ICLR 2026 论文列表

Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. While GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale, its inner workings are described as a sequence of algebraic updates that obscure geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: first, the GPTQ error propagation step gains an intuitive geometric interpretation; second, GPTQ inherits the error upper bound of Babai's algorithm under the assumption that no weights are clipped. Leveraging this bound, we design post-training quantization methods that avoid clipping, and outperform the original GPTQ. In addition, we provide efficient GPU inference kernels for the resulting representation. Taken together, these results place GPTQ on a firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models.

Despite the flourishing in time series (TS) forecasting backbones, the training mostly relies on regression losses like Mean Square Error (MSE). However, MSE assumes a one-mode Gaussian distribution, which struggles to capture complex patterns, especially for real-world scenarios where multiple diverse outcomes are possible. We propose the Multi-Mode Patch Diffusion (MMPD) loss, which can be applied to any patch-based backbone that outputs latent tokens for the future. Models trained with MMPD loss generate diverse predictions (modes) with the corresponding probabilities. Technically, MMPD loss models the future distribution with a diffusion model conditioned on latent tokens from the backbone. A lightweight Patch Consistent MLP is introduced as the denoising network to ensure consistency across denoised patches. Multi-mode predictions are generated by a multi-mode inference algorithm that fits an evolving variational Gaussian Mixture Model (GMM) during diffusion. Experiments on eight datasets show its superiority in diverse forecasting. Its deterministic and probabilistic capabilities also match the strong competitor losses, MSE and Student-T, respectively.

Reinforcement learning (RL) is widely used for humanoid control, with on-policy methods such as Proximal Policy Optimization (PPO) enabling robust training via large-scale parallel simulation and, in some cases, zero-shot deployment to real robots. However, the low sample efficiency of on-policy algorithms limits safe adaptation to new environments. Although off-policy RL and model-based RL have shown improved sample efficiency, the gap between large-scale pretraining and efficient finetuning on humanoids still exists. In this paper, we find that off-policy Soft Actor-Critic (SAC), with large-batch update and a high Update-To-Data (UTD) ratio, reliably supports large-scale pretraining of humanoid locomotion policies, achieving zero-shot deployment on real robots. For adaptation, we demonstrate that these SAC-pretrained policies can be finetuned in new environments and out-of-distribution tasks using model-based methods. Data collection in the new environment executes a deterministic policy while stochastic exploration is instead confined to a physics-informed world model. This separation mitigates the risks of random exploration during adaptation while preserving exploratory coverage for improvement. Overall, the approach couples the wall-clock efficiency of large-scale simulation during pretraining with the sample efficiency of model-based learning during fine-tuning. Code and videos: https://lift-humanoid.github.io

Achieving group-robust generalization in the presence of spurious correlations remains a significant challenge, particularly when bias annotations are unavailable. Recent studies on Class-Conditional Distribution Balancing (CCDB) reveal that spurious correlations often stem from mismatches between the class-conditional and marginal distributions of bias attributes. They achieve promising results by addressing this issue through simple distribution matching in a bias-agnostic manner. However, CCDB approximates each distribution using a single Gaussian, which is overly simplistic and rarely holds in real-world applications. To address this limitation, we propose a novel Multi-stage data-Selective reTraining strategy (MST), which describes each distribution in greater detail using the hard confusion matrix. Building on these finer descriptions, we propose a fine-grained variant of CCDB, termed FG-CCDB, which enhances distribution matching through more precise confusion-cell-wise reweighting. FG-CCDB learns sample weights from a global perspective, effectively mitigating spurious correlations without incurring substantial storage or computational overhead. Extensive experiments demonstrate that MST serves as a reliable proxy for ground-truth bias annotations and can be seamlessly integrated with bias-supervised methods. Moreover, when combined with FG-CCDB, our method performs on par with bias-supervised approaches on binary classification tasks and significantly outperforms them in highly biased multi-class and multi-shortcut scenarios.

