NeurIPS 2026 Papers

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.

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.

Statistical modeling and inference for temporal networks are increasingly important across modern applications, yet remain challenging in the sparse regime with evolving network sizes and temporal dependence. We propose a tractable model that captures these key features in a unified framework. Under this model, we establish geometric ergodicity and characterize the asymptotic behavior of cycle counts. These counts provide informative low-order summaries of temporal network dynamics. Moreover, we develop method-of-moments estimators based on cycle counts. We prove identifiability and uniqueness of the parameter estimates, and establish the strong consistency and asymptotic normality. To support uncertainty quantification, we further propose a simulation-based plug-in estimator of the asymptotic variance. Extensive simulations and a real data example demonstrate that our methods are accurate and effective for sparse, size-varying temporal networks.

Animals integrate information across sensory modalities to guide exploration, suggesting that they maintain internal estimates of where actions are expected to reduce uncertainty. However, how such action-conditioned information maps are learned from multimodal sensory experience remains unclear, as previous studies have been largely confined to unimodal sensing frameworks. We introduce a multimodal predictive-coding framework for learning uncertainty-reduction maps from visual and mechanosensory observations in hawkmoth flower interaction tasks. A variational generative model trained on simulated environments recovers modality-specific information landscapes over the action space, capturing how visual patterns, surface geometry, and mechanosensory cues shape the value of exploratory actions. These learned maps account for several features of hawkmoth behavior, including angled offsets during flower tracking, probing along visual patterns, and geometry-dependent changes in exploration. Applying the model to behavioral data from flower tracking and nectary search, we find that natural trajectories tend to occupy regions of high uncertainty reduction in these learned maps. Building on these observations, we develop an uncertainty-gated lexicographic algorithm that switches between information gathering and reward exploitation based on perceptual uncertainty. Across downstream reward-learning tasks, this policy learns faster, is more sample-efficient, and generalizes better to unseen environmental conditions than exploitation-only policies, $\epsilon$-greedy exploration, and non-lexicographic baselines. Together, these results suggest that multimodal generative perception models can learn actionable information landscapes that explain biological sensing and support exploration in embodied decision-making.

Representation learning for single-cell RNA-seq has been evaluated by the identities representations capture — cell types, lineages, perturbations — rather than how faithfully they model the distribution of cell states on the gene expression manifold. As a result, density estimation, rare-state detection, perturbation scoring, and gene-level attribution are bolted onto frozen embeddings as separate models, disconnected from the geometry of the data. We argue that the density model should be the primary object and that representation quality follows from it. Building on LeJEPA, whose SIGReg objective enforces a provably optimal isotropic Gaussian latent, we introduce LeCellModel, which exploits this Gaussian latent to recover data density on the gene expression manifold via the encoder's Jacobian log-volume (JEPA-SCORE). Across several datasets, LeCellModel outperforms established methods on scIB benchmark for representation quality. Furthermore, we show that LeCellModel enables estimation of rare expression states using JEPA-SCORE as a typicality measure – applying it to a controlled cytokine panel, where it identifies stimulated cells across minority fractions and tracks pathway-response magnitude. We introduce gene-level interpretability of density estimates — to our knowledge, the first method for analyzing JEPA-SCORE in feature space. Leveraging this framework, LeCellModel recapitulates the known association of a profibrotic macrophage program with idiopathic pulmonary fibrosis, and discovers a novel CD177$^{+}$ activated regulatory T cell subpopulation previously described only in tumor contexts. Both findings emerge directly from the geometry of the learned embedding, without relying on supervised annotations.

Multimodal large language models (MLLMs) have heterogeneous strengths across OCR, chart understanding, spatial reasoning, visual question answering, cost, and latency. As a result, effective MLLM routing requires more than estimating query difficulty: a router must match the multimodal requirements of the current image-question input with the capabilities of each candidate model. We propose \textsc{LatentRouter}, a router that formulates MLLM routing as counterfactual multimodal utility prediction. Given an image-question query, \textsc{LatentRouter} extracts learned multimodal routing capsules, represents each candidate MLLM with a model capability token, and performs latent communication between these states to estimate how each model would perform if selected. A distributional outcome head predicts model-specific counterfactual quality, and a bounded capsule correction refines close decisions while limiting the influence of noisy routing signals. The resulting utility-based policy supports both performance-oriented and performance-cost routing, and can handle changing candidate pools through shared per-model scoring with availability masking. Experiments on MMR-Bench and VL-RouterBench show that \textsc{LatentRouter} outperforms strong fixed-model, feature-level, and learned-router baselines. Additional analyses show that the gains are strongest on multimodal task groups where model choice depends on visual, layout-sensitive, or reasoning-oriented requirements, and that latent communication is the main contributor to the improvement. The code is available at: https://anonymous.4open.science/r/LatentRouter-8718.

