ICLR 2026 Papers

We introduce NerVE, a unified eigenspectral framework for understanding how feed-forward networks (FFNs) in large language models (LLMs) organize and regulate information flow in high-dimensional latent space. Despite FFNs dominating the parameter budget, their high-dimensional dynamics remain poorly understood. NerVE addresses this gap through lightweight, memory-efficient tracking of eigenspectrum dynamics via four complementary metrics: Spectral Entropy (dispersion), Participation Ratio (effective dimensionality), Eigenvalue Early Enrichment (top-heaviness), and Jensen-Shannon divergence (distributional shifts). Our {\em key insight} is that FFN nonlinearities reinject and reshape variance across eigenmodes, fundamentally governing latent dimension utilization. We validate NerVE across model scales and diverse architectural configurations that each uniquely shape FFN dynamics: normalization strategies (PreLN, PostLN, MixLN, Norm-Free) controlling variance flow; FFN weight geometries constraining latent space; positional encoding and activation functions modulating information propagation. Across these settings, NerVE consistently recovers stable spectral signatures that correlate with model's generalization ability and respond predictably to design choices, providing actionable insights for architectural optimization beyond trial-and-error.

Videos captured in the wild often suffer from rain streaks, blur, and noise. In addition, even slight changes in camera pose can amplify cross-frame mismatches and temporal artifacts. Existing methods rely on optical flow or heuristic alignment, which are computationally expensive and less robust. To address these challenges, Lie groups provide a principled way to represent continuous geometric transformations, making them well-suited for enforcing spatial and temporal consistency in video modeling. Building on this insight, we propose DeLiVR, an efficient video deraining method that injects spatiotemporal Lie-group differential biases directly into attention scores of the network. Specifically, the method introduces two complementary components. First, a rotation-bounded Lie relative bias predicts the in-plane  angle of each frame using a compact prediction module, which normalized coordinates are rotated and compared with base coordinates to achieve geometry-consistent alignment before feature aggregation. Second, a differential group displacement computes angular differences between adjacent frames to estimate a velocity. These biases are combined with temporal decay and a banded attention mask to emphasize short-range reliable relations while suppressing long-range noise. DeLiVR achieves sharper details, fewer rain remnants, and stronger temporal coherence on both synthetic and real rainy benchmarks. The code is publicly available at https://github.com/Shuning0312/ICLR-DeLiVR.

Recent large language models (LLMs) have increasingly adopted the Mixture-of-Experts (MoE) architecture for efficiency. MoE-based LLMs heavily depend on a superficial safety mechanism in which harmful inputs are routed safety-critical experts. However, our analysis reveals that routing decisions for harmful inputs drift significantly after fine-tuning, exposing a critical vulnerability to harmful fine-tuning (HFT) attacks. Existing defenses, primarily designed for monolithic LLMs, are less effective for MoE LLMs as they fail to prevent drift in harmful input routing. To address this limitation, we propose SafeMoE, a safe fine-tuning method tailored to MoE LLMs. SafeMoE directly mitigates routing drift by penalizing the gap between the routing weights of a fine-tuned model and those of the initial safety-aligned model, thereby preserving the safety-aligned routing of harmful inputs to safety-critical experts. Experiments on open-source MoE LLMs ranging from 7B to 141B parameters demonstrate that SafeMoE effectively mitigates HFT attacks, reducing the harmfulness score of OLMoE from 62.0 to 5.0, for example, while maintaining task utility within 1% degradation and incurring only 2\% overhead. It significantly outperforms state-of-the-art defense methods for safeguarding LLM fine-tuning and remains effective in recent large-scale MoE LLMs such as gpt-oss and Llama 4. Our implementation is available at https://anonymous.4open.science/r/SafeMoE.

Integrating multimodal screening data is challenging because biological signals only partially overlap and cell-level pairing is frequently unavailable. Existing approaches either require pairing or fail to capture both shared and modality-specific information in an end-to-end manner. We present PETRI, an early-fusion transformer that learns a unified cell embedding from unpaired cellular images and gene expression profiles. PETRI groups cells by shared experimental context into multimodal “documents” and performs masked joint reconstruction with cross-modal attention, permitting information sharing while preserving modality-specific capacity. The resulting latent space supports construction of perturbation-level profiles by simple averaging across modalities. Applying sparse autoencoders to the embeddings reveals learned concepts that are biologically meaningful, multimodal, and retain perturbation-specific effects. To support further machine learning research, we release a blinded, matched optical pooled screen (OPS) and Perturb-seq dataset in HepG2 cells.

