NeurIPS 2025 Papers

The growing integration of machine learning (ML) and artificial intelligence (AI) models into high-stakes domains such as healthcare and scientific research calls for models that are not only accurate but also interpretable. Among the existing explainable methods, counterfactual explanations offer interpretability by identifying minimal changes to inputs that would alter a model’s prediction, thus providing deeper insights. However, current counterfactual generation methods suffer from critical limitations, including gradient vanishing, discontinuous latent spaces, and an overreliance on the alignment between learned and true decision boundaries. To overcome these limitations, we propose LeapFactual, a novel counterfactual explanation algorithm based on conditional flow matching. LeapFactual generates reliable and informative counterfactuals, even when true and learned decision boundaries diverge. LeapFactual is not limited to models with differentiable loss functions. It can even handle human-in-the-loop systems, expanding the scope of counterfactual explanations to domains that require the participation of human annotators, such as citizen science. We provide extensive experiments on benchmark and real-world datasets highlighting that LeapFactual generates accurate and in-distribution counterfactual explanations that offer actionable insights. We observe, for instance, that our reliable counterfactual samples with labels aligning to ground truth can be beneficially used as new training data to enhance the model. The proposed method is diversely applicable and enhances scientific knowledge discovery as well as non-expert interpretability.

Short videos are an effective tool for promoting contents and improving knowledge accessibility. While existing extractive video summarization methods struggle to produce a coherent narrative, existing abstractive methods cannot `quote' from the input videos, i.e., inserting short video clips in their outputs. In this work, we explore novel video editing models for generating shorts that feature a coherent narrative with embedded video insertions extracted from a long input video. We propose a novel retrieval-embedded generation framework that allows a large language model to quote multimodal resources while maintaining a coherent narrative. Our proposed REGen system first generates the output story script with quote placeholders using a finetuned large language model, and then uses a novel retrieval model to replace the quote placeholders by selecting a video clip that best supports the narrative from a pool of candidate quotable video clips. We examine the proposed method on the task of documentary teaser generation, where short interview insertions are commonly used to support the narrative of a documentary. Our objective evaluations show that the proposed method can effectively insert short video clips while maintaining a coherent narrative. In a subjective survey, we show that our proposed method outperforms existing abstractive and extractive approaches in terms of coherence, alignment, and realism in teaser generation.

Distillation has shown remarkable success in transferring knowledge from a Large Language Model (LLM) teacher to a student LLM. However, current distillation methods require similar tokenizers between the teacher and the student, restricting their applicability to only a small subset of teacher--student pairs. In this work, we develop a principled cross-tokenizer distillation method to solve this crucial deficiency. Our method is the first to enable effective distillation across fundamentally different tokenizers, while also substantially outperforming prior methods in all other cases. We verify the efficacy of our method on three distinct use cases. First, we show that viewing tokenizer transfer as self-distillation enables unprecedentedly effective transfer across tokenizers, including rapid transfer of subword models to the byte-level. Transferring different models to the same tokenizer also enables ensembling to boost performance. Secondly, we distil a large maths-specialised LLM into a small general-purpose model with a different tokenizer, achieving competitive maths problem-solving performance. Thirdly, we use our method to train state-of-the-art embedding prediction hypernetworks for training-free tokenizer transfer. Our results unlock an expanded range of teacher--student pairs for distillation, enabling new ways to adapt and enhance interaction between LLMs.

The softmax-contaminated mixture of experts (MoE) model is deployed when a large-scale pre-trained model, which plays the role of a fixed expert, is fine-tuned for learning downstream tasks by including a new contamination part, or prompt, functioning as a new, trainable expert. Despite its popularity and relevance, the theoretical properties of the softmax-contaminated MoE have remained unexplored in the literature. In the paper, we study the convergence rates of the maximum likelihood estimator of gating and prompt parameters in order to gain insights into the statistical properties and potential challenges of fine-tuning with a new prompt. We find that the estimability of these parameters is compromised when the prompt acquires overlapping knowledge with the pre-trained model, in the sense that we make precise by formulating a novel analytic notion of distinguishability. Under distinguishability of the pre-trained and prompt models, we derive minimax optimal estimation rates for all the gating and prompt parameters. By contrast, when the distinguishability condition is violated, these estimation rates become significantly slower due to their dependence on the prompt convergence rate to the pre-trained model. Finally, we empirically corroborate our theoretical findings through several numerical experiments.

