NeurIPS 2026 Papers

Intracortical brain–computer interfaces (iBCIs) can restore movement and communication, but neural drift can degrade performance across recording sessions. Because recalibration adds user burden, there is a need for decoders that adapt from minimal calibration data. Although session-specific input layers are a common way to handle cross-session drift, they can underperform in the extreme few-shot regime because the shared decoder is trained downstream of well-estimated session-specific layers, but must rely at deployment on a new-session layer fit from only a few calibration trials. To avoid this dependence, we propose a two-stage approach: first, train a single GRU decoder on pooled held-in sessions without session-specific input layers, encouraging the backbone to handle cross-session variability directly; second, freeze this backbone and meta-learn a lightweight alignment layer for rapid calibration. We evaluate on FALCON H2, an official human handwriting iBCI benchmark designed for few-shot cross-session decoding, and achieve 7.41\% word error rate using only three released calibration sentences per held-out session. These results suggest that, under extreme calibration limits, learning a transferable backbone before adding session-specific adaptation can be more effective than jointly training flexible session-specific layers.

World models enable agents to predict future dynamics conditioned on actions, making the choice of latent state representation central to planning and control. Existing latents are often either learned directly from pixels with limited semantic structure or inherited from frozen visual foundation models with excessive task-irrelevant detail, yielding state spaces that are poorly matched to downstream planning and control. This is especially challenging in reward-free offline settings, where the model must learn from fixed trajectories without reward supervision or online interaction. To address this, we propose TC-WM, a framework for turning foundation-model embeddings into compact, task-sufficient world representations. The key design is to treat the pretrained embedding space as a semantic scaffold rather than as the final state space: TC-WM linearly projects high-dimensional visual embeddings into a compact latent, aligns a designated subspace with the agent’s physical state via contrastive learning, and reconstructs embeddings to preserve useful visual structure. This combines the generality of foundation features with the controllability of task-centric dynamics. Theoretically, we show that TC-WM suffices to identify the task-centric latent factors up to a simple transformation. Empirically, TC-WM enables test-time planning across diverse environments, e.g., Robomimic and D4RL, achieving better world modeling quality and more precise control compared to state-of-the-art world model approaches. Webpage: https://tc-wm.github.io/

Survival analysis provides statistical methods to model the time until an event occurs. Reporting delays arise when event times are not observed at their occurrence but are only revealed upon reporting. This issue is particularly critical for timely risk evaluation when the observation window is short due to administrative censoring. In this study, we incorporate right-censored reporting delays by jointly modeling parametric hazards for the event and reporting processes. We then construct a consistent estimator for the model parameters and develop a Monte Carlo expectation-maximization algorithm to compute it. To address the challenges posed by administrative censoring, we leverage these findings and propose a transfer-learning procedure. Experimental results demonstrate that our method improves the accuracy of timely risk evaluation under administrative censoring.

State-of-the-art machine learning weather prediction systems achieve strong upper-air forecast skill but degrade at longer lead times, with mesoscale structures progressively vanishing and ensemble forecasts becoming under-dispersive. While these limitations are often attributed to the training objective, we find that message-passing processors significantly contribute to this degradation. Repeated neighborhood aggregation at each autoregressive step acts as a smoothing operator that, over rollout steps, suppresses high-frequency information in latent space. This effect is particularly limiting in regional weather prediction, where fine-scale structures are already partially unresolved, further eroding mesoscale variability and hindering long-horizon forecasting. We propose GraphMet, a graph-based weather model motivated by Koopman theory that replaces stacked message-passing layers with a single linear Koopman operator step. GraphMet learns linear evolution in a spectral latent basis while preserving the encoder, decoder, and multi-scale icosahedral mesh structure. A two-term spectral objective jointly learns a stable Koopman basis and preserves latent geometry, enabling efficient long-range propagation without repeated nonlinear aggregation. Empirically, GraphMet reduces the 15-day activity and improves regional RMSE by 11-14% at 5km resolution, and enables efficient probabilistic forecasting with lower inference cost than state-of-the-art methods. Our code available at : https://anonymous.4open.science/w/GraphMet-54ED/.

