NeurIPS 2026 论文列表

Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions, such as stationarity or limited emission models, and typically rely on variational autoencoder (VAE) estimators, which introduce approximation gaps that limit the recovery of the latent structure. In this work, we address both the theoretical and practical limitations of this setting. First, we establish identifiability of a broad class of recurrent nonlinear switching dynamical systems under flexible assumptions, significantly extending prior results. Second, we introduce $\Omega$SDS, a flow-based estimator that enables exact likelihood optimization using expectation-maximisation. Through empirical validation on both synthetic and real-world data, our results demonstrate that $\Omega$SDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.

Denoising score matching (DSM) is the cornerstone of scalable diffusion model training. However, DSM becomes inapplicable on curved manifolds: the curved geometry makes the forward diffusion process nonlinear and the transition kernel is no longer tractable. Existing approaches therefore revert to implicit score matching (ISM) with expensive Brownian simulation, approximate the intractable heat kernel, or bypass the transition kernel altogether via flow matching with the logarithm map, each incurring significant computational cost or approximation error on general manifolds. We propose \emph{splitting diffusion}, a new framework that restores DSM-like training on general Riemannian manifolds by replacing the intractable Brownian forward process with a splitting scheme that alternates two steps: (1) an Ornstein-Uhlenbeck velocity update in the tangent space, whose transition kernel has a closed-form solution; (2) a deterministic geodesic transport step. This splitting yields a fully tractable transition kernel locally, enabling DSM-style training while requiring only the exponential map as a geometric oracle. The effectiveness of splitting diffusion is demonstrated on complicated manifolds and high-dimensional data.

Diffusion models promise iterative refinement, yet masked diffusion language models (MDMs) suffer from two shortcomings: (1) inability to revise tokens, and (2) sparse training signal. The root cause is structural: MDMs control information flow only through input masking, so unmasked positions cannot be supervised, and self-correction is never learned. We propose the Leave-One-Out Transformer (LOOT), which addresses both issues. With LOOT, MDMs predict the distribution over potential replacements conditioned on the rest of the sequence at each position, in a single forward pass. Supervision can then be applied at masked and unmasked positions alike, yielding a lower-variance training objective with a dense loss signal at every token. Our method empowers MDMs to learn self-correction during training and supports continuous refinement at inference time via Gibbs sampling. LOOT achieves a new best validation perplexity on LM1B in a parameter-matched setting. Finetuned from a MDM checkpoint on OpenWebText, LOOT establishes a generative quality-vs-diversity frontier that surpasses prior remasking methods across NFE budgets.

Kolmogorov–Arnold Networks (KANs) expand each input coordinate through a fixed basis family, yet the optimization role of this basis lifting remains poorly understood. We identify basis lifting as a structural source of ill-conditioning in KANs and provide a mechanism-level analysis linking lifted feature geometry to convergence, accuracy, and seed sensitivity. Our analysis studies the evolution of lifted empirical Gram matrices under stochastic gradient descent (SGD) and shows that fixed basis lifting induces and preserves near-rank deficiency through eigenvalue and determinant drift. It further concentrates feature energy into a smaller number of directions, amplifying dominant eigenvalues and worsening condition numbers. These results show that basis selection is not merely an expressivity choice, but also an optimization and conditioning choice. Motivated by this mechanism, we introduce T-KAN, a learnable basis-coordinate transformation that aligns basis directions before the learned linear map. It reshapes lifted Gram geometries while preserving the expressivity and introducing negligible parameter overhead. In controlled small-to-moderate KAN regimes, T-KAN often improves conditioning and optimization with B-spline, Chebyshev, and RBF KANs.

Classifier-free guidance (CFG) is the de facto standard for conditional sampling in diffusion models, yet it often reduces sample diversity. Using tools from statistical physics, we analyze the emergence of generative distortions induced by CFG, namely the mismatch between the CFG sampling distribution and the true conditional distribution. We study this phenomenon in analytically tractable settings with exact score functions, characterizing its dependence on data dimensionality and the number of classes. For high-dimensional Gaussian mixtures, we use dynamic mean-field theory to show that distortions arise when the number of classes scales exponentially with the data dimension, whereas they vanish in the sub-exponential regime due to a dynamical phase transition. We further prove that, in the infinite-class limit, distortions remain unavoidable regardless of dimensionality because of the increasing density of classes. Finally, we show that standard CFG schedules cannot prevent variance shrinkage, and we propose a theoretically grounded guidance schedule incorporating a negative-guidance window that improves both class separability and sample diversity in real-world latent diffusion models.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 13.4\% improvement in accuracy while reducing generated tokens by 11.8\% to 52.8\%. Code and models will be publicly available.

