NeurIPS 2026 Papers

Decoding cognitive functions and brain diseases from functional magnetic resonance imaging (fMRI) is a foundational problem in neuroscience advanced by recent deep learning across task and resting-state (rs) settings. Existing region-level decoders capture spatial structure through region-of-interest (ROI)-aware graph or Transformer architectures, but apply a uniform temporal operator across all regions. Consequently, they do not explicitly model how cortical regions integrate information over heterogeneous timescales. We propose CoRTeX, a region-resolved recurrent architecture for fMRI in which each cortical region carries its own learnable parameters and evolves on its own learned timescale. At its core, per-region differentiable temporal integration windows allow each ROI to learn how far back in time to integrate information through a soft mask over a private buffer. Cross-region information is restricted to a single identity-aware attention channel, additionally biased by a co-activation-driven memory whose learning and forgetting rates are themselves region-specific. Experiments on stimulus classification using task-fMRI (NSD) and on two disease diagnosis tasks using rs-fMRI (ABIDE, COBRE) demonstrate that CoRTeX achieves competitive performance with strong baselines while enabling region-level analyses that are not well-defined for models with exchangeable units: the learned per-region timescales exhibit interpretable spatial organization, and class-specific regional attribution aligns with category-selective cortex. Code is available at: https://anonymous.4open.science/r/CoRTeX-F.

In tool-integrated reinforcement learning with verifiable rewards (RLVR), sequence-level verifier signals are issued for trajectories whose outcomes are determined by a sparse subset of tokens—tool names, argument keys, and argument values. Standard RLVR assigns the same advantage to every token in a rollout, diluting credit at precisely the positions that matter. We propose **Correctable Fork Tokens (CFT)**, which decomposes selective credit assignment into two subproblems: *where* to update, and *how much* to update at those positions. To this end, CFT introduces a training-only answer-conditioned branch sharing parameters with the student policy. The key insight is that conditioning on the ground-truth answer concentrates the model's distribution at decision-fork positions, providing hindsight localization without additional parameter capacity or imitation targets. Critically, this benefit requires accurate answer information: a larger-capacity teacher without the answer fails to replicate these gains, confirming that privileged answer information—not teacher capacity—is the active ingredient. CFT uses this entropy reduction ($IG_t$) to identify correctable fork positions, then rescales token-level credit at those positions while preserving the verifier advantage as the sole signal for update direction. On BFCL v3/v4, CFT improves multi-turn accuracy by **4.2/6.5** pp and overall accuracy by **3.1/2.2** pp over GRPO; it further surpasses On-policy distillation—which employs a larger Expert Model as teacher—by **3.6/6.7** pp on multi-turn, confirming that answer-conditioned fork localization rather than teacher capacity drives the improvement. On Tau3, the average score improves by **8.3** pp. We additionally present a three-level structured verifier for tool-call settings; ablations confirm that finer-grained verifier feedback and selective token credit are complementary. Our reproducible implementation is available at [https://anonymous.4open.science/r/CFT](https://anonymous.4open.science/r/CFT).

Biological recurrent circuits can reuse a common substrate by changing its operating regime rather than replacing the circuit itself. This principle is difficult to isolate in fully adaptive neural models, where recurrence, controllers, readouts, and internal representations can all absorb task structure. As a result, successful multi-context behavior does not reveal which route made the computation possible. We introduce Constrained Modulatory Reservoirs (CMR), a fixed-substrate framework for studying such reconfiguration with the main bypasses removed. The primary dynamics and low-rank perturbation basis are fixed, and the readout is denied direct access to the cue, forcing input-dependent adaptation to act through a limited set of recurrent connectivity changes. In transient-cue channel-selection tasks, this restriction makes a capacity transition visible. Low-loss behavior appears only when the available perturbation directions are sufficient, the selected change is retained across the cue-to-signal gap, and the primary dynamics express it during the response window. Controls show that this effect is not explained by low-dimensional cue representation alone. Allowing the substrate to learn hides the bottleneck, while activity- and gain-level alternatives fail to reproduce the same regime. CMR therefore reframes flexible recurrent computation as a question of where adaptive influence is allowed to enter a fixed dynamical system, making capacity, memory, and expression experimentally separable.

