NeurIPS 2026 论文列表

Compositional score-based approaches to simulation-based inference (SBI) approximate the posterior over a shared parameter given $n$ independent observations by aggregating individually learned posterior scores: currently, there are two main propositions of such methods (Geffner et al., 2023; Linhart et al., 2026). As the resulting composite score does not correspond to the score of any distribution along the forward diffusion path of the true multi-observation posterior, sampling from it via a reverse SDE leads to an irreducible bias. Annealed Langevin dynamics provides a principled alternative: it treats the composite score as the genuine score of a sequence of tractable bridging densities and samples from them in succession. When properly tuned, it could lead to a controllable bias. However, its hyperparameters, namely step sizes, the number of steps per level, and the number of annealing levels, have so far been chosen empirically. We derive Wasserstein bounds for annealed Langevin with approximate scores and translate them into explicit decision rules for these hyperparameters that guarantee a prescribed sampling accuracy, while highlighting different theoretical aspects of each composite score formulation. In the Gaussian setting, we obtain closed-form expressions for all relevant quantities and prove that the bridging densities of Linhart et al. (2026) consistently admit larger step sizes and require fewer total Langevin steps than those of Geffner et al. (2023). Furthermore, we show empirically that the tuning obtained in the Gaussian setting generalizes to more complex problems, thus providing a well-understood and theoretically grounded starting point for practitioners using compositional score-based approaches.

Multi-parameter persistent homology is a rapidly developing branch of topological data analysis that improves the robustness of single-parameter persistent homology to outliers, while still capturing the metric characteristics of the data. However, a notable limitation is its lack of scalability. In this paper, we introduce a novel approach for efficiently computing 2-parameter persistent homology on large point sets. Our work extends the Flood filtration, originally developed for single-parameter persistence. Our construction, called the sublevel Flood bifiltration, offers a scalable approximation of the sublevel Flood bifiltration. We show that it benefits from theoretical stability properties and describe how to compute it efficiently. We demonstrate the performance of our approach in classification tasks on low-dimensional synthetic datasets, where density awareness is critical, as well as on real-world time series datasets.

With the rapid advancement of generative models, AI-generated images (AIGIs) have become increasingly realistic, posing new challenges for reliable detection. In this work, we revisit the root causes of poor generalization in AIGI detectors from the perspective of shortcut learning. We find that detectors often rely on spurious semantic cues or a single prominent artifact, causing the feature space to collapse toward low diversity and severely limiting generalization. To characterize this issue, we propose the Generative Artifact Manifold Clustering (GAMC) hypothesis, which shows that although generative artifacts are multi-dimensional, different generators occupy distinct distributions along these dimensions, making detectors that rely on local artifact cues inherently fragile. To address this, we shift AIGI detection from “single-cue reliance” to “multi-dimensional discrimination” and introduce the Semantic–Artifact Self-Adversarial Feature Learning (SA-AFL) framework. SA-AFL progressively disentangles semantics from artifacts and employs a self-adversarial mechanism to balance learning across artifact dimensions, enabling the model to retain richer and more shared generative features. As a result, SA-AFL reduces shortcut reliance and learns more transferable evidence for cross-generator detection. Comprehensive experiments on images from 23 generative models show that SA-AFL improves ACC by 6.84\% and mAP by 8.25\% over state-of-the-art methods.

Understanding what individual components of a neural network do is a central goal of mechanistic interpretability, and a valuable tool for auditing or editing trained models. The dominant approach picks a behavior and reverse-engineers the circuit that implements it. This gives a local picture, since we learn what a weight does in service of one task on one distribution, but not what it does in general. We therefore ask the reverse question. Can we pick any single nonzero parameter in a trained transformer and say what it does, without first choosing a behavior? Until recently, this was out of reach, because the weight basis of a standard transformer is not aligned with the computations the network performs (Elhage, et al. 2022). However, weight-sparse transformers (Gao et al. 2025) offer an alternative path forward. By training most weights to zero, the surviving weights align more cleanly with computation, which opens the door to per-weight interpretation. In this work, we introduce an automated LLM-pipeline that produces a short, human-readable account of when a given weight matters, verifies the account on held-out data, and applies it at scale to compare two weight-sparse transformers against two dense controls. Empirically, we find that a significant percentage of nonzero weights (17-35%) on sparse transformers are interpretable, compared to 5-9% on the equivalent dense model and Pythia-70m. Together these results suggest that sparse training produces transformers whose individual weights are interpretable to a degree not achievable in conventional transformers, providing a potential starting point for per-weight interpretation of larger models

