ICLR 2026 Papers

Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.

Given the query, key and value matrices $Q, K, V\in \mathbb{R}^{n\times d}$, the attention matrix is defined as $\mathrm{Att}(Q, K, V)=D^{-1}AV$ where $A=\exp(QK^\top/\sqrt{d})$ with $\exp(\cdot)$ applied entrywise, $D=\mathrm{diag}(A{\bf 1}_n)$. The attention matrix is the backbone of modern transformers and large language models, but explicitly forming the softmax matrix $D^{-1}A$ incurs $\Omega(n^2)$, motivating numerous approximation schemes that reduce runtime to $\widetilde O(nd)$ via sparsity or low-rank factorization. We propose a quantum data structure that approximates any row of $\mathrm{Att}(Q, K, V)$ using only row queries to $Q, K, V$. Our algorithm preprocesses these matrices in $\widetilde{O}\left( \epsilon^{-1} n^{0.5} \left( s_\lambda^{2.5} + s_\lambda^{1.5} d + \alpha^{0.5} d \right) \right)$ time, where $\epsilon$ is the target accuracy, $s_\lambda$ is the $\lambda$-statistical dimension of the exponential kernel defined by $Q$ and $K$, and $\alpha$ measures the row distortion of $V$ that is at most $d/{\rm srank}(V)$, the stable rank of $V$. Each row query can be answered in $\widetilde{O}(s_\lambda^2 + s_\lambda d)$ time. To our knowledge, this is the first quantum data structure that approximates rows of the attention matrix in sublinear time with respect to $n$. Our approach relies on a quantum Nystr{\"o}m approximation of the exponential kernel, quantum multivariate mean estimation for computing $D$, and quantum leverage score sampling for the multiplication with $V$.

We introduce the challenging problem of multi-object system identification from videos, for which prior methods are ill-suited due to their focus on single-object scenes or discrete material classification with a fixed set of material prototypes. To address this, we propose MOSIV, a new framework that directly optimizes for continuous, per-object material parameters using a differentiable simulator guided by geometric objectives derived from video. We also present a new synthetic benchmark with contact-rich, multi-object interactions to facilitate evaluation. On this benchmark, MOSIV substantially improves grounding accuracy and long-horizon simulation fidelity over adapted baselines, establishing it as a strong baseline for this new task. Our analysis shows that object-level fine-grained supervision and geometry-aligned objectives are critical for stable optimization in these complex, multi-object settings. The source code and dataset will be released.

Diffusion-based Large Language Models (dLLMs) parallelize text generation by framing decoding as a denoising process, but suffer from high computational overhead since they predict all future suffix tokens at each step while retaining only a small fraction. We propose $\textbf{Diffusion Scratchpad} (\textbf{\textit{DPad}})$, a training-free method that restricts attention to a structured subset of suffix tokens, preserving fidelity while eliminating redundancy. $\textit{DPad}$ integrates two strategies: (i) a $\textit{sliding window}$, which maintains a fixed-length suffix window, and (ii) $\textit{distance-decay dropout}$, which deterministically removes distant suffix tokens before attention computation. This concise design is compatible with existing optimizations such as parallel decoding and prefix caching, and lends itself to a lightweight implementation. Comprehensive evaluations across multiple benchmarks on $\texttt{LLaDA}$ and $\texttt{Dream}$ models demonstrate that $\textit{DPad}$ delivers up to $\mathbf{61.4\times}$ speedup over vanilla dLLMs while maintaining comparable accuracy, highlighting its potential for efficient and scalable long-sequence inference.

