NeurIPS 2025 Papers

We present *Fractional Diffusion Bridge Models* (FDBM), a novel generative diffusion bridge framework driven by the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove that the resulting bridge is a coupling-preserving process and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_\alpha$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.

We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs---a problem well motivated by the minima stability and edge-of-stability phenomena in gradient-descent training. Existing work either requires interpolation or focuses only on univariate inputs. This paper presents new and somewhat surprising theoretical results for multivariate inputs. On two natural settings (1) generalization gap for flat solutions, and (2) mean-squared error (MSE) in nonparametric function estimation by stable minima, we prove upper and lower bounds, which establish that while flatness does imply generalization, the resulting rates of convergence necessarily deteriorate exponentially as the input dimension grows. This gives an exponential separation between the flat solutions compared to low-norm solutions (i.e., weight decay), which are known not to suffer from the curse of dimensionality. In particular, our minimax lower bound construction, based on a novel packing argument with boundary-localized ReLU neurons, reveals how flat solutions can exploit a kind of "neural shattering" where neurons rarely activate, but with high weight magnitudes. This leads to poor performance in high dimensions. We corroborate these theoretical findings with extensive numerical simulations. To the best of our knowledge, our analysis provides the first systematic explanation for why flat minima may fail to generalize in high dimensions.

For classical PDE solvers, adjusting the spatial resolution and time step offers a trade-off between speed and accuracy. Neural emulators often achieve better speed-accuracy trade-offs by operating accurately on a compact representation of the PDE system. Coarsened PDE fields are a simple and effective representation, but cannot exploit fine spatial scales in the high-fidelity numerical solutions. Alternatively, unstructured latent representations provide efficient autoregressive rollouts, but cannot enforce local interactions or physical laws as inductive biases. To overcome these limitations, we introduce hybrid representations that augment coarsened PDE fields with spatially structured latent variables extracted from high-resolution inputs. Hybrid representations provide efficient rollouts, can be trained on a simple loss defined on coarsened PDE fields, and support hard physical constraints. When predicting fine- and coarse-scale features across multiple PDE emulation tasks, they outperform or match the speed-accuracy trade-offs of the best convolutional, attentional, Fourier operator-based and autoencoding baselines.

Conformal prediction has been explored as a general and efficient way to provide uncertainty quantification for time series. However, current methods struggle to handle time series data with change points — sudden shifts in the underlying data-generating process. In this paper, we propose a novel Conformal Prediction for Time-series with Change points (CPTC) algorithm, addressing this gap by integrating a model to predict the underlying state with online conformal prediction to model uncertainties in non-stationary time series. We prove CPTC's validity and improved adaptivity in the time series setting under minimum assumptions, and demonstrate CPTC's practical effectiveness on 6 synthetic and real-world datasets, showing improved validity and adaptivity compared to state-of-the-art baselines.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty --- often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce _neurosymbolic diffusion models_ (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks — including high-dimensional visual path planning and rule-based autonomous driving — NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

We show that across architecture (Transformer vs. Mamba vs. RWKV), training dataset (OpenWebText vs. The Pile), and scale (14 million parameters to 12 billion parameters), autoregressive language models exhibit highly consistent patterns of change in their behavior over the course of pretraining. Based on our analysis of over 1,400 language model checkpoints on over 110,000 tokens of English, we find that up to 98\% of the variance in language model behavior at the word level can be explained by three simple heuristics: the unigram probability (frequency) of a given word, the $n$-gram probability of the word, and the semantic similarity between the word and its context. Furthermore, we see consistent behavioral phases in all language models, with their predicted probabilities for words overfitting to those words' $n$-gram probabilities for increasing $n$ over the course of training. Taken together, these results suggest that learning in neural language models may follow a similar trajectory irrespective of model details.

Pre-training large language models (LLMs) on vast text corpora enhances natural language processing capabilities but risks encoding social biases, particularly gender bias. While parameter-modification methods like fine-tuning mitigate bias, they are resource-intensive, unsuitable for closed-source models, and lack adaptability to evolving societal norms. Instruction-based approaches offer flexibility but often compromise general performance on normal tasks. To address these limitations, we propose $\textit{FaIRMaker}$, an automated and model-independent framework that employs an $\textbf{auto-search and refinement}$ paradigm to adaptively generate Fairwords, which act as instructions to reduce gender bias and enhance response quality. $\textit{FaIRMaker}$ enhances the debiasing capacity by enlarging the Fairwords search space while preserving the utility and making it applicable to closed-source models by training a sequence-to-sequence model that adaptively refines Fairwords into effective debiasing instructions when facing gender-related queries and performance-boosting prompts for neutral inputs. Extensive experiments demonstrate that $\textit{FaIRMaker}$ effectively mitigates gender bias while preserving task integrity and ensuring compatibility with both open- and closed-source LLMs.