Path-integration-trained recurrent neural networks (RNNs) can reproduce grid-like and head-direction-like representations, but most existing models rely on low-dimensional velocity inputs and do not capture the hierarchical organisation of the brain's self-localisation circuit. We introduce a hierarchical recurrent neural network (HRNN) that separately processes angular velocity and linear speed to perform simultaneous angular and positional path integration. Trained on these tasks, the HRNN generalises to longer timescales than seen during training and develops neural response properties resembling all the key cell types: angular velocity cells, head direction cells, speed cells, conjunctive and pure grid cells. The learned circuit also recovers key motifs of the navigation system, including attractor dynamics and asymmetric connectivity patterns. Perturbation analyses reveal functional information flow across the hierarchy, consistent with experimental observations. Finally, introducing theta-paced mutual inhibition between two learned angular-velocity subpopulations enables the HRNN to reproduce the bidirectional theta sweeps observed in empirical data. These results establish hierarchical task-driven RNNs as a biologically interpretable framework for linking neural representations, circuit motifs, and population dynamics in spatial navigation, while enabling targeted in silico perturbations and the generation of experimentally testable predictions.

Over the past decade, a growing body of work has established that implicit biases in learning dynamics fundamentally shape the solutions found by neural networks, governing their learned features and generalisation performance. However, despite these strides in deep learning theory, far less is known about representation learning in generative models based on dynamical systems, from normalising flows to diffusion. Importantly, continuous-time generative models can be prone to mode collapse, yet the learning dynamics underpinning such biases remain elusive. To address this, we use tools from dynamical systems and operator theory to show that bounds on the rank of the gradient of the model weights can explain how collapse occurs in generative models. We show that, in both variational inference and flow matching tasks, optimisation induces low-rank biases that encourage parsimonious representation learning but may also cause the learned distribution to collapse. Together these findings point to a trade-off between promoting feature learning while avoiding both memorisation and collapse in dynamical systems-based generative models.

Understanding how deep neural networks learn representations remains a central challenge in machine learning theory. In this work, we propose a feature-centric framework for analyzing neural network training by relating weight updates to feature evolution. We introduce a simple identity, the *Feature Learning Equation*, which identifies the weight Gram matrix as the key object capturing feature dynamics. This enables us to interpret gradient descent as implicitly inducing a hypothetical evolution of features, whose covariance structure — termed the *Virtual Covariance* — characterizes how representations evolve during training. Building on this perspective, we introduce *Target Linearity*, a measure quantifying the linear alignment between features and targets. By analyzing the training and layer-wise dynamics, we show that deep networks learn to *sequentially* transform representations toward target-linear structure. This linearization perspective provides a unified interpretation of several empirical phenomena, including Neural Collapse and linear interpolation in generative models.

Large Language Models (LLMs) have shown promise for empowering search agents to tackle complex information-seeking tasks. However, since acquiring external information necessitates web search, these agents are highly susceptible to various adversarial attacks (e.g., malicious information injection or stealthy context manipulation). Existing attack strategies inevitably rely on static and human-crafted templates, failing to emulate the dynamic and complex nature of real-world threats. In this paper, we propose an adversarial self-evolution framework that integrates bi-level optimization between the attacker's strategy evolution and the defender's adaptive mitigation, to expose the vulnerabilities of search agents. Specifically, we introduce the Contrastive Rollout Evolutionary Optimization (CREO) method to drive the directional evolution of the attack strategy population via contrastive evolutionary signals. To provide a stable environment for this continuous evolution, we further construct a controlled sandbox and design fine-grained metrics to quantify internal vulnerabilities. Extensive experiments across various multi-hop QA benchmarks and frontier LLMs demonstrate that the proposed framework yields attack efficacy superior to static baselines, underscoring the urgent need to develop more robust defense frameworks. The anonymized code repository is available at https://anonymous.4open.science/r/adversarial_rag-3EFA.

