NeurIPS 2026 Papers

We present a neuro-inspired framework for embodied planning and control. Building on three principles that enable fast and highly effective goal-directed behavior in the mammalian brain — paired forward/inverse internal models, open-loop multi-step motor commands, and sequential organization of action — our *Inverter* framework combines analytic and trained components, the latter trained end-to-end through *Inverse Learning* (IL), a paradigm we formalize and delineate from supervised, reinforcement, and imitation learning. IL bridges RL-style amortization, which runs in a single forward pass but emits one action at a time, and optimal-control-style sequence reasoning, which plans whole trajectories but with iterative test-time computation. Single Inverters or hierarchical n=2 Inverter stacks match or improve over comparable offline-RL and diffusion-planner baselines on all 3 `maze2d-v1` and 6 `antmaze-v2` D4RL variants by an average of $+24.2\%$ (range $-1.9\%$ to $+78.2\%$), at one-to-two orders of magnitude less inference compute. As one mechanism behind this effectiveness, we show that Inverters can learn control policies closer to the analytic optimum than the data-generating policy itself. We also identify a failure mode of IL: forward-model hacking under narrow training-data coverage, which we mitigate by using *random* training data with broader coverage. As an application example, a Pulse Inverter synthesizes arbitrary single-qubit quantum gates with fidelity matching the standard iterative numerical baseline (GRAPE), at more than $1000\times$ lower per-gate compute. We propose deeper hierarchical, probabilistic, and latent extensions of the Inverter framework as a differentiable world-interface, especially for latency- and compute-critical embodied AI.

Local field potentials (LFPs) are population-level neural signals central to brain-computer interfaces and systems neuroscience, yet unlike spike-based population codes, their dynamics lack a principled geometric description that connects spectral structure to latent state-space geometry. Here we establish, analytically and empirically, that the lag-embedded dynamics of LFP signals lie on a low-dimensional K-torus, where K equals the number of sustained oscillatory modes present in the signal. Modeling LFPs as bounded autoregressive processes, we show that each oscillatory component contributes an independent circular degree of freedom, while aperiodic 1/f structure and noise contribute only geometric thickness around the manifold without altering its topology. To apply this theory to real nonstationary recordings, we introduce DeepLagField, a physics-informed network that jointly estimates time-varying AR structure and effective model order, with formal guarantees that local toroidal geometry is preserved despite drifting oscillatory dynamics.We validate the predicted toroidal geometry using persistent homology across primate visual cortex LFP, rodent hippocampal LFP, and mouse cortical EEG recordings, confirming the expected Betti number signatures across species and recording modalities. Critically, we demonstrate that this geometric structure is not merely descriptive but carries behaviorally relevant information inaccessible to standard spectral summaries — as evidenced by torus parameters derived purely from manifold geometry outperforming multi-band spectral features for sleep-state decoding without any hand-crafted frequency design. This proof of concept points toward broad downstream utility wherever oscillatory field signals are recorded, from neural decoding and brain-state monitoring to clinical biomarker development. These results reframe neural oscillations not as isolated spectral features but as coordinate directions of a low-dimensional delay manifold, opening a geometry-first approach to neural signal analysis that is simultaneously theoretically grounded, empirically validated across species, and predictive of behaviorally relevant brain states.

Demand-side flexibility, i.e., forecasting, shifting, and curtailing residential energy loads, depends on thermal models trusted across millions of heterogeneous buildings. Existing tools force a hard tradeoff: high-fidelity physics simulators such as EnergyPlus are accurate but sequential and require per-building calibration, while purely data-driven sequence models scale but abandon the physical structure that makes their predictions trustworthy. We introduce NeuralBES (Building Energy Simulation), a differentiable emulator that resolves this tradeoff by parameterizing a resistance--capacitance (RC) based thermal model with a shared neural encoder: static building metadata such as floor area, vintage, and HVAC type is mapped to physically bounded capacitances, conductances, and equipment coefficients, which become the coefficients of a scalar linear recurrence solved via a log-space parallel scan, and a predictor--corrector loop closes the thermostat--temperature nonlinearity while preserving full-horizon gradient flow. Trained on the ResStock dataset across three climate zones, NeuralBES handles heterogeneous building archetypes, vintages, and climate zones within a single trained encoder, while black-box baselines produce statistically plausible but physically inconsistent trajectories. On the annual full-year rollout, NeuralBES is the only data-conditioned model that is simultaneously physics-valid and accurate to within 4 MAPE points of the strongest raw-error baseline, while operating at roughly an order of magnitude fewer parameters than the transformer and recurrent baselines; among physics-valid baselines at parameter parity it more than halves the MAPE of the grey-box RC alternative.

