ICLR 2026 Papers

We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior theory largely focuses on shallow (depth-2) models and does not fully explain the implicit low-rank bias observed in deeper networks. We identify coupled dynamics as a key mechanism behind this bias and show that it intensifies with increasing depth. Focusing on gradient flow under diagonal observations, we prove: (a) networks of depth $\geq 3$ exhibit coupling unless initialized diagonally, and (b) convergence to rank-1 occurs if and only if the dynamics is coupled—resolving an open question by Menon (2024) for a family of initializations. We also revisit the loss of plasticity phenomenon in matrix completion (Kleinman et al., 2024), where pre-training on few observations and resuming with more degrades performance. We show that deep models avoid plasticity loss due to their low-rank bias, whereas depth-2 networks pre-trained under decoupled dynamics fail to converge to low-rank, even when resumed training (with additional data) satisfies the coupling condition—shedding light on the mechanism behind this phenomenon.

Although recent studies on time-series anomaly detection have increasingly adopted ever-larger neural network architectures such as transformers and foundation models, they incur high computational costs and memory usage, making them impractical for real-time and resource-constrained scenarios. Moreover, they often fail to demonstrate significant performance gains over simpler methods under rigorous evaluation protocols. In this study, we propose Patch-based representation learning for time-series Anomaly detection (PaAno), a lightweight yet effective method for fast and efficient time-series anomaly detection. PaAno extracts short temporal patches from time-series training data and uses a 1D convolutional neural network to embed each patch into a vector representation. The model is trained using a combination of triplet loss and pretext loss to ensure the embeddings capture informative temporal patterns from input patches. During inference, the anomaly score at each time step is computed by comparing the embeddings of its surrounding patches to those of normal patches extracted from the training time-series. Evaluated on the TSB-AD benchmark, PaAno achieved state-of-the-art performance, significantly outperforming existing methods, including those based on heavy architectures, on both univariate and multivariate time-series anomaly detection across various range-wise and point-wise performance measures.

As 3D Gaussian Splatting (3DGS) is increasingly adopted in various academic and commercial applications due to its high-quality and real-time rendering capabilities, the need for copyright protection is growing. At the same time, its large model size requires efficient compression for storage and transmission. However, compression techniques, especially quantization-based methods, degrade the integrity of existing 3DGS watermarking methods, thus creating the need for a novel methodology that is robust against compression. To ensure reliable watermark detection under compression, we propose a compression-tolerant 3DGS watermarking method that preserves watermark integrity and rendering quality. Our approach utilizes an anchor-based 3DGS, embedding the watermark into anchor attributes, particularly the anchor feature, to enhance security and rendering quality. We also propose a quantization distortion layer that injects quantization noise during training, preserving the watermark after quantization-based compression. Moreover, we employ a frequency-aware anchor growing strategy that enhances rendering quality by effectively identifying Gaussians in high-frequency regions, and an HSV loss to mitigate color artifacts for further rendering quality improvement. Extensive experiments demonstrate that our proposed method preserves the watermark even under compression and maintains high rendering quality.