What if the best way to search a video with a vision-language model (VLM) is to stop asking the model to search? Recent approaches give the VLM control over temporal navigation, tying search quality to the model's reasoning ability. We propose the opposite: BeliefSearch treats the VLM as a noisy sensor and delegates navigation to an external Bayesian controller. A single belief over video segments anchors the system: the question sets the prior, each VLM observation updates it, and the same belief decides whether to search, which segment to examine next, and when to stop. Because the belief is explicit, we can trace why each choice was made. The same signal also drives training: each turn earns credit for the uncertainty it reduces, and the final reward is gated by how much the search lowered entropy. This blocks a reward-hacking shortcut where the model otherwise learns to skip search and guess from the preview frames. On long-video benchmarks, our method outperforms all prior search-based methods by up to 8.8 points while using $5$ to $13\times$ fewer frames than recent RL search baselines.

Large language models consistently fail at elementary counting tasks despite strong performance on complex reasoning benchmarks. Recent work has characterized counting failures behaviorally or identified circuits through which counting succeeds, but a mechanistic account of where and why counting breaks down remains absent. In this work, we provide such an account by tracing the count signal from embedding to output and identifying the geometric bottleneck that prevents correct readout for single digit counting problems. Using a dual-metric framework combining Signal-to-Noise Ratio (SNR) with linear probing, we show that counting information is computed correctly and persists in a linearly decodable subspace through the final layer. The failure in counting is not representational but geometric i.e the digit-token columns of the unembedding matrix $W_U$ are orthogonal to the count subspace in the residual stream, rendering correctly computed counts unreadable at the output. We term this as the $\textbf{Unembedding Bottleneck}$ and to causally validate it, we apply a $\textbf{Probe-Informed LoRA}$ correction targeting $W_U$, which restores single-digit counting accuracy by up to 80-95% across six models while updating only ${\sim}$0.001% of parameters and preserving general capabilities. Our findings reveal a broader class of failure in LLMs where information is internally present but geometrically inaccessible to the output projection.

The method of types, pioneered by Csiszar (1998), uses combinatorial arguments to approximate the probabilities of empirical measures and has become a standard tool for deriving error rates in hypothesis testing, source coding, and related information-theoretic problems. Although the technique is widely used across machine learning, computer science, and econometrics, rigorous type-theoretic guarantees for stationary Markov decision processes and reinforcement learning remain limited. This paper addresses that gap by developing a method-of-types framework for the empirical pair measure of the state--action process of a stationary Markov decision process. We establish finite-sample type bounds for the state--action process and characterize the associated entropy cost through the conditional Kullback--Leibler divergence relative to the true pair kernel. These results yield large deviation principles for learned MDP dynamics and variational rate functions for plug-in value- and Q-function estimators in offline reinforcement learning. We further develop finite-sample uncertainty-quantification and hypothesis-testing guarantees based on KL uncertainty sets, including applications to pessimistic value and Q-function estimation under model misspecification. Finally, we apply the same framework to universal source coding and obtain explicit coding error exponents for controlled Markov trajectories. Together, these results provide a unified type-theoretic approach to rare-event analysis, uncertainty quantification, offline reinforcement learning, and information-theoretic coding for finite controlled Markov systems.

Existing Large Language Model (LLM) benchmarks primarily focus on syntactically correct inputs, leaving a significant gap in evaluation on imperfect text. In this work, we study how word-boundary corruption affects how LLMs detect targeted information. By inserting whitespace characters within words to break them into fragments, LLMs' detection accuracy follows a U-shaped curve with the increase in insertion rate. We refer to this curve as the Text Uncanny Valley. To explain such observation, we propose a mode transition hypothesis: LLMs operate in a word-level mode for near-normal text and a character-level mode for heavily fragmented text, with the valley marking the disordered transition where neither mode is effective. Four experiments and one analysis are consistent with this account: in-context learning fails to rescue valley-bottom performance; regularizing the perturbation substantially reduces the U-shape; a math reasoning task replicates the U-shape for Gemini 3.0 Flash but not for stronger models, suggesting the effect is attenuated when tasks rely less on exact lexical alignment; and tokenization entropy peaks before the F1 minimum, consistent with a regime-conflict interpretation. These findings reveal a failure mode invisible to clean-text benchmarks yet directly relevant to any deployment scenario involving noisy or uncurated text inputs.