Large Vision Transformers (ViTs) must often be compressed before they can be deployed on resource-constrained edge devices. However, many edge devices require only part of the *all-classes* knowledge of a pre-trained ViT in their corresponding application scenarios. This is overlooked by existing compression methods. Lightweight models produced by these methods retain a substantial amount of class-irrelevant knowledge and suffer suboptimal performance on target classes. To address this, we analyze the knowledge distribution of ViT and reveal a knowledge disentanglement within it: neurons in the feed-forward network (FFN) modules encode class-specific knowledge, while the multi-head attention (MHA) modules capture class-agnostic patterns. Building on this insight, we introduce Vulcan, a pruning-oriented post-training method for deriving compact class-specific models from a pre-trained ViT under given resource budgets. Vulcan follows a novel *train-then-prune* paradigm, which introduces redundancy into ViTs deliberately by collapsing FFN neurons onto those with the highest class-specific activations and by enforcing low-rankness in MHA weights. This design mitigates the irreversible knowledge loss of direct pruning, so that the post-trained model can be compressed into a compact one with negligible performance loss. Notably, the derived edge ViTs not only achieve significant reductions in size and computation but also even surpass the original ViTs in performance on specific classes. Comprehensive experiments with five base ViTs covering three representative visual tasks on four datasets demonstrate that Vulcan-derived ViTs outperform the base ViTs on class-specific tasks by up to 15.12\% in accuracy, with only 20\%–40\% of their sizes. Compared with state-of-the-art structured pruning methods, Vulcan improves class-specific accuracy by up to 13.92\%. Code is available at [Vulcan](https://github.com/CGCL-codes/Vulcan).

Large Language Models (LLMs) are pre-trained on large data from different sources and domains. These data most often contain trillions of tokens with large portions of copyrighted or proprietary content, which hinders the usage of such models under AI legislation. This raises the need for truly open pre-training data that is compliant with the data security regulations. In this paper, we introduce Common Corpus, the largest open dataset for LLM pre-training. The data assembled in Common Corpus are either uncopyrighted or under permissible licenses and amount to about two trillion tokens. The dataset contains a wide variety of languages, ranging from the high-resource European languages to some low-resource languages rarely represented in pre-training datasets. In addition, it includes a large portion of code data. The diversity of data sources in terms of covered domains and time periods opens up the paths for both research and entrepreneurial needs in diverse areas of knowledge. In this paper, we present the detailed provenance of data assembling and the details of dataset filtering and curation. We train two small language models on Common Corpus and find that the resulting model performs comparably to other models of their size, indicating that our dataset is suitable for multilingual pretraining. Common Corpus represents a key contribution to the ecosystem for open science research on large language models.

Reinforcement learning (RL) has become a central paradigm for post-training large language models (LLMs) to elicit stronger reasoning. Yet, most recent RL for LLMs (RL4LLM) methods avoid explicit critics, replacing them with average advantage baselines. This shift is largely pragmatic: conventional value functions are computationally expensive to train at LLM scale and often fail under sparse rewards and long reasoning horizons. We revisit this bottleneck from an architectural perspective and introduce Asymmetric Proximal Policy Optimization (**AsyPPO**), a simple and scalable framework that restores the critic’s role while remaining efficient in large-model settings. **AsyPPO** employs a set of lightweight *mini-critics*, each trained on disjoint prompt shards. This design encourages diversity while preserving calibration, reducing value-estimation bias. Beyond robust estimation, **AsyPPO** leverages inter-critic uncertainty to refine the policy update: (i) masking advantages in states where critics agree and gradients add little learning signal, and (ii) filtering high-divergence states from entropy regularization, suppressing spurious exploration. Across multiple reasoning benchmarks, **AsyPPO** consistently improves learning stability and performance over strong baselines, e.g., GRPO, achieving performance gains of $> 6$% on *Qwen3-4b-Base* and about $3$% on *Qwen3-8b-Base* and *Qwen3-14b-Base* over classic PPO. Such results highlight the importance of architectural innovations in critics for scalable, efficient algorithms.

Optimizing inference for long-context large language models (LLMs) is increasingly important due to the quadratic compute and linear memory cost of Transformers. Existing approximate inference methods, including key-value (KV) cache dropping, sparse attention, and prompt compression, typically rely on coarse predictions of token or KV pair importance. We unify and extend recent work by introducing a framework for approximate LLM inference that leverages small draft models to more accurately predict token and KV pair importance. We provide novel theoretical and empirical analyses justifying lookahead-based importance estimation techniques. Within this framework, we present: (i) **SpecKV**, the first method to use lookahead with a small draft model to enable precise KV cache dropping; (ii) **SpecPC**, which leverages draft model attention activations to identify and discard less important prompt tokens; and (iii) **SpecKV-PC**, a cascaded compression strategy combining both techniques. Extensive experiments on long-context benchmarks demonstrate that our methods consistently achieve higher accuracy than existing baselines while retaining the same efficiency gains in memory usage, latency, and throughput.

