NeurIPS 2025 论文列表

Intracranial recordings have opened a unique opportunity to simultaneously measure activity across multiregional networks in the human brain. Recent works have focused on developing transformer-based neurofoundation models of such recordings that can generalize across subjects and datasets. However, these recordings exhibit highly complex spatiotemporal interactions across diverse spatial scales, from the single-channel scale to the scale of brain regions. As such, there remain critical open questions regarding how best to encode spatial information and how to design self-supervision tasks that enable the learning of brain network patterns and enhance downstream decoding performance using such high-dimensional, multiregional recordings. To allow for exploring these questions, we propose a new spatiotemporal transformer model of multiregional neural activity and a corresponding self-supervised masked latent reconstruction task, designed to enable flexibility in the spatial scale used for token encoding and masking. Applying this model on publicly available multiregional intracranial electrophysiology (iEEG) data, we demonstrate that adjusting the spatial scale for both token encoding and masked reconstruction significantly impacts downstream decoding. Further, we find that spatial encoding at larger scales than channel-level encoding, which is commonly used in existing iEEG transformer models, improves downstream decoding performance. Finally, we demonstrate that our method allows for region-level token encoding while also maintaining accurate channel-level neural reconstruction. Taken together, our modeling framework enables exploration of the spatial scales used for token encoding and masking, reveals their importance towards self-supervised pretraining of neurofoundation models of multiregional human brain activity, and enhances downstream decoding performance.

We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a global latent variable and struggle with uncertainty calibration and capturing local data dependencies. DNP addresses these limitations by introducing a global latent variable to model task-level variations and a local latent variable to capture input similarity within a distance-preserving latent space. This is achieved through bi-Lipschitz regularization, which bounds distortions in input relationships and encourages the preservation of relative distances in the latent space. This modeling approach allows DNP to produce better-calibrated uncertainty estimates and more effectively distinguish in- from out-of-distribution data. Empirical results demonstrate that DNP achieves strong predictive performance and improved uncertainty calibration across regression and classification tasks.

Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper, we introduce a novel Hybrid Boundary PINN (HB-PINN) method that combines a pretrained network for efficient initialization with a boundary-constrained mechanism. The HB-PINN method features a primary network focused on inner domain points and a distance metric network that enhances predictions at the boundaries, ensuring accurate solutions for both boundary and interior regions. Comprehensive experiments have been conducted on the NSE under complex boundary conditions, including the 2D cylinder wake flow and the 2D blocked cavity flow with a segmented inlet. The proposed method achieves state-of-the-art (SOTA) performance on these benchmark scenarios, demonstrating significantly improved accuracy over existing PINN-based approaches.

Recent studies have demonstrated that fine-tuning language models with brain data can improve their semantic understanding, although these findings have so far been limited to English. Interestingly, similar to the shared multilingual embedding space of pretrained multilingual language models, human studies provide strong evidence for a shared semantic system in bilingual individuals. Here, we investigate whether fine-tuning language models with bilingual brain data changes model representations in a way that improves them across multiple languages. To test this, we fine-tune monolingual and multilingual language models using brain activity recorded while bilingual participants read stories in English and Chinese. We then evaluate how well these representations generalize to the bilingual participants’ first language, their second language, and several other languages that the participants are not fluent in. We assess the fine-tuned language models on brain encoding performance and downstream NLP tasks. Our results show that bilingual brain-informed fine-tuned language models outperform their vanilla (pretrained) counterparts in both brain encoding performance and most downstream NLP tasks across multiple languages. These findings suggest that brain-informed fine-tuning improves multilingual understanding in language models, offering a bridge between cognitive neuroscience and NLP research. We make our code publicly available.