Automated knowledge graph (KG) construction is essential for navigating the rapidly expanding body of scientific literature. However, existing approaches face persistent challenges: they struggle to recognize long multi-word entities, often fail to generalize across domains, and typically overlook the hierarchical and logically constrained nature of scientific knowledge. While general-purpose large language models (LLMs) offer some adaptability, they are computationally expensive and yield inconsistent accuracy on specialized, domain-heavy tasks such as scientific knowledge graph construction. As a result, current KGs are shallow and inconsistent, limiting their utility for exploration and synthesis. We propose a two-stage framework for scalable, zero-shot scientific KG construction. The first stage, Z-NERD, introduces (i) Orthogonal Semantic Decomposition (OSD), which promotes domain-agnostic entity recognition by isolating semantic “turns” in text, and (ii) a Multi-Scale TCQK attention mechanism that captures coherent multi-word entities through n-gram–aware attention heads. The second stage, HGNet, performs relation extraction with hierarchy-aware message passing, explicitly modeling parent, child, and peer relations. To enforce global consistency, we introduce two complementary objectives: a Differentiable Hierarchy Loss to discourage cycles and shortcut edges, and a Continuum Abstraction Field (CAF) Loss that embeds abstraction levels along a learnable axis in Euclidean space. To the best of our knowledge, this is the first approach to formalize hierarchical abstraction as a continuous property within standard Euclidean embeddings, offering a simpler and more interpretable alternative to hyperbolic methods. To address data scarcity, we also release SPHERE, a large-scale, multi-domain benchmark for hierarchical relation extraction. Our framework establishes a new state of the art on benchmarks such as SciERC, SciER and SPHERE benchmarks, improving named entity recognition (NER) by 8.08\% and relation extraction (RE) by 5.99\% on the official out-of-distrubtion test sets. In zero-shot settings, the gains are even more pronounced, with improvements of 10.76\% for NER and 26.2\% for RE, marking a significant step toward reliable and scalable scientific knowledge graph construction.

Large language models (LLMs) can solve complex real-world tasks when prompted to generate chain-of-thought (CoT) reasoning, motivating their use for preference reasoning in recommender systems. However, applying LLM reasoning on recommendation faces two practical challenges. First, LLMs struggle to reason over long, noisy user histories that often span hundreds of items while truncation discards signals needed to capture long-term interests. Second, in decoder-only architectures, CoT requires generating rationale tokens autoregressively, leading to prohibitive inference latency for real-world deployment. To address the challenges, we propose SIREN, a framework that enables effective LLM-based rating prediction via long-term interest sketching and internalized reasoning. First, instead of prompting raw histories, we build a compact, token-bounded interest sketch that preserves persistent preferences and suppresses noise. Specifically, we encode and cluster item descriptions to discover semantic topics, then compress each user’s history into a short list of liked and disliked topics, facilitating LLM reasoning. Second, we develop an internalized reasoning strategy for efficient inference. We adopt a two-stage training paradigm: (i) train the LLM to reason explicitly for rating prediction with rule-based reinforcement learning, since ground-truth CoTs are unavailable in recommendation; and (ii) learn to internalize CoT into model parameters through hidden alignment. At inference, the LLM directly generates the rating with near-CoT quality. Extensive experiments show that SIREN reduces average input tokens by $48.7\%$ compared to raw-history prompting, outperforms existing methods while delivering over $100\times$ lower inference latency than CoT-based LLM recommenders. Code and data are available at https://anonymous.4open.science/r/LLM4Rec-C7CF.

Inspired by the remarkable reasoning capabilities of Deepseek-R1 in complex textual tasks, many works attempt to incentivize similar capabilities in Multimodal Large Language Models (MLLMs) by directly applying reinforcement learning (RL). However, they still struggle to activate complex reasoning. In this paper, rather than examining multimodal RL in isolation, we delve into current training pipelines and identify three crucial phenomena: 1) Effective cold start initialization is critical for enhancing MLLM reasoning. Intriguingly, we find that initializing with carefully selected text data alone can lead to performance surpassing many recent multimodal reasoning models, even before multimodal RL.2) Standard GRPO applied to multimodal RL suffers from gradient stagnation, which degrades training stability and performance. 3) Subsequent text-only RL training, following the multimodal RL phase, further enhances multimodal reasoning. This staged training approach effectively balances perceptual grounding and cognitive reasoning development. By incorporating the above insights and addressing multimodal RL issues, we introduce \textbf{ReVisual-R1}, achieving a new state-of-the-art among open-source 7B MLLMs on challenging benchmarks including MathVerse, MathVision, WeMath, LogicVista, DynaMath, and challenging AIME2024 and AIME2025.

