NeurIPS 2026 论文列表

Spiking reservoir computing, and reservoir computing more generally, is a powerful and efficient framework for neuromorphic and biological applications, in which a fixed random reservoir drives a trained readout. Yet its performance depends critically on the reservoir initialization. Enriching the reservoir with adaptive, unsupervised plasticity rules offers a natural solution to this limitation. However, it is unclear which rules work, or why, and how to find the best-suited rules for specific tasks without exhaustive and expensive search. Here, we learn how to play the Atari game Pong in a plastic spiking reservoir network. We systematically characterize a large family of local plasticity rules that were meta-learned in prior work. We then show that their performance is predictable and structured: high-scoring rules are characterized by strong differentiation between neurons encoding the ball trajectory and the background, with stable weight dynamics, and consistent readout alignment across time. Rule performance can be estimated from rule parameters alone. Finally, conditioning simulation-based inference (SBI) on high scores allows us to sample directly from promising regions of the rule space, to discover rules that exceed the performance of those found in the prior distribution and reveal stable, high-performing configurations. Together, these results offer competitive performance against classical reservoir computing while providing a transparent, interpretable account of what makes a plasticity rule useful for neuromorphic hardware and biological computing.

We study a repeated information design setting in which the receiver, who is also the decision-maker, updates beliefs in a systematically biased way. More specifically, a distorted posterior in our model can be written as a convex combination of the prior and the Bayesian posterior, governed by a fixed but unknown parameter. Over repeated interactions, the sender chooses persuasive signaling schemes, observes only the receiver’s realized actions, and seeks to minimize regret relative to a full-information oracle that knows the receiver’s biased updating rule. We propose a safe exploration algorithm for learning the receiver’s bias while maintaining high persuasion value. The algorithm exploits the asymmetric cost of probing: conservative probes incur only local loss, whereas overly aggressive probes may lose the persuasive opportunity entirely. For general finite state and action spaces and arbitrary bounded utilities, our method achieves $O(\log\log T)$ regret. A matching $\Omega(\log\log T)$ lower bound shows that this rate is optimal. We further discuss the influence on receiver welfare, as well as extensions to jointly unknown prior and bias, and contextual settings with time-varying priors and utilities.

We study the problem of learning to bid when the bidder’s *value is dynamic*, i.e., when the current value depends on past outcomes. Specifically, we consider a bidder participating in repeated second-price auctions whose value depends on the time elapsed since their last successful bid, with auctions arriving in continuous time and only aggregated feedback revealed at the end of the horizon. Such a bidder must **(1)** balance the immediate benefit of winning the current auction against its impact on future values and **(2)** learn unknown environmental parameters. We derive regret bounds for a class of learning methods that combine plug-in estimators with a differential-equation characterization of the optimal policy, and show that a specific confidence bound algorithm learns the optimal policy with a near optimal regret of $\tilde{\mathcal{O}}(\log N)$ for piecewise linear primitives, and $\tilde{\mathcal{O}}(N^{1/3})$ for general, smooth primitives, achieving these regrets without explicit randomization. These theoretical results are supported by numerical experiments.

Visual textures, defined as spatially homogeneous image regions containing repeated elements (e.g. a field of grass, the bark of a tree), are ubiquitous in visual scenes and provide important cues for recognizing materials and objects. Existing texture models extract essential statistics from a single texture image, and can then generate high-quality samples that are visually similar to the original by matching these statistics. However, their statistics are either hand-designed or based on a network pretrained for another purpose (e.g., object recognition). Here, we develop the first principled method for unsupervised learning of a set of statistics that are used to constrain a maximum entropy probability model. We leverage methods developed for generative diffusion models to derive training and sampling procedures, and compare these to the traditional method of sampling via matching the statistics. Despite the compactness of our trained model (512 statistics), it generates texture images whose quality is as good or better than the current state-of-the-art model (~177k statistics). A more direct comparison of the two models, obtained by synthesizing images that are indistinguishable for one model but maximally different for the other, reveals their relative strengths and weaknesses. Finally, we show that, unlike previous statistical texture models, a straight trajectory in the representation space of our model generates homogeneous texture samples that interpolate smoothly between the features of the two end points.