Deploying semantic segmentation in driving and robotics requires both real-time inference and robustness to domain shifts, formalized as Real-Time Domain-Generalized Semantic Segmentation (RT-DGSS), which has not been fully addressed. Existing methods often treat real-time(RT) inference and domain generalization (DG) separately, with DG improving robustness but lacking real-time performance, and real-time models being brittle under distribution shifts. To address the RT-DGSS problem, we propose QPrompt-R1, a real-time Query-Prompt architecture built on a ViT backbone. QPrompt-R1 injects a small set of learnable queries only at the final transformer block, performing a single query–image alignment step and eliminating decoder overhead. To further enhance alignment without test-time cost, we introduce a Group Relative Query Alignment (GRQA) objective, which uses group-relative supervision within each group to align queries with features, improving domain generalization through group-relative rewards. QPrompt-R1 achieves 54 FPS, delivering strong performance in synthetic-to-real transfer, real-to-real generalization, and robustness under adverse conditions. Additionally, GRQA is plug-and-play, improving state-of-the-art DGSS methods like REIN (+1.2) and SoMA (+0.5) without inference-time overhead.

We study the challenge of achieving theoretically grounded feature recovery using Sparse Autoencoders (SAEs) for the interpretation of Large Language Models. Existing SAE training algorithms often lack rigorous mathematical guarantees and suffer from practical limitations such as hyperparameter sensitivity and instability. We rethink this problem from the perspective of neuron activation frequencies, and through controlled experiments, we identify a striking phenomenon we term neuron resonance: neurons reliably learn monosemantic features when their activation frequency matches the feature's occurrence frequency in the data. Building on this finding, we introduce a new SAE training algorithm based on ``bias adaptation'', a technique that adaptively adjusts neural network bias parameters to ensure appropriate activation sparsity. We theoretically prove that this algorithm correctly recovers all monosemantic features when input data is sampled from our proposed statistical model. Furthermore, we develop an improved empirical variant, Group Bias Adaptation (GBA), and demonstrate its superior performance against benchmark methods when applied to LLMs with up to 2 billion parameters. This work represents a foundational step in demystifying SAE training by providing the first SAE algorithm with theoretical recovery guarantees and practical effectiveness for LLM interpretation.

Robotic systems can require multimodal reasoning under stringent constraints of latency, memory, and energy. Standard instruction tuning and token-level distillation fail to deliver decision quality, reliability, and interpretability under these constraints. We introduce BOLT, a decision-aligned distillation and budget-aware routing framework that treats multi-choice prediction as a decision surface to be aligned during training and selectively refined at inference. During training, BOLT introduces Option-level Decision Distillation to align student models directly on the decision surface of multi-choice answers, thereby eliminating prompt artifacts, improving calibration, and optimizing the exact output space. At inference, BOLT activates Budget-aware Test-time Augmentation, a calibrated router that uses low-cost signals such as confidence, margin, entropy, retrieval affinity, and agreement across short question decompositions to trigger high-resolution reevaluation, type-matched retrieval exemplars, or question decomposition only when their expected benefit outweighs cost. On Robo2VLM-1, a 2B BOLT student distilled from LLaVA-1.5-13B improves accuracy from 28.66 in zero-shot to 42.89 with decision distillation and to 50.50 with budgeted routing, surpassing the 13B teacher at 36.74. It lowers expected calibration error, strengthens the risk-coverage frontier, and slashes GPU memory from 26,878 MB for the teacher to 3,035 MB for the distilled student, and 3,817 MB with all augmentations enabled. By constraining outputs to valid options while exposing retrieved evidence and decomposition traces, BOLT reduces hallucination and provides transparent decision-making, enabling large-model quality on edge robots.