Large language models (LLMs) have achieved remarkable success across diverse domains, due to their strong instruction-following capabilities. This raised interest in optimizing instructions for black-box LLMs, whose internal parameters are inaccessible but popular for their strong performance and ease of use. Recent approaches leverage white-box LLMs to assist instruction optimization for black-box LLMs by generating instructions from soft prompts. However, white-box LLMs often map different soft prompts to the same instruction, leading to redundant queries to the black-box model. While previous studies regarded this many-to-one mapping as a redundancy to be avoided, we reinterpret it as useful prior knowledge that can enhance the optimization performance. To this end, we introduce PREimage-informed inSTruction Optimization (PRESTO), a novel framework that leverages the preimage structure of soft prompts to improve query efficiency. PRESTO consists of three key components: (1) score sharing, which shares the evaluation score with all soft prompts in a preimage; (2) preimage-based initialization, which select initial data points that maximize search space coverage using preimage information; and (3) score consistency regularization, which enforces prediction consistency within each preimage. By leveraging preimages, PRESTO observes 14 times more scored data under the same query budget, resulting in more efficient optimization. Experimental results on 33 instruction optimization tasks demonstrate the superior performance of PRESTO.

Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. \textbf{In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology.} Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.

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.

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.

Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the Text8 dataset, the informed corrector improves sample quality by generating text with significantly fewer errors than the baselines. On tokenized ImageNet 256x256, this approach consistently produces superior samples with fewer steps, achieving improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion.

The FAIR Universe – HiggsML Uncertainty Challenge focused on measuring the physical properties of elementary particles with imperfect simulators. Participants were required to compute and report confidence intervals for a parameter of interest regarding the Higgs boson while accounting for various systematic (epistemic) uncertainties. The dataset is a tabular dataset of 28 features and 280 million instances. Each instance represents a simulated proton-proton collision as observed at CERN’s Large Hadron Collider in Geneva, Switzerland. The features of these simulations were chosen to capture key characteristics of different types of particles. These include primary attributes, such as the energy and three-dimensional momentum of the particles, as well as derived attributes, which are calculated from the primary ones using domain-specific knowledge. Additionally, a label feature designates each instance’s type of proton-proton collision, distinguishing the Higgs boson events of interest from three background sources. As outlined in this paper, the permanent dataset release allows long-term benchmarking of new techniques. The leading submissions, including Contrastive Normalising Flows and Density Ratios estimation through classification, are described. Our challenge has brought together the physics and machine learning communities to advance our understanding and methodologies in handling systematic uncertainties within AI techniques.

Unsupervised anomaly detection of multivariate time series remains challenging in complex nonstationary dynamics, due to the high false-positive rates and limited interpretability. We propose PhysDiff, combining physics-guided decomposition with diffusion-based reconstruction, to address these issues. The physics-guided signal decomposition is introduced to disentangle overlapping dynamics by isolating high frequency oscillations and low frequency trends, which can reduce interference and provide meaningful physical priors. The reconstruction through conditional diffusion modeling captures deviations from learned normal behavior, making anomalies more distinguishable. Notably, PhysDiff introduces an amplitude-sensitive permutation entropy criterion to adaptively determine the optimal decomposition depth, and automatically extract adaptive frequency components used as explicit physics-based constraints for the diffusion process. Furthermore, the proposed conditional diffusion network employs a dual-path conditioning mechanism that integrates high-frequency and low-frequency physical priors, dynamically regulating the denoising process via a novel time frequency energy routing mechanism. By weighting reconstruction errors across frequency bands, our method improves anomaly localization and enhances interpretability. Extensive experiments on five benchmark datasets and two NeurIPS-TS scenarios demonstrate that PhysDiff outperforms 18 state-of-the-art baselines, with average F1-score improvements on both standard and challenging datasets. Experimental results validate the advantages of combining principled signal decomposition with diffusion-based reconstruction for robust, interpretable anomaly detection in complex dynamic systems.