Naturalistic language encoding models based on large language model features can predict cortical responses well, but their learned representations remain difficult to interpret. Three challenges are central: semantic selectivity is fundamentally non-identifiable in high-dimensional correlated feature spaces, cortical organization remains implicit in voxelwise weight maps, and cross-subject structure is usually addressed only after model fitting. We introduce a multisubject coupled sparse autoencoder that jointly reconstructs language-model features and predicts subject-specific brain responses, learning a sparse basis of semantic-cortical atoms that makes semantic structure, cortical organization, and cross-subject correspondence explicit within a single model. In naturalistic story-listening fMRI, the model retains 88\% of matched dense-feature ridge brain prediction performance using 50 atoms and $k{=}5$ active atoms per TR. Relative to matched two-stage baselines, joint training yields the strongest overall tradeoff between prediction and interpretability. The learned atoms are semantically coherent and interpretable, recover more reproducible cross-subject brain maps than standard post hoc encoding-model analyses, align with large-scale cortical structure from Yeo~7 and Neurosynth, and transfer better than ridge to held-out subjects in the low-data regime. This framework provides a more interpretable basis for cognitive neuroscience analyses of semantic-to-brain encoding by linking semantic features to corresponding cortical response patterns across subjects.

Open-vocabulary dense perception requires grounding language-specified concepts in local regions for recognition, localization, and segmentation beyond closed category sets. CLIP learns image-level vision-language alignment, whereas dense prediction requires spatially precise and semantically reliable local features. Although recent dense CLIP adaptation methods reduce this gap through region-level semantic transfer and spatial correlation guidance, maintaining stable local semantics under contextual variation remains challenging. Specifically, the global contextual modeling in CLIP may introduce undesirable dependencies into local features. Changes in background, scale, viewpoint, or scene layout may cause identical object regions to yield inconsistent dense representations, leading to unstable correspondences and semantic drift. Moreover, spatial correlation guidance from visual foundation models captures visual relatedness between patches, but not whether coherent regions correspond to the queried textual concept, leaving concept-level dense alignment under-constrained. To address these issues, we introduce Semantic Spatial Consistency Learning $\textbf{(SSCL)}$, an adaptation method with two complementary objectives: 1) Context-Invariant Spatiotemporal Consistency (CISC) enforces semantic consistency for the same anchor region under varying contexts to mitigate context-induced feature drift; 2) Structure-Guided Semantic Refinement (SGSR) leverages spatial affinities from a frozen visual foundation model to refine CLIP text-patch responses, producing text-conditioned dense supervision with improved spatial coherence and concept-level alignment. Experiments on video instance segmentation, region classification, semantic segmentation, and object detection show consistent gains over the baseline methods, demonstrating the effectiveness and generalization capability of the proposed SSCL. Our code and models will be made publicly available.

Continual learning under adversarial perturbations remains underexplored, despite its importance in security-critical deployments where attack patterns evolve over time. Existing continual adversarial defense methods mainly rely on replay or prediction-space regularization, but often fail to preserve robust representations across sequentially arriving attack types. In this paper, we study continual adversarial defense, where a model receives a sequence of tasks induced by different white-box attacks and must acquire robustness to new attacks without forgetting previously learned defenses. We address this challenging learning scenario by proposing the Learning Robust Representation Framework (LRRF), a representation-centric framework that improves robustness through hierarchical alignment at three complementary levels. First, we introduce the Dynamic Representation Matching (DRM) mechanism that aligns clean and adversarial feature distributions within each task to reduce the clean-robustness trade-off. Second, a Cross-Task Invariant Representation (CTIR) mechanism is proposed to regularize the current representation network against an accumulated network from previous tasks, encouraging attack-invariant features to persist over time. Third, a Knowledge Consolidation Optimization (KCO) mechanism is proposed to match class-consistent clean and adversarial features using replayed samples, which further stabilizes category structure across tasks. The empirical results show that the proposed approach achieves state-of-the-art performance.

