NeurIPS 2025 Papers

Diversified recommendation has attracted increasing attention from both researchers and practitioners, which can effectively address the homogeneity of recommended items. Existing approaches predominantly aim to infer the diversity of user preferences from observed user feedback. Nonetheless, due to inherent data biases, the observed data may not fully reflect user interests, where underexplored preferences can be overwhelmed or remain unmanifested. Failing to capture these preferences can lead to suboptimal diversity in recommendations. To fill this gap, this work aims to study diversified recommendation from a data-bias perspective. Inspired by the outstanding performance of large language models (LLMs) in zero-shot inference leveraging world knowledge, we propose a novel approach that utilizes LLMs' expertise to uncover underexplored user preferences from observed behavior, ultimately providing diverse and relevant recommendations. To achieve this, we first introduce Tree of Preferences (ToP), an innovative structure constructed to model user preferences from coarse to fine. ToP enables LLMs to systematically reason over the user's rationale behind their behavior, thereby uncovering their underexplored preferences. To guide diversified recommendations using uncovered preferences, we adopt a data-centric approach, identifying candidate items that match user preferences and generating synthetic interactions that reflect underexplored preferences. These interactions are integrated to train a general recommender for diversification. Moreover, we scale up overall efficiency by dynamically selecting influential users during optimization. Extensive evaluations of both diversity and relevance show that our approach outperforms existing methods in most cases and achieves near-optimal performance in others, with reasonable inference latency.

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.

Symbolic regression (SR) seeks interpretable analytical expressions that uncover the governing relationships within data, providing mechanistic insight beyond 'black-box' models. However, existing SR methods often suffer from two key limitations: (1) *redundant representations* that fail to capture mathematical equivalences and higher-order operand relations, breaking permutation invariance and hindering efficient learning; and (2) *sparse rewards* caused by incomplete incorporation of constraints that can only be evaluated on full expressions, such as constant fitting or physical-law verification. To address these challenges, we propose a unified framework, **Graph-based Symbolic Regression (GSR)**, which compresses the search space through a permutation-invariant representation, Expression Graphs (EGs), that intrinsically encode expression equivalences via a term-rewriting system (TRS) and a directed acyclic graph (DAG) structure; and mitigates reward sparsity via employing hybrid neural-guided Monte-Carlo tree search (hnMCTS) on EGs, where the constraint-informed neural guidance enables direct incorporation of expression-level constraint priors, and an adaptive $\epsilon$-UCB policy balances exploration and exploitation. Theoretical analyses establish the uniqueness of our proposed EG representation and the convergence of the hnMCTS algorithm. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of GSR in discovering underlying expressions and adhering to physical laws, offering practical solutions for scientific discovery.

Diffusion models have recently emerged as a powerful approach for trajectory planning. However, their inherently non-sequential nature limits their effectiveness in long-horizon reasoning tasks at test time. The recently proposed Monte Carlo Tree Diffusion (MCTD) offers a promising solution by combining diffusion with tree-based search, achieving state-of-the-art performance on complex planning problems. Despite its strengths, our analysis shows that MCTD incurs substantial computational overhead due to the sequential nature of tree search and the cost of iterative denoising. To address this, we propose Fast-MCTD, a more efficient variant that preserves the strengths of MCTD while significantly improving its speed and scalability. Fast-MCTD integrates two techniques: Parallel MCTD, which enables parallel rollouts via delayed tree updates and redundancy-aware selection; and Sparse MCTD, which reduces rollout length through trajectory coarsening. Experiments show that Fast-MCTD achieves up to 100× speedup over standard MCTD while maintaining or improving planning performance. Remarkably, it even outperforms Diffuser in inference speed on some tasks, despite Diffuser requiring no search and yielding weaker solutions. These results position Fast-MCTD as a practical and scalable solution for diffusion-based inference-time reasoning.

The mean of a random variable can be understood as a *linear* functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this paper, we investigate whether a similar quadratic speedup is achievable for estimating *non-linear* functionals of probability distributions. We propose a \textit{quantum-inside-quantum} algorithm that achieves this speedup for the broad class of nonlinear estimation problems known as nested expectations. Our algorithm improves upon the direct application of the quantum-accelerated multilevel Monte Carlo algorithm introduced by An et. al.. The existing lower bound indicates that our algorithm is optimal up to polylogarithmic factors. A key innovation of our approach is a new sequence of multilevel Monte Carlo approximations specifically designed for quantum computing, which is central to the algorithm's improved performance.