Facial expression recognition (FER) models are employed in many video-based affective computing applications, such as human-computer interaction and healthcare monitoring. However, deep FER models often struggle with subtle expressions and high inter-subject variability, limiting their performance in real-world applications. To improve their performance, source-free domain adaptation (SFDA) methods have been proposed to personalize a pretrained source model using only unlabeled target domain data, thereby avoiding data privacy, storage, and transmission constraints. This paper addresses a challenging scenario, where source data is unavailable for adaptation, and only unlabeled target data consisting solely of neutral expressions is available. SFDA methods are not typically designed to adapt using target data from only a single class. Further, using models to generate facial images with non-neutral expressions can be unstable and computationally intensive. In this paper, personalized feature translation (PFT) is proposed for SFDA. Unlike current image translation methods for SFDA, our lightweight method operates in the latent space. We first pre-train the translator on the source domain data to transform the subject-specific style features from one source subject into another. Expression information is preserved by optimizing a combination of expression consistency and style-aware objectives. Then, the translator is adapted on neutral target data, without using source data or image synthesis. By translating in the latent space, PFT avoids the complexity and noise of face expression generation, producing discriminative embeddings optimized for classification. Using PFT eliminates the need for image synthesis, reduces computational overhead (using a lightweight translator), and only adapts part of the model, making the method efficient compared to image-based translation. Extensive experiments on four challenging video FER benchmark datasets, BioVid, StressID, BAH, and AffWild2, show that PFT consistently outperforms state-of-the-art SFDA methods, providing a cost-effective approach that is suitable for real-world, privacy-sensitive FER applications.

Latent generative modeling has become the standard strategy for Diffusion Transformers (DiTs), but the autoencoder has barely evolved. Most DiTs still use the legacy VAE encoder, which introduces several limitations: large convolutional backbones that compromise architectural simplicity, low-dimensional latent spaces that restrict information capacity, and weak representations resulting from purely reconstruction-based training. In this work, we investigate replacing the VAE encoder–decoder with pretrained representation encoders (e.g., DINO, SigLIP, MAE) combined with trained decoders, forming what we call \emph{Representation Autoencoders} (RAEs). These models provide both high-quality reconstructions and semantically rich latent spaces, while allowing for a scalable transformer-based architecture. A key challenge arises in enabling diffusion transformers to operate effectively within these high-dimensional representations. We analyze the sources of this difficulty, propose theoretically motivated solutions, and validate them empirically. Our approach achieves faster convergence without auxiliary representation alignment losses. Using a DiT variant with a lightweight wide DDT-head, we demonstrate state-of-the-art image generation performance, reaching FIDs of 1.18 @256 resolution and 1.13 @512 on ImageNet.

Recent advances have shown success in eliciting strong reasoning abilities in multimodal large language models (MLLMs) through rule-based reinforcement learning (RL) with outcome rewards. However, this paradigm typically lacks supervision over the thinking process leading to the final outcome. As a result, the model may learn sub-optimal reasoning strategies, which can hinder its generalization ability. In light of this, we propose SophiaVL-R1, as an attempt to add reward signals for the thinking process in this paradigm. To achieve this, we first train a thinking reward model that evaluates the quality of the entire thinking process. Given that the thinking reward may be unreliable for certain samples due to reward hacking, we propose the Trust-GRPO method, which assigns a trustworthiness weight to the thinking reward during training. This weight is computed based on the thinking reward comparison of responses leading to correct answers versus incorrect answers, helping to mitigate the impact of potentially unreliable thinking rewards. Moreover, we design an annealing training strategy that gradually reduces the thinking reward over time, allowing the model to rely more on the accurate rule-based outcome reward in later training stages. Experiments show that our SophiaVL-R1 surpasses a series of reasoning MLLMs on various benchmarks (\textit{e.g.}, MathVisita, MMMU), demonstrating strong reasoning and generalization capabilities. Notably, our SophiaVL-R1-7B even outperforms LLaVA-OneVision-72B on most benchmarks, despite the latter having 10 $\times$ more parameters. All code, models, and datasets will be made publicly available.