The emergence of large language models (LMs) as versatile problem-solving systems marks a paradigm shift comparable to the advent of digital computers. Traditional computer science provides theoretical foundations for understanding computational processes through complexity theory, algorithms, and formal methods, this position paper argues that language models require their own distinct theoretical framework, termed as Computer Science of Language Models (**CSLM**). We identify seven fundamental differences between traditional computing and language model: 1) the generating-solving-verifying triad versus the solving-verifying dichotomy, 2) token-based rather than operation-based computation, 3) probabilistic reliability with hallucinations rather than deterministic correctness, 4) native multimodal understanding beyond pixel-level processing, 5) general-purpose capabilities versus problem-specific algorithms, 6) essential two-stage training-inference processes, and 7) inherent knowledge. We argue these differences necessitate new theoretical frameworks, complexity measures, and evaluation methodologies. Then, we define the **token complexity** as the core concept in CSLM and discuss connections to existing research in scaling laws, memory systems, tool use, and fine-tuning, while identifying critical open questions about LM-complete problems, reliability bounds, emergence phenomena, and multimodal complexity. Drawing parallels to complexity theory's 50-year development, we present a 5-year research roadmap (2026-2030) to build the mature CSLM. CSLM promises to transform LM development from empirical scaling to principled engineering grounded in rigorous theory and strengthen our understanding about both the problems, LMs and their relationships.

Advances in large language models (LLMs) have created new opportunities in data science, but their deployment is often limited by the challenge of finding relevant data in large data lakes. Existing methods struggle with this: both single- and multi-agent systems are quickly overwhelmed by large, heterogeneous files, and master–slave multi-agent systems rely on a rigid central controller that requires precise knowledge of each sub-agent’s capabilities, which is not possible in large-scale settings where the main agent lacks full observability over sub-agents’ knowledge and competencies. We propose a novel multi-agent paradigm inspired by the blackboard architecture for traditional AI models. In our framework, a central agent posts requests to a shared blackboard, and autonomous subordinate agents--either responsible for a partition of the data lake or retrieval from web--volunteer to respond based on their capabilities. This design improves scalability and flexibility by removing the need for a central coordinator to know each agent’s expertise or internal knowledge. We evaluate the approach on three benchmarks that require data discovery: KramaBench and modified versions of DSBench and DA-Code. Results show that the blackboard architecture substantially outperforms strong baselines, achieving 13%–57% relative improvements in end-to-end success and up to a 9% relative gain in data discovery F1 over the best baseline.

Fast linear algebra in deep learning usually comes with a choice: fixed geometry and exact computation, as in the Fourier transform, or adaptive geometry paid for by dense parameters, random features, or low-rank surrogates. To move beyond this trade-off, we introduce LAPLEX, a class of exact, trainable (phased) Laplace-kernel operators. A LAPLEX layer is a typically full-rank dense matrix, implicitly defined by learnable coordinate anchors, with FFT-like scaling. Consequently, it supports trainable matrix--vector operations at vector dimensions up to $10^9$ on modern GPUs. As a neural layer, it yields compact projections and classification heads interpretable as soft, trainable routing models. The same primitive also serves as an efficient Gram operator, enabling high-dimensional covariance models on flattened images of dimension $3 \cdot 10^6$ that preserve visible spatial structure without imposing convolutional bias. These applications reflect a single principle: dense geometry can be learned without storing a dense matrix, which enables data-adaptive global interactions in regimes where ordinary dense layers are out of reach. In this sense, LAPLEX separates expressivity from storage cost: it behaves like a dense trainable matrix, but is represented and applied through a small structured set of parameters.

We introduce a novel Longitudinal Focused Attention Meditation Electroencephalography (L-FAME) dataset and an accompanying benchmark, designed to foster research into the neural effects of various meditation practices and the evolution of these effects over a six-week training period. The dataset contains EEG recordings and psychological assessments from 74 healthy college participants, collected at two distinct time points: pre-intervention and post-intervention. Participants were randomly assigned to one of three distinct meditation groups: two mantra-based techniques (SA-TA-NA-MA and Hare Krishna) and one Breath Focus practice. Leveraging this unique longitudinal and comparative dataset, we propose a benchmark suite comprising three distinct classification tasks: (1) cognitive state decoding to distinguish between resting and meditation states, (2) fine-grained classification of the specific meditation techniques, and (3) cross-session adaptation to evaluate model generalization across the longitudinal time gap. We provide comprehensive baseline results for these tasks utilizing a range of classical machine learning algorithms and deep learning architectures. The complete dataset, preprocessing pipelines, and benchmark evaluation code will be publicly released, offering a valuable resource and a standardized framework for the development and comparison of new analytical methods in computational meditation research and EEG-based machine learning.