Understanding how neural activity encodes behavioral and sensory variables is a key challenge in systems neuroscience. This requires models that go beyond predicting activity from labels and instead support source-conditioned counterfactual editing: given a recorded source response, we should be able to edit one behavioral or stimulus variable and predict how neural activity would change while preserving other observed factors and source-specific variability not explained by the labels. Here, we introduce **Neural-DISCO**, a disentangled representation learning framework for counterfactual modeling of neural activity. Neural-DISCO partitions the latent space into label-specific components, each associated with an observed behavioral or stimulus variable, together with a residual latent that captures variability not supplied through observed labels. Across simulated and real neural recording datasets, we show that this structure enables selective manipulation of individual labels to generate counterfactual neural responses while preserving the remaining content of the original activity. Further, to gain insight into how behavioral and stimulus variables are encoded at single-neuron resolution, we pair this disentangled framework with feature attribution methods that identify which neurons are most important for each label. We find that disentanglement enhances the recovery of known functional cell roles in both synthetic and real data. Together, these results support Neural-DISCO as a framework for controlled counterfactual modeling of neural activity and provide a practical interface for probing how neural populations encode behavior and sensory information.

In the context of computational materials science, analytical homogenization theories, such as Strong Contrast Expansion (SCE), develop PDE-induced power expansions that map microstructural statistics of material samples to their macroscopic effective properties. However, low-order truncations of such expansions for computational feasibility often trade off prediction accuracy, especially when high-order correlations, finite-resolution effects, or strong contrast regimes become important. While learned residual surrogates, e.g., neural operators, can alleviate this tradeoff, they do not ensure reliable inference of structure-property sensitivities, hampering downstream material design tasks. To this end, we propose Neural-Corrected Operator (NCO) that learns a correction directly to the analytical PDE kernel to compensate for the low-order truncation, and show that NCO intrinsically bounds sensitivity inferences. We evaluate NCO on structure-property prediction and inverse-design tasks for heterogeneous bi-phase composite materials governed by linear second-order PDEs. NCO improves the accuracy of low-order SCE models for structure-property prediction and produces sensitivities that facilitate more effective microstructure design optimization than output-level residual baselines.

Understanding how cortical activity represents natural whole-body behavior in primates remains challenging. Limited by diversity of movements and inaccessible of large-scale neural feature programming whole-body kinematics, previous motor decoding studies rely on constrained tasks and limited limb movements. Here, we present a neural-behavioral recording and modeling framework for freely moving monkeys, combining epidural cortical signals from distributed sensorimotor areas with synchronized multi-view motion capture through a data custom collection platform. We reconstruct whole-body monkey kinematics and learn a compact motion prior using an autoregressive encoder-decoder model. Conditioned on epidural signals, the model decodes more accurate and realistic full-body movements without explicit physical constraints. Our results provides a novel proof-of-concept approach for decoding natural whole-body movements in primates using large-scale intracranial neural activity.

Modern Transformer design and compression both reduce to allocating capacity under a budget. The standard scalars for these decisions, #Params and #FLOPs, capture size and compute but not architectural structure—two architectures with identical parameter budgets but different depth-width, head, or FFN allocations receive identical scores yet behave differently. We propose Neural Spectral Capacity (NSC), a closed-form scalar grounded in the singular-value spectrum of each weight matrix. Under standard random initialization, the Marchenko–Pastur law renders NSC computable from the architectural specification alone, with no model instantiation, data, or gradients. Its layer-wise additive structure admits NSC-DP, an exact dynamic-programming solver returning the architecture globally maximizing NSC under resource constraints in seconds on a CPU—a guarantee that black-box search over existing training-free proxies cannot provide. Empirically, NSC outperforms #Params, #FLOPs, and representative training-free proxies in ranking across seven Transformer and CNN families (on FlexiBERT, τ=0.505 on pairs differing in #Params by <10%, where #Params collapses to 0.082); NSC-DP discovers a Transformer-XL architecture on WikiText-103 that beats the human-designed baseline in 2 seconds; and prunes LLaMA-7B to the best 5.7B model across eight commonsense reasoning tasks without any calibration data, ∼5900× faster than the strongest training-free proxy baseline.