Reinforcement learning (RL) post-training aligns diffusion-based generators with human preferences, yet existing RL methods suffer from poor compatibility with off-policy learning and few-step distilled models. These limitations are especially severe in the video generation area, as practical video generation pipelines often rely on few-step distilled generators. Furthermore, due to complex spatial-temporal dynamics and higher dimensions, near-on-policy video rollouts are both expensive to collect and often imperfect. Relying on such rollouts alone can amplify artifacts and is prone to reward hacking. To address these issues, we propose Forward-Consistent Reward Matching (FCRM), an efficient off-policy RL framework for video generation. FCRM converts the forward denoising loss into a positive loss-induced score and formulates the reward alignment as a one-step GFlowNet matching problem. The resulting residual is pointwise in a clean sample space that naturally supports off-policy learning and few-step generators. To avoid biased gradients, we introduce a double-sampling estimator for the squared residual objective. Theoretically, minimizing the proposed matching residual bounds the KL divergence between the learned distribution and the optimal reward-tilted distribution. Experiments on standard video generation benchmarks validate FCRM across online, replay, offline, and few-step settings and outperform SOTA methods.

With the rise of large language models (LLMs), generative engines have become powerful alternatives to traditional search, reshaping retrieval tasks. In e-commerce, for instance, conversational shopping agents now guide consumers to relevant products. This shift has created the need for generative engine optimization (GEO)---improving content visibility and relevance for generative engines. Despite its growing importance, current GEO practices are largely ad hoc, and their impacts remain poorly understood, especially in the e-commerce setting. We address this gap by introducing E-GEO, the first dataset built specifically for e-commerce GEO. E-GEO contains 13,747 realistic, multi-sentence consumer product queries, each paired with 10 relevant Amazon listings, capturing rich intent, constraints, preferences, and shopping contexts that existing datasets miss. Using this dataset, we conduct the first large-scale empirical study of e-commerce GEO across five frontier generative engines, seven popular LLM rewriters with a simple prompt, and fifteen hand-crafted rewriting heuristics. We further formulate GEO as a tractable optimization problem and develop a lightweight prompt meta-optimization algorithm that significantly improves over heuristic baselines. Notably, the optimized prompts reveal a stable, domain-agnostic pattern, suggesting the existence of a "universally effective" GEO strategy. Finally, we red-team the GEO system through both heuristic and optimization-based attacks and show that, under a simple in-prompt defense, gains from GEO reflect genuine content improvement rather than manipulation, anchoring GEO as a substantive, well-defined optimization problem.

While novel view synthesis (NVS) for dynamic scenes has seen significant progress, reconstructing temporally consistent geometric surfaces remains a challenge. Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) offer powerful dynamic scene rendering capabilities; however, relying solely on photometric optimization often leads to geometric ambiguities. This results in discontinuous surfaces, severe artifacts, and broken surfaces over time. To address these limitations, we present DySurface, a novel framework that bridges the effectiveness of explicit Gaussians with the geometric fidelity of implicit Signed Distance Functions (SDFs) in dynamic scenes. Our approach tackles the structural discrepancy between the forward deformation of 3DGS ($canonical \rightarrow dynamic$) and the backward deformation required for volumetric SDF rendering ($dynamic \rightarrow canonical$). Specifically, we propose the VoxGS-DSDF branch that leverages deformed Gaussians to construct a dynamic sparse voxel grid, providing explicit geometric guidance to the implicit SDF field. This explicit anchoring effectively regularizes the volumetric rendering process, significantly improving surface reconstruction quality, containing watertight boundaries and detailed representations. Quantitative and qualitative experiments demonstrate that DySurface significantly outperforms state-of-the-art baselines in geometric accuracy metrics while maintaining competitive rendering performance. Codes will be publicly available.

Drifting Models have recently achieved state-of-the-art performance in one-step image generation by training generators to follow corrective vector fields. However, their standard reverse-style drift improves samples from the model side, which can severely underutilize training samples and bottleneck early convergence. To address this, we introduce DualDrift, a unified framework that augments the original reverse drift with a novel forward drift. The forward drift lets each data sample assign correction to generated rollouts, providing denser data-side signals and accelerating early training. At the same time, this dense data-side signal can overemphasize dominant regions when used alone. DualDrift therefore uses a parameter-free scheduler driven by empirical batch statistics to balance the fast early correction of forward drift with the stable refinement of reverse drift. Evaluated on ImageNet $256\times256$, DualDrift achieves faster convergence and significantly improves over the baseline Drifting Models in both FID and Inception Score.