Continual learning (CL) enables models to acquire new tasks sequentially while retaining previously learned knowledge. However, most theoretical analyses focus on simplified, converged models or restrictive data distributions and therefore fail to capture how forgetting and generalization evolve during training in more general settings. Current theory faces two fundamental challenges: (i) analyses confined to the converged regime cannot characterize intermediate training dynamics; and (ii) establishing forgetting bounds requires two-sided bounds on the population risk for each task. To address these challenges, we analyze the training-time dynamics of forgetting and generalization in standard CL within the Neural Tangent Kernel (NTK) regime, showing that decreasing the loss’s Lipschitz constant and minimizing the cross-task kernel jointly reduce forgetting and improve generalization. Specifically, we (i) characterize intermediate training stages via kernel gradient flow and (ii) employ Rademacher complexity to derive both upper and lower bounds on population risk. Building on these insights, we propose \emph{OGD+}, which projects the current task’s gradient onto the orthogonal complement of the subspace spanned by gradients of the most recent task evaluated on all prior samples. We further introduce \emph{Orthogonal Penalized Gradient Descent} (OPGD), which augments OGD+ with gradient-norm penalization to jointly reduce forgetting and enhance generalization. Experiments on multiple benchmarks corroborate our theoretical predictions and demonstrate the effectiveness of OPGD, providing a principled pathway from theory to algorithm design in CL.

Bridging the gap between the formal precision of system specifications and the nuances of human language is critical for reliable engineering, robotics, and AI safety, but it remains a major bottleneck. Prior efforts in grounding formal logic remain fragmented, resulting in datasets that are very small-scale (~2-5k examples), domain-specific, or translate logic into overly technical forms rather than context-rich natural language (NL). Thus, failing to adequately bridge formal methods and practical NLP. To address this gap, we introduce VERIFY, the first large-scale dataset meticulously designed to unify these elements. This dataset contains more than 200k+ rigorously generated triplets, each comprising a Linear Temporal Logic (LTL) formula, a structured, human-readable 'Intermediate Technical Language' (ITL) representation designed as a bridge between logic and text, and a domain-specific NL description contextualized across 13 diverse domains. VERIFY's construction pipeline ensures high fidelity: LTL formulas are enumerated and verified via model checking, mapped to the novel ITL representation using a provably complete formal grammar, and then translated into context-aware NL via LLM-driven generation. We guarantee data quality through extensive validation protocols, i.e., manual expert verification of 10,000 diverse samples. Furthermore, automated semantic consistency checks judged by Llama 3.3 confirmed an estimated >97% semantic correctness. From the initial experiments, we demonstrate VERIFY's scalability, logical complexity, and contextual diversity, significantly challenging standard models such as T5 and Llama 3.

Sequential recommendation models are widely used in applications, yet they face stringent latency requirements. Mainstream models leverage the Transformer attention mechanism to improve performance, but its computational complexity grows with the sequence length, leading to a latency challenge for long sequences. Consequently, KV cache technology has recently been explored in sequential recommendation systems to reduce inference latency. However, KV cache introduces substantial storage overhead in sequential recommendation systems, which often have a large user base with potentially very long user history sequences. In this work, we observe that KV sequences across different users exhibit significant similarities, indicating the existence of collaborative signals in KV. Furthermore, we analyze the KV using singular value decomposition (SVD) and find that the information in KV can be divided into two parts: the majority of the information is shareable across users, while a small portion is user-specific. Motivated by this, we propose CollectiveKV, a cross-user KV sharing mechanism. It captures the information shared across users through a learnable global KV pool. During inference, each user retrieves high-dimensional shared KV from the pool and concatenates them with low-dimensional user-specific KV to obtain the final KV. Experiments on five sequential recommendation models and three datasets show that our method can compress the KV cache to only 0.8\% of its original size, while maintaining or even enhancing model performance.

