ICLR 2026 论文列表

Exogenous variables offer valuable supplementary information for predicting future endogenous variables. Forecasting with exogenous variables needs to consider both past-to-future dependencies (i.e., temporal correlations) and the influence of exogenous variables on endogenous variables (i.e., channel correlations). This is pivotal when future exogenous variables are available, because they may directly affect the future endogenous variables. Many methods have been proposed for time series forecasting with exogenous variables, focusing on modeling temporal and channel correlations. However, most of them use a two-step strategy, modeling temporal and channel correlations separately, which limits their ability to capture joint correlations across time and channels. Furthermore, in real-world scenarios, recorded time series are frequently affected by various forms of noises, underscoring the critical importance of robustness in such correlations modeling. To address these limitations, we propose GCGNet, a Graph-Consistent Generative Network for time series forecasting with exogenous variables. Specifically, GCGNet first employs a Variational Generator to produce coarse predictions. A Graph Discriminator then further guides it by evaluating the consistency between the generated and true correlations, where the correlations are represented as graphs, and are robust to noises. Finally, a Graph Refiner is proposed to refine the predictions to prevent degeneration and improve accuracy. Extensive experiments on 12 real-world datasets demonstrate that GCGNet outperforms state-of-the-art baselines.

Sparse autoencoders (SAEs) are a cornerstone of interpretability for large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the $\ell_0$ sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method—a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

High computational costs and slow inference hinder the practical application of video generation models. While prior works accelerate the generation process through feature caching, they often suffer from notable quality degradation. In this work, we reveal that this issue arises from their inability to distinguish truly redundant features, which leads to the unintended skipping of computations on important features. To address this, we propose \textbf{PreciseCache}, a plug-and-play framework that precisely detects and skips truly redundant computations, thereby accelerating inference without sacrificing quality. Specifically, PreciseCache contains two components: LFCache for step-wise caching and BlockCache for block-wise caching. For LFCache, we compute the Low-Frequency Difference (LFD) between the prediction features of the current step and those from the previous cached step. Empirically, we observe that LFD serves as an effective measure of step-wise redundancy, accurately detecting highly redundant steps whose computation can be skipped through reusing cached features. To further accelerate generation within each non-skipped step, we propose BlockCache, which precisely detects and skips redundant computations at the block level within the network. Extensive experiments on various backbones demonstrate the effectiveness of our PreciseCache, which achieves an average of $2.6\times$ speedup without noticeable quality loss. Source code will be released.

Contrastive Language-Image Pre-training (CLIP) has become a cornerstone in vision-language representation learning, powering diverse downstream tasks and serving as the default vision backbone in multimodal large language models (MLLMs). Despite its success, CLIP's dense and opaque latent representations pose significant interpretability challenges. A common assumption is that interpretability and performance are in tension: enforcing sparsity during training degrades accuracy, motivating recent post-hoc approaches such as Sparse Autoencoders (SAEs). However, these post-hoc approaches often suffer from degraded downstream performance and loss of CLIP's inherent multimodal capabilities, with most learned features remaining unimodal. We propose a simple yet effective approach that integrates sparsity directly into CLIP training, yielding representations that are both interpretable and performant. Compared to SAEs, our Sparse CLIP representations preserve strong downstream task performance, achieve superior interpretability, and retain multimodal capabilities. We show that multimodal sparse features enable straightforward semantic concept alignment and reveal training dynamics of how cross-modal knowledge emerges. Finally, as a proof of concept, we train a vision-language model on sparse CLIP representations that enables interpretable, vision-based steering capabilities. Our findings challenge conventional wisdom that interpretability requires sacrificing accuracy and demonstrate that interpretability and performance can be co-optimized, offering a promising design principle for future models.

Multimodal data are prevalent across various domains, and learning robust representations of such data is paramount to enhancing generation quality and downstream task performance. To handle heterogeneity and interconnections among different modalities, recent multimodal generative models extract shared and private (modality-specific) information with two separate variables. Despite attempts to enforce disentanglement between these two variables, these methods struggle with challenging datasets where the likelihood model is insufficient. In this paper, we propose Information-Disentangled Multimodal VAE (IDMVAE) to explicitly address this issue, with rigorous mutual information-based regularizations, including cross-view mutual information maximization for extracting shared variables, and a cycle-consistency style loss for redundancy removal using generative augmentations. We further introduce diffusion models to improve the capacity of latent priors. These newly proposed components are complementary to each other. Compared to existing approaches, IDMVAE shows a clean separation between shared and private information, demonstrating superior generation quality and semantic coherence on challenging datasets.