Large Language Models (LLMs) often lack meaningful confidence estimates for the semantic content of their outputs. While base LLMs are known to exhibit next-token calibration, it remains unclear whether they can assess confidence in the actual meaning of their responses beyond the token level. We find that, when using a certain sampling-based notion of semantic calibration, base LLMs are remarkably well-calibrated: they can meaningfully assess confidence in various open-ended question-answering tasks, despite training only on next-token prediction. To formalize this phenomenon, we introduce "$B$-calibration," a notion of calibration parameterized by the choice of equivalence classes. Our main theoretical contribution establishes a mechanism for why semantic calibration emerges in base LLMs, leveraging a recent connection between calibration and local loss optimality. This theoretical mechanism leads to a testable prediction: base LLMs will be semantically calibrated when they can easily predict their own distribution over semantic answer classes before generating a response. We state three implications of this prediction, which we validate through experiments: (1) Base LLMs are semantically calibrated across question-answering tasks, (2) instruction-tuning procedures systematically break this calibration, and (3) chain-of-thought reasoning breaks calibration (intuitively because models cannot predict their final answers before completing their generation). To our knowledge, our work provides the first principled explanation of when and why semantic calibration emerges in LLMs.

We present an algorithm for the empirical group distributionally robust (GDR) least squares problem. Given $m$ groups, a parameter vector in $\mathbb{R}^d$, and stacked design matrices and responses $\mathbf{A}$ and $\bm{b}$, our algorithm obtains a $(1+\varepsilon)$-multiplicative optimal solution using $\widetilde{O}(\min\{\mathsf{rank}(\mathbf{A}),m\}^{1/3}\varepsilon^{-2/3})$ linear-system-solves of matrices of the form $\mathbf{A}^{\top}\mathbf{B}\mathbf{A}$ for block-diagonal $\mathbf{B}$. Our technical methods follow from a recent geometric construction, block Lewis weights, that relates the empirical GDR problem to a carefully chosen least squares problem and an application of accelerated proximal methods. Our algorithm improves over known interior point methods for moderate accuracy regimes and matches the state-of-the-art guarantees for the special case of $\ell_{\infty}$ regression. We also give algorithms that smoothly interpolate between minimizing the average least squares loss and the distributionally robust loss.

MambaVoiceCloning (MVC) asks whether the conditioning path of diffusion-based TTS can be made fully SSM-only at inference—removing all attention and recurrence across text, rhythm, and prosody—while preserving or improving quality under controlled conditions. MVC combines a gated bidirectional Mamba text encoder, a Temporal Bi-Mamba supervised by a lightweight alignment teacher discarded after training, and an expressive Mamba with AdaLN modulation, yielding linear-time $\mathcal{O}(T)$ conditioning with bounded activation memory and practical finite look-ahead streaming. Unlike prior Mamba–TTS systems that remain hybrid at inference, MVC removes attention-based duration and style modules under a fixed StyleTTS2 mel–diffusion–vocoder backbone. Trained on LJSpeech/LibriTTS and evaluated on VCTK, CSS10 (ES/DE/FR), and long-form Gutenberg passages, MVC achieves modest but statistically reliable gains over StyleTTS2, VITS, and Mamba–attention hybrids in MOS/CMOS, F$_0$ RMSE, MCD, and WER, while reducing encoder parameters to 21M and improving throughput by $1.6\times$. Diffusion remains the dominant latency source, but SSM-only conditioning improves memory footprint, stability, and deployability. Code: \url{https://github.com/aiai-9/MVC}.

Large Language Models (LLMs) achieve remarkable success, but their massive parameter counts present significant deployment challenges. Post-training tensor decomposition offers a promising, data-free compression strategy by exploiting structural redundancies within the model weights. However, existing tensor methods face a critical limitation: the dense core tensor bottleneck. While these methods find a shared low-rank basis, the resulting dense core tensor grows polynomially with the chosen ranks, becoming a new storage bottleneck and capping the maximum achievable compression. To overcome this fundamental barrier, we introduce LeSTD (\textbf{Le}arning-based \textbf{S}parse \textbf{T}ensor \textbf{D}ecomposition), a novel two-stage framework for the high-ratio compression of Multi-Head Attention (MHA) blocks. LeSTD first employs an iterative algorithm to identify a high-quality, and shared orthogonal basis that jointly represents all attention heads. Subsequently, it introduces a principled, importance-based pruning algorithm that learns an ultra-sparse core tensor by systematically removing the least salient elements and refitting the remaining ones to preserve model fidelity. By decoupling basis optimization from core sparsification, LeSTD breaks the compression ceiling imposed by the dense core, enabling significantly higher compression ratios than prior methods.