Infinite-dimensional orthonormal basis expansions play a central role in representing and computing with function spaces due to their favorable linear algebraic properties. However, common bases such as Fourier or wavelets are fixed and do not adapt to the structure of a given problem or dataset. In this paper, we aim to represent these bases with neural networks and optimize them. Our key idea is that any target infinite-dimensional orthonormal basis can be viewed either as a point on the Lie manifold of the orthogonal group, or equivalently, as the endpoint of a continuous path on that manifold that connects a reference basis, e.g. Fourier, to that target. Paths on the Lie manifold satisfy ordinary differential equations (ODEs) governed by skew-adjoint integral operators. Using neural networks to define finite-rank generators of such ODEs allows us to parameterize and optimize orthonormal bases in function space. While relying on finite-rank generators to model infinite operators might seem restrictive, we prove a universality result: even with a rank-2 generator, the integrated solutions of the ODE are dense in the orthogonal group under the appropriate operator topology. In other words, for any target orthonormal basis, there exists a path originating from a reference basis and driven by finite-rank generators that gets arbitrarily close to that target basis. We demonstrate the flexibility of our framework by transforming the Fourier basis into the principal components of a functional dataset, eigenfunctions of linear operators, or dynamic modes of energy-preserving physical simulations.

Optimal Transport (OT) provides a principled framework for comparing probability distributions. Classical solvers remain the gold standard for this task, providing exact solutions. At the same time, OT is an ideal testbed for studying whether learning-based amortized models can internalize the structure of OT type problems. Here, ground-truth solutions are available, constraints are explicit, and exact discrete solutions have well-characterized sparsity. We describe ToR-OT, a transformer-based model that learns to predict discrete OT plans through autoregressive token regression. We reframe OT into a structured sequence generation task. ToR-OT decodes sparse transport plans as sequences rather than solving an optimization task at test time. We focus on three properties: (a) Zero-shot generalization: pretraining on a large synthetic corpus of OT instances allows a single model to generalize to unseen distribution pairs and heterogeneous cost metrics without retraining. (b) Sparse primal decoding: by exploiting the inherent sparsity in exact discrete OT solutions, the decoder predicts only nonzero entries (avoids dense coupling outputs). (c) Amortized inference: on low-dimensional discrete problems, ToR-OT gives accurate approximate plans and compares favorably with per-instance neural OT baselines. Overall, ToR-OT is not yet a replacement for classical solvers, but best viewed as a step toward understanding how autoregressive transformers can learn structure of constrained optimization problems like OT.

Learning parity functions, more general modular addition, is a challenging machine learning task due to its input sensitivity. A recent study substantially scaled modular addition learning in both the number of summands and the modulus. Its key idea is to increase zeros in training sequences, reducing the effective number of summands and thus controlling training difficulty; however, this induces covariate shift between training and test input distributions. This study theoretically and empirically analyzes this side effect and proposes a covariate-shift-free method for modular addition. Specifically, we introduce an auxiliary modulus $Kq$ during training, which reduces wrap-around frequency and problem difficulty while preserving the same input distribution across training and testing. Experiments show strong scalability and sample efficiency: even for large input length $N$, large modulus $q$, and small datasets---where the sparse method fails to learn---our method achieves equal or better match accuracy and relaxed $\tau$-accuracy. For example, at $N=64$ and $q=974269$, our method trained on 100K samples achieves $97.0\%$ $\tau$-accuracy at $\tau=0.05$, while the sparse method achieves only $9.5\%$ with the same data size and $93.9\%$ even when extended to 1M samples.

Budget-feasible mechanisms (BFMs) are a fundamental tool for budget-constrained procurement, but designing strong BFMs remains challenging, particularly for general valuation classes. Classical approaches rely on problem-specific analysis and worst-case approximations, often yielding conservative mechanisms in practice. This motivates data-driven methods for discovering mechanisms with stronger empirical performance. However, strict budget constraints expose a key limitation of existing neural automated mechanism design (AMD): they either fail to provide exact economic guarantees or suffer from severe scalability bottlenecks. We propose BFMNet, a scalable menu-based neural framework for learning truthful budget-feasible procurement mechanisms. BFMNet first learns *self-bid-independent* menus from market context, ensuring dominant-strategy incentive compatibility (DSIC) and individual rationality (IR) by construction, and then applies an ex-post, instance-level menu transformation to enforce budget feasibility. We prove that the resulting mechanism satisfies exact DSIC, IR, and budget feasibility. By avoiding intractable global discretization grids and restrictive Lipschitz constraints, BFMNet remains both expressive and scalable. Extensive experiments show that BFMNet improves utility over classical baselines by up to $34.1$%, remains competitive with state-of-the-art neural baselines that provide only approximate economic guarantees, and scales robustly to larger auction instances.

Domain generalization aims to learn models that generalize to unseen target domains using labeled data from multiple source domains. Many existing approaches focus on learning domain-invariant representations, but enforcing invariance alone may fail to preserve sufficient task-relevant information under domain shift. We propose BLENDER, a reconstruction-aware framework for domain generalization that employs a hierarchical latent decomposition to separate domain-invariant and domain-specific factors. This structure prioritizes informativeness in the domain-invariant representation and captures residual domain-specific variation through conditional modeling. We further provide a theoretical analysis establishing a bound on the reconstruction risk for unseen target domains, revealing how domain invariance and latent disentanglement contribute to generalization beyond the observed domains. Experiments on standard domain generalization datasets demonstrate strong performance under substantial domain shifts, and qualitative analyses show that BLENDER promotes a structured allocation of information between domain-invariant and domain-specific latent representations.

