ICLR 2026 Papers

Persistent homology (PH) based schemes help encode information, such as cycles, and are thus increasingly being integrated with graph neural networks (GNNs) and higher order message-passing networks. Many PH based schemes in graph learning employ inclusion-based filtration mechanisms that trace a sequence of subgraphs of increasing size, maintaining bookkeeping information about the evolution (e.g., in terms of birth and death of components). We offer a novel perspective that goes beyond this inclusion paradigm. Specifically, we introduce topological descriptors for graphs, simplices, and cells that interleave a sequence of inclusions with a sequence of contractions and related families parametrized by two functions. The resulting descriptors on the extended sequence are provably more expressive than many existing PH methods with suitable stability conditions. Empirical results substantiate the merits of the proposed approach.

Model pruning is an effective approach for compressing large language models (LLMs). However, this process often leads to significant degradation of model capabilities. While post-training techniques such as instruction tuning are commonly employed to recover model performance, existing methods often overlook the uneven deterioration of model capabilities and incur high computational costs. Moreover, some irrelevant instructions may also introduce negative effects to model capacity recovery. To address these challenges, we propose the **P**ost-training d**A**ta **S**election method for **E**fficient pruned large language model **R**ecovery (**PASER**). PASER aims to identify instructions to recover the most compromised model capacities with a certain data budget. Our approach first applies manifold learning and spectral clustering to group recovery instructions in the semantic space, revealing capability-specific instruction sets. Then, the data budget is adaptively allocated across clusters by the degree of corresponding model capability degradation. In each cluster, we prioritize data samples that lead to the most decline of model performance. To mitigate potential negative tuning effects, we also detect and filter out conflicting or irrelevant recovery data. Extensive experiments demonstrate that PASER significantly outperforms conventional baselines, effectively recovering the general capabilities of pruned LLMs while utilizing merely 4\%-20\% of the original post-training data. We provide the anonymous code repository in [Link](https://anonymous.4open.science/r/PASER-E606).

Dynamic reconstruction has achieved remarkable progress, but there remain challenges in monocular input for more practical applications. The prevailing works attempt to construct efficient motion representations, but lack a unified spatiotemporal decomposition framework, suffering from either holistic temporal optimization or coupled hierarchical spatial composition. To this end, we propose WorldTree, a unified framework comprising Temporal Partition Tree (TPT) that enables coarse-to-fine optimization based on the inheritance-based partition tree structure for hierarchical temporal decomposition, and Spatial Ancestral Chains (SAC) that recursively query ancestral hierarchical structure to provide complementary spatial dynamics while specializing motion representations across ancestral nodes. Experimental results on different datasets indicate that our proposed method achieves 8.26% improvement of LPIPS on NVIDIA-LS and 9.09% improvement of mLPIPS on DyCheck compared to the second-best method. Code: https://github.com/iCVTEAM/WorldTree.

As new optimizers gain traction and model quantization becomes standard for efficient deployment, a key question arises: how does the choice of optimizer affect model performance in the presence of quantization? Despite progress in both areas, systematic evidence on optimizer–quantization interactions remains limited. To fill this gap, we study the impact of optimizer choice on model robustness under quantization, considering both post-training quantization (PTQ), and quantization-aware training (QAT). We first train full-precision models, ranging from 50M to 1.5B parameters, with six optimizers, to explore the hyperparameter landscape, and establish well-tuned baselines. We then apply PTQ to evaluate how model performance degrades when trained with different optimizers. We find that outlier-related metrics, such as the max-to-mean ratio (MMR) and Kurtosis, fail to predict the PTQ performance across different optimizers. We show analytically that this is due to the MMR capturing only isolated layer errors, while ignoring how quantization errors accumulate and propagate through the network. To study the QAT degradation, we train quantized models from scratch and compare them to our original-precision baselines. We find that optimizers performing well in the original pretraining setup may not remain optimal under QAT, and that models trained with Shampoo show the lowest accuracy degradation. Finally, we derive scaling laws for quantization-aware training under different optimizers, showing that Shampoo achieves the highest parameter efficiency of all tested optimizers.