Determinantal point processes allow efficient sampling of diverse subsets of data. However, (exact) sampling under additional constraints is often computationally intractable under complexity-theoretic assumptions. We take an algebraic approach to designing novel algorithms that allow exact constrained sampling with theoretical efficiency guarantees. Our algorithms apply to a general class of point processes based on Bombieri inner products of polynomials, which we call Bombieri $k$-point processes. This perspective recovers known algorithms for constrained $k$-DPPs and extends them to a broader class of simple $k$-point processes. As applications, we obtain exact samplers for matching-, path-, subgraph-, and budget-constrained processes, as well as distributions combining diversity with clustering. While common complexity-theoretic assumptions rule out polynomial-time algorithms in many of these settings, our algorithms are efficient with respect to the relaxed notion of fixed-parameter tractability when the sample size $k$ is kept bounded.

Uncertainty quantification (UQ) for large language models (LLMs) aims to provide reliable measures of predictive confidence, yet current methods often fail to remain stable under simple, meaning-preserving perturbations. We identify an important source of instability: semantically equivalent paraphrases of the same input can induce substantial variability in predictive confidence, even for methods with formal guarantees such as conformal prediction. To address this issue, we propose a paraphrase-aware UQ framework that explicitly enforces invariance to semantic rewordings. Instead of relying on a single input, our approach constructs uncertainty scores by aggregating predictions across a set of its paraphrases, using a lightweight proxy model to produce calibrated and comparable outputs. This aggregation yields uncertainty estimates that are both more stable and more informative, while remaining compatible with conformal calibration techniques to retain coverage guarantees. Across multiple UQ benchmarks and model families, our method achieves nominal coverage with smaller and more stable prediction sets under paraphrase perturbations. Code is available at https://anonymous.4open.science/r/PA_Score-8C0D.

Ranking models define probability distributions over rankings and are fundamental in applications such as preference learning and decision-making. Without structural assumptions, these models are intractable due to their factorial complexity. Although independence assumptions are key to reducing complexity and enabling interpretability, standard notions of conditional independence do not directly apply to rankings because they are subject to mutual exclusivity constraints. We introduce \emph{relative rank models}, a probabilistic framework based on structured coarsenings of the ranking space that relax these constraints while preserving relative order information. This representation enables a well-defined notion of conditional independence for rankings and allows rankings to be modeled using Bayesian networks. As a result, relative rank models support tractable learning, probabilistic inference, and interpretable representations. We further show that two prominent ranking models based on independence assumptions tailored to rankings arise as special cases, providing a unifying framework for independence in ranking models.

Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction–abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.

We study the computational relationship between replicability (Impagliazzo et al. [STOC `22], Ghazi et al. [NeurIPS `21]) and other stability notions. Specifically, we focus on replicable PAC learning and its connections to differential privacy (Dwork et al. [TCC 2006]) and to the statistical query (SQ) model (Kearns [JACM `98]). Statistically, it was known that differentially private learning and replicable learning are equivalent and strictly more powerful than SQ-learning. Yet, computationally, all previously known efficient (i.e., polynomial-time) replicable learning algorithms were confined to SQ-learnable tasks or restricted distributions, in contrast to differentially private learning. Our main contribution is the first computationally efficient replicable algorithm for realizable learning of parities over arbitrary distributions, a task that is known to be hard in the SQ-model, but possible under differential privacy. This result provides the first evidence that efficient replicable learning over general distributions strictly extends efficient SQ-learning, and is closer in power to efficient differentially private learning, despite computational separations between replicability and privacy. Additionally, we leverage our parity learner to prove that, assuming $RP \neq NP$, converting replicability to pure differential privacy requires a strict loss in sample complexity. Our main building block is a new, efficient and replicable algorithm that, given a set of vectors, outputs a subspace of their linear span that covers most of them.