For decades, philosophers and musicologists have debated which features of a performance are constitutive of the work and which are expressions of how it is being played. Computational evidence has been hard to assemble: audio embedding models conflate work identity with performance style, and existing interpretability tools for music generators treat learned representations as flat dictionaries that mix the two. We turn the question into an empirical one by introducing the dual-contrastive sparse autoencoder (DC-SAE), a two-branch sparse autoencoder that uses cheap work-level metadata to factor a generative music transformer's residual stream into work-identity and performance-content subspaces. Across jazz-standard, classical-work, and pop-cover corpora, the resulting decomposition is supported by probes and feature galleries that surface musically interpretable concepts on each side. Without performer supervision, the variation branch acquires structure related to performer identity, and steering along these directions can shift the perceived performer of generated audio while preserving the underlying work. Together, these results show that a generative music model has internalized a representation of interpretation that can be recovered, named, and steered.

While one-step text-to-image generators, a fast and deployment-friendly class of visual generative models, can produce samples with a single forward pass, existing preference-finetuning methods fail to simultaneously achieve efficient adaptation, reward-model agnosticism, and diverse generation. In this work, we propose Drifting Preference Optimization (DrPO), an online preference-finetuning method for one-step generators. Inspired by the recent work of Drifting Models, DrPO first uses the target reward model to construct an on-policy dipole reward model from positive and negative samples. This dipole model induces a preference drifting field in latent feature space, whose gradients are then used to optimize the generator without backpropagating through the target reward model. Empirically, we evaluate DrPO across multiple reward models and SD-Turbo and SDXL-Turbo one-step generators, including HPSv3 and GenEval as representative alignment benchmarks, and validate that DrPO can efficiently and effectively finetune one-step generative models. Preliminary experiments further suggest that this sample-based gradient synthesis can be extended to offline preference finetuning.

Sparse autoencoders (SAEs) have become an important tool for unsupervised concept discovery in large models. To make the resulting feature spaces more interpretable and manageable, recent approaches have begun imposing hierarchical structure, either explicitly or as an implicit effect of training constraints, yet rigorous comparison remains difficult. There are no agreed-upon requirements for what a meaningful feature hierarchy should satisfy, and evaluation has largely relied on qualitative illustrations with fragmented quantitative protocols. To address this, we derive a set of key requirements for generalization/specialization hierarchies in unsupervised concept discovery, drawing on semantic net and taxonomy research alongside recent SAE work, and use them to derive a concrete evaluation protocol. Applying this protocol to current SAE approaches trained on visual data, we find that while feature spaces generally provide a basis for sensible hierarchies, establishing good hierarchical structure remains challenging. In particular, feature absorption, both in its well-known hard form and in a continuous, soft form, systematically compromises hierarchy quality, pointing to a fundamental tension that future approaches will need to navigate.

The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds only weak pointwise similarity between models. In this paper, we show that what models share is not the location of samples in representation space, but the directions (displacement vectors) between them. Under a single orthogonal alignment---rotation and reflection only---these displacement vectors are substantially preserved across 44 independently trained vision and language encoders spanning modalities and asymmetric capability pairs, consistent with the PRH evidence. The samples' absolute positions are not, consistent with recent counter-evidence. Both arise from a single decomposition: representations split into a *shared semantic component* that is linearly aligned across models, and a *private capability component* that is not. We trace this geometry to concept-level structure: within a model, parent concepts are orthogonal to their child variation vectors; across models, concept displacements are parallel. Our theory falsifiably predicts (and experiments confirm) that fine-tuning preserves pointwise similarity but collapses displacement, and that relational distillation does the opposite. A major implication is that, because semantics align linearly but capabilities do not, capabilities can be imported from one model to another using a single cached forward pass through the source. We call this Shadow Casting. As a proof of concept, our ShadowCLIP instantiation matches or outperforms strong fine-tuned baselines at orders of magnitude less compute. A cache can be released alongside open model weights, letting one model's capabilities be downloaded and imported into any number of other models without fine-tuning.

We characterise disentanglement for smooth generative pushforward models, such as in VAEs and GANs. For a generator/decoder $g:\\mathcal{Z}\\to\\mathcal{X}$ and factorised prior $p(z)=\\prod_i p_i(z_i)$, we define disentanglement as standard statistical independence expressed over the generated manifold: {the pushforward density} $p_\\mu = g_\\#p$ factorises into one–dimensional "seam" factors, each controlled by a distinct latent coordinate. We prove that $p_\\mu$ factorises according to the SVD of $g$'s Jacobian; that disentanglement equates to two conditions on $g$ (C1-C2); and that under such conditions the seam factors are identifiable, up to permutation and sign. In the special case of Gaussian ($\\beta$-)VAEs, we show via an identity how diagonal posteriors promote C1-C2, in expectation, explaining why disentanglement arises modulated by $\\beta$. Experiments illustrate this mechanism on Gaussian data, dSprites, and CelebA.