In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.

The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems. So far, however, the focus has been almost exclusively on *polynomial-time* algorithms, where predictions improve competitive ratios, approximation guarantees, or running times. In this paper, we raise the question of whether predictions can push the frontier of *exact exponential-time* algorithms for NP-hard problems. We answer this question affirmatively by proposing a *general approach* that augments an entire family of state-of-the-art exact algorithms for a variety of subset selection problems. We show that a noisy predictor that is only marginally better than random guessing suffices to provably reduce the search space, and that the resulting runtime speedup scales smoothly with the prediction quality. Importantly, our algorithms require only *pairwise* independence of predictions or, alternatively, do not require the knowledge of the predictor's accuracy–both strictly weaker and more realistic settings than typically assumed.

Generative models, from diffusion models to large language models, achieve remarkable performance but at a cost in training data orders of magnitude larger than what biological learners require. An alternative paradigm has emerged in which networks are trained to predict their \emph{own} latent representations of related views or masked regions, as in data2vec and JEPA -- an idea related to predictive-coding accounts of the cortex. Despite strong empirical results, the theoretical understanding of these methods remains limited. Central questions include: by how much does latent prediction actually improve data efficiency? Is there a benefit to stacking such methods into multi-scale hierarchies? We answer both using as data a tractable probabilistic context-free grammar that captures the compositional structure of natural language and images. We prove that latent prediction recovers the full latent tree of depth $L$ from a number of samples scaling as $m^3$, where $m$ is the number of production rules per symbol. This is much fewer than the $m^L$ samples required by supervised learning and the $m^{L+1}$ required by token-level SSL. We confirm this bound with (i) a hierarchical clustering algorithm, (ii) an end-to-end neural network whose predictor-clusterer modules predict their own latents at each level via gradient descent, and (iii) the first sample-complexity analysis of data2vec, which we show implicitly performs hierarchical latent prediction. This suggests that explicit stacking such as H-JEPA is largely redundant.

Personalization is essential for general-purpose robots to transition into household environments and achieve true practicality. While general robotic manipulation has been extensively studied, personalized robotic manipulation (PeRM) lacks a unified formulation and remains significantly underexplored. In this paper, we identify user preference as the cornerstone of PeRM and introduce LIBERO-PeRM, a novel benchmark designed for personalized preference learning in embodied agents. Specifically, LIBERO-PeRM highlights five key research topics in personalization: 1) how policies follow preferences in zero-shot settings; 2) how to learn single preferences from demonstrations; 3) how efficiently policies acquire preferences as demonstrations increase; 4) how learned preferences generalize across layouts and preference settings; and 5) how policies compose multiple preferences and resolve conflicts. To this end, we propose a unified formulation of personalized manipulation with three preference levels that jointly cover common daily personalization scenarios. Building on this formulation and the LIBERO framework, we develop an extensible procedural generation pipeline that generates paired demonstrations with and without preferences. For benchmarking purposes, we create five task suites (312 tasks in total) with corresponding high-quality demonstrations, rich metadata, and preference satisfaction metrics to probe the aforementioned research topics. Experimental results show that current VLA policies struggle with zero-shot personalization, while SFT makes preferences learnable; preference learning benefits from mixed training, broader layout diversity, and same-layout no-preference data, but generalization, decomposition, and conflict resolution remain difficult.

Inverse reinforcement learning (IRL) is a well-established paradigm for circumventing the need for explicit reward. In this paper, we study the problem of estimating the reward function from a single sequence of actions (i.e., a demonstration) of a stochastic linear bandit algorithm. Our main result is a unified approach for inverse linear bandits, based on the idea of formulating a linear program by tightly characterizing the confidence intervals of pulled actions. We show that the estimation error of our algorithms matches the information-theoretic lower bound, up to polynomial factors in $d$ and $\log T$, where $d$ is the dimensionality of the feature space and $T$ is the length of the demonstration. Compared to prior approaches, our approach (i) gives a unified reward estimator that works when the demonstrator employs LinUCB or Phased Elimination, two popular algorithms for stochastic linear bandits, while existing estimator only works for Phased Elimination; (ii) does not require access to hyperparameters or internal states of the demonstrator algorithm as required by prior work; and (iii) works for general action sets, while existing estimator requires assumptions on the density and geometry of the action set. We further demonstrate the practicality of our new approach by validating our new algorithms on synthetic data and demonstrations constructed from real-world datasets, where our estimators significantly outperform existing ones.

Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local geometric framework in which semantically equivalent inputs occupy structured regions in latent space, with paraphrastic variation along nuisance directions and semantic identity preserved in invariant subspaces. Building on this view, we make three contributions: (1) a geometric characterization of invariant latent features, (2) a contrastive subspace discovery method that separates semantic-changing from semantic-preserving variation, and (3) an application of invariant representations to zero-shot model attribution. Across models and layers, empirical results support these contributions. Invariant structure emerges in specific depth regions, semantic displacement lies largely outside the nuisance subspace, and representation-level interventions indicate a causal role of invariant components in model outputs. Invariant representations also capture model-specific geometric patterns, enabling accurate attribution. These findings suggest that semantic invariance can be viewed as a local geometric property of latent representations, offering a principled perspective on how language models organize meaning.

Mutual information (MI) is fundamental to representation-learning analysis in deep networks, but in high dimensions MI estimators depend on hyperparameters --- bin widths, kernel bandwidths, neighbourhood radii, auxiliary networks --- whose bias often dominates the signal. We show that continuous piecewise-linear (CPWL) networks, including ReLU networks, admit an intrinsic information-theoretic analysis that avoids this pitfall: their inherent partition of the input space into convex linear regions assigns to every input a discrete region label $\Pi$ alongside the continuous representation $T$. We decompose $I(Y; T)$ exactly into geometric terms, where the \emph{routing information} $I(Y; \Pi)$ admits a hyperparameter-free plug-in estimator that approximates a population lower bound on every other MI term in the decomposition. When the partition saturates, a functional-equivalence quotient at relative Frobenius tolerance $\varepsilon \in [0, 2]$ collapses regions implementing the same linear operator and restores informativeness. Empirically, the routing estimator correlates strongly with three established MI baselines {\it without any hyperparameter}, and the functional quotient at moderate $\varepsilon$ recovers informative estimates in the regime where the raw partition is bounded by $\log_2 N$ rather than $H(Y)$. We provide a parameter-free framework for analysing the internal information geometry of CPWL networks, grounded in their inherent piecewise-linear structure rather than in external discretisation.

Although numerous algorithms have been proposed for unsupervised anomaly detection, there is currently no widely acknowledged internal evaluation method tailored specifically to this task. Existing internal evaluation methods typically assess score distributions alone or depend on auxiliary classifiers, limiting their reliability and interpretability. To address these problems, we propose SSSD (Similar Scores, Similar Data), an evaluation framework inspired by the smoothness assumption in machine learning—that similar inputs should yield similar outputs. We adapt this principle to anomaly detection by requiring that locally similar data points be assigned similar anomaly scores. Instead of testing this assumption directly, SSSD identifies violations of this principle by comparing the similarity of data with similar anomaly scores, interpreting a significant difference as a higher probability of erroneous detection. This evaluation of similarity is measured through nearby-score and nearby-distance, which is calculated based on the distances between neighboring data points and their corresponding anomaly scores. SSSD is highly interpretable, providing valuable insights for identifying mislabeled data. Experimental results show that our proposed method is both effective and robust for evaluating the performance of unsupervised anomaly detection algorithms across artificial and real-world datasets.

Large language models can hallucinate confidently, making uncertainty quantification essential for reliable deployment. Existing approaches rely predominantly on token-level signals from the final (unembedding) layer, while the rich geometric structure of intermediate hidden states remains largely unexplored. Aggregating token-level scores to the response level is itself non-trivial, and no single signal reliably catches the confident-but-wrong failure mode where a model commits to every token with high confidence yet produces an incorrect answer. We address this gap by extracting complementary signals from two distinct representational layers: hidden-state geometric complexity (global uncertainty) from the embedding layer, and token-level entropy (local uncertainty) from the unembedding layer. We show empirically that the two signals cover different regimes that are weakly correlated and thus combining them captures failure modes invisible to either alone. Building on this insight, we propose Global Local Uncertainty (GLU), an unsupervised, single-pass framework that fuses the two signals via a multiplicative gate. Experiments across three benchmarks and three model families show that GLU matches or outperforms all unsupervised baselines and remains competitive with supervised methods that lack cross-dataset generalization.

We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, leave non-vanishing remainder terms that prevent adaptation to a vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lower bound, up to logarithmic factors, across both dense-tail and sparse-tail regimes under a mild nondegeneracy condition. The analysis yields a linearization of Oja's iterates, which in turn enables a high-dimensional Gaussian approximation for the general-rank subspace estimation error with an explicit limiting covariance. We also establish a row-wise Berry--Esseen theorem for the aligned difference, recovering prior rank-one results as special cases. For practical inference, we develop an online multiplier bootstrap algorithm and prove its consistency. Beyond streaming PCA, our techniques contribute to Gaussian approximation and bootstrap inference for nonconvex stochastic approximation.