NeurIPS 2026 论文列表

We identify, for the first time, a new model modification attack—the cross-task model repurposing attack—that can render fingerprints generated by existing model fingerprinting approaches inapplicable. To address this challenge, we propose UniReFP—a novel unified model fingerprinting framework applicable to diverse vision models across different tasks—that utilizes ownership evidence in a shared class-level semantic space rather than original task-specific output space, enabling effective ownership verification when a protected model is repurposed across tasks with heterogeneous output formats. Specifically, UniReFP constructs a surrogate classifier by repurposing the protected model, enabling fingerprints to be generated independently of the original task-dependent output space of the protected model. Moreover, it optimizes grouped fingerprints to encode ownership evidence: fingerprints within the same group are encouraged to induce consistent semantic responses and intermediate representations on the surrogate classifier, while producing dispersed responses on independently trained reference classifiers. During verification, UniReFP uses a task-aware semantic projection mechanism to map heterogeneous suspect-model outputs into unified semantic-presence vectors, and determines ownership by measuring inner-group consistency. Extensive experimental results validate the effectiveness of UniReFP, consistently showing superior performance under cross-task repurposing attacks, commonly studied model modification attacks, and even their combinations.

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called "target alignment", which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

Decades of cognitive science establish that humans navigate environments by forming cognitive maps, defined as allocentric and topology-preserving representations of 3D space. While modern Vision-Language Models (VLMs) demonstrate emergent spatial reasoning from 2D egocentric inputs, it remains unclear whether they construct an analogous 3D internal representation. In this paper, we demonstrate that current VLMs do possess a latent topological map of 3D scenes, but it is heavily overshadowed by non-geometric visual semantics, such as color and shape. By isolating this spatial subspace through cross-scene linear feature extraction, we extract a clean spatial subspace that causally controls the model's spatial outputs. We mathematically shape this latent representation and prove its correspondence to the Laplacian eigenmaps of the scene's 3D Gaussian-kernel graph, converging to the physical 3D space in the continuous limit. Motivated by this geometric identification, we further introduce a mathematically principled latent regularization method for VLMs, based on Dirichlet energy. Applying this single-term regularizer to a minimal 500-step supervised VLM fine-tuning (SFT) on simple synthetic data yields significant improvements on real-world spatial benchmarks, outperforming standard SFT and competitive baselines by up to 12.1\% in spatial tasks involving scene topology understanding.

Pairwise constrained clustering typically relies on hard must-link/cannot-link labels, whereas realistic pairwise supervision may be real-valued and entangle intrinsic ambiguity, expert judgment, and stochastic corruption. Existing deep constrained clustering (DCC) methods mainly target hard, expert-agnostic constraints, treating soft labels mostly numerically rather than semantically. We formalize this setting as uncertainty-aware probabilistic constrained clustering (UPCC), defining a canonical aleatoric target through a heterogeneous observation process and analyzing its conditional identifiability. We introduce ProbPair, an angular pairwise objective for probabilistic relations, and build ECI-PP, an estimator--corrector--integrator framework that refines imperfect supervision via belief estimation, correction, and reliability-aware integration. Across challenging probabilistic supervision settings, experiments on diverse benchmarks show that ECI-PP outperforms state-of-the-art DCC methods and remains robust with a shared default configuration.

The proliferation of multimodal data has underscored the imperative for efficiency in cross-modal retrieval. By mapping data into a unified Hamming space, Cross-modal hashing (CMH) significantly enhances both storage and computational efficiency, thereby establishing itself as a preferred favored paradigm for retrieval tasks. However most methods assume complete data, which rarely holds in practice. In incomplete settings, missing modalities (e.g., text or image) break semantic correspondence and make unsupervised hashing unreliable. Therefore, we propose Unsupervised Generative Completion and Graph-attention Refinement for Incomplete Cross-modal Hashing (UGGRH) method. Specifically, UGGRH leverages pretrained generative models for modality completion and employs a discriminator-guided similarity refinement module to fuse intra-modal relations with paired image-text matching signals, thereby constructing a robust cross-modal similarity matrix that yields a noise-tolerant similarity target for training. After that, it learns discriminative binary codes via hash-aware graph attention and cross-modal fusion, to refine modality embeddings and produce unified hash codes. Experiments on MIRFlickr25K, NUS-WIDE, and MS COCO datasets demonstrate that UGGRH consistently achieves superior performance under high missing rates and modality imbalance, showing significant improvements in retrieval accuracy and robustness across challenging incomplete scenarios.