Reinforcement learning from verifiable rewards (RLVR) produces strong reasoning models, yet these models can fail catastrophically when the conditioning context is fallible (e.g., corrupted chain-of-thought, misleading partial solutions, or mild input perturbations), because standard RLVR optimizes final-answer correctness only under clean conditioning. We introduce GASP (Guided Adversarial Self-Play), a robustification method that explicitly trains error detection and repair capabilities using only outcome verification. Without human labels or external teachers, GASP instantiates an adversarial self-play game within a single model: a polluter learns to induce failure through locally coherent corruptions, while an agent learns to diagnose and recover under the same corrupted conditioning. To address the scarcity of successful recoveries early in training, we propose in-distribution repair guidance, an auxiliary imitation objective on self-generated repairs that increases recovery probability while preserving previously acquired capabilities. Across four open-weight models (1.5B–8B), GASP converts strong-but-brittle reasoners into substantially more robust ones that better withstand misleading and perturbed context, while often improving clean accuracy. Further analysis shows that adversarial corruptions create an effective curriculum, and that in-distribution guidance enables rapid recovery learning with minimal representational drift.

Learning in neural systems arises from synaptic changes that reshape the representations underlying behavior. While low-rank recurrent neural networks (RNNs) have emerged as a powerful framework for linking connectivity to function, a theoretical understanding of their learning process remains elusive. Here, we extend the low-rank framework from activity to learning by deriving gradient-descent dynamics directly in a reduced overlap space. We formulate a closed-form, low-dimensional system of ODEs that governs learning in this space, exact for linear RNNs and asymptotically exact for nonlinear RNNs in the large-$N$ Gaussian limit. Central to our analysis is a distinction between two classes of overlaps: _loss-visible_ overlaps, which fully determine network activity, output, and loss, and _loss-invisible_ overlaps, which do not affect function but are required to describe learning. We illustrate the consequences of this decomposition through two phenomena. First, we show that learning can serve as a perturbation that exposes differences in connectivity between functionally equivalent networks. Second, we show that loss-invisible overlaps can act as memory variables that encode training history, and characterize the conditions under which this occurs. Finally, we present several testable predictions for biological learning experiments derived from our theory.

Animals generate complex behaviors by flexibly recombining a finite set of motor primitives, but existing behavior segmentation methods oversimplify this process by imposing discrete syllables under restrictive generative assumptions. Here, we introduce Motif-based Continuous Dynamics (MCD), a framework that models behavior as a continuous, compositional process driven by reusable motor motifs. MCD leverages reinforcement learning (RL) to (1) discover interpretable motif representations via transition-based representation learning, and (2) model behavior as a time-varying mixture of these motifs through motif-based policies. This formulation avoids restrictive dynamics assumptions while capturing continuity, compositionality, and long-term dependencies in behavior. Across simulated gridworld tasks, maze navigation, and animal behavior datasets, MCD identifies reusable motifs and interprets the trajectories with them. These results provide a generative account of behavior as combinations of fundamental motifs, offering a flexible and interpretable framework for studying natural behavior.

Deep neural networks are highly vulnerable to bit corruption in stored weights, whether from naturally occurring memory faults or deliberate fault-injection attacks. Existing defenses remain fundamentally limited: fault-tolerance methods degrade under cumulative corruption and remain vulnerable to strong white-box attacks, while ECC-based recovery methods are often tied to specific precisions or architectures and expose concentrated vulnerable surfaces. We propose a simple training-based recovery framework that endows model weights with recoverable structure through block-wise zero-sum constraints enforced by differentiable projection. The resulting method incurs no parameter-space overhead and generalizes naturally across architectures and numerical precisions. We further develop adaptive adversarial bit-flip attacks tailored to recovery-based defenses, covering both our method and prior ECC-based approaches. Across diverse architectures, precisions, datasets, and threat models, our method consistently delivers strong robustness and recoverability while preserving clean performance.