Transformers have demonstrated strong performance in time series forecasting, yet they often fail to capture the intrinsic structure of temporal data, making them susceptible to real-world noise and anomalies. Unlike in vision or language, the local geometry of temporal patterns is a critical feature in time series forecasting, but it is frequently disrupted by corruptions. In this work, we address this gap with two key contributions. First, we propose Local Geometry Attention (LGA), a novel attention mechanism theoretically grounded in local Gaussian process theory. LGA adapts to the intrinsic data geometry by learning query-specific distance metrics, enabling it to model complex temporal dependencies and enhance resilience to noise. Second, we introduce TSRBench, the first comprehensive benchmark for evaluating forecasting robustness under realistic, statistically-grounded corruptions. Experiments on TSRBench show that LGA significantly reduces performance degradation, consistently outperforming both Transformer and linear model. These results establish a foundation for developing robust time series models that can be deployed in real-world applications where data quality is not guaranteed. Our code is available at: https://anonymous.4open.science/r/LGA-5454.

Reinforcement Learning (RL) has shown remarkable success in enhancing the reasoning capabilities of Large Language Models (LLMs). Process-Supervised RL (PSRL) has emerged as a more effective paradigm compared to outcome-based RL. However, existing PSRL approaches suffer from limited exploration efficiency, both in terms of branching positions and sampling. In this paper, we introduce a novel PSRL framework (AttnRL), which enables efficient exploration for reasoning models. Motivated by preliminary observations that steps exhibiting high attention scores correlate with reasoning behaviors, we propose to branch from positions with high values. Furthermore, we develop an adaptive sampling strategy that accounts for problem difficulty and historical batch size, ensuring that the whole training batch maintains non-zero advantage values. To further improve sampling efficiency, we design a one-step off-policy training pipeline for PSRL. Extensive experiments on multiple challenging mathematical reasoning benchmarks demonstrate that our method consistently outperforms prior approaches in terms of performance and sampling and training efficiency.

Combining Chain-of-Thought (CoT) with Reinforcement Learning (RL) improves text-to-image (T2I) generation, yet the underlying interaction between CoT's exploration and RL's optimization remains unclear. We present a systematic entropy-based analysis that yields three key insights: (1) CoT expands the generative exploration space, while RL contracts it toward high-reward regions; (2) final reward is strongly negatively correlated with both the mean and variance of image-token entropy, highlighting the need to reduce uncertainty and instability; and (3) the entropy of the textual CoT directly governs downstream image quality, with lower-entropy CoTs leading to better generations. Motivated by these findings, we propose Entropy-Guided Group Relative Policy Optimization (EG-GRPO), a fine-tuning strategy that reallocates optimization budget by uncertainty: low-entropy tokens are excluded from reward-driven updates to preserve stability, while high-entropy tokens receive an entropy bonus that encourages structured exploration without collapse. Experiments on standard T2I benchmarks demonstrate that EG-GRPO achieves state-of-the-art performance.

Multimodal large language models (MLLMs) have demonstrated remarkable potential in bridging visual and textual reasoning, yet their reliance on text-centric priors often limits their ability to disentangle semantically similar actions in open-vocabulary scenarios. To address this, we propose Video-STAR, a framework that harmonizes contextual sub-motion decomposition with tool-augmented reinforcement learning for open-vocabulary action recognition (OVAR). Unlike prior methods that treat actions as monolithic entities, our approach innovatively decomposes actions into discriminative sub-motions for fine-grained matching while dynamically invokes domain-specific tools for cross-modal interleaving, thereby enabling category-specific reasoning capacity and reducing cross-modal hallucination. Moreover, by designing a hierarchical reward that balances tool-usage efficiency, sub-motion relevance, and structural coherence in reasoning, our method autonomously leverages external tools to prioritize sub-motion patterns without explicit supervision, transmitting from text-centric reasoning to visually grounded inference. Extensive evaluations on HMDB-51, UCF-101, SSv2, Kinetics-400, and Kinetics-600 datasets demonstrate our state-of-the-art performance, outperforming existing methods in distinguishing fine-grained actions and handling cross-modal hallucination, while maintaining computational efficiency.