Training loss and accuracy are the standard signals used to monitor generalization during deep neural network training. Two well-documented phenomena complicate this picture: in grokking, train loss falls rapidly while test performance improves abruptly only after a long delay; in epoch-wise double descent, train loss decreases monotonically while test loss or error rises and falls. Existing accounts are often task-specific, and a task-agnostic analysis framework for diagnosing and explaining these phenomena across realistic tasks and architectures is missing. We address this challenge by analyzing two competing processes that underlie learning dynamics: representation learning in the encoder and readout calibration in the final classifier. Using tools from representational geometry, neural tangent kernels, and linear probing, we show that both processes are active throughout training, with the fluctuations of their relative speed giving rise to seemingly anomalous generalization dynamics. Applying the representation-readout decomposition to grokking across a wide range of tasks and architectures, we find that the readout is train-biased before grokking onset, and representation learning is gradual but not absent—contrary to the lazy-to-rich account. The framework further provides diagnostic signatures distinguishing spurious from genuine generalization: in a previously reported MNIST grokking example and an epoch-wise double descent example, apparent delayed or non-monotone generalization is shown to arise from representation degradation and readout misalignment induced by non-standard training recipes. Together, these results establish the representation-readout decomposition as a top-down framework for understanding learning dynamics and revealing underlying algorithms for interpretability research.

We introduce Rapid Simulation Based Inference (RSBI), a diffusion-based variational approach to likelihood-free Bayesian inference that achieves high posterior sample efficiency under large and multi-dimensional prior-to-posterior volumes. RSBI builds on recent advances in Schrödinger Bridge (SB) diffusion sampling to handle multi-modal posteriors, with the likelihood supplied either by a neural ratio estimator or kernal surrogate via a differentiable simulator. Furthermore, a key observation is that an appropriate surrogate likelihood gives a proposal distribution covering most of the generally multi-modal posterior mass, replacing the sequential rounds of standard methods with a one-shot proposal step. Subsequent NRE refinement recovers exact inference under the simulator and original model prior. As a variational method, RSBI does not suffer from prior leakage and implicit target drift commonly observed in standard sequential posterior estimation methods. To improve mode coverage we optionally utilize the well-tempered meta-dynamics framework, which also provides a mechanism through which to encourage exploration of the prior volume. We observe strong performance not only on standard SBI benchmarks, but also as prior volume is scaled up to 2500 times the original, achieving a performance degradation of only $\sim$5% on the two moons benchmark under a highly constrained simulation budget. Additionally, we evaluate RSBI's potential for gravitational wave ring-down posterior estimation, highlighting a real-world use-case where our method excels.

CLIP has become a cornerstone of multimodal representation learning, yet improving its performance typically requires a prohibitively costly process of training from scratch on billions of samples. We ask a different question: *Can we improve the performance of open-weight CLIP models across various downstream tasks using only existing self-supervised datasets?* Unlike supervised fine-tuning, which adapts a pretrained model to a single downstream task, our setting seeks to improve general performance across various tasks. However, as both our experiments and prior studies reveal, simply applying standard training protocols starting from an open-weight CLIP model often fails, leading to performance degradation. In this paper, we introduce **TuneCLIP**, a self-supervised fine-tuning framework that overcomes the performance degradation. TuneCLIP has two key components: (1) a warm-up stage of recovering optimization statistics to reduce cold-start bias, inspired by theoretical analysis, and (2) a fine-tuning stage of optimizing a new contrastive loss to mitigate the penalization on false negative pairs. Our extensive experiments show that TuneCLIP consistently improves performance across model architectures and scales. Notably, it elevates leading open-weight models like SigLIP (ViT-B/16), achieving gains of up to +2.5% on ImageNet and related out-of-distribution benchmarks, and +1.2% on the highly competitive DataComp benchmark, setting a new strong baseline for efficient post-pretraining adaptation.