Understanding the dynamics of optimization algorithms in deep learning has become increasingly critical, especially as models grow in scale and complexity. Despite the empirical success of stochastic gradient descent (SGD) and its variants in finding solutions that generalize well, the precise mechanisms underlying this generalization remain poorly understood. A particularly intriguing aspect of this phenomenon is the bias of optimization algorithms towards certain types of minima—often flatter or simpler—especially in overparameterized regimes. While prior works have associated flatness of the loss landscape with better generalization, tools to mechanistically connect data, optimization algorithms, and the nature of the resulting minima are still limited. For instance, methods like Sharpness-Aware Minimization (SAM) have shown practical gains by explicitly promoting flatness, but lack a unified theoretical framework explaining their influence across different data structures and model architectures. In this work, we introduce a comprehensive linear stability analysis framework to dissect the behavior of optimization algorithms—SGD, random perturbations, and SAM—in neural networks, focusing particularly on two-layer ReLU models. Our approach is built upon a novel coherence measure that captures the interaction between data geometry and gradient similarity, providing new insights into why and how certain solutions are favored.

Emerging world models autoregressively generate video frames in response to actions, such as camera movements and text prompts, among other control signals. Due to limited temporal context window sizes, these models often struggle to maintain scene consistency during revisits, leading to severe forgetting of previously generated environments. Inspired by the mechanisms of human memory, we introduce a novel framework to enhancing long-term consistency of video world models through a geometry-grounded long-term spatial memory. Our framework includes mechanisms to store and retrieve information from the long-term spatial memory and we curate custom datasets to train and evaluate world models with explicitly stored 3D memory mechanisms. Our evaluations show improved quality, consistency, and context length compared to relevant baselines, paving the way towards long-term consistent world generation.

Designing models that can learn to reason in a systematic way is an important and long-standing challenge. In recent years, a wide range of solutions have been proposed for the specific case of systematic relational reasoning, including Neuro-Symbolic approaches, variants of the Transformer architecture, and specialized Graph Neural Networks. However, existing benchmarks for systematic relational reasoning focus on an overly simplified setting, based on the assumption that reasoning can be reduced to composing relational paths. In fact, this assumption is hard-baked into the architecture of several recent models, leading to approaches that can perform well on existing benchmarks but are difficult to generalize to other settings. To support further progress in the field of systematic relational reasoning with neural networks, we introduce a new benchmark that adds several levels of difficulty, requiring models to go beyond path-based reasoning.

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets. Our project page for accessing the source code is available at https://camlab-ethz.github.io/GAOT.

Continual Test-Time Adaptation (CTTA) aims to online adapt a pre-trained model to changing environments during inference. Most existing methods focus on exploiting target data, while overlooking another crucial source of information, the pre-trained weights, which encode underutilized domain-invariant priors. This paper takes the geometric attributes of pre-trained weights as a starting point, systematically analyzing three key components: magnitude, absolute angle, and pairwise angular structure. We find that the pairwise angular structure remains stable across diverse corrupted domains and encodes domain-invariant semantic information, suggesting it should be preserved during adaptation. Based on this insight, we propose PAID (Pairwise Angular Invariant Decomposition), a prior-driven CTTA method that decomposes weight into magnitude and direction, and introduces a learnable orthogonal matrix via Householder reflections to globally rotate direction while preserving the pairwise angular structure. During adaptation, only the magnitudes and the orthogonal matrices are updated. PAID achieves consistent improvements over recent SOTA methods on four widely used CTTA benchmarks, demonstrating that preserving pairwise angular structure offers a simple yet effective principle for CTTA. Our code is available at https://github.com/wangkunyu241/PAID.

Model merging has emerged as a promising technique for enhancing large language models, though its application in large-scale pre-training remains relatively unexplored. In this paper, we present a comprehensive investigation of model merging techniques during the pre-training process. Through extensive experiments with both dense and Mixture-of-Experts (MoE) architectures ranging from millions to over 100 billion parameters, we demonstrate that merging checkpoints trained with constant learning rates not only achieves significant performance improvements but also enables accurate prediction of annealing behavior. These improvements lead to both more efficient model development and significantly lower training costs. Our detailed ablation studies on merging strategies and hyperparameters provide new insights into the underlying mechanisms while uncovering novel applications. Through comprehensive experimental analysis, we offer the open-source community practical pre-training guidelines for effective model merging.

Designing analog circuits from performance specifications is a complex, multi-stage process encompassing topology selection, parameter inference, and layout feasibility. We introduce FALCON, a unified machine learning framework that enables fully automated, specification-driven analog circuit synthesis through topology selection and layout-constrained optimization. Given a target performance, FALCON first selects an appropriate circuit topology using a performance-driven classifier guided by human design heuristics. Next, it employs a custom, edge-centric graph neural network trained to map circuit topology and parameters to performance, enabling gradient-based parameter inference through the learned forward model. This inference is guided by a differentiable layout cost, derived from analytical equations capturing parasitic and frequency-dependent effects, and constrained by design rules. We train and evaluate FALCON on a large-scale custom dataset of 1M analog mm-wave circuits, generated and simulated using Cadence Spectre across 20 expert-designed topologies. Through this evaluation, FALCON demonstrates >99\% accuracy in topology inference, <10\% relative error in performance prediction, and efficient layout-aware design that completes in under 1 second per instance. Together, these results position FALCON as a practical and extensible foundation model for end-to-end analog circuit design automation.