Generating clinical reports that summarize abnormal patterns, diagnostic findings, and clinical interpretations from long-term EEG recordings remains labor-intensive. We present CELM, the first clinical EEG-to-Language foundation model capable of summarizing long-duration, variable-length EEG recordings and performing end-to-end clinical report generation at multiple scales. CELM integrates pretrained EEG foundation models with language models to enable scalable multimodal learning. We curate a large-scale clinical EEG dataset containing 9,922 reports paired with approximately 11,000 hours of EEG recordings from 9,048 patients to train CELM, and release the benchmark with an automated report-structuring pipeline to facilitate future research. Experimental results show that CELM consistently outperforms existing methods across all evaluation settings. Importantly, we further conduct human evaluation with clinical experts, demonstrating that CELM generates reports that are more clinically coherent, diagnostically reliable, and better aligned with expert interpretation. We release our model and benchmark construction pipeline at https://anonymous.4open.science/r/CELM-3AF4.

LiDAR sensors are critical for autonomous driving perception, yet remain vulnerable to spoofing attacks. Jamming attacks inject high-frequency laser pulses that completely blind LiDAR sensors by overwhelming authentic returns with malicious signals. We discover that while point clouds become randomized, the underlying full-waveform data retains distinguishable signatures between attack and legitimate signals. In this work, we propose PULSAR-Net, capable of reconstructing authentic point clouds under jamming attacks by leveraging previously underutilized intermediate full-waveform representations and simultaneous laser sensing in modern LiDAR systems. PULSAR-Net adopts a novel U-Net architecture with axial spatial attention mechanisms specifically designed to identify attack-induced signals from authentic object returns in the full-waveform representation. To address the lack of full-waveform representations in existing LiDAR datasets under jamming attacks, we introduce a physics-aware dataset generation pipeline that synthesizes realistic full-waveform representations under jamming attacks. Despite being trained exclusively on synthetic data, PULSAR-Net achieves reconstruction rates of 92\% and 73\% for vehicles obscured by jamming attacks in real-world static and driving scenarios, respectively.

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically requires large input–output paired datasets generated by costly high-fidelity PDE solvers. Unsupervised operator learning frameworks alleviate data dependency but remain hindered by computational bottlenecks. To address this, we propose Neural Variational Quantum Linear Solver (NVQLS), the first hybrid quantum–classical operator learning framework leveraging the Legendre-Galerkin weak formulation. We critically resolve the sign ambiguity in VQLS energy minimization, preventing erroneous solution representations. Additionally, we introduce a neural embedding, a novel encoding scheme to map varying forcings and PDE coefficients into parameterized quantum circuit representations. These structural innovations provide theoretical computational complexity advantages under efficient state preparation schemes, while achieving superior accuracy compared to a representative classical baseline. Validations on 1D and 2D parametric PDEs under diverse boundary conditions demonstrate NVQLS's capability to simultaneously process varying inputs, offering a scalable unsupervised approach to quantum-enhanced operator learning.

Functional data such as time series, trajectories, and fields are increasingly central in machine learning and are naturally modeled in infinite-dimensional Hilbert spaces. We study Semi-dual Neural Optimal Transport (SNOT) for learning transport maps between probability measures on separable Hilbert spaces. A critical challenge in this setting is the spurious solution problem: a neural map can globally optimize the SNOT objective while failing to recover an optimal transport map. We show that this failure arises from non-regular source measures, which make the inner minimization in the semi-dual objective non-identifiable. We prove that regular source measures, defined via Gaussian null sets, restore inner-minimizer uniqueness and recover the Monge map. For singular sources, we introduce Gaussian smoothing and establish a necessary and sufficient kernel condition for smoothing to restore regularity. We further prove plan-level consistency: as smoothing vanishes, every Wasserstein accumulation point of the induced optimal plans solves the original Kantorovich problem. Experiments on synthetic singular transports and real-world unpaired time-series imputation benchmarks validate the theory, achieving the best performance on several benchmarks and competitive performance on the remaining ones.

In this paper, we tackle the critical failure modes of Physics-Informed Neural Networks (PINNs), such as spectral bias, which lead to poor convergence on complex PDEs. We identify two key shortcomings in existing curriculum learning methods for PINNs: unreliable knowledge transfer between stages and a reliance on manual, ad-hoc curriculum design. To overcome these limitations, we present Neural Operator-based Curriculum Learning (NOCL), a unified framework that leverages Neural Tangent Kernel (NTK) theory to automate curriculum generation and employs neural operators to enable robust, dynamic knowledge transfer across curriculum stages. By dynamically training neural operators and filtering data for PINN initialization, our approach ensures scalable and effective learning across progressively difficult tasks. Experiments verify that NOCL leads to marked gains in convergence and generalization relative to prior methods, resulting in substantially better performance on test suite.