Test-Time Adaptation (TTA) methods are often computationally expensive, require a large amount of data for effective adaptation, or are brittle to hyperparameters. Based on a theoretical foundation of the geometry of the latent space, we are able to significantly improve the alignment between source and distribution-shifted samples by re-centering target data embeddings at the origin. This insight motivates NEO – a hyperparameter-free fully TTA method, that adds no significant compute compared to vanilla inference. NEO is able to improve the classification accuracy of ViT-Base on ImageNet-C from 55.6\% to 59.2\% after adapting on just one batch of 64 samples. When adapting on 512 samples NEO beats all 7 TTA methods we compare against on ImageNet-C, ImageNet-R and ImageNet-S and beats 6/7 on CIFAR-10-C, while using the least amount of compute. NEO performs well on model calibration metrics and additionally is able to adapt from 1 class to improve accuracy on 999 other classes in ImageNet-C. On Raspberry Pi and Jetson Orin Nano devices, NEO reduces inference time by 63\% and memory usage by 9\% compared to baselines. Our results based on 3 ViT architectures and 4 datasets show that NEO can be used efficiently and effectively for TTA.

Knowledge Graph Question Answering (KGQA) aims to interpret natural language queries and perform structured reasoning over knowledge graphs by leveraging their relational and semantic structures to retrieve accurate answers. Existing methods primarily follow either the retrieve-then-reason paradigm, which relies on Graph Neural Networks (GNNs) or heuristic rules to extract static candidate paths, or dynamic path generation strategies that employ large language models (LLMs) with prompting to jointly perform retrieval and reasoning. However, the former lacks adaptability due to static path extraction and the absence of contextual refinement, while the latter suffers from high computational costs and limited evaluation accuracy because of their dependence on fixed scoring functions and repeated LLM calls. To address these issues, this paper proposes Dynamically Adaptive MCTS-based Reasoning (DAMR), a novel framework that integrates LLM-guided Monte Carlo Tree Search (MCTS) with adaptive path evaluation to enable efficient and context-aware KGQA. DAMR leverages MCTS as a backbone, where an LLM-based planner selects the top-$k$ semantically relevant relations at each expansion step to effectively reduce the search space. To enhance evaluation accuracy, we introduce a lightweight Transformer-based scorer that performs context-aware plausibility estimation by jointly encoding the question and relation sequence through cross-attention, thereby capturing fine-grained semantic shifts during multi-hop reasoning. Furthermore, to mitigate the scarcity of high-quality supervision, DAMR incorporates a dynamic pseudo-path refinement mechanism that periodically generates training signals from partial paths explored during search, enabling the scorer to continually adapt to the evolving distribution of reasoning trajectories. Extensive experiments on multiple KGQA benchmarks show that DAMR significantly outperforms state-of-the-art methods.

Large language models (LLMs) have demonstrated impressive capabilities across a wide range of natural language processing tasks. However, their outputs often exhibit social biases, raising fairness concerns. Existing debiasing methods, such as fine-tuning on additional datasets or prompt engineering, face scalability issues or compromise user experience in multi-turn interactions. To address these challenges, we propose a framework for detecting stereotype-inducing words and attributing neuron-level bias in LLMs, without the need for fine-tuning or prompt modification. Our framework first identifies stereotype-inducing adjectives and nouns via comparative analysis across demographic groups. We then attribute biased behavior to specific neurons using two attribution strategies based on integrated gradients. Finally, we mitigate bias by directly intervening on their activations at the projection layer. Experiments on three widely used LLMs demonstrate that our method effectively reduces bias while preserving overall model performance.