Data quantity and quality play a vital role in determining the performance of Large Language Models (LLMs). High-quality data, in particular, can significantly boost the LLM's ability to generalize on a wide range of downstream tasks. In this paper, we introduce **GneissWeb**, a large dataset of around 10 trillion tokens that caters to the data quality and quantity requirements of training LLMs. Our GneissWeb recipe that produced the dataset consists of sharded exact sub-string deduplication and a judiciously constructed ensemble of quality filters. GneissWeb goes beyond simple model-based quality filtering used in recent datasets by designing an ensemble of filters incorporating novel quality filters. Novel components enable us to achieve a favorable trade-off between data quality and quantity, producing models that outperform models trained on state-of-the-art open large datasets (5+ trillion tokens). We show that models trained using GneissWeb outperform those trained on FineWeb-V1.1.0 by 2.73 percentage points in terms of average scores on a set of 11 commonly used benchmarks (both zero-shot and few-shot) for pre-training dataset evaluation. When the evaluation set is extended to 20 benchmarks (both zero-shot and few-shot), models trained using GneissWeb still achieve a 1.75 percentage points gain over those trained on FineWeb-V1.1.0.

We propose \textbf{ABSignSGD}, a block‑coordinate variant of sign-based descent with flexible block selection that enables memory‑ and runtime‑efficient full‑parameter fine‑tuning of large language models. We present a unified convergence analysis under mild conditions, covering both the base method and a \textit{majority‑vote} extension for distributed training. The latter improves communication efficiency by aggregating only gradient signs rather than averaging full gradients. Experiments on \textcolor{blue}{Qwen3‑8B, Llama3-8B, and Qwen3-32B}, spanning mathematical reasoning and general instruction‑following tasks, show that ABSignSGD converges faster per iteration and delivers superior downstream performance while reducing both runtime and memory usage compared to existing methods. Ablation studies further indicate that the memoryless sign-based update naturally complements block‑wise updates, explaining the method’s strong empirical performance.

Understanding 3D scenes requires flexible combinations of visual reasoning tasks, including depth estimation, novel view synthesis, and object manipulation, all of which are essential for perception and interaction. Existing approaches have typically addressed these tasks in isolation, preventing them from sharing a common representation or transferring knowledge across tasks. A conceptually simpler but practically non-trivial alternative is to unify these diverse tasks into a single model, reducing different tasks from separate training objectives to merely different prompts and allowing for joint training across all datasets. In this work, we present a physical world model for unified 3D understanding and interaction 3WM, formulated as a probabilistic graphical model in which nodes represent multimodal scene elements such as RGB, optical flow, and camera pose. Diverse tasks emerge from different inference pathways through the graph: novel view synthesis from RGB and dense flow prompts, object manipulation from RGB and sparse flow prompts, and depth estimation from RGB and camera conditioning, all zero-shot without task-specific training. 3WM outperforms specialized baselines without the need for finetuning by offering precise controllability, strong geometric consistency, and robustness in real-world scenarios, achieving state-of-the-art performance on NVS and 3D object manipulation. Beyond predefined tasks, the model supports composable inference pathways, such as moving objects aside while navigating a 3D environment, enabling complex geometric reasoning. This demonstrates that a unified model can serve as a practical alternative to fragmented task-specific systems, taking a step towards a general-purpose visual world model.

This paper advances the theoretical understanding of active learning label complexity for decision trees as binary classifiers. We make two main contributions. First, we provide the first analysis of the **disagreement coefficient** for decision trees—a key parameter governing active learning label complexity. Our analysis holds under two natural assumptions required for achieving polylogarithmic label complexity: (i) each root-to-leaf path queries distinct feature dimensions, and (ii) the input data has a regular, grid-like structure. We show these assumptions are essential, as relaxing them leads to polynomial label complexity. Second, we present the first general active learning algorithm for binary classification that achieves a **multiplicative error guarantee**, producing a $(1+\epsilon)$-approximate classifier. By combining these results, we design an active learning algorithm for decision trees that uses only a **polylogarithmic number of label queries** in the dataset size, under the stated assumptions. Finally, we establish a label complexity lower bound, showing our algorithm’s dependence on the error tolerance $\epsilon$ is close to optimal.