How little of a pretrained large language model has to change for it to acquire new capabilities? We find that zeroing fewer than 0.05% of its weights, with no other modification, matches full-parameter fine-tuning (FPT) at scale across the three dominant LLM fine-tuning paradigms: on-policy reinforcement learning with verifiable rewards (GRPO), supervised fine-tuning (SFT), and on-policy distillation (SDFT). We call the method Bit-Mask Tuning (BMT): a learnable binary keep/zero mask over the gate projection of transformer blocks. BMT reaches FPT accuracy at our largest backbones, with the GRPO gap closing monotonically across model sizes from 0.5B to 8B. Two practical advantages follow: the trained mask is several 1000x smaller than the full-parameter checkpoint, and BMT forgets substantially less than FPT, retaining prior-task accuracy throughout training where FPT measurably drifts. To understand why masking alone suffices, we analyze the update geometry on GRPO and find that BMT's weight delta lands closer to full-parameter updates than other adapters on three measures: effective rank, spectrum drift, and principal-weight overlap. In sum, deletion alone produces a tiny yet high-performing adapter, reduced forgetting, and an update geometry that tracks FPT's more closely than any baseline we evaluate.

Concept vectors aim to enhance model interpretability by linking internal representations with human-understandable semantics, but their practical utility is often limited by noisy and inconsistent activations. In this work, we uncover the SuperActivator Mechanism: a transformer dynamic that amplifies concept activation gaps, concentrating the most reliable concept evidence into a small set of high-activation tokens. To develop a theoretical understanding of this mechanism, we prove that concept-aligned attention heads multiplicatively amplify pairwise activation gaps, with already-extreme activations growing fastest. We find that this amplification is not just theoretical, but also occurs empirically on large-scale models: while in- and out-of-concept activation distributions overlap considerably, the in-concept distribution develops a positive tail clearly separated from the noise. These high-tail tokens, which we call SuperActivators, appear consistently across concept-positive samples, making them reliable indicators of concept presence. Accordingly, SuperActivator-based detection improves F1 by up to 14% over standard concept activation aggregators and prompting baselines across image and text modalities, models, layers, and concept extraction techniques, demonstrating the generality and practicality of our insights. Further empirical analysis demonstrates that the most reliable SuperActivators are sparse, with detection typically peaking when using only 5-10% of in-concept token activations, and capture more faithful localized semantics than global concept vectors.

Machine learning models—including large language models (LLMs)—are often said to exhibit *monoculture*, where outputs agree strikingly often. However, we present two experiments that substantially disagree with prior findings of monoculture. In particular, we find that monoculture virtually disappears in one dataset when we include item difficulty compared to previous works that do not. Informed by these findings, we theoretically formalize what it means to measure monoculture. We show that monoculture is inherently subjective, relying on two key decisions: 1) the baseline null model for what "independence" should look like; and 2) the population of models and items under consideration. We conclude with concrete guidelines for future evaluators to ensure the robustness of their results.

