NeurIPS 2026 Papers

Many engineering building blocks behave as multi-port linear time-invariant systems. RF cavities, photonic devices, and superconducting quantum chips, despite their different underlying physics, all share a common mathematical structure for their port-level response. Each entry of the response matrix is a sum of contributions from a small number of intrinsic resonant modes, the pole-residue form. A model capable of predicting such responses for arbitrary geometries and arbitrary port configurations, while simultaneously extracting the underlying eigenmode structure, would therefore establish a foundational design principle spanning all these domains. We propose a neural framework that learns this modal decomposition end-to-end, supervised only by system-level observables and without supervising the modal parameters themselves. The architecture decomposes into a port-independent pole predictor and two port-dependent coupling predictors whose outputs are combined entry-wise, separating intrinsic from port-dependent features. This factorization yields a single trained model that generalizes to port counts unseen during training, dissolving the $\mathcal{O}(N^2)$ scaling barrier of direct regression. Despite no modal supervision, the freely-parameterized poles converge to physically meaningful eigenmodes, verified by cross-validation against the AAA rational approximation algorithm. We instantiate the framework in radio-frequency electromagnetic surrogate modeling. A model trained only on 2-port data accurately predicts $N$-port responses unseen during training.

One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the transition density function between consecutive observation times, which is needed to derive the likelihood function. Extending previous studies that solve Fokker-Planck (FP) type partial differential equations with Normalizing Flows, we propose a new Normalizing Flow architecture to learn the transition density function of the diffusion process between two observation times. We do so by solving in a Neural Galerkin framework the associated FP equation with a Dirac mass as initial condition, over a specified training distribution of the initial datum and the coefficients of the diffusion. We specifically focus on processes whose diffusion matrix vanishes in certain inaccessible boundary regions, such as Stochastic Volatility models that satisfy a Feller condition. The product of the obtained transition densities evaluated along the observed trajectory approximates the likelihood function, thereby enabling cheap posterior sampling via Markov chain Monte Carlo (MCMC). After the offline training phase, inference becomes significantly more efficient, as it avoids the need to solve the FP equation in real time for each parameter proposed by the MCMC sampler or to rely on other likelihood-free methods for Bayesian inference that involve repeated simulation of diffusion bridges.

Inverse problems for stiff parabolic partial differential equations (PDEs), such as the inverse heat conduction problem (IHCP), are severely ill-posed: the forward map rapidly damps high-frequency interior structure before it reaches the boundary. Soft-constrained physics-informed neural networks (PINNs), which embed the PDE as a residual penalty, suffer from gradient pathology in this regime and tend to fit boundary measurements while leaving the interior field essentially untouched. We propose Neural Field Thermal Tomography (NeFTY), a hard-constrained neural field framework for label-free three-dimensional inverse heat conduction. NeFTY represents the unknown diffusivity as a continuous coordinate-based neural network, and at every optimization step passes the candidate field through a differentiable implicit-Euler heat solver with harmonic-mean interface flux, so that the governing PDE holds exactly on the discretization rather than as a soft penalty. Adjoint gradients propagate the surface reconstruction error back to the network weights at solver-level memory cost, making test-time inversion tractable on a single GPU. Across synthetic 3D benchmarks, NeFTY substantially outperforms soft-constrained PINN variants and a voxel-grid baseline on label-free volumetric recovery, and it transfers to real thermography data, surpassing classical signal-processing baselines in both defect segmentation and depth estimation.