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on specific integrated solvers. This integration limits their applicability, including their use in neural network architectures and bi-level optimization tasks, restricting users to a narrow selection of solver choices. To address this limitation, we introduce **dQP**, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver. A key insight we leverage to achieve modularity is that, once the active set of inequality constraints is known, both the solution and its derivative can be expressed using simplified linear systems that share the same matrix. This formulation fully decouples the computation of the QP solution from its differentiation. Building on this result, we provide a minimal-overhead, open-source implementation (<https://github.com/cwmagoon/dQP>) that seamlessly integrates with over 15 state-of-the-art solvers. Comprehensive benchmark experiments demonstrate dQP’s robustness and scalability, particularly highlighting its advantages in large-scale sparse problems.

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely $\lambda$-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: \href{https://github.com/miccunifi/lambda_orthogonality.git}{https://github.com/miccunifi/lambda\_orthogonality}.

The Schrödinger bridge problem seeks the optimal stochastic process that connects two given probability distributions with minimal energy modification. While the Sinkhorn algorithm is widely used to solve the static optimal transport problem, a recent work (Pooladian and Niles-Weed, 2024) proposed the *Sinkhorn bridge*, which estimates Schrödinger bridges by plugging optimal transport into the time-dependent drifts of SDEs, with statistical guarantees in the one-sample estimation setting where the true source distribution is fully accessible. In this work, to further justify this method, we study the statistical performance of intermediate Sinkhorn iterations in the two-sample estimation setting, where only finite samples from both source and target distributions are available. Specifically, we establish a statistical bound on the squared total variation error of Sinkhorn bridge iterations: $\mathcal{O}(1/m+1/n + r^{2k})~(r \in (0,1))$, where $m$ and $n$ are the sample sizes from the source and target distributions, respectively, and $k$ is the number of Sinkhorn iterations. This result provides a theoretical guarantee for the finite-sample performance of the Schrödinger bridge estimator and offers practical guidance for selecting sample sizes and the number of Sinkhorn iterations. Notably, our theoretical results apply to several representative methods such as [SF]$^2$M, DSBM-IMF, BM2, and lightSB(-M) under specific settings, through the previously unnoticed connection between these estimators.

The widespread use of generative models has created a feedback loop in which each generation of models is trained on data partially produced by its predecessors. This process has raised concerns about model collapse: A critical degradation in performance caused by repeated training on synthetic data. However, different analyses in the literature have reached different conclusions as to the severity of model collapse. As such, it remains unclear how concerning this phenomenon is, and under which assumptions it can be avoided. To address this, we theoretically study model collapse for maximum likelihood estimation (MLE), in a natural setting where synthetic data is gradually added to the original training set. Under standard assumptions (similar to those long used for proving asymptotic consistency and normality of MLE), we establish non-asymptotic bounds showing that collapse can be avoided even as the fraction of real data vanishes. On the other hand, we prove that some assumptions (beyond MLE consistency) are indeed necessary: Without them, model collapse can occur arbitrarily quickly, even when the original data is still present in the training set. To the best of our knowledge, these are the first rigorous examples of iterative generative modeling with accumulating data that rapidly leads to model collapse.

Vision Transformers have demonstrated exceptional performance across various computer vision tasks, yet their quadratic computational complexity concerning token length remains a significant challenge. To address this, token reduction methods have been widely explored. However, existing approaches often overlook the frequency characteristics of self-attention, such as rank collapsing and over-smoothing phenomenon. In this paper, we propose a frequency-aware token reduction strategy that improves computational efficiency while preserving performance by mitigating rank collapsing. Our method partitions tokens into high-frequency tokens and low-frequency tokens. high-frequency tokens are selectively preserved, while low-frequency tokens are aggregated into a compact direct current token to retain essential low-frequency components. Through extensive experiments and analysis, we demonstrate that our approach significantly improves accuracy while reducing computational overhead and mitigating rank collapsing and over smoothing. Furthermore, we analyze the previous methods, shedding light on their implicit frequency characteristics and limitations. The code is available in https://github.com/jhtwosun/frequency-aware-token-pruning.