To mitigate the trade-offs between performance and costs, LLM providers route user tasks to different models based on task difficulty and latency. We study the effect of LLM routing with respect to user behavior. We propose a game between an LLM provider with two models (standard and reasoning) and a user who can re-prompt or abandon tasks if the routed model cannot solve them. The user's goal is to maximize their utility minus the delay from using the model, while the provider minimizes the cost of servicing the user. We solve this Stackelberg game by fully characterizing the user best response and simplifying the provider problem. We observe that in nearly all cases, the optimal routing policy involves a static policy with no cascading that depends on the expected utility of the models to the user. Furthermore, we reveal a misalignment gap between the provider-optimal and user-preferred routes when the user's and provider's rankings of the models with respect to utility and cost differ. Finally, we demonstrate conditions for extreme misalignment where providers are incentivized to throttle the latency of the models to minimize their costs, consequently depressing user utility. The results yield simple threshold rules for single-provider, single-user interactions and clarify when routing, cascading, and throttling help or harm.

Large language models (LLMs) demand extensive memory capacity during both fine-tuning and inference. To enable memory-efficient fine-tuning, existing methods apply block-wise quantization techniques, such as NF4 and AF4, to the network weights. We show that these quantization techniques incur suboptimal quantization errors. Therefore, as a first novelty, we propose an optimization approach for block-wise quantization. Using this method, we design a family of quantizers named 4-bit block-wise optimal float (BOF4), which consistently reduces the quantization error compared to both baseline methods. We provide both a theoretical and a data-driven solution for the optimization process and prove their practical equivalence. Secondly, we propose a modification to the employed normalization method based on the signed absolute block maximum (BOF4-S), enabling further reduction of the quantization error and empirically achieving less degradation in language modeling performance. Thirdly, we explore additional variations of block-wise quantization methods applied to LLMs through an experimental study on the importance of accurately representing zero and large-amplitude weights on the one hand, and optimization towards various error metrics on the other hand. Lastly, we introduce a mixed-precision quantization strategy dubbed outlier-preserving quantization (OPQ) to address the distributional mismatch induced by outlier weights in block-wise quantization. By storing outlier weights in 16-bit precision (OPQ) while applying BOF4-S, we achieve top performance among 4-bit block-wise quantization techniques w.r.t. perplexity.

Multimodal spatiotemporal learning on real-world experimental data is constrained by two challenges: within-modality measurements are sparse, irregular, and noisy (QA/QC artifacts) but cross-modally correlated; the set of available modalities varies across space and time, shrinking the usable record unless models can adapt to arbitrary subsets at train and test time. We propose OmniField, a continuity-aware framework that learns a continuous neural field conditioned on available modalities and iteratively fuses cross-modal context. A multimodal crosstalk block architecture paired with iterative cross-modal refinement aligns signals prior to the decoder, enabling unified reconstruction, interpolation, forecasting, and cross-modal prediction without gridding or surrogate preprocessing. Extensive evaluations show that OmniField consistently outperforms eight strong multimodal spatiotemporal baselines. Under heavy simulated sensor noise, performance remains close to clean-input levels, highlighting robustness to corrupted measurements.

The prevailing paradigm for enhancing the reasoning abilities of Large Language Models (LLMs) revolves around post-training on high-quality, reasoning-intensive data. While emerging literature suggests that reasoning data is increasingly incorporated also during the mid-training stage---a practice that is relatively more proprietary and less openly characterized---the role of such data in pretraining remains unclear. In particular, due to the opaqueness of pretraining corpora in most frontier models, the effect of reasoning data introduced at different phases of pre- and/or post-training is relatively less reported in the scientific literature. This raises several important but unsettled questions: Is adding reasoning data earlier during pre-training any better than introducing it during post-training, when the token counts are controlled? Could earlier inclusion risk overfitting and harm generalization, or instead establish durable foundations that later fine-tuning cannot recover? To address these questions, we conduct the first systematic study of how reasoning data—varying in scale, diversity, and quality—affects LLM performance when introduced at different stages of training. Our findings reveal that front-loading reasoning data into pretraining is critical (19% average gain), establishing foundational capabilities that cannot be fully replicated by later-stage SFT, even with more data. We uncover an asymmetric principle for optimal data allocation: pretraining benefits most from broad diversity in reasoning patterns (11% average gain), while SFT is more sensitive to data quality (15% average gain with high quality data). Furthermore, we show that high-quality pretraining data has latent effects, activated only after SFT, and that naively scaling SFT data can be detrimental, washing away the benefits of early reasoning injection. Collectively, our results challenge the conventional separation of language modeling and reasoning, providing a principled guide for strategically allocating data across the entire training pipeline to build more capable models.