Real-world data frequently exhibit latent hierarchical structures, which can be naturally represented by hyperbolic geometry. Although recent hyperbolic neural networks have demonstrated promising results, many existing architectures remain partially intrinsic, mixing Euclidean operations with hyperbolic ones or relying on extrinsic parameterizations. To address it, we propose the \emph{Intrinsic Lorentz Neural Network} (ILNN), a fully intrinsic hyperbolic architecture that conducts all computations within the Lorentz model. At its core, the network introduces a novel \emph{point-to-hyperplane} fully connected layer (FC), replacing traditional Euclidean affine logits with closed-form hyperbolic distances from features to learned Lorentz hyperplanes, thereby ensuring that the resulting geometric decision functions respect the inherent curvature. Around this fundamental layer, we design intrinsic modules: GyroLBN, a Lorentz batch normalization that couples gyro-centering with gyro-scaling, consistently outperforming both LBN and GyroBN while reducing training time. We additionally proposed a gyro-additive bias for the FC output, a Lorentz patch-concatenation operator that aligns the expected log-radius across feature blocks via a digamma-based scale, and a Lorentz dropout layer. Extensive experiments conducted on CIFAR-10/100 and two genomic benchmarks (TEB and GUE) illustrate that ILNN achieves state-of-the-art performance and computational cost among hyperbolic models and consistently surpasses strong Euclidean baselines.

Fine-tuning large language models (LLMs) often faces GPU memory bottlenecks: the backward pass of first-order optimizers like Adam increases memory usage to more than 10 times the inference level (e.g., 633~GB for OPT-30B). Zeroth-order (ZO) optimizers avoid this cost by estimating gradients only from forward passes, yet existing methods like MeZO usually need tens of times more steps to converge. Can this trade-off between speed and memory in ZO be fundamentally improved? Normalized-SGD, for instance, demonstrates strong empirical performance with greater memory efficiency than Adam. In light of this, we introduce FZOO, a Fast Zeroth-Order Optimizer towards Adam-Scale Speed. On the one hand, FZOO reduces the total forward passes needed for convergence by employing batched one-sided estimates that adapt step-sizes based on the standard deviation of batch losses. On the other hand, it accelerates per-batch computation through the use of Rademacher random vector (±1) perturbations, which also enables further speedups through batched evaluation. Extensive experiments on diverse models (including RoBERTa-large, the OPT family (350M-66B), Phi-2, and Llama3) across 11 varied downstream tasks validate FZOO's effectiveness. On average, FZOO outperforms MeZO by +3% in accuracy while requiring 3$\times$fewer forward passes. Notably, for the RoBERTa-large model, FZOO achieves average improvements of +5.6% in accuracy and 18$\times$reduction in forward passes compared to MeZO, achieving convergence speeds comparable to Adam. We also provide theoretical analysis proving FZOO’s formal equivalence to a normalized-SGD update rule and establishing its convergence guarantees. Beyond full-parameter tuning, FZOO plugs smoothly into PEFT techniques, unlocking even larger memory savings. Taken together, our results make single-GPU, high-speed, full-parameter fine-tuning realistic today and point toward future work on memory-efficient pre-training. Code: https://github.com/DKmiyan/FZOO

Retrieval Augmented Generation (RAG) systems are increasingly vital in dynamic domains like online gaming, yet the lack of a dedicated benchmark has impeded standardized evaluation in this area. The core difficulty lies in Dual Dynamics: the constant interplay between game content updates and the shifting focus of the player community. Furthermore, the necessity of automating such a benchmark introduces a critical requirement for player-centric authenticity to ensure generated questions are realistic. To address this integrated challenge, we introduce ChronoPlay, a novel framework for the automated and continuous generation of game RAG benchmarks. ChronoPlay utilizes a dual-dynamic update mechanism to track both forms of change, and a dual-source synthesis engine that draws from official sources and player community to ensure both factual correctness and authentic query patterns. We instantiate our framework on three distinct games to create the first dynamic RAG benchmark for the gaming domain, offering new insights into model performance under these complex and realistic conditions.

Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are based on neural dynamics such as the (leaky) integrate-and-fire (IF/LIF) models, which are described by \emph{first-order} ordinary differential equations (ODEs) with Markovian characteristics. This means the potential state at any time depends solely on its immediate past value, potentially limiting network expressiveness. Empirical studies of real neurons, however, reveal long-range correlations and fractal dendritic structures, suggesting non-Markovian behavior better modeled by \emph{fractional-order} ODEs. Motivated by this, we propose a \emph{fractional-order} spiking neural network (\emph{f}-SNN) framework that strictly generalizes integer-order SNNs and captures long-term dependencies in membrane potential and spike trains via fractional dynamics, enabling richer temporal patterns. We also release an open-source toolbox to support the \emph{f}-SNN framework, applicable to diverse architectures and real-world tasks. Experimentally, fractional adaptations of established SNNs into the \emph{f}-SNN framework achieve superior accuracy, comparable energy efficiency, and improved robustness to noise, underscoring the promise of \emph{f}-SNNs as an effective extension of traditional SNNs.

We introduce Horseshoe Splatting, a Bayesian extension of 3D Gaussian Splatting (3DGS) that jointly addresses structured sparsity in per-splat covariances and delivers calibrated uncertainty. While neural radiance fields achieve high-fidelity view synthesis and 3DGS attains real-time rendering with explicit anisotropic Gaussians, existing pipelines do not explicitly encode structural sparsity in the covariance—e.g., axis-wise variances or pairwise correlations—leaving noise-dominated components insufficiently regularized. Uncertainty is likewise essential for trustworthy and robust novel-view prediction, yet most 3DGS variants remain deterministic. We place a global-local Horseshoe prior on the covariance scales, whose spike-at-zero and heavy-tails adaptively shrink irrelevant directions while preserving the salient structure. We fit the model with a factorized variational inference scheme that mirrors the Horseshoe's inverse-Gamma augmentation, enabling Monte Carlo rendering and pixel-wise posterior uncertainty with minimal overhead. Theoretically, we establish posterior contraction rates for the scale parameters and transfer them to the rendered image via a local Lipschitz mapping, providing guarantees that estimation error and predictive uncertainty diminish with data. Empirically, Horseshoe Splatting produces high-quality uncertainty maps while matching state-of-the-art 3DGS visual fidelity and runtime, yielding a practical, uncertainty-aware renderer that is robust to structured sparsity in the radiance field. The code is available at https://github.com/HKU-MedAI/Horseshoe-Splatting.

Visual prompt tuning offers significant advantages for adapting pre-trained visual foundation models to specific tasks. However, current research provides limited insight into the interpretability of this approach, which is essential for enhancing AI reliability and enabling AI-driven knowledge discovery. In this paper, rather than learning abstract prompt embeddings, we propose the first framework, named Interpretable Visual Prompt Tuning (IVPT), to explore interpretability for visual prompts by introducing cross-layer concept prototypes. Specifically, visual prompts are linked to human-understandable semantic concepts, represented as a set of category-agnostic prototypes, each corresponding to a specific region of the image. IVPT then aggregates features from these regions to generate interpretable prompts for multiple network layers, allowing the explanation of visual prompts at different network depths and semantic granularities. Comprehensive qualitative and quantitative evaluations on fine-grained classification benchmarks show its superior interpretability and performance over visual prompt tuning methods and existing interpretable methods. Our code is available at https://github.com/ThomasWangY/IVPT.