We study cross-domain lossy compression, where the encoder observes a degraded source while the decoder reconstructs samples from a distinct target distribution. The problem is formulated as constrained optimal transport with two constraints on compression rate and classification loss. With shared common randomness, the one-shot setting reduces to a deterministic transport plan, and we derive closed-form distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoffs for Bernoulli sources under Hamming distortion. In the asymptotic regime, we establish analytic DRC/RDC expressions for Gaussian models under mean-squared error. The framework is further extended to incorporate perception divergences (Kullback-Leibler and squared Wasserstein), yielding closed-form distortion-rate-perception-classification (DRPC) functions. To validate the theory, we develop deep end-to-end compression models for super-resolution (MNIST), denoising (SVHN, CIFAR-10, ImageNet, KODAK), and inpainting (SVHN) problems, demonstrating the consistency between the theoretical results and empirical performance.

We introduce EasyCreator, a novel 4D video creation framework capable of both generating and editing 4D content from a single monocular video input. By leveraging a powerful video inpainting foundation model as a generative prior, we reformulate 4D video creation as a video inpainting task, enabling the model to fill in missing content caused by camera trajectory changes or user edits. To facilitate this, we generate composite masked inpainting video data to effectively fine-tune the model for 4D video generation. Given an input video and its associated camera trajectory, we first perform depth-based point cloud rendering to obtain invisibility masks that indicate the regions that should be completed. Simultaneously, editing masks are introduced to specify user-defined modifications, and these are combined with the invisibility masks to create a composite masks dataset. During training, we randomly sample different types of masks to construct diverse and challenging inpainting scenarios, enhancing the model’s generalization and robustness in various 4D editing and generation tasks. To handle temporal consistency under large camera motion, we design a self-iterative tuning strategy that gradually increases the viewing angles during training, where the model is used to generate the next-stage training data after each fine-tuning iteration. Moreover, we introduce a temporal packaging module during inference to enhance generation quality. Our method effectively leverages the prior knowledge of the base model without degrading its original performance, enabling the generation of 4D videos with consistent multi-view coherence. In addition, our approach supports prompt-based content editing, demonstrating strong flexibility and significantly outperforming state-of-the-art methods in both quality and versatility.

The proliferation of diverse data across users and organizations has driven the development of machine learning methods that enable multiple entities to jointly train models while minimizing data sharing. Among these, *multitask learning* (MTL) is a powerful paradigm that leverages similarities among multiple tasks, each with insufficient samples to train a standalone model, to solve them simultaneously. MTL accomplishes this by learning a *shared representation* that captures common structure between tasks and generalizes well across them all. Despite being designed to be the smallest unit of shared information necessary to effectively learn patterns across multiple tasks, these shared representations can inadvertently leak sensitive information about the particular tasks they were trained~on. In this work, we investigate privacy leakage in shared representations through the lens of inference attacks. Towards this, we propose a novel, *black-box task-inference* threat model where the adversary, given the embedding vectors produced by querying the shared representation on samples from a particular task, aims to determine whether the task was present in the multitask training dataset. Motivated by analysis of tracing attacks on mean estimation over mixtures of Gaussian distributions, we develop efficient, purely black-box attacks on machine learning models that exploit the dependencies between embeddings from the same task without requiring shadow models or labeled reference data. We evaluate our attacks across vision and language domains when MTL is used for personalization and for solving multiple distinct learning problems, and demonstrate that even with access only to fresh task samples rather than training data, a black-box adversary can successfully infer a task's inclusion in training.

LLMs are known to store vast amounts of knowledge in their parametric memory. However, learning and recalling facts from this memory is known to be unreliable, depending largely on the prevalence of particular facts in the training data and other factors which are poorly understood. Practitioners are lacking tools which will allow them to ensure that the models learn a given body of knowledge reliably and consistently. To this end, we propose Active Reading: a framework where we train models to study a given set of material with self-generated learning strategies. First, we demonstrate models trained with Active Reading on expert domains absorb significantly more knowledge than vanilla finetuning and other data augmentations. We train expert 8B models that achieve 66% on a Wikipedia-grounded subset of SimpleQA (+313% relative over vanilla finetuning) and 26% on FinanceBench (+160% relative over vanilla finetuning) by applying Active Reading to the source documents for each benchmark. Finally, we show that Active Reading can be utilized at pre-training scale to build more factual models. As a demonstration of this, we release WikiExpert-8B, a Wikipedia-expert model trained on 1 trillion generated tokens, which outcompetes models with hundreds of billions of parameters on factual QA.

Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden neurons. This limitation arose from the choice of nonlinearity between the visible and hidden units, which enforced winner-takes-all dynamics in the hidden layer, thereby restricting each hidden unit to encode only a single memory. We overcome this limitation by introducing a novel associative memory network with a threshold nonlinearity that enables distributed representations. In contrast to winner-takes-all dynamics, where each hidden neuron is tied to an entire memory, our network allows hidden neurons to encode basic components shared across many memories. Consequently, complex patterns are represented through combinations of hidden neurons. These representations reduce redundancy and allow many correlated memories to be stored compositionally. Thus, we achieve much higher capacity: exponential in the number of hidden units, provided the number of visible units is sufficiently larger than the number of hidden neurons. Exponential capacity arises because all binary states of the hidden units can become stable memory patterns with an appropriately chosen threshold. Moreover, the distributed hidden representation, which has much lower dimensionality than the visible layer, preserves class-discriminative structure, supporting efficient nonlinear decoding. These results establish a new regime for associative memory, enabling high-capacity, robust, and scalable architectures consistent with biological constraints.

Large language models (LLMs) have revolutionized natural language processing. Understanding their internal mechanisms is crucial for developing more interpretable and optimized architectures. Mechanistic interpretability has led to the development of various methods for assessing layer relevance, with cosine similarity being a widely used tool in the field. On this work, we demonstrate that cosine similarity is a poor proxy for the actual performance degradation caused by layer removal. Our theoretical analysis shows that a layer can exhibit an arbitrarily low cosine similarity score while still being crucial to the model's performance. On the other hand, empirical evidence from a range of LLMs confirms that the correlation between cosine similarity and actual performance degradation is often weak or moderate, leading to misleading interpretations of a transformer's internal mechanisms. We propose a more robust metric for assessing layer relevance: the actual drop in model accuracy resulting from the removal of a layer. Even though it is a computationally costly metric, this approach offers a more accurate picture of layer importance, allowing for more informed pruning strategies and lightweight models. Our findings have significant implications for the development of interpretable LLMs and highlight the need to move beyond cosine similarity in assessing layer relevance.

Recent diffusion-based Multimodal Large Language Models (dMLLMs) suffer from high inference latency and therefore rely on caching techniques to accelerate decoding. However, the application of cache mechanisms often introduces undesirable repetitive text generation, a phenomenon we term the Repeat Curse. To better investigate underlying mechanism behind this issue, we analyze repetition generation through the lens of information flow. Our work reveals three key findings: (1) context tokens aggregate semantic information as anchors and guide the final predictions; (2) as information propagates across layers, the entropy of context tokens converges in deeper layers, reflecting the model’s growing prediction certainty; (3) Repetition is typically linked to disruptions in the information flow of context tokens and to the inability of their entropy to converge in deeper layers. Based on these insights, we present CoTA, a plug-and-play method for mitigating repetition. CoTA enhances the attention of context tokens to preserve intrinsic information flow patterns, while introducing a penalty term to the confidence score during decoding to avoid outputs driven by uncertain context tokens. With extensive experiments, CoTA demonstrates significant effectiveness in alleviating repetition and achieves consistent performance improvements on general tasks. Code will be made available.

The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures---Mamba-2 and Gated DeltaNet---and find they perform well compared to their linear-time variants.

Conformal prediction can be used to construct prediction sets that cover the true outcome with a desired probability, but can sometimes lead to large prediction sets that are costly in practice. The most useful outcome is a singleton prediction---an unambiguous decision---yet existing efficiency-oriented methods primarily optimize average set size. Motivated by this, we propose a new non-conformity score that is motivated by minimizing the probability of producing non-singleton sets while maintaining coverage. Starting from a non-convex constrained optimization problem as a motivation, we provide a convex-geometric reformulation and associated algorithm for computing the non-conformity score and associated split conformal prediction sets in $O(K)$ time for $K$-class problems. Using this score in split conformal prediction, we introduce Singleton-Optimized Conformal Prediction (SOCOP). We evaluate our method in experiments on image classification and LLM multiple-choice answering, comparing with standard non-conformity scores such as the (negative) label probability estimates and their cumulative distribution function; both of which are motivated by aiming to optimize average length. The results show that SOCOP increases singleton frequency (sometimes by over 20\%) compared to the above scores, with minimal impact on average set size.