Discriminative models are trained with task-specific objectives such as classification, detection, or representation learning, yet their practical utility depends on generalizing beyond the training task to unseen samples from the same domain. This suggests that a discriminative model may retain an implicit trace of the data manifold beyond its task labels. We ask whether this trace can be exposed as a generative signal without task-specific guidance. We introduce the Discriminative Score Function (DSF), which extracts an image-space generative field from the loss-gradient geometry of a pretrained discriminative model. DSF provides a training-free update rule that moves images toward model-consistent visual regions without retraining or task-specific targets. We apply DSF to diverse pretrained discriminative models, including ResNet classifiers, DETR detectors, and DINOv2 ViT encoders. DSF generates unconditional images from noise and supports conditional guidance, editing, inpainting, and explanation through the same field. DSF-generated samples also provide effective zero-shot quantization calibration when real images or labels are unavailable, preserving feature geometry better than data-free calibration baselines. These results show that discriminative training leaves a generative functional signal for synthesis and calibration.

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and $\mu_1$, and on a deterministic or stochastic bridge to define an interpolating process between the two distributions. The time marginals of this process can then be approximately sampled by estimating the transition rates, or more generally the generator, of its Markovian projection. This framework has recently been extended to the case of discrete source and target distributions, under the name *Discrete Flow Matching* (DFM). However, theoretical guarantees for such models remain scarce. In this paper, we study two DFM models on $\mathbb{Z}_m^d = \\{0,\ldots,m-1\\}^d$, sampled through time discretization, and derive non-asymptotic associated bounds for both of them. In contrast to previous work, we establish non-asymptotic bounds in Kullback--Leibler divergence for the early-stopped version of the target distribution. We also derive explicit convergence guarantees in total variation distance with respect to the true target distribution. Importantly, these bounds rely only on an approximation error assumption, relaxing standard score assumptions used in earlier works, while also yielding improved dependence on the vocabulary size $m$ and the dimension $d$.

Discrete diffusion is a promising framework for categorical generative modeling, but current evaluation protocols often fail to reveal whether models have actually learned the target distribution. We introduce the Discrete Diffusion Playground, a diagnostic benchmark that converts known 2D continuous distributions into binary token sequences through an exact discretized bijection. This creates a rare setting in which models are trained on discrete sequences, but generated samples can be decoded back into 2D and compared directly against a known ground-truth distribution. The benchmark spans smooth Gaussian mixtures and tilted checkerboards with sharp boundaries, disconnected support, and coordinate-dependent structure, allowing it to expose failures that are invisible in standard proxy metrics. It supports exact grid divergences, Wasserstein distances, density visualizations, and nonparametric two-sample tests, providing both quantitative evaluation and interpretable failure diagnosis. Using this testbed, we show that masked diffusion models can learn meaningful adaptive reveal orders but remain less stable than autoregressive baselines on smooth targets and largely fail on tilted checkerboards, where autoregressive models preserve the target geometry. Control experiments with reversed and interleaved token orderings show that autoregressive performance is not explained by favorable bit order alone.The Playground provides a simple but stringent benchmark for stress-testing discrete generative models and for developing evaluation metrics that detect real distributional mismatch rather than proxy performance. Our code is available at https://anonymous.4open.science/r/DiscreteDiffusionPlayground-0CCA/

Discrete diffusion models are often said to outperform autoregressive models on planning tasks, but the specific mechanisms enabling this are not yet well understood. To explain why, we abstract the complexity of studying ``planning'' into graph traversal problems, which offer a minimal setup for evaluating language models' planning and lookahead capabilities. We find that non-autoregressive language models are able to leverage an inherent directional asymmetry in lookahead planning tasks to outperform the training efficiency of their autoregressive counterparts. Through a mechanistic study of the training and inference dynamics of autoregressive and non-autoregressive models, we discover that while forward traversal through junctions in the graph requires complex sequential planning, the reverse path remains deterministic. Consequently, non-autoregressive models naturally develop a fundamentally different solution strategy. Effectively, they learn a reverse-decoding pattern which reduces an $\ell^{th}$-order lookahead problem to a sequence of simple $1^{st}$-order transitions. Latent-space analysis further confirms these divergent strategies by demonstrating the distinct internal representations formed during generation. Ultimately, these findings highlight the advantages of non-autoregressive modeling while clarifying the inherent planning limitations induced by autoregressive architectures.