Understanding simplicity biases in deep learning offers a promising path toward developing reliable AI. A common metric for this, inspired by Boolean function analysis, is average sensitivity, which captures a model's robustness to single-token perturbations. We argue that average sensitivity has two key limitations: it lacks a natural generalization to real-valued domains and fails to explain the "junta-like" input dependence we empirically observe in modern LLMs. To address these limitations, we propose *noise stability* as a more comprehensive simplicity metric. Noise stability expresses a model's robustness to correlated noise applied to *all* input coordinates simultaneously. We provide a theoretical analysis of noise stability for single-layer attention and ReLU MLP layers and tackle the multi-layer propagation problem with a covariance interval propagation approach. Building on this theory, we develop a practical *noise stability regularization* method. Experiments on algorithmic and next-token-prediction tasks show that our regularizer consistently catalyzes grokking and accelerates training by approximately $35$\% and $75$\% respectively. Our results establish noise stability as a powerful tool for understanding and improving modern Transformers.

Test-time prompt tuning (TPT) has emerged as a promising technique for adapting large vision-language models (VLMs) to unseen tasks without relying on labeled data. However, the lack of dispersion between textual features can hurt calibration performance, which raises concerns about VLMs' reliability, trustworthiness, and safety. Current TPT approaches primarily focus on improving prompt calibration by either maximizing average textual feature dispersion or enforcing orthogonality constraints to encourage angular separation. However, these methods may not always have optimal angular separation between class-wise textual features, which implies overlooking the critical role of angular diversity. To address this, we propose A-TPT, a novel TPT framework that introduces angular diversity to encourage uniformity in the distribution of normalized textual features induced by corresponding learnable prompts. This uniformity is achieved by maximizing the minimum pairwise angular distance between features on the unit hypersphere. We show that our approach consistently surpasses state-of-the-art TPT methods in reducing the aggregate average calibration error while maintaining comparable accuracy through extensive experiments with various backbones on different datasets. Notably, our approach exhibits superior zero-shot calibration performance on natural distribution shifts and generalizes well to medical datasets. We provide extensive analyses, including theoretical aspects, to establish the grounding of A-TPT. These results highlight the potency of promoting angular diversity to achieve well-dispersed textual features, significantly improving VLM calibration during test-time adaptation. Our code will be made publicly available.

Recently, significant progress has been made in developing reasoning-capable Large Language Models (LLMs) through long Chain-of-Thought (CoT) techniques. However, this long-CoT reasoning process imposes substantial memory overhead due to the large Key-Value (KV) Cache memory overhead. Post-training KV Cache quantization has emerged as a promising compression technique and has been extensively studied in short-context scenarios. However, directly applying existing methods to long-CoT LLMs causes significant performance degradation due to the following two reasons: (1) Large cumulative error: Existing methods fail to adequately leverage available memory, and they directly quantize the KV Cache during each decoding step, leading to large cumulative quantization error. (2) Short-context calibration: Due to Rotary Positional Embedding (RoPE), the use of short-context data during calibration fails to account for the distribution of less frequent channels in the Key Cache, resulting in performance loss. We propose Progressive Mixed-Precision KV Cache Quantization (PM-KVQ) for long-CoT LLMs to address the above issues in two folds: (1) To reduce cumulative error, we design a progressive quantization strategy to gradually lower the bit-width of KV Cache in each block. Then, we propose block-wise memory allocation to assign a higher bit-width to more sensitive transformer blocks. (2) To increase the calibration length without additional overhead, we propose a new calibration strategy with positional interpolation that leverages short calibration data with positional interpolation to approximate the data distribution of long-context data. Extensive experiments on 7B–70B long-CoT LLMs show that PM-KVQ improves reasoning benchmark performance by up to 8% over SOTA baselines under the same memory budget and achieves 2.73–5.18$\times$ throughput over the original 16-bit LLMs. Our code will be released soon.

Large Language Models (LLMs) have shown impressive capabilities in many scenarios, but their performance depends, in part, on the choice of prompt. Past research has focused on optimizing prompts specific to a task. However, much less attention has been given to optimizing the general instructions included in a prompt, known as a system prompt. To address this gap, we propose SPRIG, an edit-based genetic algorithm that iteratively constructs prompts from prespecified components to maximize the model's performance in general scenarios. We evaluate the performance of system prompts on a collection of 47 different types of tasks to ensure generalizability. Our study finds that a single optimized system prompt performs on par with task prompts optimized for each individual task. Moreover, combining system and task-level optimizations leads to further improvement, which showcases their complementary nature. Experiments also reveal that the optimized system prompts generalize effectively across model families, parameter sizes, and languages. This study provides insights into the role of system-level instructions in maximizing LLM potential.