Fine-tuning large language models (LLMs) poses significant computational burdens, especially in federated learning (FL) settings. We introduce Layer-wise Efficient Federated Fine-tuning (LEFF), a novel method designed to enhance the efficiency of FL fine-tuning while preserving model performance and minimizing client-side computational overhead. LEFF strategically selects layers for fine-tuning based on client computational capacity, thereby mitigating the straggler effect prevalent in heterogeneous environments. Furthermore, LEFF incorporates an importance-driven layer sampling mechanism, prioritizing layers with greater influence on model performance. Theoretical analysis demonstrates that LEFF achieves a convergence rate of $\mathcal{O}(1/\sqrt{T})$. Extensive experiments on diverse datasets demonstrate that LEFF attains superior computational efficiency and model performance compared to existing federated fine-tuning methods, particularly under heterogeneous conditions.

Machine unlearning algorithms aim to remove the influence of specific training samples, ideally recovering the model that would have resulted from training on the remaining data alone. We study unlearning in the overparameterized setting, where many models interpolate the data, and defining the solution as any loss minimizer over the retained set—as in prior work in the underparameterized setting—is inadequate, since the original model may already interpolate the retained data and satisfy this condition. In this regime, loss gradients vanish, rendering prior methods based on gradient perturbations ineffective, motivating both new unlearning definitions and algorithms. For this setting, we define the unlearning solution as the minimum-complexity interpolator over the retained data and propose a new algorithmic framework that only requires access to model gradients on the retained set at the original solution. We minimize a regularized objective over perturbations constrained to be orthogonal to these model gradients, a first-order relaxation of the interpolation condition. For different model classes, we provide exact and approximate unlearning guarantees and demonstrate that an implementation of our framework outperforms existing baselines across various unlearning experiments.

Large Language Models (LLMs) achieve impressive reasoning capabilities at the cost of substantial inference overhead, posing substantial deployment challenges. Although distilled Small Language Models (SLMs) significantly enhance efficiency, their performance suffers as they fail to follow LLMs' reasoning paths. Luckily, we reveal that only a small fraction of tokens genuinely diverge reasoning paths between LLMs and SLMs. Most generated tokens are either identical or exhibit neutral differences, such as minor variations in abbreviations or expressions. Leveraging this insight, we introduce **Roads to Rome (R2R)**, a neural token router that selectively utilizes LLMs only for these critical, path-divergent tokens, while leaving the majority of token generation to the SLM. We also develop an automatic data generation pipeline that identifies divergent tokens and generates token-level routing labels to train the lightweight router. We apply R2R to combine R1-1.5B and R1-32B models from the DeepSeek family, and evaluate on challenging math, coding, and QA benchmarks. With an average activated parameter size of 5.6B, R2R surpasses the average accuracy of R1-7B by 1.6×, outperforming even the R1-14B model. Compared to R1-32B, it delivers a 2.8× wall-clock speedup with comparable performance, advancing the Pareto frontier of test-time scaling efficiency.

Can we build accurate world models out of large language models (LLMs)? How can world models benefit LLM agents? The gap between the prior knowledge of LLMs and the specified environment's dynamics usually bottlenecks LLMs' performance as world models. To bridge the gap, we propose a training-free "world alignment" that learns an environment's symbolic knowledge complementary to LLMs. The symbolic knowledge covers action rules, knowledge graphs, and scene graphs, which are extracted by LLMs from exploration trajectories and encoded into executable codes to regulate LLM agents' policies. We further propose an RL-free, model-based agent "WALL-E" through the model-predictive control (MPC) framework. Unlike classical MPC requiring costly optimization on the fly, we adopt an LLM agent as an efficient look-ahead optimizer of future steps' actions by interacting with the neurosymbolic world model. While the LLM agent's strong heuristics make it an efficient planner in MPC, the quality of its planned actions is also secured by the accurate predictions of the aligned world model. They together considerably improve learning efficiency in a new environment. On open-world challenges in Mars (Minecraft like) and ALFWorld (embodied indoor environments), WALL-E significantly outperforms existing methods, e.g., surpassing baselines in Mars by 16.1%–51.6% of success rate and by at least 61.7% in score. In ALFWorld, it achieves a new record 98% success rate after only 4 iterations.

Tensorized Incomplete Multi-View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across multiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., $\ell_1$ or $\ell_{2,1}$), which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus on modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limitations, we propose a novel approach, GaUssian regressIon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model to characterize complex noise distributions in a more realistic and flexible manner. Meanwhile, a dual manifold regularization is introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the high-preservation $\ell_{\delta}$-norm tensor rank constraint, which applies differentiated penalties to the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demonstrate that our method outperforms SOTA approaches.