A central challenge in program induction has long been the trade-off between symbolic and neural approaches. Symbolic methods offer compositional generalisation and data efficiency, yet their scalability is constrained by formalisms such as domain-specific languages (DSLs), which are labor-intensive to create and may not transfer to new domains. In contrast, neural networks flexibly learn from data but fail to generalise systematically. We bridge this divide with the Neural Language Interpreter (NLI), an architecture that learns its own discrete, symbolic-like programming language end-to-end. NLI autonomously discovers a vocabulary of subsymbolic primitive operations and uses a novel differentiable neural executor to interpret variable-length sequences of these primitives. This allows NLI to represent programs that are not bound to a constant number of computation steps, enabling it to solve more complex problems than those seen during training. To make these discrete, compositional program structures amenable to gradient-based optimisation, we employ the Gumbel-Softmax relaxation, enabling the entire model to be trained end-to-end. Crucially, this same differentiability enables powerful test-time adaptation. At inference, NLI's program inductor provides an initial program guess. This guess is then refined via gradient descent through the neural executor, enabling efficient search for the neural program that best explains the given data. We demonstrate that NLI outperforms in-context learning, test-time training, and continuous latent program networks (LPNs) on tasks that require combinatorial generalisation and rapid adaptation to unseen tasks. Our results establish a new path toward models that combine the compositionality of discrete languages with the gradient-based search and end-to-end learning of neural networks.

Constraint-based causal discovery relies on numerous conditional independence tests (CITs), but its practical applicability is severely constrained by the prohibitive computational cost, especially as CITs themselves have high time complexity with respect to the sample size. To address this key bottleneck, we introduce the Ensemble Conditional Independence Test (E-CIT), a general and plug-and-play framework. E-CIT operates on an intuitive divide-and-aggregate strategy: it partitions the data into subsets, applies a given base CIT independently to each subset, and aggregates the resulting p-values using a novel method grounded in the properties of stable distributions. This framework reduces the computational complexity of a base CIT to linear in the sample size when the subset size is fixed. Moreover, our tailored p-value combination method offers theoretical consistency guarantees under mild conditions on the subtests. Experimental results demonstrate that E-CIT not only significantly reduces the computational burden of CITs and causal discovery but also achieves competitive performance. Notably, it exhibits an improvement in complex testing scenarios, particularly on real-world datasets.

Indirect editing methods for 3D Gaussian Splatting (3DGS) have recently witnessed significant advancements. These approaches operate by first applying edits in the rendered 2D space and subsequently projecting the modifications back into 3D. *However, this paradigm inevitably introduces cross-view inconsistencies and constrains both the flexibility and efficiency of the editing process*. To address these challenges, we present **VF-Editor**, which enables native editing of Gaussian primitives by predicting attribute variations in a feedforward manner. To accurately and efficiently estimate these variations, we design a novel variation predictor distilled from 2D editing knowledge. The predictor encodes the input to generate a variation field and employs two learnable, parallel decoding functions to iteratively infer attribute changes for each 3D Gaussian. Thanks to its unified design, VF-Editor can seamlessly distill editing knowledge from diverse 2D editors and strategies into a single predictor, allowing for flexible and effective knowledge transfer into the 3D domain. Extensive experiments on both public and private datasets reveal the inherent limitations of indirect editing pipelines and validate the effectiveness and flexibility of our approach.

Thinking LLMs solve complex tasks at the expense of increased compute and overthinking on simpler problems, while non-thinking LLMs are faster and cheaper but underthink on harder reasoning problems. This has led to the development of separate thinking and non-thinking LLM variants, leaving the onus of selecting the optimal model for each query on the end user. In this work, we introduce OptimalThinkingBench, a unified benchmark that jointly evaluates overthinking and underthinking in LLMs and also encourages the development of optimally-thinking models that balance performance and efficiency. Our benchmark comprises two sub-benchmarks: OverthinkingBench, featuring simple general queries in 72 domains along with simple math problems, and UnderthinkingBench, containing 11 challenging reasoning tasks along with tough math problems. Using novel thinking-adjusted accuracy metrics, we perform an extensive evaluation of 33 different thinking and non-thinking models and show that no model is able to optimally think on our benchmark. Thinking models often overthink for hundreds of tokens on the simplest user queries without improving performance. In contrast, large non-thinking models ``underthink'', often falling short of much smaller thinking models. We further explore several methods to encourage optimal thinking, but find that these approaches often improve on one sub-benchmark at the expense of the other, highlighting the need for better unified and optimal models in the future.