A meaningful text can be hidden inside another, completely different yet still coherent and plausible, text of the same length. For example, a tweet containing a harsh political critique could be embedded in a tweet that celebrates the same political leader, or an ordinary product review could conceal a secret manuscript. This uncanny state of affairs is now possible thanks to Large Language Models, and in this paper we present *Calgacus*, a simple and efficient protocol to achieve it. We show that even modest 8‑billion‑parameter open‑source LLMs are sufficient to obtain high‑quality results, and a message as long as this abstract can be encoded and decoded locally on a laptop in seconds. The existence of such a protocol demonstrates a radical decoupling of text from authorial intent, further eroding trust in written communication, already shaken by the rise of LLM chatbots. We illustrate this with a concrete scenario: a company could covertly deploy an unfiltered LLM by encoding its answers within the compliant responses of a safe model. This possibility raises urgent questions for AI safety and challenges our understanding of what it means for a Large Language Model to know something.

Vision–language models (VLMs) align images and text with remarkable success, yet the geometry of their shared embedding space remains poorly understood. To probe this geometry, we begin from the Iso-Energy Assumption, which exploits cross-modal redundancy: a concept that is truly shared should exhibit the same average energy across modalities. We operationalize this assumption with an Aligned Sparse Autoencoder (SAE) that encourages energy consistency during training while preserving reconstruction. We find that this inductive bias changes the SAE solution without harming reconstruction, giving us a representation that serves as a tool for geometric analysis. Sanity checks on controlled data with known ground truth confirm that alignment improves when Iso-Energy holds and remains neutral when it does not. Applied to foundational VLMs, our framework reveals a clear structure with practical consequences: **(*i*)** sparse *bimodal* atoms carry the entire *cross-modal* alignment signal; **(*ii*)** *unimodal* atoms act as *modality-specific* biases and fully explain the modality gap; **(*iii*)** removing unimodal atoms collapses the gap without harming performance; **(*iv*)** restricting vector arithmetic to the bimodal subspace yields in-distribution edits and improved retrieval. These findings suggest that the right inductive bias can both preserve model fidelity and render the latent geometry interpretable and actionable.

With the rise of deep neural networks, especially in safety-critical applications, robustness and interpretability are crucial to ensure their trustworthiness. Recent advances in 3D-aware classifiers that map image features to volumetric representation of objects, rather than relying solely on 2D appearance, have greatly improved robustness on out-of-distribution (OOD) data. Such classifiers have not yet been studied from the perspective of interpretability. Meanwhile, current concept-based XAI methods often neglect OOD robustness. We aim to address both aspects with CAVE - Concept Aware Volumes for Explanations - a new direction that unifies interpretability and robustness in image classification. We design CAVE as a robust and inherently interpretable classifier that learns sparse concepts from 3D object representation. We further propose 3D Consistency (3D-C), a metric to measure spatial consistency of concepts. Unlike existing metrics that rely on human-annotated parts on images, 3D-C leverages ground-truth object meshes as a common surface to project and compare explanations across concept-based methods. CAVE achieves competitive classification performance while discovering consistent and meaningful concepts across images in various OOD settings.

Recent advances in Large Language Model (LLM) compression, such as quantization and pruning, have achieved notable success. However, as these techniques gradually approach their limits, relying on a single method for further compression has become increasingly challenging. In this work, we explore an alternative solution by combining quantization and sparsity. This joint approach, though promising, introduces new difficulties due to the inherently conflicting requirements on weight distributions: quantization favors compact ranges, while pruning benefits from high variance. To attack this problem, we propose Optimal Brain Restoration (OBR), a general and training-free framework that aligns pruning and quantization by error compensation between both. OBR minimizes performance degradation on downstream tasks by building on a second-order Hessian objective, which is then reformulated into a tractable problem through surrogate approximation and ultimately reaches a closed-form solution via group error compensation. Experiments show that OBR incurs only a 1.4 perplexity degradation on Llama2-7B to enable aggressive W4A4KV4 quantization with 50% sparsity, delivering up to 4.72x speedup and 6.4x memory reduction compared to the FP16-dense baseline.