Despite the importance of causal reasoning, training LLMs to perform causal reasoning remains underexplored. Existing data efforts mostly focus on benchmarking LLMs on specific aspects of causality, rendering them less suitable for training generalizable causal reasoners. To address this, we propose UniCo, a data generation framework that both (1) addresses 18 causal query types across Pearl's Causal Ladder and (2) translates symbolic samples into code and narrative domains to simulate real-world use cases where causal terms are not explicitly specified. To ensure data quality, UniCo grounds answers with exact causal inference and filter cases with reasoning shortcuts. Upon supervised-finetuning with 66.6K UniCo-generated instances, Qwen3-4B, Qwen3-8B and Olmo-3-7B-Instruct achieve an average of 22.9% improvements across all 18 in-distribution query types, and 8.1% over state-of-the-art causal data generation frameworks on 7 established causal benchmarks outside the training distribution. Furthermore, in real-world medical understanding, legal decision, and tabular reasoning, UniCo-trained models consistently display more faithful reasoning traces, outperforming the base models by an average of 20.2% in faithfulness metrics. These suggest that causality-centered training not only strengthens causal reasoning, but also equips LLMs with a causal mindset in general reasoning tasks.

Proximal Policy Optimization (PPO) and it's variants are the most widely used policy-gradient methods in reinforcement learning, yet the role of its actor update mechanism is still poorly understood theoretically. In particular, standard PPO combines clipped surrogate gradients, multiple epochs of minibatch updates, and reuse of rollout data, but existing convergence analyses do not fully capture this update structure. In this work, we theoretically study PPO policy updates with symmetric clipping from a policy-gradient perspective and interpret its actor updates as a cyclic biased-gradient method with sample reuse and random reshuffling. Our first contribution is a clean formalization of PPO clipped actor updates through surrogate gradients that approximate the true policy gradient. Using the performance difference lemma, we prove a linear bias bound which quantifies how the surrogate gradient drifts as the policy moves away from the sampling policy. Our second contribution is a convergence analysis of cyclic surrogate-gradient ascent, showing that additional PPO-style biased updates can improve progress under conservative learning rates without requiring additional samples. Finally, we analyze the stochastic minibatch version with reshuffling and obtain convergence-to-stationarity guarantees under standard smoothness assumptions and a bounded critic-bias condition. Overall, our results provide a theoretical interpretation of PPO’s multi-epoch actor updates: extra clipped surrogate steps introduce bias, but can still improve optimization efficiency by compensating for small, stable step sizes through sample reuse.

Tuning-free customized generation has gained popularity for its efficiency, particularly with the rise of rectified flow transformers. However, it often suffers from semantic inconsistency, degrading both concept fidelity and prompt alignment. We attribute this failure to their tendency for inference-time superficial feature fusion, which is intrinsic to the tuning-free paradigm. In this paper, we propose SemanticFlow for semantically consistent tuning-free customization, introducing explicit semantic control to jointly enhance concept fidelity and prompt alignment. SemanticFlow operates through a cohesive "perceive-and-manipulate" mechanism for aligned fusion of visual and textual features at the early denoising stage. Specifically, we first devise lightweight semantic token streams as run-time probes to accurately perceive the spatial responses of the target semantics. We then formulate semantic manipulation as an energy-guided rectification of these semantic responses within the rectified flow framework, steering the generation process toward the desired outcome. Experiments demonstrate that SemanticFlow jointly enhances concept fidelity and prompt alignment in previously challenging scenarios, effectively enabling semantically-consistent customization.