Educational LLM systems generate assessment questions on demand and depend on the assumption that a model can be controlled to a specified cognitive level. We test the assumption. CogBench is a benchmark for cognitive-level control in LLM question generation, grounded in the Revised Bloom's Taxonomy. Its central design choice is a two-mode protocol that separates cognition from imitation: in standard mode the model is asked to generate at level L_t; in adversarial mode it must do so while restricted to verbs from a different level L_v, demonstrating the requested level structurally rather than lexically. CogBench spans 8 subjects, 6 Bloom levels, and 120 CC-BY OpenStax passages, with ~17,000 graded generations across 13 models (six frontier closed APIs and seven open-source local models), each scored by a deliberately dual evaluator: a 28-rule constraint checker, and the Cognitive Complexity Score (CCS), a fine-tuned BERT classifier at 82.0% exact accuracy that outperforms a four-model LLM-as-judge panel by 7.8 points. We find that (1) adversarial vocabulary collapses strict adherence by 24-56 pp across the 12 models above floor, with the strongest standard performer suffering the largest collapse; (2) Remember-level adherence under adversarial vocabulary is essentially 0% in all 13 models, suggesting Remember lives almost entirely in its surface verbs; (3) the two evaluators rank models differently, including on the leader, a divergence we argue benchmarks should report rather than hide; and (4) the most adversarially robust models on CCS are not frontier flagships but gpt-4o-mini (46.8%) and llama3.1-8b (45.6%). What current LLMs offer educational systems looks like cognitive control and is largely verb-level imitation that resembles it. We release the dataset (CC-BY 4.0; Croissant 1.0 with Responsible-AI fields), the evaluation harness, and a 13-model leaderboard at https://huggingface.co/spaces/cogbench-anonymous/cogbench-leaderboard.

We study path--flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving path network and a flow network using the same alignment loss: the flow learns to match the path velocity, and the path learns to align its velocity to the current flow. Although every fixed learned path defines a valid flow-matching objective, the alignment loss alone is not a reliable criterion for path learning. We identify *path overfitting*, a failure mode in which the alignment loss decreases while sample quality worsens. We trace this failure to low-entropy bottlenecks in the induced probability path, where the learned interpolant routes samples through overly concentrated intermediate marginals. Motivated by this diagnosis, we introduce a stochastic path regularizer that hides part of the source information from the path network while preserving exact endpoints. The resulting regularized objective controls entropy collapse and makes joint path--flow training effective. On ImageNet-$256\times256$ with SiT backbones, our method consistently improves FID across model scales, extends to model-guidance training, and leaves the inference-time architecture and sampler unchanged. Code is available at https://anonymous.4open.science/r/traj_opt_paper-4D80.

Clustering is a fundamental task in unsupervised learning, serving as a core tool for data mining and exploratory data analysis. Classical $k$-clustering objectives such as $k$-median and $k$-means formalize this task, but typically assume access to exact pairwise distances. This assumption is increasingly unrealistic in modern applications where distances are estimated through proxy embedding models, learned similarity functions, human feedback, or other low-cost procedures that may be noisy. We study $k$-clustering in an unknown metric space where the algorithm has access only to a weak distance oracle: for each pair of objects, the oracle returns the true distance with probability of $1/2+\varepsilon$ , where $\varepsilon$ is a constant, and otherwise may return an arbitrary corrupted value. We present randomized algorithms that, given a metric space with $n$ vertices and a parameter $k$, use only weak distance-oracle queries to compute a set of representative centers together with a mapping from every input object to one of these centers, such that the total mapping cost is within a constant factor of the optimal $k$-clustering cost. Our first algorithm returns $O(k\cdot\mathsf{polylog}(n))$ centers using $O(n\cdot k\cdot \mathsf{polylog}(n))$ weak-oracle queries and runs in quasi-polynomial time. We also give a polynomial-time algorithm that returns $O(k^2\cdot\mathsf{polylog}(n))$ centers using $O(n\cdot k\cdot \mathsf{polylog}(n))$ weak-oracle queries. Preliminary experiments for $k$-means clustering show that our approach remains close to the optimum under substantial oracle noise, while noise-oblivious baselines degrade sharply.

Large perturbation models require training data encompassing chemical, cellular, and assay diversity. Current transcriptomic resources for small-molecule modeling, however, are fragmented across technologies, metadata conventions, controls, doses, and preprocessing pipelines. We introduce Chem-PerturBridge, a harmonized multi-dataset resource comprising over 37k compounds, 136 cellular contexts, and 1.25M transcriptomic samples across eight assay types, with standardized identifiers, metadata, and replicate-aware condition-level effects. We use the resource to evaluate matched-condition agreement across datasets and replicate agreement within datasets. Matched same-compound conditions generally show weak agreement in fine-grained logFC rankings and magnitudes across most dataset pairs, often falling below same-context different-compound baselines. In contrast, logFC direction agreement is substantially more stable and usually exceeds these baselines. We further evaluate Chem-PerturBridge as a pretraining resource for compound representation learning. Under a compound-held-out OP3 evaluation split, embeddings pretrained on Chem-PerturBridge improve over L1000-only embeddings, Morgan fingerprints, and the descriptor-free OP3 baseline across metrics. Chem-PerturBridge therefore supports both diagnostic evaluation of cross-dataset signature agreement and model-oriented reuse of heterogeneous perturbation transcriptomic data.