Reconstructing the connectome of the brain is a central goal of modern neuroscience, but the required electron microscopy (EM) imaging is extremely time-consuming. EM image super-resolution (SR) accelerates this acquisition for downstream neuron segmentation, yet existing methods do not adequately couple SR with segmentation for EM: SR lacks segmentation guidance, and segmentation cannot adapt to super-resolved features. In this work, we propose a joint SR and segmentation framework specifically designed for EM images. In the super-resolution part, we introduce segmentation as an auxiliary task via a shared encoder with task-specific decoders to provide a semantic prior, improving reconstruction fidelity. In the segmentation part, we introduce a lightweight partial diffusion model that initializes denoising from a partially noised SR embedding, producing a structural prior that closely approximates real HR features and enhances segmentation accuracy on super-resolved EM images. Extensive experiments across multiple datasets and degradation settings demonstrate the superior performance of our framework.

Inferring the latent processes that generate observable neural activity is a central challenge in neuroscience, with direct implications for brain-machine interfaces and neural engineering. Existing inverse approaches typically summarize the recording into low-dimensional features or learn black-box latents that lack a direct biophysical interpretation. A promising alternative is to fit a differentiable biophysical simulator end-to-end against the full extracellular signal, using direct and scalable gradient optimization. In practice, however, recovering a per-neuron input via backpropagation through neuronal dynamics is difficult because the loss landscape is nearly flat in the subthreshold regime and jumps sharply at spike threshold, leaving gradient descent without a useful signal. We observe that per-neuron spike times, routinely available from spike sorting, expose discrete millisecond-scale anchors at which the loss does carry information. Gradients from these anchors flow back in time through the differentiable simulator and shape the subthreshold drive that produced each spike. Building on this, we present a fully differentiable pipeline coupling biophysical membrane dynamics to a volume conductor model of the multi-electrode array. For each neuron in a recorded population, the method jointly recovers a time-varying latent input current and a probe-relative position consistent with both the extracellular trace and the observed spike times. No explicit likelihood or posterior estimation is required, and every fitted latent corresponds to a named biophysical quantity. On paired patch-clamp / Neuropixels SPE-1 data, the model localizes the patched neuron to within $40 \mu m$ on average across cells, while reproducing observed spatio-temporal activity patterns under realistic noise. These results position scalable differentiable biophysical simulation as a practical route to mechanistic, gradient-based analysis of high-density neural recordings.

Rapid advancements in large language models (LLMs) have sparked the question whether these models possess some form of consciousness. To tackle this challenge, Butlin et al. introduced a list of indicators for consciousness in artificial systems based on neuroscientific theories. In this work, we evaluate a key indicator from this list, called HOT-3, which tests for agency guided by a general belief-formation and action selection system that updates beliefs based on meta-cognitive monitoring. We view beliefs as representations in the model's latent space that emerge in response to a given input, and introduce a metric to quantify their dominance during generation. Analyzing the dynamics between competing beliefs across models and tasks reveals three key findings: (1) external inputs systematically modulate internal belief formation, (2) belief formation causally drives the model's action selection, and (3) models can monitor and report their own belief states and adjust behavior in response to internal conflict. Together, these results provide empirical support for the existence of belief-guided agency and meta-cognitive monitoring in LLMs. More broadly, our work lays methodological groundwork for investigating the emergence of agency, beliefs, and meta-cognition in LLMs.

Illusory pattern perception is a well-documented human cognitive tendency to infer meaningful relationships in data that is actually random. Such a tendency, often described as “connecting the dots” where none exist, can result in systematic reasoning errors. This paper investigates whether Large Language Models (LLMs) exhibit such perceptual tendencies, which can lead to systematic errors in downstream applications. To our knowledge, this work presents the first systematic study of illusory pattern perception in LLMs, adapting classic psychological paradigms to three tasks with direct empirical comparison to human behaviors. We find that LLMs frequently exhibit stronger illusory pattern perception than humans. In particular, models tend to over-associate frequent positive attributes with majority groups or large organizations, and show increased tendencies to construct causal narratives from ambiguous events. To uncover the mechanism behind these behaviors, we develop a feature interpretability framework based on Sparse Autoencoders (SAEs) to analyze internal representations. Our results reveal that holistic frequency perception and analytic cognitive orientation are linked to the emergence of illusory perceptions. These findings highlight a previously underexplored cognitive-like illusion that may affect the reliability of LLM reasoning. Code available at [Anonymous Github](https://anonymous.4open.science/r/illusory-8E27/).