Neural network verification is key to certifying robustness in safety-critical systems. Sound verifiers commit to abstract domains that propagate soundly through the network's operations, paying for that commitment with looseness at scale and applicability largely confined to piecewise-linear architectures. Probabilistic verifiers relax soundness, but they too commit to a fixed family of shapes for the network's reachable outputs. When the network's true output geometry differs from the chosen shape, the verifier over-approximates the reach-set and fails to certify networks that are in fact safe. We propose instead to learn the reach-set geometry from the network's behavior. A flow-matching model trained on input-output samples and calibrated by conformal prediction yields a probabilistic reach set whose shape adapts to the true shape of the reach-set rather than to an a priori choice. The resulting set has no closed-form description, so we reframe the specification check as a rare-event estimation problem on the learned distribution, restricted to the calibration's coverage region, and solve it with bounded adaptive multilevel splitting. The pipeline produces a probabilistic safety certificate combining the conformal coverage with a rare-event upper bound. Our pipeline performs comparably to sound verifiers on a subset of VNN-COMP 2025 benchmarks where sound verification is tractable and matches or exceeds fixed-shape probabilistic baselines on most benchmarks in the same suite. On a synthetic family of growing-depth networks, it scales sub-exponentially where sound verifiers time out or abstain.

The Normalized Transformer, or nGPT (Loshchilov et al., 2025) achieves impressive training speedups and does not require weight decay or learning rate warmup. However, despite having hyperparameters that explicitly scale with model size, we observe that nGPT does not exhibit learning rate transfer across model dimension and token horizon. To rectify this, we combine numerical experiments with a principled use of alignment exponents (Everett et al., 2024) to revisit and modify the $\mu$P approach to yperparameter transfer (Yang and Hu, 2021). The result is a novel nGPT parameterization we call $\nu$GPT. Through extensive empirical validation, we find $\nu$GPT exhibits learning rate transfer across width, depth, and token horizon.

We study learning rate (LR) scaling for hybrid architectures combining Transformer and State-Space Model (SSM) blocks, a class adopted by several recent production language models. In particular, we focus on the gap between the theoretical scaling rules derived for SSMs under zero-order-hold (ZOH) discretization at infinite width with proportional state size, and the field-standard practical implementations using simplified-ZOH Mamba at fixed state size. Surprisingly, in this practical regime hybrid architectures achieve a near-zero LR transfer gap across widths 256-2048 and depths 4-32 at sub-billion-parameter scale using only the original $\mu$P prescription, even though SSM operations fall outside its Tensor Programs representability conditions and every parameterization we test fails the standard coordinate-check diagnostic of $\mu$P correctness. We attribute this to a two-condition decomposition of LR transfer in hybrid architectures: a global update-to-weight invariance, enforced by $\mu$P's initialization and LR scaling; and a local per-component balance, provided by AdamW's $g/\sqrt{v}$ per-parameter normalization. Our observations show that the optimal LR is invariant to width up to $8\times$, as well as to depth, sequence length, batch size, and Transformer-to-SSM ratio, and transfers to Nemotron-H, a production hybrid outside our custom architecture set. We hope these findings fill the gap between theoretical scaling rules and practical hybrid implementations, and stimulate further research toward bridging it.

Low-Rank Adaptation (LoRA) is the prevailing approach for efficient large language model (LLM) fine-tuning. Building on this paradigm, recent studies have proposed alternative initialization strategies and architectural modifications, reporting substantial improvements over vanilla LoRA. However, these gains are often demonstrated under fixed or narrowly tuned hyperparameter settings, despite the known sensitivity of neural networks to training configurations. In this work, we systematically re-evaluate nine representative LoRA variants alongside vanilla LoRA through extensive hyperparameter searches. Across tasks spanning mathematical reasoning, commonsense reasoning, code generation, and instruction following at diverse model scales, we find that different LoRA methods favor distinct learning rate ranges. Crucially, once learning rates are properly tuned, all methods achieve similar peak performance (within 1-2\%), with only subtle rank-dependent behaviors. These results suggest that vanilla LoRA remains a competitive baseline and that improvements reported under a single training configuration may not reflect consistent methodological advantages. Finally, a second-order analysis attributes the differing optimal learning rate ranges to variations in the largest Hessian eigenvalue, aligning with classical learning theories.