As AI increasingly shapes daily life, energy consumption and data privacy have become pressing concerns. On-device learning trains models directly on edge devices, cutting energy consumption and safeguarding data privacy. However, the expanding scale of modern neural networks creates a major obstacle for on-device training. Although prior work has concentrated on compact convolutional architectures, we instead apply subspace-based training to transformer models. Motivated by the idea that a model's essential information lies in a fixed subspace, we introduce Weight-Activation Subspace Iteration (WASI), a method that mitigates the memory bottleneck of backpropagation and boosts inference efficiency in transformer models by restricting training to this subspace. Our results demonstrate that WASI maintains accuracy comparable to vanilla training while reducing memory usage by up to $62\times$ and computational cost (FLOPs) by up to $2\times$. On a Raspberry Pi 5, WASI achieves roughly $1.4\times$ faster training and inference than vanilla training. The code is available at https://github.com/Le-TrungNguyen/ICLR2026-WASI.git.

Video understanding has made remarkable progress in recent years, largely driven by advances in deep models and the availability of large-scale annotated datasets. However, the robustness of these models to domain shifts encountered in real-world video applications remains a critical yet underexplored problem, limiting their practical reliability. To address this problem, we introduce \textbf{V}ideo \textbf{U}nderstanding \textbf{D}omain \textbf{G}eneralization (\textbf{VUDG}), the first dataset designed specifically for evaluating domain generalization in video understanding. VUDG contains videos from 11 distinct domains that cover three types of domain shifts, and maintains semantic consistency across different domains to ensure fair and meaningful evaluation. We propose a multi-expert progressive annotation framework to efficiently annotate videos with structured question-answer pairs designed for domain generalization. Extensive experiments on 9 representative Large Vision-Language Models (LVLMs) and several traditional video question answering methods show that most models (including state-of-the-art LVLMs) suffer performance degradation under domain shifts. These results highlight the challenges posed by VUDG and the difference in the robustness of current models to data distribution shifts. We believe VUDG provides a critical resource to benefit future research in domain generalization for video understanding.

Scaling test-time compute has emerged as an effective strategy for improving the performance of large language models. However, existing methods typically allocate compute uniformly across all queries, overlooking variation in query difficulty. To address this inefficiency, we formulate test-time compute allocation as a novel bandit learning problem and propose adaptive algorithms that estimate query difficulty on the fly and allocate compute accordingly. Compared to uniform allocation, our algorithms allocate more compute to challenging queries while maintaining accuracy on easier ones. Among challenging queries, our algorithms further learn to prioritize solvable instances, effectively reducing excessive computing on unsolvable queries. We theoretically prove that our algorithms achieve better compute efficiency than uniform allocation and empirically validate their effectiveness on math and code benchmarks. Specifically, our algorithms achieve up to an 11.10\% performance improvement (15.04\% relative) on the MATH-500 dataset, up to 10.82\% (14.44\% relative) on the AIME25 dataset, and up to an 11.23\% performance improvement (15.29\% relative) on the LiveCodeBench dataset.

Due to tractable analysis and control, linear state-space models (LSSMs) provide a fundamental mathematical tool for time-series data modeling in various disciplines. In particular, many LSSMs have sparse system matrices because interactions among variables are limited or only a few significant relationships exist. However, current learning algorithms for LSSMs lack the ability to learn system matrices with the sparsity constraint due to the similarity transformation. To address this issue, we impose sparsity-promoting priors on system matrices to balance modeling error and model complexity. By taking hidden states of LSSMs as latent variables, we then explore the expectation-maximization (EM) algorithm to derive a maximum a posteriori (MAP) estimate of both hidden states and system matrices from noisy observations. Based on the Global Convergence Theorem, we further demonstrate that the proposed learning algorithm yields a sequence converging to a local maximum or saddle point of the joint posterior distribution. Finally, experimental results on simulation and real-world problems illustrate that the proposed algorithm can preserve the inherent topological structure among variables and significantly improve prediction accuracy over classical learning algorithms.