Out-of-distribution (OOD) detection is essential for reliably deploying machine learning models in the wild. Yet, most methods treat large pre-trained models as monolithic encoders and rely solely on their final-layer representations for detection. We challenge this wisdom. We reveal the intermediate layers of pre-trained models, shaped by residual connections that subtly transform input projections, can encode surprisingly rich and diverse signals for detecting distributional shifts. Importantly, to exploit latent representation diversity across layers, we introduce an entropy-based criterion to automatically identify layers offering the most complementary information in a training-free setting, without access to OOD data. We show that selectively incorporating these intermediate representations can increase the accuracy of OOD detection by up to $10\%$ in far-OOD and over $7\%$ in near-OOD benchmarks compared to state-of-the-art training-free methods across various model architectures and training objectives. Our findings reveal a new avenue for OOD detection research and uncover the impact of various training objectives and model architectures on confidence-based OOD detection methods.

Deep generative models, particularly diffusion models, have achieved remarkable success but face significant challenges when trained on real-world, long-tailed datasets- where few "head" classes dominate and many "tail" classes are underrepresented. This paper develops a theoretical framework for long-tailed learning via diffusion models through the lens of deep mutual learning. We introduce a novel regularized training objective that combines the standard diffusion loss with a mutual learning term, enabling balanced performance across all class labels, including the underrepresented tails. Our approach to learn via the proposed regularized objective is to formulate it as a multi-player game, with Nash equilibrium serving as the solution concept. We derive a non-asymptotic first-order convergence result for individual gradient descent algorithm to find the Nash equilibrium. We show that the Nash gap of the score network obtained from the algorithm is upper bounded by $\mathcal{O}(\frac{1}{\sqrt{T_{train}}}+\beta)$ where $\beta$ is the regularizing parameter and $T_{train}$ is the number of iterations of the training algorithm. Furthermore, we theoretically establish hyper-parameters for training and sampling algorithm that ensure that we find conditional score networks (under our model) with a worst case sampling error $\mathcal{O}(\epsilon+1), \forall \epsilon>0$ across all class labels. Our results offer insights and guarantees for training diffusion models on imbalanced, long-tailed data, with implications for fairness, privacy, and generalization in real-world generative modeling scenarios.

Dynamic view synthesis has seen significant advances, yet reconstructing scenes from uncalibrated, casual video remains challenging due to slow optimization and complex parameter estimation. In this work, we present **Instant4D**, a monocular reconstruction system that leverages native 4D representation to efficiently process casual video sequences within minutes, without calibrated cameras or depth sensors. Our method begins with geometric recovery through deep visual SLAM, followed by grid pruning to optimize scene representation. Our design significantly reduces redundancy while maintaining geometric integrity, cutting model size to under **10%** of its original footprint. To handle temporal dynamics efficiently, we introduce a streamlined 4D Gaussian representation, achieving a **30×** speed-up and reducing training time to within two minutes, while maintaining competitive performance across several benchmarks. Our method reconstruct a single video within 10 minutes on the Dycheck dataset or for a typical 200-frame video. We further apply our model to in-the-wild videos, showcasing its generalizability. Our project website is published at https://instant4d.github.io/.

Despite their impressive performance across a wide range of tasks, Large Vision-Language Models (LVLMs) remain prone to hallucination. In this study, we propose a comprehensive intervention framework aligned with the transformer’s causal architecture in LVLMs, integrating the effects of different intervention paths on hallucination. We find that hallucinations in LVLMs do not arise from a single causal path, but rather from the interplay among image-to-input-text, image-to-output-text, and text-to-text pathways. For the first time, we also find that LVLMs rely on different pathways depending on the question–answer alignment format. Building on these insights, we propose simple yet effective methods to identify and intervene on critical hallucination heads within each pathway, tailored to discriminative and generative formats. Experiments across multiple benchmarks demonstrate that our approach consistently reduces hallucinations across diverse alignment types.

We study matching markets with ties, where workers on one side of the market may have tied preferences over jobs, determined by their matching utilities. Unlike classical two-sided markets with strict preferences, no single stable matching exists that is utility-maximizing for all workers. To address this challenge, we introduce the \emph{Optimal Stable Share} (OSS)-ratio, which measures the ratio of a worker's maximum achievable utility in any stable matching to their utility in a given matching. We prove that distributions over only stable matchings can incur linear utility losses, i.e., an $\Omega (N)$ OSS-ratio, where $N$ is the number of workers. To overcome this, we design an algorithm that efficiently computes a distribution over (possibly non-stable) matchings, achieving an asymptotically tight $O (\log N)$ OSS-ratio. When exact utilities are unknown, our second algorithm guarantees workers a logarithmic approximation of their optimal utility under bounded instability. Finally, we extend our offline approximation results to a bandit learning setting where utilities are only observed for matched pairs. In this setting, we consider worker-optimal stable regret, design an adaptive algorithm that smoothly interpolates between markets with strict preferences and those with statistical ties, and establish a lower bound revealing the fundamental trade-off between strict and tied preference regimes.