Humans develop perception through a bottom-up hierarchy: from basic primitives and Gestalt principles to high-level semantics. Current Multimodal Large Language Models (MLLMs) are trained directly on complex downstream tasks. Does it guarantee their performance on these foundational visual capabilities? To systematically investigate this gap, we introduce VisFactor, a benchmark that digitizes 20 vision-centric subtests from FRCT, a well-established cognitive psychology assessment spanning four domains of human visual cognition. Furthermore, we design algorithms to automatically construct and validate unlimited test cases with controllable difficulty. Using VisFactor, we evaluate 39 frontier MLLMs, including both proprietary (e.g., GPT, Gemini) and open-source (e.g., LLaMA, Qwen) models. The best model achieves a score of only 55.9%. Analysis reveals good internal consistency (Cronbach's alpha = 0.94) and construct validity (compared to existing vision benchmarks). Models consistently fail on tasks such as mental rotation, spatial relation inference, and figure–ground discrimination, regardless of model size or prompting strategy. These findings suggest that performance improvements on existing general benchmarks might represent castles in the air instead of a genuine mastery of human-like visual cognition.

Characterizing the properties of neuronal cell types is central to understanding brain function. Yet, biophysically realistic neuron models remain difficult to scale to large populations while preserving the richness of cellular dynamics and within-cell-type variability. We present a cell-type-specific neural-operator framework for scalable neuronal population modeling. Rather than training separate surrogate models for individual neurons, the proposed framework learns a shared operator across multiple modeled neurons from the same cell type, conditioned on biologically interpretable electrophysiological features. This enables efficient generation of large ensembles of somatic voltage responses while preserving variability across cells and model configurations. We evaluate the approach using membrane dynamics metrics, action potential waveform metrics, spike timing accuracy, input-output firing relationships, and electrophysiological feature distributions. Our framework reproduces subthreshold membrane dynamics, spike waveforms, and firing-rate responses across major cortical inhibitory neuron types, while accurately preserving spike timing despite the sensitivity of threshold-crossing dynamics. The predicted electrophysiological feature distributions show strong agreement with detailed simulator outputs and human experimental recordings, including high explained variability in properties such as inter-spike intervals, firing frequency, action-potential shape, and post-spike recovery. By enabling fast ensemble simulation of cell-type-specific neuronal responses, the proposed framework provides a scalable tool for studying cellular diversity, probing variability near functional thresholds, and generating synthetic but biophysically grounded neuronal populations.

Dynamic Sparse Training (DST) is an effective paradigm for sparse to sparse training of neural network connectivity under a fixed parameter budget. Recent advances in network-science for AI introduced epitopological learning methods, such as Cannistraci-Hebb Training (CHT), demonstrating that network automata applied to the mere network topology enables gradient-free predictions of the sparse connectivity evolution that can trigger significant increase in task performance. However, these methods were currently developed for standard MLP-like fully-connected architectures and need significant rethinking to be extended to convolutional neural networks (CNNs) due to element-wise weight sharing and spatially repeated interactions. In this work, we bridge this gap by introducing epitopological learning DST for CNNs through channel-wise network modeling to address the prohibitive complexity of element-wise modeling, which treats each kernel-channel as a single network node. Results show orders-of-magnitude improvements in time complexity of link-regrowth when applied at channel-level with respect to element-level. We also enhance the channel-wise formulation with lightweight contextual modulation to improve expressivity. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet with ResNet and VGG architectures demonstrate that our method achieves performance comparable to dense training using only 30% of the parameters, which significantly reduces computational cost. Furthermore, our approach improves robustness under noisy inputs. These results highlight the effectiveness of topology-aware sparse training and the benefit of decoupling graph construction from sparse update rules in convolutional networks.