Animals generate behavior through continuous interactions between their neural circuits, bodies, and environment. Embodied simulations provide a means to study these interactions by testing neural circuit models in biologically realistic settings. Recent efforts have developed embodied simulations of diverse animals, and emerging work on biologically grounded neural architectures has begun to integrate circuit connectivity and single-unit dynamics from experimental data into artificial neural networks, introducing stronger inductive biases and closer mechanistic alignment with biology. How can we develop embodied simulations that enable the study of increasingly complex bodies and neural circuits? In this work, we address the challenge through coordinated advances in the simulated body, neural architecture, and training algorithm. We introduce *Rat v2*, a biomechanical model that provides an efficient and flexible tool for simulating rat behavior. To control this body, we develop *Rat NCAP*, a biologically grounded neural architecture for locomotion based on mammalian spinal circuits that incorporates cell-type-specific connectivity and a novel flexor-extensor neuromechanical interface. To optimize circuit parameters, we refine an evolutionary algorithm to support reliable and efficient training. The integrated system learns to locomote at different speeds without imitation learning, producing locomotion statistics and gaits that match experimental data. Systematic analyses reveal that neuromechanical interface choice substantially affects trainability and gait quality, and that specific neural populations play distinct roles in gait generation. Together, these findings support the view that embodied simulations at an intermediate level of abstraction can simultaneously reproduce complex behavior and yield mechanistic insights into the neural circuits that generate it.

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

Generative models play a rapidly growing role in the design and simulation of molecules. The most widely used applications of generative models are in large language models (LLMs), owing to the natural flexibility of language for specifying and answering queries. However, generalist LLMs do not effectively handle large sets of 3D coordinates, whereas specialist generative models of 3D molecules cannot reach the controllability afforded by language. To bridge these capabilities, we propose Nahual, a decoder-only autoregressive diffusion model for any sequence of text and 3D molecules. To enable autoregression on continuous coordinates to scale to long sequences, we propose next-token diffusion, whereby a standard causal transformer backbone is grounded in the clean current sequence while denoising the next sequence. We train Nahual on a curated set of twelve 3D chemistry tasks ranging from microsolvation to molecular conformer search to adsorption on metal surfaces, with associated evaluation metrics and baselines. The result is a single set of end-to-end-trained weights that simultaneously performs all tasks and surpasses state-of-the-art models specialized for crystal structure prediction and property-conditional molecule generation. Our results demonstrate the viability of scaling generalist decoder-only models for native multimodal understanding and generation across language and chemistry.

Transformer-based autoregressive models offer an efficient alternative to diffusion- and flow-matching-based approaches for generating 3D molecules. One challenge remains: standard transformer architectures require a sequential ordering of tokens, which is not inherently defined for the atoms in a molecule. Prior works have addressed this by using canonical atom orderings. However, these approaches are not permutation invariant w.r.t. atoms and bias next-token prediction towards ordering conventions. We overcome this limitation by introducing a novel neighborhood-guided training strategy. Our model, NEAT (Neighborhood-Guided, Efficient, Autoregressive Set Transformer) treats molecular graphs as sets of atoms and learns an order-agnostic distribution over admissible tokens at the graph boundary, thereby ensuring atom-level permutation invariance. NEAT achieves state-of-the-art generation quality on the QM9 and GEOM-Drugs datasets while offering a significant speed advantage over existing baselines.

We introduce NAGO, a noise-aware generative operator for efficient sampling from invariant measures of stochastic partial differential equations (SPDEs) in function space. Our central idea is to treat the noise measure as a design variable rather than a fixed default. While existing generative approaches mainly shape the sampling process through interpolation schedules or guidance heuristics, NAGO directly controls the marginal velocity field in functional flow matching by choosing a noise measure with suitable regularity. We establish conditions under which the resulting noise-induced flows are well defined in infinite-dimensional settings, and show how noise regularity affects the spectral geometry and stiffness of the marginal velocity field. This analysis leads to a principled design rule: match the regularity of the noise measure to that of the target invariant measure. The resulting method enables stable training and fast sampling without relying on downstream correction mechanisms. Experiments on three representative SPDEs with multiscale invariant measures show that NAGO consistently improves the accuracy--efficiency trade-off over standard flow matching baselines, while achieving up to two orders of magnitude speedup compared with classical numerical solvers.