Large language models (LLMs) typically generate identical or similar responses for all users given the same prompt, posing serious safety risks in high-stakes applications where user vulnerabilities differ widely. Existing safety evaluations primarily rely on context-independent metrics—such as factuality, bias, or toxicity—overlooking the fact that the same response may carry divergent risks depending on the user's background or condition. We introduce ``personalized safety'' to fill this gap and present PENGUIN—a benchmark comprising 14,000 scenarios across seven sensitive domains with both context-rich and context-free variants. Evaluating six leading LLMs, we demonstrate that personalized user information significantly improves safety scores by 43.2%, confirming the effectiveness of personalization in safety alignment. However, not all context attributes contribute equally to safety enhancement. To address this, we develop RAISE—a training-free, two-stage agent framework that strategically acquires user-specific background. RAISE improves safety scores by up to 31.6% over six vanilla LLMs, while maintaining a low interaction cost of just 2.7 user queries on average. Our findings highlight the importance of selective information gathering in safety-critical domains and offer a practical solution for personalizing LLM responses without model retraining. This work establishes a foundation for safety research that adapts to individual user contexts rather than assuming a universal harm standard.

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation---a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates promising improvements over existing learning-based methods. Our PyTorch implementation is available at https://github.com/jiajunhe98/FEAT.

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operations. Although we discover that the corresponding problems are NP-complete in general, we provide a comprehensive parameterized-complexity analysis with the aim of determining those properties of the problems that explain the hardness and those that make the problems tractable. For instance, we show that the problems remain hard for a small number $d$ of features or small domain size $D$ but the combination of both yields fixed-parameter tractability. That is, the problems are solvable in $(D + 1)^{2d} \cdot |\mathcal{I}|^{O(1)}$ time, where $|\mathcal{I}|$ is the size of the input. We also provide a proof-of-concept implementation of this algorithm and report on empirical results.

Decision tree, despite its unmatched interpretability and lightweight structure, faces two key issues that limit its broader applicability: non-differentiability and low testing accuracy. This study addresses these issues by developing a differentiable oblique tree that optimizes the entire tree using gradient-based optimization. We propose an exact reformulation of hard-split trees based on "ReLU+Argmin" mechanism, and then cast the reformulated tree training as an unconstrained optimization task. The ReLU-based sample branching, expressed as exact-zero or non-zero values, preserve a unique decision path, in contrast to soft decision trees with probabilistic routing. The subsequent Argmin operation identifies the unique zero-violation path, enabling deterministic predictions. For effective gradient flow, we approximate Argmin behaviors by scaling softmin function. To ameliorate numerical instability, we propose a warm-start annealing scheme that solves multiple optimization tasks with increasingly accurate approximations. This reformulation alongside distributed GPU parallelism offers strong scalability, supporting 12-depth tree even on million-scale datasets where most baselines fail. Extensive experiments demonstrate that our optimized tree achieves a superior testing accuracy against 14 baselines, including an average improvement of 7.54\% over CART.

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10% improvements on the challenging benchmarks.

Recent advances in flow-based generative modelling have provided scalable methods for computing the Schrödinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The successful Iterative Markovian Fitting (IMF) procedure solves the SB problem via sequential bridge-matching steps, presenting an elegant and practical approach with many favourable properties over the more traditional Iterative Proportional Fitting (IPF) procedure. Beyond the standard setting, optimal transport can be generalised to the multi-marginal case in which the objective is to minimise a cost defined over several marginal distributions. Of particular importance are costs defined over a tree structure, from which Wasserstein barycentres can be recovered as a special case. In this work, we extend the IMF procedure to solve for the tree-structured SB problem. Our resulting algorithm inherits the many advantages of IMF over IPF approaches in the tree-based setting. In the case of Wasserstein barycentres, our approach can be viewed as extending the widely used fixed-point approach to use flow-based entropic OT solvers, while requiring only simple bridge-matching steps at each iteration.

