Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic regression. We construct a random mask-based diffusion and denoising process to generate diverse and high-quality equations. We integrate this generative processes with a token-wise Group Relative Policy Optimization (GRPO) method to conduct efficient reinforcement learning on the given measurement dataset. In addition, we introduce a long short-term risk-seeking policy to expand the pool of top-performing candidates, further enhancing performance. Extensive experiments and ablation studies have demonstrated the effectiveness of our approach.

Neural Algorithmic Reasoning (NAR) trains neural networks to simulate classical algorithms, enabling structured and interpretable reasoning over complex data. While prior research has predominantly focused on learning exact algorithms for polynomial-time-solvable problems, extending NAR to harder problems remains an open challenge. In this work, we introduce a general NAR framework grounded in the primal-dual paradigm, a classical method for designing efficient approximation algorithms. By leveraging a bipartite representation between primal and dual variables, we establish an alignment between primal-dual algorithms and Graph Neural Networks. Furthermore, we incorporate optimal solutions from small instances to greatly enhance the model's reasoning capabilities. Our empirical results demonstrate that our model not only simulates but also outperforms approximation algorithms for multiple tasks, exhibiting robust generalization to larger and out-of-distribution graphs. Moreover, we highlight the framework's practical utility by integrating it with commercial solvers and applying it to real-world datasets.

The think-aloud method, where participants voice their thoughts as they solve a task, is a valuable source of rich data about human reasoning processes. Y et, it has declined in popularity in contemporary cognitive science, largely because labor-intensive transcription and annotation preclude large sample sizes. Here, we develop methods to automate the transcription and annotation of verbal reports of reasoning using natural language processing tools, allowing for large-scale analysis of think-aloud data. In our study, 640 participants thought aloud while playing the Game of 24, a mathematical reasoning task. We automatically transcribed the recordings and coded the transcripts as search graphs, finding moderate inter-rater reliability with humans. We analyze these graphs and characterize consistency and variation in human reasoning traces. Our work demonstrates the value of think-aloud data at scale and serves as a proof of concept for the automated analysis of verbal reports.

Computer-aided synthesis planning (CASP) algorithms have demonstrated expert-level abilities in planning retrosynthetic routes to molecules of low to moderate complexity. However, current search methods assume the sufficiency of reaching arbitrary building blocks, failing to address the common real-world constraint where using specific molecules is desired. To this end, we present a formulation of synthesis planning with starting material constraints. Under this formulation, we propose Double-Ended Synthesis Planning ( \texttt{DESP}), a novel CASP algorithm under a _bidirectional graph search_ scheme that interleaves expansions from the target and from the goal starting materials to ensure constraint satisfiability. The search algorithm is guided by a goal-conditioned cost network learned offline from a partially observed hypergraph of valid chemical reactions. We demonstrate the utility of \texttt{DESP} in improving solve rates and reducing the number of search expansions by biasing synthesis planning towards expert goals on multiple new benchmarks.

This paper proposed a method for doing active learning (AL) where in each AL iteration the optimization is done over network architecture and the underlying parameters, as opposed to other methods which fixes the architecture and only optimizes the parameters. These two optimizations are done separately, by first performing a local search among models of monotonically increasing complexity and then optimizing parameters of the obtained architecture. The authors used this method with three different active learning algorithms and showed that their method improved performance of these ALs. The paper is very well-written and clear. The problem of architectural optimization is also of great importance in the field.

My concern about generalization still remains, and I hope the authors can devote maybe a sentence or two to it in the final draft - even something to the effect of "it is a concern; experimental evidence suggests it is not a great concern."] Summary: For any given ML algorithm, e.g., random forests, the paper proposes a transfer-learning approach for selection of hyperparameters (limited to those parameters that can be ordered) wherein a bounding space is constructed from previous evaluations of that algorithm on other datasets. Two types of bounding spaces are described. The box space is the tightest bounding box covering the best known hyperparameter settings for previous datasets. The ellipsoid is found as the smallest-volume ellipsoid covering the best known settings (via convex optimization).

Weaknesses: Lack of ablation study for the two rejection protocols is my mean concern and is the principle component of my rating. While the experiments focused intensively on various architectures and normalization-activation layers, it is not clear how those two rejection protocols contribute to the final results. Although both of them are very well motivated by the two observations, the observations themselve are not sufficient to justify the two rejection protocol. Evolution is extremely creative and the more constraint we manually put on it, the more we limit its creativity. More specifically, the search space for complex problems are usually very deceptive, for example, a candidate might be numerically unstable based on the stability criterion, however this candidate may have potential to be evolved into a surprisingly powerful one later on, but based on the current protocol it might be rejected early on. In table 3, random search with rejection also achieved very good results and authors' EvoNorm only outperformed it by a small margin, which also concerns me about the effectiveness of the search method itself.

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training.

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the estimation problem can be thought of as solving a zero-sum game between a modeler who is optimizing over the hypothesis space of the target model and an adversary who identifies violating moments over a test function space. We analyze the statistical estimation rate of the resulting estimator for arbitrary hypothesis spaces, with respect to an appropriate analogue of the mean squared error metric, for ill-posed inverse problems. We show that when the minimax criterion is regularized with a second moment penalty on the test function and the test function space is sufficiently rich, then the estimation rate scales with the critical radius of the hypothesis and test function spaces, a quantity which typically gives tight fast rates. Our main result follows from a novel localized Rademacher analysis of statistical learning problems defined via minimax objectives.

Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives -- using principles from classical search. We propose a general framework that orchestrates local and global search to efficiently navigate the generative space. It employs a theoretically grounded local search via annealed Langevin MCMC and performs compute-efficient global exploration using breadth-first and depth-first tree search. We evaluate our approach on a range of challenging domains, including planning, offline reinforcement learning, and image generation. Across all tasks, we observe significant gains in both performance and efficiency. These results show that classical search provides a principled and practical foundation for inference-time scaling in diffusion models. Project page at diffusion-inference-scaling.github.io.