Neural scaling laws predict how language model performance improves with increased training inputs. While aggregate metrics like validation loss can follow smooth power-law curves, individual downstream tasks exhibit diverse scaling behaviors: some improve monotonically, others plateau, and some even degrade with scale. We argue that predicting downstream performance from validation loss suffers from two limitations: averaging token-level losses obscures signal, and no simple parametric family can capture the full spectrum of scaling behaviors. To address this, we propose Neural Neural Scaling Laws (NeuNeu), a neural network that frames scaling law prediction as time-series extrapolation. NeuNeu combines temporal context from observed accuracy trajectories with token-level validation losses, learning to predict future performance without the limitations inherent in assuming a specific functional form. Trained entirely on open-source model checkpoints from HuggingFace, NeuNeu achieves 1.99\% mean absolute error in predicting model accuracy on 66 downstream tasks---a 44\% reduction compared to logistic scaling laws (3.56\% MAE). Furthermore, NeuNeu generalizes zero-shot to unseen model families, architectures, parameter counts, and downstream tasks. Our work suggests that predicting downstream scaling directly from data outperforms parametric alternatives.

We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions when there are no restrictions on the weights, we show that dense neural networks do not possess this universality. Our argument is based on a model compression approach, combining the weak regularity lemma with an interpretation of feedforward networks as message passing graph neural networks. We consider ReLU neural networks subject to natural constraints on weights and input and output dimensions, which model a notion of dense connectivity. Within this setting, we demonstrate the existence of Lipschitz continuous functions that cannot be approximated by such networks. This highlights intrinsic limitations of neural networks with dense layers and motivates the use of sparse connectivity as a necessary ingredient for achieving true universality.

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.

Chain-of-thought reasoning has driven striking advances in language model capability, yet every reasoning step grows the KV cache, creating a bottleneck to scaling this paradigm further. Current approaches manage these constraints on the model’s behalf using hand-designed criteria. A more scalable approach would let end-to-end learning subsume this design choice entirely, following a broader pattern in deep learning. After all, if a model can learn to reason, why can't it learn to forget? We introduce \textbf{Neural Garbage Collection (NGC)}, in which a language model learns to forget while learning to reason, trained \emph{end-to-end} from outcome-based task reward alone. As the model reasons, it periodically pauses, decides which KV cache entries to evict, and continues to reason conditioned on the remaining cache. By treating tokens in a chain-of-thought and cache eviction decisions as discrete actions sampled from the language model, we can use reinforcement learning to jointly optimize how the model reasons and how it manages its own memory: what the model evicts shapes what it remembers, what it remembers shapes its reasoning, and the correctness of that reasoning determines its reward. Crucially, the model learns this behavior entirely from a \emph{single learning signal} — the outcome-based task reward — without supervised fine-tuning or proxy objectives. On Countdown, AMC, and AIME tasks, NGC maintains strong accuracy relative to the full-cache upper bound at a 2–3x compression in peak KV cache size and substantially outperforms eviction baselines. Our results are a first step towards a broader vision where end-to-end optimization drives both capability and efficiency in language models.

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.

Fractional differential equations (FDEs) excel at modelling systems with long-range memory, while stochastic differential equations (SDEs) capture inherent randomness. Existing neural differential equation models address either memory (Neural FDEs) or stochasticity (Neural SDEs), but a unified framework combining both with a learnable scalar memory exponent and an efficient adjoint remains absent. We introduce the Neural Fractional Stochastic Differential Equation (Neural FSDE), which learns continuous-time dynamics with both memory and randomness from data via a Caputo FSDE with neural drift, neural diffusion, and a learnable fractional order. To enable scalable training, we derive a discrete adjoint method that computes gradients with respect to the initial state, the drift and diffusion network parameters, and the fractional order, with memory cost independent of the autograd graph depth. We validate the framework on two real-world domains. On the stochastic-fractional COVID-19 model of Bonyah et al., the NeuralFSDE provides the first end-to-end real-data calibration under a rolling-origin forecasting protocol, recovering a fractional order less than 1. On S&P~500 index option pricing, we recast rough Bergomi, rough Heston, Neural SDE, and NeuralFSDE as Caputo-FSDE special cases under a single calibration pipeline; the NeuralFSDE achieves the lowest implied-volatility error across schedules and instruments, with a matched-architecture comparison against the memoryless Neural SDE, isolating the contribution of fractional memory. Code is available at https://anonymous.4open.science/r/NeuralFSDE.

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.