Learning robust representations from functional magnetic resonance imaging (fMRI) is fundamentally challenged by the temporal irregularity and noise inherent in data from heterogeneous sources. Existing self-supervised learning (SSL) methods often discard critical temporal information by discretizing or averaging fMRI signals. To address this, we introduce a novel framework that reframes SSL as a Stochastic Optimal Control (SOC) problem. Our approach models brain activity as continuous-time latent dynamics, learning a robust representation of brain dynamics by optimizing a control policy that is agnostic to the temporal irregularity. This SOC framework naturally unifies masked autoencoding (MAE) and joint-embedding prediction (JEPA) to extract compact, control-derived representations. Furthermore, a simulation-free inference strategy ensures computational efficiency and scalability for large-scale fMRI datasets. Our model demonstrates state-of-the-art performance across diverse downstream applications, highlighting the potential of the SOC-based continuous-time representation learning framework.

Model merging plays a crucial role in consolidating multiple specialized models into a single, unified model, especially in the era of large language models (LLMs). Recent research has primarily focused on developing strategies to enhance merging performance with the trained models, while the impact of training paradigms, such as supervised fine-tuning (SFT) and reinforcement learning (RL), on the effectiveness of model merging remains underexplored. In this study, we systematically explore the merging behavior of RL-trained LLMs compared to those trained with traditional SFT. Through comprehensive evaluations across five representative tasks, we find that RL significantly reduces task conflicts and results in less performance degradation after merging, making RL-trained models particularly well-suited for this process. To unearth the reasons behind the superior suitability of RL for model merging, we conduct extensive empirical experiments and theoretical analyses. Our findings highlight three key factors: (1) On-policy training data in RL control the gradient updates in a smaller magnitude, reducing the risk of overwriting existing knowledge for other tasks in the model. (2) The RL optimization objective, which favors "\textit{enough is as good as a feast}", progressively reduces the magnitude of parameter updates as the model converges, thereby alleviating inter-task conflicts. (3) Joint optimization of positive and negative examples in RL steers the model towards an unbiased task-specific parameter subspace, ensuring robust performance while further preventing parameter conflicts.

The quadratic complexity of softmax attention poses a major bottleneck for long-context modeling, motivating a surge of linear attention variants with linear complexity. Unlike softmax attention, which benefits from optimized kernels, linear attention lacks general-purpose, hardware-efficient support and scalable distributed implementations. We introduce Forge, a domain-specific compiler that automates the generation of high-performance, scalable kernels for a wide range of linear attention models directly from high-level PyTorch code. At its core, Forge employs an intuitive programming abstraction that decomposes any linear attention algorithm into three canonical phases: intra-chunk computation, inter-chunk state propagation, and output merging. This unified abstraction enables Forge to perform domain-specific optimizations, automatically generating kernels that fuse computation and communication at a fine-grained tile level and eliminating host synchronization. Our evaluation demonstrates that Forge combines programmability with performance: a wide range of linear attention variants can be implemented in just a few dozen lines of code, while the generated kernels deliver 1.01x-4.9x the performance of sate-of-the-art expert-optimized library and scale with near-linear efficiency on scalar gated linear attention to 16 million tokens on 128 GPUs, surpassing the state-of-the-art distributed baseline by up to 7.2x.

Reconstructing dynamic 3D scenes with photorealistic detail and temporal coherence remains a significant challenge. Existing Gaussian splatting approaches modeling scenes rely on per-frame optimization, causing them to overfit to instantaneous states rather than learning true motion dynamics. To address this, we present Mango-GS, a multi-frame, node-guided framework for high-fidelity 4D reconstruction. Our approach leverages a temporal Transformer to learn complex motion dependencies across a window of frames, ensuring the generation of plausible trajectories. For efficiency, this temporal modeling is confined to a sparse set of control nodes. These nodes are uniquely designed with decoupled position and latent codes, which provide a stable semantic anchor for motion influence and prevents correspondence errors for large movements. Our framework is trained end-to-end, enhanced by a input masking strategy and two multi-frame loss to ensure robustness. Extensive experiments demonstrate that Mango-GS achieves state-of-the-art quality and fast rendering speed, enabling high-fidelity reconstruction and real-time rendering of dynamic scenes.