Estimating curvature information from gradients alone is a fundamental problem in machine learning. The challenge becomes particularly acute in settings where only aggregate mini-batch gradients are available, yet curvature information is still required for applications such as preconditioning in optimisation, sampling, and early stopping. Perhaps surprisingly, we show that a simple target-perturbation scheme suffices to recover such curvature information from gradients alone. Our method injects zero-mean noise into the targets, with variance calibrated to the local output curvature. The covariance of the resulting noisy batch gradients then recovers practical curvature matrices, without requiring per-sample gradients, second-order derivatives, or other internal network quantities. For a broad class of non-linear models, our scheme recovers the Generalised Gauss--Newton (GGN) matrix; for feed-forward ReLU networks, it additionally recovers the diagonal blocks of the population Hessian. We demonstrate that the resulting estimator is simple, lightweight, and easy to integrate into existing training pipelines. Experiments demonstrate accurate curvature recovery, faster optimisation when the estimator is used for preconditioning, and the utility of the estimated GGN for early stopping.

While LLM-based coding agents have advanced to repository-scale engineering, existing benchmarks predominantly focus on software maintenance, overlooking the foundational capability of system construction. We introduce CSBench, a benchmark evaluating project-level Spec-to-Code implementation across core computer science domains (e.g., OS, compilers, databases). CSBench features 100 expert-curated tasks from top-tier university assignments within containerized environments. Evaluating 12 state-of-the-art LLMs reveals a stark performance disparity: even top-tier models like GPT-5.2 see success rates plummet from over 90% in algorithmic tasks to below 35% in system-level domains. Our analysis identifies a fundamental deficiency in systemic reasoning and construction knowledge as the primary bottleneck, where agents either terminate prematurely due to overconfidence or fail to translate execution feedback into valid architectural fixes, highlighting CSBench as a necessary tool to bridge this gap and advance autonomous agents toward deep computer science mastery.

Intracranial electrocorticography (ECoG) offers high–signal-to-noise access to cortical activity for brain–computer interfaces, yet limited per-patient data has led most prior work to rely on small, subject-specific decoders that neglect information shared across patients. We investigate whether large pretrained scalp-EEG foundation models (EEG FMs) can be adapted to ECoG, enabling cross-patient learning and competitive decoding performance while calibrating to a held-out patient in $10$--$30$ minutes on a single GPU. We introduce CORTEG, a cross-modality transfer framework that combines a pretrained EEG FM backbone, an electrode-aware KNNSoftFourier spatial adapter, a dual-stream tokenizer for low-frequency and high-gamma activity, and a leave-one-subject-out fine-tuning strategy. We evaluate CORTEG on two challenging regression tasks: public finger trajectory regression (n=9) and private audio envelope regression (n=16). CORTEG matches or exceeds the strongest task-specific baselines on both tasks: it reaches the highest mean correlation among compared methods on the public finger benchmark (gain not statistically significant on $n{=}9$ subjects), with larger and statistically significant gains on the audio task and in low-data per-patient calibration. Feature analyses align with neurophysiology, and latent manifolds capture low-dimensional finger-movement structure. CORTEG provides systematic evidence that scalp-EEG pretraining can be repurposed for ECoG decoding, enabling data-efficient intracranial BCIs that can adapt to new patients.

Quantifying variability in a target population relative to a reference population is central to many scientific and clinical problems (e.g., diseased vs. healthy). Yet, without paired data and in the presence of heterogeneous target variation, existing methods struggle to separate multiple modes of target-specific variation. We propose CASL-VAE, a deep contrastive latent variable model that learns structured latent generative factors from unpaired data. CASL-VAE factorizes variation into continuous common latent factors shared across populations and hierarchical salient latent factors that model target-specific heterogeneity as discrete subtypes and continuous within-subtype variation. Using variational inference, we show how approximate joint likelihood optimization over reference and target domains can be performed using unpaired data, providing a principled basis for paired-sample generation and cross-domain analysis. We validate CASL-VAE on semi-synthetic neuroimaging data, demonstrating improved subtype recovery and paired-sample generation compared to baseline clustering and generative models. We also validate its ability to reveal biologically plausible heterogeneity in Alzheimer's disease. Code will be released upon acceptance.