Athletic performance represents the pinnacle of human motor intelligence, demanding rapid choices, precise control, agility, and coordinated physical execution. Replicating this seamless combination of capabilities remains elusive in current artificial intelligence and robotic systems. Concurrently, understanding the biological mastery of these movements is hindered because complex muscle coordination is rarely measured in vivo due to the limitations of physical equipment. To bridge this fundamental gap in understanding, $\textit{MyoChallenge}$ at NeurIPS 2025 established a pioneering benchmark for motor control intelligence in sports, leveraging high-fidelity musculoskeletal models within physics simulation combined with machine learning-driven algorithms. The competition introduces two distinct tracks emphasizing either upper or lower limbs control: a table tennis rally task utilizing a biomechanic upper limb composed of an arm with a hand (MyoArm) and a trunk (MyoTorso); and a soccer penalty kick using a biomechanic model of legs (MyoLeg) and a trunk (MyoTorso). Marking the fourth iteration of the MyoChallenge series, this event attracted almost 70 teams and over 560 submissions globally, uniting a diverse community ranging from physicians and neuroscientists to machine learning experts. The competition facilitated the development of several state-of-the-art control algorithms for a musculoskeletal system capable of sports agility, leveraging techniques such as physics-based motion planners, on-policy behaviour cloning, hierarchical planning, and muscle synergies that significantly surpassed our provided baseline performance. By integrating standardized tasks and physiologically realistic models into the open-source framework of MyoSuite, MyoChallenge'25 serves as a reproducible and reusable testbed to accelerate interdisciplinary research across machine learning, biomechanics, sports science, and neuroscience. Project page: https://www.myosuite.org//myochallenge/myochallenge-2025

Contemporary large language model (LLM) chat systems treat conversation history as an immutable sequence of turns that defines the model’s working context. However, user intent in real interactions is not static: it evolves through correction, refinement, and shifting constraints. This mismatch between dynamic intent and static transcripts can result in context pollution, where outdated or irrelevant information persists and continues to influence subsequent responses. We introduce mutable transcripts, a new interaction paradigm that enables users to revise prior turns through natural language edit requests, allowing the conversation history itself to be updated rather than appended. This reframes the transcript from a passive record into an editable representation of conversational state. We present a working prototype that integrates transcript-level revision into a standard chat interface and evaluate its feasibility through a controlled user study (n=17) and an illustrative transcript analysis of representative interaction scenarios. Participants significantly preferred mutable transcripts over standard chat across measures of clarity, confidence, and ease of use, with reduced intent to restart conversations. Transcript analysis of representative user study conversations shows that mutable transcripts can reduce conversation length and eliminate obsolete retained context. These findings provide initial evidence that user-driven revision of conversational history can improve interaction quality and help maintain a more current representation of user intent.

Due to the challenge of uncovering biologically meaningful spatial tissue patterns from standard H\&E-stained whole-slide images (WSIs) without relying on multiplexed staining or fixed-scale modeling, a unified framework is proposed for spatial biomarker discovery that integrates cell classification, adaptive multi-scale microenvironment construction, and colocalization pattern analysis. Cell-level predictions assign discrete, semantically meaningful types that serve as the basis for microenvironment modeling, where physical adjacency initializes local ecological features and a combination of spatial competition-based seed selection with homogeneity-constrained recursive region growing allows microenvironments to expand from locally pure regions in a data-driven manner, capturing heterogeneity across scales without predefined spatial ranges. Microenvironment-level cell composition features are then used to construct a colocalization feature space, explicitly modeling spatial relationships among cell types, and differential biomarkers are identified via a distributional comparison framework that systematically detects group-specific colocalization patterns. Experiments demonstrate that this framework reliably discovers discriminative and biologically interpretable spatial biomarkers from H\&E images alone, exhibiting robustness in tissues with complex structures and heterogeneous scales, and offering a flexible, extensible paradigm for spatial phenotypic biomarker discovery in standard histopathology.

