning depth, and (4) PRMs generalize poorly out of distribution. This underperformance stems from tree search's greater reliance on unreliable PRM scores, suggesting different reward modeling is necessary before tree search can effectively enhance mathematical reasoning in LLMs.

Vine copulas offer flexible multivariate dependence modeling and have become widely used in machine learning, yet structure learning remains a key challenge. Early heuristics like the greedy algorithm of Dissmann are still considered the gold standard, but often suboptimal. We propose random search algorithms that improve structure selection and a statistical framework based on model confidence sets, which provides theoretical guarantees on selection probabilities and a powerful foundation for ensembling. Empirical results on several real-world data sets show that our methods consistently outperform state-of-the-art approaches.

Autonomous web agents powered by large language models (LLMs) show strong potential for performing goal-oriented tasks such as information retrieval, report generation, and online transactions. These agents mark a key step toward practical embodied reasoning in open web environments. However, existing approaches remain limited in reasoning depth and efficiency: vanilla linear methods fail at multi-step reasoning and lack effective backtracking, while other search strategies are coarse-grained and computationally costly. We introduce Branch-and-Browse, a fine-grained web agent framework that unifies structured reasoning-acting, contextual memory, and efficient execution. It (i) employs explicit subtask management with tree-structured exploration for controllable multi-branch reasoning, (ii) bootstraps exploration through efficient web state replay with background reasoning, and (iii) leverages a page action memory to share explored actions within and across sessions. On the WebArena benchmark, Branch-and-Browse achieves a task success rate of 35.8\% and reduces execution time by up to 40.4\% relative to state-of-the-art methods. These results demonstrate that Branch-and-Browse is a reliable and efficient framework for LLM-based web agents.

Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between the problem's variables. While the framework has yielded promising results in various combinatorial problems, we show that the performance of PI-GNNs systematically plummets with an increasing density of the combinatorial problem graphs. Our analysis reveals an interesting phase transition in the PI-GNNs' training dynamics, associated with degenerate solutions for the denser problems, highlighting a discrepancy between the relaxed, real-valued model outputs and the binary-valued problem solutions. To address the discrepancy, we propose principled alternatives to the naive strategy used in PI-GNNs by building on insights from fuzzy logic and binarized neural networks. Our experiments demonstrate that the portfolio of proposed methods significantly improves the performance of PI-GNNs in increasingly dense settings.

Combinatorial optimization problems are central to both practical applications and the development of optimization methods. While classical and quantum algorithms have been refined over decades, machine learning-assisted approaches are comparatively recent and have not yet consistently outperformed simple, state-of-the-art classical methods. Here, we focus on a class of Quadratic Unconstrained Binary Optimization (QUBO) problems, specifically the challenge of finding minimum energy configurations in three-dimensional Ising spin glasses. We use a Global Annealing Monte Carlo algorithm that integrates standard local moves with global moves proposed via machine learning. We show that local moves play a crucial role in achieving optimal performance. Benchmarking against Simulated Annealing and Population Annealing, we demonstrate that Global Annealing not only surpasses the performance of Simulated Annealing but also exhibits greater robustness than Population Annealing, maintaining effectiveness across problem hardness and system size without hyperparameter tuning. These results provide, to our knowledge, the first clear and robust evidence that a machine learning-assisted optimization method can exceed the capabilities of classical state-of-the-art techniques in a combinatorial optimization setting.

Mixed-Integer Linear Programming (MILP) is a powerful framework used to address a wide range of NP-hard combinatorial optimization problems, often solved by Branch and Bound (B&B). A key factor influencing the performance of B&B solvers is the variable selection heuristic governing branching decisions. Recent contributions have sought to adapt reinforcement learning (RL) algorithms to the B&B setting to learn optimal branching policies, through Markov Decision Processes (MDP) inspired formulations, and ad hoc convergence theorems and algorithms. In this work, we introduce BBMDP, a principled vanilla MDP formulation for variable selection in B&B, allowing to leverage a broad range of RL algorithms for the purpose of learning optimal B\&B heuristics. Computational experiments validate our model empirically, as our branching agent outperforms prior state-of-the-art RL agents on four standard MILP benchmarks.

Interpretable reinforcement learning policies are essential for high-stakes decision-making, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing decision tree policies, which formulates the optimization problem as a mixed-integer linear program (MILP). To enhance efficiency, we employ a reduced-space branch-and-bound approach that decouples the MDP dynamics from tree-structure constraints, enabling efficient parallel search. This significantly improves runtime and scalability compared to previous methods. Our approach ensures that each iteration yields the optimal decision tree. Experimental results on standard benchmarks demonstrate that SPOT achieves substantial speedup and scales to larger MDPs with a significantly higher number of states. The resulting decision tree policies are interpretable and compact, maintaining transparency without compromising performance. These results demonstrate that our approach simultaneously achieves interpretability and scalability, delivering high-quality policies an order of magnitude faster than existing approaches.

Feature selection is a combinatorial optimization problem that is NP -hard. Conventional approaches often employ heuristic or greedy strategies, which are prone to premature convergence and may fail to capture subtle yet informative features. This limitation becomes especially critical in high - dimensional datasets, where complex and interdependent feature relationships prevail. We introduce the HeFS (Helper - Enhanced Feature Selection) framework to refine feature subsets produced by existing algorithms. HeFS systematically searches the residual feature space to identify a Helper Set-- features that complement the original subset and improve classification performance. The approach employs a biased initialization scheme and a ratio-guided mutation mechanism within a genetic algorithm, coupled with Pareto - based multi - objective optimization to jointly maximize predictive accuracy and feature complementarity. Experiments on 18 benchmark datasets demonstrate that HeFS consistently identifies overlooked yet informative features and achieves superior performance over state-of-the - art methods, including in challenging domains such as gastric cancer classification, drug toxicity prediction, and computer science applications.