Tool-Integrated Reasoning (TIR) enables large language models (LLMs) to enhance their internal reasoning ability by integrating external tools. However, models with TIR often exhibit suboptimal behaviors, including insufficient tool calls, excessive tool calls, and overthinking after receiving tool call results. How to empower LLMs to perform TIR efficiently and accurately, while stabilizing the reasoning process, remains an open challenge. In this paper, we first analyze the impact of tool calls on model reasoning from the perspective of information entropy. We find that when tool call results are provided, the information entropy of subsequent reasoning content will show a clear trend of change, and the overall information entropy of the reasoning chain will vary depending on the number of tool calls. Based on these observations, we propose Tool-Light, a framework designed to encourage LLMs to perform TIR efficiently and accurately. Our framework consists of dataset construction and multi-stage fine-tuning. For dataset construction, we use the trained model for continuous self-evolved sampling, integrating two methods: vanilla sampling and entropy-guided sampling. At the same time, during the sampling process, we design strict criteria for selecting positive-negative pairs. For the training process, we introduce a two-stage method, which includes a Supervised Fine-Tuning (SFT), and Self-Evolved Direct Preference Optimization (DPO). Test results on 10 datasets reveal the effectiveness of Tool-Light, significantly improving the efficiency and accuracy of the model in completing TIR tasks.

Recent attempts to transfer features from 2D Vision–Language Models (VLMs) to 3D semantic segmentation expose a persistent trade-off. Directly projecting 2D features into 3D yields noisy and fragmented predictions, whereas enforcing geometric coherence necessitates costly training pipelines and large-scale, annotated 3D data. We argue that this limitation stems from the dominant \textit{segmentation-and-matching} paradigm, which fails to reconcile 2D semantics with 3D geometric structure. The geometric cues are not eliminated during the 2D-to-3D transfer but remain latent within the noisy and view-aggregated features. To exploit this property, we propose \textbf{GeoPurify} that applies a small Student Affinity Network to purify 2D VLM-generated 3D point features using geometric priors distilled from a 3D self-supervised teacher model. During inference, we devise a Geometry-Guided Pooling module to further denoise the point cloud and ensure the semantic and structural consistency. Benefiting from latent geometric information and the learned affinity network, GeoPurify effectively mitigates the trade-off and achieves superior data efficiency. Extensive experiments on major 3D benchmarks demonstrate that GeoPurify achieves or surpasses state-of-the-art performance while utilizing only \textbf{$\sim$1.5\%} of the training data.

Classifier-Free Guidance (CFG) is a widely used technique for conditional generation and improving sample quality in continuous diffusion models, and its extensions to discrete diffusion has recently started to be investigated. In order to improve the algorithms in a principled way, this paper starts by analyzing the exact effect of CFG in the context of a low-dimensional masked diffusion model, with a special emphasis on the guidance schedule. Our analysis shows that high guidance early in sampling (when inputs are heavily masked) harms generation quality, while late-stage guidance has a larger effect. These findings provide a theoretical explanation for empirical observations in recent studies on guidance schedules. The analysis also reveals an imperfection of the current CFG implementations. These implementations can unintentionally cause imbalanced transitions, such as unmasking too rapidly during the early stages of generation, which degrades the quality of the resulting samples. To address this, we draw insight from the analysis and propose a novel classifier-free guidance mechanism. Intuitively, our method smoothens the transport between the data distribution and the initial (masked) distribution, which results in improved sample quality. Remarkably, our method is achievable via a simple one-line code change. Experiments on conditional image and text generation empirically confirm the efficacy of our method.