We investigate the problem of sequentially selecting elements of an unknown matroid in an online manner to form an independent set, with the goal of maximizing the minimum probability of acceptance across all elements, a property we define as $f$-fairness. Under adversarial arrival orders, we design an $\alpha(\ln(k)+1)$-fair algorithm, where $\alpha$ is the arboricity of the matroid and $k$ is the rank, a result that is nearly optimal. For laminar matroids, we develop an $(2\alpha-1)$-fair algorithm, which is optimal up to constant factors, achieved through a novel online coloring scheme. In the random arrival order setting, we achieve a $(4+o(1))\alpha$-fair algorithm for graphic matroids, matching the optimal result up to constant factors, relying on a novel technique for learning a degeneracy ordering using a sampled subset of edges. We further generalize our result to $p$-matchoids, obtaining a $\beta(p\ln k+1)$-fair algorithm for the adversarial arrival model, where $\beta$ is the optimal offline fairness. Notably, all our results can be extended to a setting with no prior knowledge of the matroid with only a logarithmic increase in the fairness factor.

Large language models (LLMs) often produce reasoning steps that are superficially coherent yet internally inconsistent, leading to unreliable outputs. Since such failures typically arise from implicit or poorly-grounded knowledge, we introduce \emph{Grounded Reasoning in Dependency (GRiD)}, a novel dependency-aware reasoning framework that explicitly grounds reasoning steps in structured knowledge. GRiD represents reasoning as a graph consisting of interconnected knowledge extraction nodes and reasoning nodes, enforcing logical consistency through explicit dependencies. Each reasoning step is validated via a lightweight, step-wise verifier that ensures logical correctness relative to its premises. Extensive experiments across diverse reasoning benchmarks—including StrategyQA, CommonsenseQA, GPQA, and TruthfulQA—demonstrate that GRiD substantially improves reasoning accuracy, consistency, and faithfulness compared to recent state-of-the-art structured reasoning methods. Notably, GRiD enhances performance even when applied purely as a lightweight verification module at inference time, underscoring its generalizability and practical utility. Code is available at: https://github.com/cure-lab/GRiD.

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.

Large language models often possess latent capabilities that lie dormant unless explicitly elicited, or surfaced, through fine-tuning or prompt engineering. Predicting, assessing, and understanding these latent capabilities pose significant challenges in the development of effective, safe AI systems. In this work, we recast elicitation as an information-constrained fine-tuning problem and empirically characterize upper bounds on the minimal number of parameters needed to achieve specific task performances. We find that training as few as 10–100 randomly chosen parameters—several orders of magnitude fewer than state-of-the-art parameter-efficient methods—can recover up to 50\% of the performance gap between pretrained-only and full fine-tuned models, and 1,000s to 10,000s of parameters can recover 95\% of this performance gap. We show that a logistic curve fits the relationship between the number of trained parameters and model performance gap recovery. This scaling generalizes across task formats and domains, as well as model sizes and families, extending to reasoning models and remaining robust to increases in inference compute. To help explain this behavior, we consider a simplified picture of elicitation via fine-tuning where each trainable parameter serves as an encoding mechanism for accessing task-specific knowledge. We observe a relationship between the number of trained parameters and how efficiently relevant model capabilities can be accessed and elicited, offering a potential route to distinguish elicitation from teaching.

Large language models are increasingly used to support high-stakes decisions, potentially influencing who is granted bail or receives a loan. Naive chain-of-thought sampling can improve average decision accuracy, but has also been shown to amplify unfair bias. To address this challenge and enable the trustworthy use of reasoning models in high-stakes decision-making, we propose a framework for training a generalizable Fairness Reward Model (FRM). Our model assigns a fairness score to LLM reasoning, enabling the system to down-weight biased trajectories and favor equitable ones when aggregating decisions across reasoning chains. We show that a single Fairness Reward Model, trained on weakly supervised, LLM-annotated examples of biased versus unbiased reasoning, transfers across tasks, domains, and model families without additional fine-tuning. When applied to real-world decision-making tasks including recidivism prediction and social media moderation, our approach consistently improves fairness while matching, or even surpassing, baseline accuracy.