Computational RNA design methods routinely evaluate designed sequences by refolding them with the same structure-prediction model used during optimization, measuring agreement with the design target. While scalable, this practice carries a fundamental risk: when optimization and evaluation share the same underlying model, high scores can reflect model-specific idiosyncrasies rather than genuine structural quality. To characterize the severity and mechanism of this problem, we audited nine RNA design methods spanning four algorithmic paradigms, evaluating approximately 11,000 sequences against predictors from two independent model families: physics-based thermodynamic models and machine-learning models, alongside five tertiary-structure predictors and large-scale SHAPE chemical-mapping data. We find that 78.1% of designs produced by single-objective optimization pass one predictor yet fail another, while ensemble-based methods reduce this disagreement 30-fold. A controlled experiment identifies optimization objective breadth, not search strategy, as the primary driver of this fragility. Cross-predictor disagreement carries a calibrated experimental signal: lower disagreement predicts higher SHAPE accuracy across 40,000 sequences, yet remains null-to-anti-predictive for biological function, establishing a clear scope boundary. We release **ACCORD** (**A**cross-oracle **C**alibration for **CO**mputational **R**NA **D**esign), a benchmarking workflow that reports per-predictor scores, experimentally calibrated uncertainty tiers, and explicit warnings for invalid use cases, providing the community with a principled foundation for RNA design evaluation.

Differentiable physics solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented. Integration effort, computational cost, gradient accuracy, and numerical conditioning vary widely across solvers and are discoverable only by trial and error. We introduce Mosaic, an extensible benchmarking framework for differentiable PDE solvers that standardizes access to solver gradients. Each solver is packaged as a containerized component (Tesseract) exposing a uniform gradient API regardless of language or automatic differentiation (AD) strategy, enabling researchers to evaluate, compare, and build on non-trivial physical solvers. Our evaluation of 14 solvers across fluid dynamics, structural mechanics, and heat transfer demonstrates that the benchmark surfaces practically relevant differences: order-of-magnitude variation in computational cost and Jacobian conditioning, alongside structural incompatibilities that eliminate solvers from realistic tasks entirely. Despite this variation, all solvers that produce gradients converge to similar optima, indicating that the practical barriers are memory limits, numerical stability, and setup compatibility rather than gradient accuracy alone. Mosaic is open-source and available at https://anonymous.4open.science/r/mosaic-bench.

Bioassay activity prediction is often data-limited because drug-discovery datasets rely on time-consuming and expensive wet-lab experiments for data generation and evaluation. This challenge has inspired recent research into molecular foundation models (MFMs), which aim to encode general-purpose chemical knowledge into molecular representations that generalize well in data-constrained scenarios. This paper presents Monroe, a new MFM with several innovations over the existing state of the art: increased scale allowing pre-training on over 80 million molecules from the PM6 quantum chemistry dataset; improved graph representation of stereochemistry; improved training losses including conformer denoising and embedding decorrelation; improved multi-task learning; and the use of a prior-data-fitted model (TabPFN) for downstream in-context prediction. Our evaluations use a principled pairwise comparison framework that measures statistically significant performance differences. Across established Polaris benchmarks, Monroe matches or exceeds existing MFMs, while on activity cliff benchmarks, designed to assess utility for molecular discovery, it achieves significant improvements over prior methods. Finally, ablation and transfer experiments show that PFN-based downstream predictors also substantially improve two leading existing models, MiniMol and CheMeleon, yielding new state-of-the-art variants we call MiniMol_PFN and Chemeleon_PFN, suggesting that our downstream adaptation strategy generalizes beyond Monroe. Full source code is at https://anonymous.4open.science/r/monroe-0E0D, and will be openly released.

Existing inverse physics methods recover physical parameters from multi-view videos, where geometric constraints across views resolve scale and 3D structure. In monocular settings, however, such constraints are absent, leading to severe scale ambiguity, inaccurate geometry, and weak coupling between appearance optimization and physical simulation. We propose MonoPhysics, a framework for monocular inverse physics estimation of deformable objects using differentiable MPM simulation and 3D Gaussian Splatting, which jointly optimizes geometry, appearance, and physical parameters from a single camera view. We address these challenges through three visual-physical bridges: global scale alignment, physics-aware geometry refinement, and a differentiable position map, which together enable accurate optimization from image-space losses alone. We evaluate on Vid2Sim and our new dataset of elastic and plastic objects, showing that MonoPhysics outperforms existing baselines in monocular settings and achieves performance comparable to multi-view baselines using only a single camera.