We explore if it is possible to learn data structures end-to-end with neural networks, with a focus on the problem of nearest-neighbor (NN) search. We introduce a framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned from scratch, and does not require careful initialization or seeding with candidate data structures. In several settings, we are able to reverse-engineer the learned data structures and query algorithms. For 1D nearest neighbor search, the model discovers optimal distribution (in)dependent algorithms such as binary search and variants of interpolation search. In higher dimensions, the model learns solutions that resemble k-d trees in some regimes, while in others, elements of locality-sensitive hashing emerge. Additionally, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.

Understanding the remarkable efficacy of Adam when training transformer-based language models has become a central research topic within the optimization community. To gain deeper insights, several simplifications of Adam have been proposed, such as the signed gradient and signed momentum methods. In this work, we conduct an extensive empirical study — training over 1,500 language models across different data configurations and scales — comparing Adam to several known simplified variants. We find that signed momentum methods are faster than SGD, but consistently underperform relative to Adam, even after careful tuning of momentum, clipping setting and learning rates. However, our analysis reveals a compelling option that preserves near-optimal performance while allowing for new insightful reformulations: constraining the Adam momentum parameters to be equal, $\beta_1=\beta_2$. Beyond robust performance, this choice affords new theoretical insights, highlights the "secret sauce" on top of signed momentum, and grants a precise statistical interpretation: we show that Adam in this setting implements a natural online algorithm for estimating the mean and variance of gradients—one that arises from a mean-field Gaussian variational inference perspective.

Public model repositories now contain millions of models, yet most remain undocumented and effectively lost: their capabilities, provenance, and constraints cannot be reliably determined. As a result, the field wastes training time and compute, propagates hidden biases, faces intellectual-property risks, and misses opportunities for model reuse and transfer. In this position paper, we advocate charting the world's model population in a unified structure we call the Model Atlas: a graph that captures models, their attributes, and the weight transformations connecting them. The Model Atlas enables applications in model forensics, meta-ML research, and model discovery, challenging tasks given today's unstructured model repositories. However, because most models lack documentation, large atlas regions remain uncharted. Addressing this gap motivates new machine learning methods that treat models themselves as data and infer properties such as functionality, performance, and lineage directly from their weights. We argue that a scalable path forward is to bypass the unique parameter symmetries that plague model weights. Charting all the world's models will require a community effort, and we hope its broad utility will rally researchers toward this goal.

Monitoring individual tree mortality at scale has been found to be crucial for understanding forest loss, ecosystem resilience, carbon fluxes, and climate-induced impacts. However, the fine-granularity monitoring faces major challenges on both the data and methodology sides because: (1) finding isolated individual-level tree deaths requires high-resolution remote sensing images with broad coverage, and (2) compared to regular geo-objects (e.g., buildings), dead trees often exhibit weaker contrast and high variability across tree types, landscapes and ecosystems. Existing datasets on tree mortality primarily rely on moderate-resolution satellite imagery (e.g., 30m resolution), which aims to detect large-patch wipe-outs but is unable to recognize individual-level tree mortality events. Several efforts have explored alternatives via very-high-resolution drone imagery. However, drone images are highly expensive and can only be collected at local scales, which are therefore not suitable for national-scale applications and beyond. To bridge the gaps, we introduce TreeFinder, the first high-resolution remote sensing benchmark dataset designed for individual-level tree mortality mapping across the Contiguous United States (CONUS). Specifically, the dataset uses NAIP imagery at 0.6m resolution that provides wall-to-wall coverage of the entire CONUS. TreeFinder contains images with pixel-level labels generated via extensive manual annotation that covers forested areas in 48 states with over 23,000 hectares. All annotations are rigorously validated using multi-temporal NAIP images and auxiliary vegetation indices from remote sensing imagery. Moreover, TreeFinder includes multiple evaluation scenarios to test the models' ability in generalizing across different geographic regions, climate zones, and forests with different plant function types. Finally, we develop benchmarks using a suite of semantic segmentation models, including both convolutional architectures and more recent foundation models based on vision transformers for general and remote sensing images. Our dataset and code are publicly available on Kaggle and GitHub: https://www.kaggle.com/datasets/zhihaow/tree-finder and https://github.com/zhwang0/treefinder.