Classification with rejection (CwR) generalizes the standard classification task by providing an extra option of rejection with a cost $c$ smaller than misclassification costs, and the design of its convex calibrated surrogate loss is our central topic. While typical surrogate losses for $K$-class classification operates on $K$-dimensional scoring functions, it has been proved that this dimensionality can be reduced to $\lceil\log_2K\rceil$ for CwR with $c\in(0,0.5]$, rendering more efficient computation. This logarithmic dependency is commonly conjectured to be the lowest possible among any convex calibrated surrogate losses for CwR. Through the lens of property elicitation, we explore even lower-dimensional structures for CwR, by constructing a $2$-dimensional convex calibrated surrogate loss under $c\in(0,0.5)$. This loss dimension is provably optimal among all convex calibrated surrogate losses. The boundary cost $c=0.5$ is more nuanced---we construct a $4$-dimensional convex calibrated loss, improving over the $\lceil\log_2 K\rceil$-dimension when $K>16$. Notably, this breaks the optimal logarithmic dimensionality attainable by the *embedding framework* [Finocchiaro et al., 2024], a widely used loss design principle for polyhedral losses, negatively resolving their conjecture on the dimension optimality.

Despite the remarkable progress in Multimodal Large Language Models (MLLMs), the prevailing Chain-of-Thought (CoT) paradigms remain predominantly confined to the linguistic space. While recent advancements have focused on bridging the Perception Gap through high-resolution cropping (e.g., Thinking with Images), they overlook a more fundamental bottleneck: the Reference Gap. The inherent ambiguity of natural language often fails to provide precise, unambiguous pointers to complex spatial layouts, leading to logical collapse in tasks requiring rigorous grounding. In this work, we introduce Thinking with Visual Primitives, a novel reasoning framework that elevates spatial markers (e.g., points and bounding boxes) to "minimal units of thought". By interleaving these visual primitives directly into the thinking process, our model can "point" while it "reasons", effectively grounding its cognitive trajectory in the physical coordinates of the image. Notably, our framework is built on a highly optimized architecture with extreme visual token efficiency. Despite its compact model scale and significantly lower image-token budget, our model achieves frontier-competitive performance on a focused suite of challenging visual QA tasks, matching or exceeding models such as GPT-5.4, Claude-Sonnet-4.6, and Gemini-3-Flash. This demonstrates a path toward more efficient and scalable System-2-like multimodal intelligence.

Language model (LM) alignment improves model outputs to reflect human preferences while preserving the capabilities of the base model. The most common alignment approaches are (i) reinforcement learning, which maximizes the expected reward under a KL-divergence constraint, and (ii) best-of-$N$ alignment, which selects the highest-reward output among $N$ independent samples. Despite their widespread use, the fundamental limits of reward improvement under a KL budget remain poorly understood. We characterize the information-theoretic limits of KL-regularized alignment by deriving the maximum achievable expected reward gain for a fixed KL-divergence budget. Our first result provides a closed-form expression for the optimal reward improvement, governed by a Jeffreys divergence term rather than the $\sqrt{\texttt{KL}}$ used in prior analyses. We further reformulate this expression as a covariance under the base model, yielding a practical estimator that predicts achievable alignment gains from base model samples alone. We extend our analysis to the proxy reward setting, showing that the gap between ideal and proxy alignment (reward hacking) grows with the KL penalty factor and magnitude of reward error. We then prove that reward ensembling mitigates reward hacking, providing a theoretical justification for this technique used in practice. Empirically, we compute the KL–reward Pareto frontier for two alignment tasks for LMs, safety and summarization, and show that best-of-$N$ closely approaches the theoretical limit, while PPO and GRPO remain substantially suboptimal. Our theoretical results shed light on several empirically observed phenomena in the alignment literature and suggest that algorithmic improvements are needed to achieve optimal alignment without high inference costs.

A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable $\Omega(1/T)$ path-KL error as the number of denoising steps $T$ grows. We show that matching the full posterior covariance breaks this barrier, yielding an order-wise improvement that reduces the path KL to $O(1/T^2)$. To make full covariance matching practical, we introduce the Lanczos Gaussian sampler, a training-free, matrix-free method for sampling from the optimal reverse covariance using only covariance-vector products, which are available through Jacobian-vector products of the posterior mean. The sampler avoids dense covariance storage and auxiliary covariance models. We prove that its approximation error decays exponentially in the number of Lanczos steps, where each Lanczos step requires a single Jacobian-vector product. Empirically, using only just three such steps improves sample quality over strong diagonal-covariance baselines, including OCM-DDPM, across standard image benchmarks. This identifies full covariance matching as both theoretically valuable and practically accessible for fast DDPM sampling.