Vision-Language Models (VLMs) have demonstrated impressive zero-shot capabilities across a wide range of tasks and domains. However, their performance is often compromised by learned spurious correlations, which can adversely affect downstream applications. Existing mitigation strategies typically depend on additional data, model retraining, labeled features or classes, domain-specific expertise, or external language models posing scalability and generalization challenges. In contrast, we introduce a fully interpretable, zero-shot method that requires no auxiliary data or external supervision named DIAL (Disentangle, Identify, And Label-free removal). Our approach begins by filtering the representations that might be disproportionately influenced by spurious features, using distributional analysis. We then apply a sparse autoencoder to disentangle the representations and identify the feature directions associated with spurious features. To mitigate their impact, we remove the subspace spanned by these spurious directions from the affected representations. Additionally, for cases where prior knowledge of spurious features in a dataset are not known, we introduce DIAL+ which can detect and mitigate the spurious features. We validate our method through extensive experiments on widely used spurious correlation benchmarks. Results show that our approach consistently outperforms or matches existing baselines in terms of overall accuracy and worst-group performance, offering a scalable and interpretable solution to a persistent challenge in VLMs.

Discovering the neural mechanisms underpinning cognition is one of the grand challenges of neuroscience. Addressing this challenge greatly benefits from specific hypotheses about the underlying neural network dynamics. However, previous approaches bridging neural network dynamics and cognitive behaviour required iterative refinement of network architectures and/or objectives for normative task optimization, resulting in a long, and mostly heuristic, human-in-the-loop design process. Here, we offer an alternative approach that automates this process by explicitly training recurrent neural networks (RNNs) to reproduce behaviour, including the same characteristic errors, that humans and animals produce in a cognitive task. Achieving this required two main innovations. First, as the amount of behavioural data that can be collected in experiments is often too limited to suffice for training RNNs, we use a non-parametric generative model of behavioural responses to produce surrogate data for training RNNs. Second, to capture all relevant statistical moments in the data, rather than a limited number of hand-picked low-order moments as in previous moment matching-based approaches, we developed a novel diffusion model-based approach for training RNNs. We chose a visual working memory (VWM) task as our test-bed, as behaviour in this task is well known to produce response distributions that are patently multimodal (due to so-called swap errors). The resulting network dynamics correctly predicted previously reported qualitative features of neural data recorded in macaques. Importantly, this was only the case when RNNs were trained using our approach, fitting the full richness of behavioural data -- and not when only a limited set of behavioural signatures were fitted, nor when RNNs were trained for task optimality instead of reproducing behaviour (as has been typical for RNNs used to generate dynamical hypotheses). Our model also makes novel predictions about the mechanism of swap errors, which can be readily tested in experiments. These results suggest that fitting rich patterns of behaviour provides a powerful way for the automatic discovery of neural network dynamics supporting important cognitive functions.

We address the problem of fine-tuning diffusion models for reward-guided generation in biomolecular design. While diffusion models have proven highly effective in modeling complex, high-dimensional data distributions, real-world applications often demand more than high-fidelity generation, requiring optimization with respect to potentially non-differentiable reward functions such as physics-based simulation or rewards based on scientific knowledge. Although RL methods have been explored to fine-tune diffusion models for such objectives, they often suffer from instability, low sample efficiency, and mode collapse due to their on-policy nature. In this work, we propose an iterative distillation-based fine-tuning framework that enables diffusion models to optimize for arbitrary reward functions. Our method casts the problem as policy distillation: it collects off-policy data during the roll-in phase, simulates reward-based soft-optimal policies during roll-out, and updates the model by minimizing the KL divergence between the simulated soft-optimal policy and the current model policy. Our off-policy formulation, combined with KL divergence minimization, enhances training stability and sample efficiency compared to existing RL-based methods. Empirical results demonstrate the effectiveness and superior reward optimization of our approach across diverse tasks in protein, small molecule, and regulatory DNA design.