Modern language model (LM) training has been divided into multiple stages, making it difficult for downstream developers to evaluate the impact of design choices made at each stage. We present EvoLM, a model suite that enables systematic and transparent analysis of LMs' training dynamics across pre-training, continued pre-training, supervised fine-tuning, and reinforcement learning. By training over 100 LMs with 1B and 4B parameters from scratch, we rigorously evaluate both upstream (language modeling) and downstream (problem-solving) reasoning capabilities, including considerations of both in-domain and out-of-domain generalization. Key insights highlight the diminishing returns from excessive pre-training and post-training, the importance and practices of mitigating forgetting during domain-specific continued pre-training, the crucial role of continued pre-training in bridging pre-training and post-training phases, and various intricate trade-offs when configuring supervised fine-tuning and reinforcement learning. To facilitate open research and reproducibility, we release all pre-trained and post-trained models, training datasets for all stages, and our entire training and evaluation pipeline.

While language models have shown remarkable performance across diverse tasks, they still encounter challenges in complex reasoning scenarios. Recent research suggests that language models trained on linearized search traces toward solutions, rather than solely on the final solutions, exhibit improved generalization, despite the search traces being potentially noisy or suboptimal. However, relying on such imperfect traces can result in inefficient use of test-time compute. To address this, we propose guided reinforced self-training (Guided-ReST), a fine-tuning algorithm designed to improve the model’s capability for effective search during inference. The key insight behind Guided-ReST is that optimal solutions can serve as valuable step-by-step landmarks to guide the model’s search process. Based on this insight, we introduce a novel data generation method that seamlessly incorporates optimal solutions into the model’s search procedure, enabling the generation of high-quality search traces. By fine-tuning the model on these search traces, we effectively distill improved search strategies into the model. Our method significantly enhances the search capabilities of language models on arithmetic reasoning and code self-repair tasks, including Countdown, CodeContests, and CodeForces. We release the source code at https://github.com/snu-mllab/guided-rest.

Agentic search such as Deep Research systems-where agents autonomously browse the web, synthesize information, and return comprehensive citation-backed answers-represents a major shift in how users interact with web-scale information. While promising greater efficiency and cognitive offloading, the growing complexity and open-endedness of agentic search have outpaced existing evaluation benchmarks and methodologies, which largely assume short search horizons and static answers. In this paper, we introduce Mind2Web 2, a benchmark of 130 realistic, high-quality, and long-horizon tasks that require real-time web browsing and extensive information synthesis, constructed with over 1000 hours of human labor. To address the challenge of evaluating time-varying and complex answers, we propose a novel Agent-as-a-Judge framework. Our method constructs task-specific judge agents based on a tree-structured rubric design to automatically assess both answer correctness and source attribution. We conduct a comprehensive evaluation of ten frontier agentic search systems and human performance, along with a detailed error analysis to draw insights for future development. The best-performing system, OpenAI Deep Research, can already achieve 50-70% of human performance while spending half the time, highlighting its great potential. Altogether, Mind2Web 2 provides a rigorous foundation for developing and benchmarking the next generation of agentic search systems.

Reinforcement Learning (RL) traditionally relies on scalar reward signals, limiting its ability to leverage the rich semantic knowledge often available in real-world tasks. In contrast, humans learn efficiently by combining numerical feedback with language, prior knowledge, and common sense. We introduce Prompted Policy Search (ProPS), a novel RL method that unifies numerical and linguistic reasoning within a single framework. Unlike prior work that augments existing RL components with language, ProPS places a large language model (LLM) at the center of the policy optimization loop—directly proposing policy updates based on both reward feedback and natural language input. We show that LLMs can perform numerical optimization in-context, and that incorporating semantic signals, such as goals, constraints, and strategy hints can lead to more informed exploration and sample-efficient learning. ProPS is evaluated across 15 Gymnasium tasks, spanning classic control, Atari games, and MuJoCo environments, and compared to seven widely-adopted RL algorithms (e.g., PPO, SAC, TRPO). It outperforms all baselines on 8 out of 15 tasks and demonstrates substantial gains when provided with domain knowledge. These results highlight the potential of unifying semantics and numerics for transparent, generalizable, and human-aligned reinforcement learning.