Converting pretrained attention modules such as *grouped-query attention* (GQA) into *multi-head latent attention* (MLA) can improve expressivity without increasing KV-cache cost, making it attractive for efficient inference. However, existing conversion methods typically apply naïve singular value decomposition (SVD). They focus on minimizing the difference between weight matrices rather than how those weights affect input activations, ignore the covariance structure of activations, and enforce a uniform rank across layers—causing activation drift and degraded attention fidelity. To address these issues, we propose **CARE** (**C**ovariance-**A**ware, **R**ank-**E**nhanced), a MLA conversion pipeline under a fixed KV width. CARE introduces three key steps: (i). **Activation-preserving factorization** — align the approximation with the actual input activations rather than just the weights. (ii). **Adjusted-rank allocation** — distribute a fixed KV budget across layers by giving more capacity to layers that need it most. (iii). **KV-parity mapping** — reparameterize the converted \(K\) and \(V\) to fit the MLA format while keeping the KV-cache size unchanged. Under a matched KV-cache budget, our method consistently outperforms a uniform-rank SVD baseline on Llama-3-8B, delivering up to **331%** relative gains in one-shot evaluation (higher accuracy, lower perplexity). With a brief post-SVD “healing” fine-tune, we fully recover the original model’s accuracy.

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the features learned by large language models (LLMs). By reconstructing features with sparsely activated networks, SAEs aim to recover complex superposed polysemantic features into interpretable monosemantic ones. Despite their wide applications, it remains unclear under what conditions SAEs can fully recover the ground truth monosemantic features from the superposed polysemantic ones. In this paper, we provide the first theoretical analysis with a closed-form solution for SAEs, revealing that they generally fail to fully recover the ground truth monosemantic features unless the ground truth features are extremely sparse. To improve the feature recovery of SAEs in general cases, we propose a reweighting strategy targeting at enhancing the reconstruction of the ground truth monosemantic features instead of the observed polysemantic ones. We further establish a theoretical weight selection principle for our proposed weighted SAE (WSAE). Experiments across multiple settings validate our theoretical findings and demonstrate that our WSAE significantly improves feature monosemanticity and interpretability.

We introduce *Generative Universal Verifier*, a novel concept and plugin designed for next-generation multimodal reasoning in vision-language models and unified multimodal models, providing the fundamental capability of reflection and refinement on visual outcomes during the reasoning and generation process. This work makes three main contributions: (1) We build **ViVerBench**, a comprehensive benchmark spanning $16$ categories of critical tasks for evaluating visual outcomes in multimodal reasoning. Results show that existing VLMs consistently underperform across these tasks, underscoring a substantial gap from human-level capability in reliable visual verification. (2) We design two automated pipelines to construct large-scale visual verification data and train **OmniVerifier-7B**, the first omni-capable generative verifier trained for universal visual verification and achieves notable gains on ViVerBench(+$8.3$). Through training, we identify three atomic capabilities in visual verification and demonstrate how they generalize and interact synergistically. (3) We propose **OmniVerifier-TTS**, a sequential test-time scaling paradigm that leverages the universal verifier to bridge image generation and editing within unified models, enhancing the upper bound of generative ability through iterative fine-grained optimization. Beyond generation, we extend universal verifier to broader world-modeling interleaved reasoning scenarios. Empirically, OmniVerifier-TTS achieves improvements on T2I-ReasonBench(+$3.7$), and GenEval++(+$4.3$), outperforming existing parallel test-time scaling methods, such as Best-of-N. By endowing multimodal reasoning with reliable visual verification, OmniVerifier advances both reliable reflection during generation and scalable test-time refinement, marking a step toward more trustworthy and controllable next-generation reasoning systems.

While large language models (LLMs) achieve strong performance in recommendation, they face challenges in continual learning as users, items, and user preferences evolve over time. Existing LoRA-based continual methods primarily focus on preserving performance on previous tasks, but this overlooks the unique nature of recommendation: the goal is not to predict past preferences, and outdated preferences can even harm performance when current interests shift significantly. To address this, we propose PESO (Proximally rEgularized Single evolving lOra, a continual adaptation method for LoRA in recommendation. PESO introduces a proximal regularizer that anchors the current adapter to its most recent frozen state, enabling the model to flexibly balance adaptation and preservation, and to better capture recent user behaviors. Theoretically, we show that this proximal design provides data-aware, direction-wise guidance in the LoRA subspace. Empirically, PESO consistently outperforms existing LoRA-based continual learning methods.