Stochastic Gradient Descent (SGD) is a workhorse algorithm for continuous optimization. It is a folklore belief among deep learning practitioners that learning rate decay in SGD substantially improves performance. However, it has remained unclear whether learning rate decay offers an asymptotic advantage for \emph{global} nonconvex optimization. We answer this question in the affirmative by demonstrating a natural class of nonconvex functions for which we prove that SGD with learning rate decay requires \emph{exponentially fewer} gradient queries for global optimization than SGD with any fixed learning rate. To the best of our knowledge, this is the first exponential advantage that has been demonstrated for learning rate decay. The class of functions we consider includes many popular benchmark nonconvex functions. Our results provide a robust explanatory theory for the empirically observed benefits of learning rate decay. Our technical results are built upon a new discretization analysis of SGD with decaying step size, that allows us to establish a clean correspondence with continuous-time annealing of Langevin diffusions. We then show that this annealed diffusion performs the non-logconcave sampling task associated to the optimization problem in polynomial time, via a novel application of weak Poincar\'{e} inequalities.

Graph Neural Networks (GNNs) operate under the implicit assumption that the underlying data manifold is Riemannian, where the metric tensor is strictly positive-definite. While effective for homophilic graphs, this inductive bias creates a fundamental geometric mismatch for heterophilic graphs, where edges often signify dissimilarity or structural repulsion. In this work, we propose a paradigm shift from learning on fixed manifolds to learning the manifold itself. We postulate that heterophilic graphs are naturally embedded in pseudo Riemannian manifolds endowed with an indefinite metric, allowing for negative squared distances to model repulsive interactions. To formalize this, we introduce the Graph Signature Index, a spectral invariant that diagnoses the geometric nature of a graph. This index enables our proposed Pseudo-Riemannian Attention Network (PRAT) to dynamically learn an indefinite metric tensor, effectively capturing both attractive and repulsive interactions. By unifying these opposing forces within a single framework, PRAT demonstrates how a subtle shift in the metric signature yields substantial performance gains on heterophilic benchmarks. Our analysis reveals that PRAT’s learned geometry emergently aligns with the spectral signature of the graph, validating our geometric hypothesis.

In many safety-critical applications, control of uncertain dynamical systems relies on observers that estimate states and external disturbances. Neural network observers can improve estimation accuracy, but certifying their Lyapunov stability via Linear Matrix Inequality (LMI) constraints leads to large-scale semidefinite programs (SDPs) that are difficult to solve for large networks. To overcome this scalability bottleneck, we propose a novel two-stage training framework for provably stable neural network observers. Our approach decouples the optimization into a point-guided Lyapunov pre-training phase, which rapidly achieves high estimation accuracy and local stability over sampled states, followed by an LMI fine-tuning phase that efficiently satisfies a strict global Lyapunov stability certificate. We provide formal theoretical guarantees for local stability radii and probabilistic coverage over a prescribed compact error-state domain under specified regularity and sampling assumptions. Experiments on nonlinear control benchmarks and X-29 aircraft ablations show that our LMI-certified neural network observers train significantly faster than direct LMI-based methods and generalize robustly across diverse systems, achieving improved tracking accuracy over a range of observer baselines. The code is available at https://anonymous.4open.science/r/LearningNeuralNetworkObserver-2E1E.

In many modern applications of reinforcement learning (RL), the natural reward for a task of interest is inherently sparse: a reward of 0 is given everywhere except when the task is completed, when a reward of 1 is given. Training a policy to maximize such a sparse reward requires solving a challenging credit assignment problem, leading to slow or ineffective RL improvement. We propose a simple approach to transform a sparse outcome reward into a dense process reward. Our approach relies on training a discriminator to distinguish between previous successful and unsuccessful trajectories, and using this discriminator to incentivize the RL-learned policy to match the state-action visitations of successful trajectories, while avoiding those of unsuccessful trajectories. By incentivizing the policy to match the visitations over all states, not just those that correspond to task success, this reward provides dense feedback on whether progress is being made towards task completion, and, we show, provably achieves this without changing the optimal policy. Focusing on finetuning of robotic control policies, we demonstrate that our approach leads to significantly faster RL finetuning performance on both simulated and real-world manipulation tasks, as compared to simply maximizing the sparse outcome reward.