Class-incremental learning systems trained with $\ell_2$-regularized cross-entropy and within-task softmax exhibit a structural bias on cross-task discriminators that no amount of data or regularization tuning can remove. We characterize this bias in closed form: at the population optimum, the cross-task discriminator under sequential within-task training differs from the joint-optimal by exactly $\Sigma^{-1}(\bar\mu^{(j)} - \bar\mu^{(i)})$, an offset arising from the per-task gauge fix imposed by within-task softmax, identical for all $C^2$ class pairs in a task block---this invariance, not the closed form alone, is what makes the diagnosis falsifiable and the correction one-line. Under a separation condition ($\kappa > 1$, cross-class distances exceeding inter-task distances) we prove a margin-based bound on task confusion at rate $\exp(-(\kappa - 1)^2 \gamma_{ij}/8)$. By explicit construction we show this bound cannot be uniform: when separation fails, cross-task misclassification remains $\Omega(1)$ regardless of inter-task margin, and on configurations with extreme within-task class-norm asymmetry it converges to $1$. We propose \emph{post-hoc de-centering}, an evaluation-time correction that adds the per-task offset $\Sigma^{-1}\bar\mu^{(t)}$ to each weight and a corresponding scalar to each threshold; it recovers the Bayes-optimal cross-task discriminator at the population exactly and yields a bound on task confusion that does not require the separation condition. The same operation appears in shared-covariance LDA-style heads (SLDA, FeCAM, NCM); our contribution is the gauge-theoretic derivation identifying it as the unique per-task affine correction to the structural bias of within-task cross-entropy training, the falsifiable empirical diagnostic across five published CIL methods, and the finite-sample analysis. Experiments on CIFAR-100, ImageNet-100, ImageNet-1K, ImageNet-R, and DomainNet across five frozen backbones show post-hoc de-centering recovers $82$--$94\%$ of the joint--sequential gap (mean $90.5\%$).

Transformers use the same forward computation stream to both predict the next token and store useful state for future token predictions. We formulate the \emph{state-prediction separation hypothesis}: disentangling the two roles yields better language modeling performance. We design a Transformer variant that uses separate computation streams to separate the two functions, and conduct pretraining experiments across various scales. Our experiments show that state-prediction separation consistently offers better data-- and compute--efficiency, improving validation loss and outperforming standard Transformers by 2--3 percentage points on average on downstream tasks. We also conduct extensive empirical analysis that rules out potential confounders and demonstrates the fundamental difference in the gradients our design entails.

We study the stability of data exchange among competing firms. Unlike tangible goods, data is non-rival: sharing it does not deprive the giver of its use. On one hand, competing firms-- often operating as machine-learning–driven predictors that collect observations from a shared environment to solve similar tasks-- can improve their predictive accuracies from pooling data. On the other hand, they compete for market share, which may depend on their relative predictive performance. This raises the central question of this paper: which data exchanges are stable in such competitive environments? We formalize this via a model of $n$ firms exchanging fractions of their datasets, with predictive performance feeding into market competition. We adopt core stability as our solution concept, accounting for externalities via worst-case responses by non-participating firms. Our main results reveal a sharp contrast driven by demand structure: (i) in *fully rational* markets, where customers flock entirely to the top-performing firm, a core-stable exchange always exists for any monotone continuous prediction and utility functions; (ii) in *partially rational* markets with logit-style demand, core-stable exchanges may fail to exist, and even approximate cores can be empty. Our impossibility results suggest that internal profit-sharing within coalitions can restore stability in partially rational markets. We formalize this intuition by showing that when co-operating coalitions equally redistribute market-share revenues among members, a core-stable data exchange exists. Finally, we propose a natural exchange dynamic and demonstrate empirically that it converges to a core-stable data exchange in fully rational markets on simulated instances derived from real datasets.

The mechanism governing the training dynamics of Quantum Neural Networks (QNNs) remains under-explored. In classical Deep Neural Networks (DNNs), training is known dominated by "Spectral Bias,'' i.e. prioritizing learning low-frequency while struggling with high-frequency. QNNs exhibit similar spectral limitations when the target function possesses flat spectral amplitudes. However, in this work, considering target problems with different spectral amplitudes, we theoretically and empirically identify a distinct mechanism in QNNs, which we term *Spectral Amplitude Priority*. By analyzing the frequency-domain gradients and residual dynamics via the Quantum Neural Tangent Kernel (QNTK), we prove that QNN training is governed primarily by the magnitude of spectral components rather than their frequency indices. Consequently, QNNs can efficiently capture high-frequency functions—provided they have significant amplitude—thereby overcoming the inherent limitations of their classical counterparts. We validate this principle on both synthetic high-frequency functions and quantum-advantage tasks. These results show that QNNs notably outperform DNNs in high-frequency tasks, offering an explanation for QNNs' superior expressivity.