Post-training quantization (PTQ) enables efficient deployment of deep networks using a small set of data. Its application to visual autoregressive models (VAR), however, remains relatively unexplored. We identify two key challenges for applying PTQ to VAR: (i) large reconstruction errors in attention–value products, especially at coarse scales where high attention scores occur more frequently; and (ii) a discrepancy between the sampling frequencies of codebook entries and their predicted probabilities due to limited calibration data. To address these challenges, we propose a PTQ framework tailored for VAR. First, we introduce a shift-and-sum quantization method that reduces reconstruction errors by aggregating quantized results from symmetrically shifted duplicates of value tokens. Second, we present a resampling strategy for calibration data that aligns sampling frequencies of codebook entries with their predicted probabilities. Experiments on class-conditional image generation, in-painting, out-painting, and class-conditional editing show consistent improvements across VAR architectures, establishing a new state of the art in PTQ for VAR.

Product quantisation (PQ) is a classical method for scalable vector encoding, yet it has seen limited usage for latent representations in high-fidelity image generation. In this work, we introduce PQGAN, a quantised image autoencoder that integrates PQ into the well-known vector quantisation (VQ) framework of VQGAN. PQGAN achieves a noticeable improvement over state-of-the-art methods in terms of reconstruction performance, including both quantisation methods and their continuous counterparts. We achieve a PSNR score of 37dB, where prior work achieves 27dB, and are able to reduce the FID, LPIPS, and CMMD score by up to 96\%. Our key to success is a thorough analysis of the interaction between codebook size, embedding dimensionality, and subspace factorisation, with vector and scalar quantisation as special cases. We obtain novel findings, such that the performance of VQ and PQ behaves in opposite ways when scaling the embedding dimension. Furthermore, our analysis shows performance trends for PQ that help guide optimal hyperparameter selection. Finally, we demonstrate that PQGAN can be seamlessly integrated into pre-trained diffusion models. This enables either a significantly faster and more compute-efficient generation, or a doubling of the output resolution at no additional cost, positioning PQ as a strong extension for discrete latent representation in image synthesis.

Diffusion models have shown remarkable performance in image synthesis by progressively estimating a smooth transition from a Gaussian distribution of noise to a real image. Unfortunately, their practical deployment is limited by slow inference speed, high memory usage, and the computational demands of the noise estimation process. Post-training quantization (PTQ) emerges as a promising solution to accelerate sampling and reduce the memory overhead of diffusion models. Existing PTQ methods for diffusion models typically apply uniform weights to calibration samples across timesteps, which is sub-optimal since data at different timesteps may contribute differently to the diffusion process. Additionally, due to varying activation distributions and gradients across timesteps, a uniform quantization approach is sub-optimal. Each timestep requires a different gradient direction for optimal quantization, and treating them equally can lead to conflicting gradients that degrade performance. In this paper, we propose a novel PTQ method that addresses these challenges by assigning appropriate weights to calibration samples. Specifically, our approach learns to assign optimal weights to calibration samples to align the quantized model’s gradients across timesteps, facilitating the quantization process. Extensive experiments on CIFAR-10, LSUN-Bedrooms, and ImageNet datasets demonstrate the superiority of our method compared to other PTQ methods for diffusion models.

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly inference. Consequently, quality-preserving fast sampling methods that require fewer NFEs have been an active area of research. However, prior training-free sampling methods fail to simultaneously address two key challenges: the stiffness of the ODE (i.e., the non-straightness of the velocity field) and dependence on the semi-linear structure of the DM ODE (which limits their direct applicability to flow-matching models). In this work, we introduce the Stabilized Taylor Orthogonal Runge–Kutta (STORK) method, addressing both design concerns. We demonstrate that STORK consistently improves the quality of diffusion and flow-matching sampling for image and video generation.

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers---including normalising flows, diffusion models, and controlled diffusions---to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.

Speculative decoding (SD) has emerged as a promising technique to accelerate LLM inference by employing a small, efficient draft model to propose draft tokens in advance, and subsequently validating them in parallel with the large target model. However, the existing SD methods still remain fundamentally constrained by their serialized execution, which inevitably causes mutual waiting bubbles between the draft and target models. To address this critical challenge, we draw inspiration from sophisticated branch prediction mechanisms in modern processors and propose a novel framework, \textbf{SpecBranch}, to fully unlock branch parallelism in SD. Specifically, we first conduct an in-depth analysis of the potential of branch parallelism in SD, and recognize that the key challenge lies in the intricate trade-offs between parallelization and token rollback. Based on this analysis, we introduce parallel speculative branches to preemptively hedge against likely rejections. Meanwhile, to significantly enhance parallelism, we jointly orchestrate adaptive draft lengths with a hybrid combination of the implicit draft model confidence and explicit reusing of target model features. Extensive experiments conducted across various models and benchmarks show that \textbf{SpecBranch} achieves impressive speedups of over \textbf{1.8}$\times \sim$ \textbf{4.5}$\times$ against the standard auto-regressive decoding and reduces rollback tokens by \textbf{50}\% for poorly aligned models, while maintaining an identical sampling distribution. Our code is available at \url{https://github.com/Sylvan820/Specbranch}.