Stereo depth estimation of human faces is a prerequisite for various computer vision applications, yet existing stereo benchmarks target outdoor, driving, or large object reconstruction scenarios and lack the anatomical precision and evaluation framework these applications require. We introduce HumanStereo, the first large-scale synthetic stereo dataset dedicated to human faces, comprising 417k stereo pairs from 128 photorealistic avatars across 109 unique stereo configurations and four indoor environments, with dense ground-truth annotations including depth maps, surface normals, segmentation masks, and facial landmarks. We argue that standard evaluation metrics such as $\delta_1$ and RMSE are ill-suited for facial depth estimation, and propose two complementary metrics: task-grounded absolute inlier-ratio (IR) and Landmark 3D Distance Error (L3DE) for metric anatomical accuracy. We benchmark five representative stereo methods: geometrical matchers, RAFT-Stereo, IGEV++, MASt3R, and FoundationStereo. A downstream evaluation on real optometric data for inter-pupillary distance (IPD) measurement, a parameter required in all eyeglass prescription, shows that even the best-performing model remains an order of magnitude above the sub-millimeter accuracy required for clinical deployment.

Efficient exploration in high-dimensional decision spaces remains a central challenge for decision-making systems. Humans, in contrast, can navigate large decision spaces with remarkable efficiency. Recent behavioral studies suggest that humans actively reduce dimensionality when facing large decision spaces: they probe candidate feature dimensions, rapidly identify reward-relevant ones, and use them to restrict the effective decision space. Inspired by this mechanism, we propose TDGE (Task-Dimension-Guided Exploration), a human-inspired exploration algorithm, and evaluate its performance in recommendation tasks with contextual bandit backbones. TDGE follows a top-down exploration strategy: it first selects task-relevant feature dimensions, then identifies informative features within those dimensions, and finally recommends concrete items based on the selected features. Experiments on three real-world recommendation datasets, MovieLens-20M, Last.fm, and Amazon, show that TDGE substantially improves exploration efficiency and cold-start adaptation over baseline algorithms. We further provide visualizations of recommendation trajectories showing that TDGE exhibits a human-like dimension-guided exploration process during learning. Code is available at https://anonymous.4open.science/r/Human-inspired-Task-Dimension-Guided-Exploration-for-Efficient-Learning-984B.

Large language models generate one token at a time, yet their responses show remarkably consistent length structure: step-by-step solutions converge in predictable token counts, retrievals stop after a few sentences, retractions extend responses by measurable amounts. We ask whether the model carries an internal estimate of how much response remains. Training minimal-capacity linear probes on frozen hidden states of three open-weight 7-8B models across seven completion-style datasets, we find three converging pieces of evidence. First, total response length is linearly decodable from the prompt's last hidden state alone, before any output is emitted. Second, probe directions trained on natural-language datasets transfer broadly, including to controlled synthetic completions never seen in training, outperforming a statistical baseline; the converse direction generally fails, and this asymmetry is itself informative. Third, on curated high-loss completions, the probe's per-position estimate shifts upward at the moment the model retracts and restarts a partial solution, a directional behavior no position-only predictor can reproduce (we note that this is qualitative, not aggregate). We frame this as approximate estimation of remaining generation length, distinct from exact-counting impossibility results for transformers, and interpret it as evidence that LLMs maintain a plan-like internal representation of output length (decodable, not necessarily used causally). Code: https://anonymous.4open.science/r/llm-output-length

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to the steep complexity overhead of propagating messages through combinatorial structures. To overcome this limitation, we propose HOPSE (Higher-Order Positional and Structural Encoder), a framework \emph{free of message passing layers} that uses Hasse graph decompositions to derive efficient and expressive encodings over \emph{arbitrary higher-order domains}. Notably, HOPSE scales linearly with the size of combinatorial representations while preserving the expressive power and permutation equivariance of the HOMP approaches. Experiments on molecular and topological benchmarks show that it matches or surpasses state-of-the-art performance while consistently achieving speedups over HOMP-based models, opening a new path for scalable TDL. The code is available at https://anonymous.4open.science/r/TopoBench-BF89.

Large language model (LLM) routing aims to exploit the specialized strengths of different LLMs for diverse tasks. However, existing approaches typically focus only on selecting LLM architectures, treating candidate models as static black boxes while overlooking parameter adaptation, which can substantially affect task performance. In this paper, we introduce HAPS, a hierarchical LLM routing framework that jointly searches over model architectures and parameters. Specifically, a high-level router selects among candidate LLM architectures, while a low-level router generates input-conditioned LoRA parameters for the selected architecture. To couple these two decisions, we design a shared parameter generation mechanism that enables cross-level knowledge transfer between architecture routing and parameter adaptation. We further optimize the whole framework with a reward-augmented training objective. Extensive experiments show that HAPS consistently outperforms strong routing baselines. We further conduct broad ablations and analyses on parameter sharing, architectural choices, scalability, and efficiency, providing additional evidence for the effectiveness and practicality of the proposed framework. We have released our code at https://anonymous.4open.science/r/HAPS_private-68CB.