We develop a framework for analyzing parameter symmetries in deep ReLU networks and obtain a complete characterization of the generic parameter fibers for three-layer bottleneck architectures. Our approach provides explicit semi-algebraic descriptions of these fibers and yields a polynomial time algorithm for deciding functional equivalence of two parameters. The symmetries include discrete and continuous transformations arising from layer composition, and depend on whether deeper layers hide or preserve geometric structure from preceding layers. Finally, we show that some of these symmetries induce local conservation laws along gradient flow, while others do not.

A central obstacle in nonlinear Bayesian filtering is representing the belief distribution. Moment-based filters address this by propagating polynomial moments and reconstructing a density from them. Recent work completes the predict-update loop via the maximum-entropy (MaxEnt) principle, but each step requires the partition function and its gradient, both $n$-dimensional integrals whose cost scales exponentially, restricting the demonstrated MaxEnt moment filtering to $n \le 4$. We avoid the partition function entirely by combining score matching with Stein's identity. In our setting, score matching reduces the density fit to a single linear solve whose coefficients are assembled directly from the propagated moments. The same parameters then drive Stein's identity to close the moment hierarchy during prediction and to recover posterior moments after each Bayesian update, keeping the full predict-update loop free of partition function evaluation. The resulting $\textbf{Score Kalman Filter}$ (SKF) reduces to the classical information-form Kalman filter as a special case and performs every step through linear algebra. On nonlinear coupled-oscillator networks, the SKF runs through $n=20$ and reports lower RMSE than the EKF, UKF, EnKF, and particle-filter baselines on the tested synthetic benchmarks.

We introduce the Multiscale Single-Index Model, a stylized model for deep hierarchical feature learning with scale separation. Each layer extracts a shared single-index feature at one physical scale and passes it to the next, giving a tractable setting in which to study how deep architectures learn local multiscale representations. Under non-degeneracy and delocalization assumptions on the link function and planted features respectively, we prove two complementary recovery guarantees. First, for any fixed depth $K$ and local scale $d$, corresponding to an input of size $d^K$, the first Wiener chaos expansion of the target behaves as a perturbed spiked tensor, where the perturbation comes from the non-linearity; we then leverage this fact to show that a spectral method based on tensor unfolding strongly recovers all planted directions with $O(d^{\lceil K/2\rceil}\log d)$ samples. Second, for the two hidden-layer case, we analyze joint online spherical SGD and show that it achieves weak recovery from random initialization in $O(d\log^2 d)$ samples, followed by strong recovery to accuracy $\varepsilon$ in $O(d\log(1/\varepsilon))$ additional samples. The main technical challenge is that the second layer observes non-Gaussian learned features; we overcome this through a quantitative Gaussian comparison using delocalization, combined with sharp trajectory-level control of the coupled SGD dynamics.

In this paper, we investigate the long-run behavior of discounted regularized learning with stochastic gradient feedback in general, non-concave games. Specifically, we focus on a family of implicitly regularized exponential / multiplicative weight update schemes, and we seek to determine which actions\textemdash or, more generally, which recurrent patterns of play\textemdash are more likely to arise in the long run. We approach this question through the lens of large deviations theory and randomly perturbed dynamical systems, and we obtain a precise characterization of the distribution of the process: in the long run, it follows a Boltzmann-Gibbs law with temperature equal to the method's step-size, and energy levels determined by the game and the statistics of the noise. Concretely, we show that the distribution of play concentrates exponentially around the dynamics' *internally chain transitive* (ICT) sets - i.e., irreducible invariant sets containing no smaller attractors - and the probability of visiting such a set depends exponentially on its energy. As a result, unstable ICT sets are exponentially less likely to be visited than stable ones, and the sequence of play is exponentially concentrated around the problem's ``ground state'', where energy is minimized. In this manner, learning acts as a selection mechanism: with exponentially high probability, the ground state is the only outcome observed in the long run, even in the presence of multiple equilibria and other attractors.