The differing representation spaces required for visual understanding and generation pose a challenge in unifying them within the autoregressive paradigm of large language models. A vision tokenizer trained for reconstruction excels at capturing low-level visual appearance, making it well-suited for visual generation but lacking high-level semantic representations for understanding tasks. Conversely, a vision encoder trained via contrastive learning aligns well with language but struggles to decode back into the pixel space for generation tasks. To bridge this gap, we propose DualToken, a method that unifies representations for both understanding and generation within a single tokenizer. However, directly integrating reconstruction and semantic objectives creates conflicts, leading to degraded performance in both reconstruction fidelity and semantic accuracy. Instead of forcing a single codebook to capture both visual appearance and semantics, DualToken disentangles them by introducing separate codebooks for high-level semantics and low-level visual details, effectively turning their inherent conflict into a synergistic relationship. As a result, DualToken sets a new record of 0.25 rFID and 82.0% zero-shot accuracy on ImageNet, and demonstrates strong effectiveness in downstream MLLM tasks for both understanding and generation. Specifically, our method surpasses VILA-U by 5.8 points on average across ten visual understanding benchmarks and delivers a 13% improvement on GenAI-Bench, attaining state-of-the-art performance among existing autoregressive unified models. Notably, incorporating dual visual tokens consistently outperforms using a single token type on both understanding and generation tasks. We hope our research offers a new perspective on leveraging dual visual vocabularies for building unified vision–language models.

While score-based generative models have emerged as powerful priors for solving inverse problems, directly integrating them into optimization algorithms such as ADMM remains nontrivial. Two central challenges arise: i) the mismatch between the noisy data manifolds used to train the score functions and the geometry of ADMM iterates, especially due to the influence of dual variables, and ii) the lack of convergence understanding when ADMM is equipped with score-based denoisers. To address the manifold mismatch issue, we propose ADMM plug-and-play (ADMM-PnP) with the AC-DC denoiser, a new framework that embeds a three-stage denoiser into ADMM: (1) auto-correction (AC) via additive Gaussian noise, (2) directional correction (DC) using conditional Langevin dynamics, and (3) score-based denoising. In terms of convergence, we establish two results: first, under proper denoiser parameters, each ADMM iteration is a weakly nonexpansive operator, ensuring high-probability fixed-point *ball convergence* using a constant step size; second, under more relaxed conditions, the AC-DC denoiser is a bounded denoiser, which leads to convergence under an adaptive step size schedule. Experiments on a range of inverse problems demonstrate that our method consistently improves solution quality over a variety of baselines.

Generative sequence models are typically trained on sample sequences from natural or formal languages. It is a crucial question whether—or to what extent—sample-based training is able to capture the true structure of these languages, often referred to as the "world model". Theoretical results indicate that we can hope for soundness at best, that is, generating valid sequences, but not necessarily all of them. However, it is still important to have practical tools that are able to verify whether a given sequence model is sound. In this study, we focus on chess, as it is a domain that provides enough complexity while having a simple rule-based world model. We propose adversarial sequence generation for verifying the soundness of the sequence model. Our adversaries generate valid sequences so as to force the sequence model to generate an invalid next move prediction. Apart from the falsification of soundness, this method is also suitable for a more fine-grained analysis of the failure modes and the effects of different choices during training. To demonstrate this, we propose a number of methods for adversarial sequence generation and evaluate the approach on a large set of chess models. We train models on random as well as high-quality chess games, using several training recipes. We find that none of the models are sound, but some training techniques and dataset choices are able to improve soundness remarkably. We also investigate the potential application of board state probes in both our training and attack methods. Our findings indicate that the extracted board states have no causal role in next token prediction in most of the models.

The current success of diffusion transformers are built on the compressed latent space shaped by the pre-trained variational autoencoder(VAE). However, this two-stage training paradigm inevitably introduces accumulated errors and decoding artifacts. To avoid these problems, researchers return to pixel space modeling but at the cost of complicated cascade pipelines and increased token complexity. Motivated by the simple yet effective diffusion transformer architectures on the latent space, we propose to model pixel space diffusion using a large-patch diffusion transformer and employ neural fields to decode these large patches, leading to a single-stage streamlined end-to-end solution, which we coin as pixel neural field diffusion transformer (**PixNerd**). Thanks to the efficient neural field representation in PixNerd, we achieve **1.93 FID** on ImageNet 256x256 and nearly **8x lower latency** without any complex cascade pipeline or VAE. We also extend our PixNerd framework to text-to-image applications. Our PixNerd-XXL/16 achieves a competitive 0.73 overall score on the GenEval benchmark and 80.9 overall score on the DPG benchmark.