Untargeted metabolomics produces massive numbers of tandem mass spectra, yet most spectra remain difficult to assign to molecular structures because each spectrum is only a partial, instrument-dependent observation of the underlying molecule. We study MS/MS annotation as modality-incomplete molecular--spectral inference: molecules, spectra, and fingerprints provide complementary views of the same chemical entity, but fully paired molecule--spectrum data are limited and many training examples contain only molecular or only spectral information. We introduce MolSpecFlow, a mask-conditioned heterogeneous flow framework that represents these modalities as coupled components of a shared molecular--spectral state. Availability masks encode which components exist in each example, and observation masks specify which components are conditioned on or generated, instantiating de novo annotation, molecular retrieval, and spectrum simulation within one backbone. MolSpecFlow uses a shared Mol-Spec Transformer, hybrid discrete--continuous flow dynamics, and expected mass/formula regularization over soft molecular token distributions. Experiments show consistent gains from modality-incomplete pretraining, multi-interface reuse, and external de novo transfer.

The standard mechanistic interpretation of transformer factual recall attributes storage to deep MLP modules and routing to attention. We study how module roles change when the fact distribution carries subject, relation, or answer-collision structure rather than independent facts. Which module performs the recall depends on the correlation axis and on the model's capacity load. Probes and matched-counterfactual patching disagree systematically on every motif: probes credit the deepest MLP while patching credits the first attention module. We show that probes and patching measure structurally different quantities---cumulative linear decodability versus irreplaceable causal contribution---which under correlated fact distributions need not coincide. A parameter-counting argument singles out subject-axis collision as the unique compression that the attention-routing pathway can exploit cheaply, predicting an order-of-magnitude crossover for that pathway class that we observe empirically: the layer-2 probe gap collapses sharply for subject collisions, and only subject-axis specialization survives the capacity-tight regime. Edge-level path patching uncovers a three-step chain (Attn -> MLP1 -> MLP2) whose dominance tracks the predicted threshold, with a causal-scrubbing test corroborating that the chain is causally relevant on every motif and sharpest in the subject regime. A dense joint sweep shows that subject and answer compressions compete rather than amplify, with the dominant axis set by the stronger compression. On natural CounterFact strata across four frozen pretrained LMs (Pythia-1.4B/2.8B, LLaMA-3.2-1B-Inst/3.1-8B), edge-level path patching reproduces the synthetic ranking: the answer-collision stratum is the most localized on every model. A two-hop extension shows the binding-locality structure carries to compositional facts.

Harmful fine-tuning can rapidly compromise safety alignment in Large Language Models, underscoring the vulnerability of deployed models to post-release modification. While prior work motivates model immunization by inducing ill-conditioned curvature to slow harmful optimization, this approach is not scalable due to the high computational cost of Hessian estimation. We refine this paradigm by extending the theoretical framework to prioritize plateau regions alongside curvature. We further introduce an immunization algorithm based on efficient Hessian estimation and bounds on the extremal singular values of the Hessian. We demonstrate the proposed immunization framework in three applications: (i) Fine-tuning-as-a-service settings where benign user data may be mixed with poisoned harmful data, (ii) open-weight settings where an adversary can fine-tune on harmful-only data with varied training dynamics, and (iii) robust unlearning, where immunized models better resist relearning attacks after unlearning. Extensive experiments confirm that our approach achieves robust defense against adversarial fine-tuning while maintaining general utility and downstream trainability.

Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these algorithms, with two main contributions. First, we derive minimax-optimal convergence for RF regression, showing that, under mild regularity conditions on tree growth, the eigenvalue decay of the induced kernel operator governs the statistical rate. Second, we exploit this spectral viewpoint to develop compression schemes for tree ensembles. For RFs, leading eigenfunctions of the kernel operator capture the dominant predictive directions; for GBMs, leading singular vectors of the smoother matrix play an analogous role. Learning nonlinear maps for these spectral representations yields distilled models that are orders of magnitude smaller than the originals while maintaining competitive predictive performance. Our methods compare favorably to state of the art algorithms for forest pruning and rule extraction, with applications to resource constrained computing.