Characterizing the cellular properties of neurons is fundamental to understanding their function in the brain. In this quest, the generation of bio-realistic models is central towards integrating multimodal cellular data sets and establishing causal relationships. However, current modeling approaches remain constrained by the limited availability and intrinsic variability of experimental neuronal data. The deterministic formalism of bio-realistic models currently precludes accounting for the natural variability observed experimentally. While deep learning is becoming increasingly relevant in this space, it fails to capture the full biophysical complexity of neurons, their nonlinear voltage dynamics, and variability. To address these shortcomings, we introduce $\texttt{NOBLE}$, a neural operator framework that learns a mapping from a continuous frequency-modulated embedding of interpretable neuron features to the somatic voltage response induced by current injection. Trained on synthetic data generated from bio-realistic neuron models, $\texttt{NOBLE}$ predicts distributions of neural dynamics accounting for the intrinsic experimental variability. Unlike conventional bio-realistic neuron models, interpolating within the embedding space offers models whose dynamics are consistent with experimentally observed responses. $\texttt{NOBLE}$ enables the efficient generation of synthetic neurons that closely resemble experimental data and exhibit trial-to-trial variability, offering a $4200$× speedup over the numerical solver. $\texttt{NOBLE}$ is the first scaled-up deep learning framework that validates its generalization with real experimental data. To this end, $\texttt{NOBLE}$ captures fundamental neural properties in a unique and emergent manner that opens the door to a better understanding of cellular composition and computations, neuromorphic architectures, large-scale brain circuits, and general neuroAI applications.

The integration of big data, physical laws, and machine learning algorithms has shown potential to improve the estimation and understanding of complex real-world systems. However, effectively incorporating physical laws with uncertainties into machine learning algorithms remains understudied. In this work, we bridge this gap by developing the Partial Physics Informed Diffusion Model (PPIDM), a novel framework that integrates known physical principles through a physics operator while reducing the impact of unknown dynamics by minimizing related discrepancies. We showcase PPIDM’s capabilities using ocean surface chlorophyll concentration data, which are influenced by both physical and biological processes, while the latter is poorly constrained. Experimental results reveal that PPIDM achieves substantially improved prediction accuracy and stability, significantly outperforming baseline methods that either neglect physics entirely or impose incomplete physical constraints under the assumption of completeness.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful frame- work for solving partial differential equations (PDEs). However, standard MLP- based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classi- cal spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for lin- ear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

Air pollution remains one of the most critical environmental challenges globally, posing severe threats to public health, ecological sustainability, and climate governance. While existing physics-based and data-driven models have made progress in air quality forecasting, they often struggle to jointly capture the complex spatiotemporal dynamics and ensure spatial continuity of pollutant distributions. In this study, we introduce CTENet, a novel chemical transport deep learning model that embeds the Advection-Diffusion-Reaction equation into a Physics-Informed Neural Network (PINN) framework using an Eulerian representation to model the spatiotemporal evolution of pollutants. Extensive experiments on two real-world datasets demonstrate that CTENet consistently outperforms state-of-the-art (SOTA) baselines, achieving a remarkable RMSE improvement of 45.8% on the USA dataset and 21.0% on the China dataset.

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local *gauge* symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. We use gauge equivariant networks to predict topological invariants (Chern numbers) of multiband topological insulators for the first time. The gauge symmetry of the network guarantees that the predicted quantity is a topological invariant. A major technical challenge is that the relevant gauge equivariant networks are plagued by instabilities in their training, severely limiting their usefulness. In particular, for larger gauge groups the instabilities make training impossible. We resolve this problem by introducing a novel gauge equivariant normalization layer which stabilizes the training. Furthermore, we prove a universal approximation theorem for our model. We train on samples with trivial Chern number only but show that our model generalizes to samples with non-trivial Chern number and provide various ablations of our setup.

We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.

Natural gradient methods significantly accelerate the training of Physics-Informed Neural Networks (PINNs), but are often prohibitively costly. We introduce a suite of techniques to improve the accuracy and efficiency of energy natural gradient descent (ENGD) for PINNs. First, we leverage the Woodbury formula to dramatically reduce the computational complexity of ENGD. Second, we adapt the Subsampled Projected-Increment Natural Gradient Descent algorithm from the variational Monte Carlo literature to accelerate the convergence. Third, we explore the use of randomized algorithms to further reduce the computational cost in the case of large batch sizes. We find that randomization accelerates progress in the early stages of training for low-dimensional problems, and we identify key barriers to attaining acceleration in other scenarios. Our numerical experiments demonstrate that our methods outperform previous approaches, achieving the same $L^2$ error as the original ENGD up to $75\times$ faster.