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.

Cybersecurity operations demand assistant LLMs that support diverse workflows without exposing sensitive data. Existing solutions either rely on proprietary APIs with privacy risks or on open models lacking domain adaptation. To bridge this gap, we curate 11.8B tokens of cybersecurity-focused continual pretraining data via large-scale web filtering and manual collection of high-quality resources, spanning 28.6K documents across frameworks, offensive techniques, and security tools. Building on this, we design an agentic augmentation pipeline that simulates expert workflows to generate 266K multi-turn cybersecurity samples for supervised fine-tuning. Combined with general open-source LLM data, these resources enable the training of RedSage, an open-source, locally deployable cybersecurity assistant with domain-aware pretraining and post-training. To rigorously evaluate the models, we introduce RedSage-Bench, a benchmark with 30K multiple-choice and 240 open-ended Q\&A items covering cybersecurity knowledge, skills, and tool expertise. RedSage is further evaluated on established cybersecurity benchmarks (e.g., CTI-Bench, CyberMetric, SECURE) and general LLM benchmarks to assess broader generalization. At the 8B scale, RedSage achieves consistently better results, surpassing the baseline models by up to +5.59 points on cybersecurity benchmarks and +5.05 points on Open LLM Leaderboard tasks. These findings demonstrate that domain-aware agentic augmentation and pre/post-training can not only enhance cybersecurity-specific expertise but also help to improve general reasoning and instruction-following. All models, datasets, and code will be released to advance reproducibility and open cybersecurity LLM research.

Articulated objects are ubiquitous and important in robotics, AR/VR, and digital twins. Most self-supervised methods for articulated object modeling reconstruct discrete interaction states and relate them via cross-state geometric consistency, yielding representational fragmentation and drift that hinder smooth control of articulated configurations. We introduce PD$^{2}$GS, a novel framework that learns a shared canonical Gaussian field and models the arbitrary interaction state as its continuous deformation, jointly encoding geometry and kinematics. By associating each interaction state with a latent code and refining part boundaries using generic vision priors, PD$^{2}$GS enables accurate and reliable part-level decoupling while enforcing mutual exclusivity between parts and preserving scene-level coherence. This unified formulation supports part-aware reconstruction, fine-grained continuous control, and accurate kinematic modeling, all without manual supervision. To assess realism and generalization, we release RS-Art, a real-to-sim RGB-D dataset aligned with reverse-engineered 3D models, supporting real-world evaluation. Extensive experiments demonstrate that PD$^{2}$GS surpasses prior methods in geometric and kinematic accuracy, and in consistency under continuous control, both on synthetic and real data.

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.

Evaluating progress in large language models (LLMs) is often constrained by the challenge of verifying responses, limiting assessments to tasks like mathematics, programming, and short-form question-answering. However, many real-world applications require evaluating LLMs in processing professional documents, synthesizing information, and generating comprehensive reports in response to user queries. We introduce ProfBench: a set of over 7000 response-criterion pairs as evaluated by human-experts with professional knowledge across Physics PhD, Chemistry PhD, Finance MBA and Consulting MBA. We build robust and affordable LLM-Judges to evaluate ProfBench rubrics, by mitigating self-enhancement bias and reducing the cost of evaluation by 2-3 orders of magnitude, to make it fair and accessible to the broader community. Our findings reveal that ProfBench poses significant challenges even for state-of-the-art LLMs, with top-performing models like GPT-5-high achieving only 65.9\% overall performance. Furthermore, we identify notable performance disparities between proprietary and open-weight models and provide insights into the role that extended thinking plays in addressing complex, professional-domain tasks.

Deep neural networks often fail when deployed in real-world contexts due to distribution shift, a critical barrier to building safe and reliable systems. An emerging approach to address this problem relies on _disagreement discrepancy_—a measure of how the disagreement between two models changes under a shifting distribution. The process of maximizing this measure has seen applications in bounding error under shifts, testing for harmful shifts, and training more robust models. However, this optimization involves the non-differentiable zero-one loss, necessitating the use of practical surrogate losses. We prove that existing surrogates for disagreement discrepancy are not Bayes consistent, revealing a fundamental flaw: maximizing these surrogates can fail to maximize the true disagreement discrepancy. To address this, we introduce new theoretical results providing both upper and lower bounds on the optimality gap for such surrogates. Guided by this theory, we propose a novel disagreement loss that, when paired with cross-entropy, yields a provably consistent surrogate for disagreement discrepancy. Empirical evaluations across diverse benchmarks demonstrate that our method provides more accurate and robust estimates of disagreement discrepancy than existing approaches, particularly under challenging adversarial conditions.

We develop new classifiers under group fairness in the attribute-aware setting for binary classification with multiple group fairness constraints (e.g., demographic parity (DP), equalized odds (EO), and predictive parity (PP)). We propose a novel approach based on directly intervening on the operating characteristics of a pre-trained base classifier, by: (i) identifying optimal operating characteristics using the base classifier's group-wise ROC convex hulls; (ii) post-processing the base classifier to match those targets. As practical post-processors, we consider randomizing a mixture of group-wise thresholding rules subject to minimizing the expected number of interventions. We further extend our approach to handle multiple protected attributes and multiple linear fractional constraints. On standard datasets (COMPAS and ACSIncome), our method simultaneously satisfies approximate DP, EO, and PP with few interventions and a nearly optimal drop in accuracy; and compare favorably to previous methods.

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.

The effectiveness of collective decision-making is often challenged by the bounded rationality and inherent stochasticity of individual agents. We investigate this by analyzing how to aggregate decisions from $n$ experts, each receiving a private signal about an unknown state. Assuming signals are conditionally independent and identically distributed, we depart from the fully rational paradigm and model expert behavior using quantal response—a stochastic choice model capturing bounded rationality. Within a minimax regret framework, we show that majority voting is the optimal robust aggregator when individual rationality falls below a certain threshold. Interestingly, such groups can outperform perfectly rational agents, as their decision randomness encodes weak but informative signals lost in deterministic behavior. We validate these findings using large language models (LLMs), which naturally exhibit quantal response via their temperature parameter. Aggregating moderately stochastic LLM outputs significantly improves accuracy on complex reasoning tasks, highlighting bounded rationality not as a limitation, but as a potential strength in collective intelligence.

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.

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilities can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

Training time-series forecast models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach seeks to minimize the conditional negative log-likelihood of the label sequence, typically estimated using the mean squared error. However, this estimation proves to be biased in the presence of label autocorrelation. In this paper, we propose DistDF, which achieves alignment by alternatively minimizing a discrepancy between the conditional forecast and label distributions. Because conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a newly proposed joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. This discrepancy admits tractable, differentiable estimation from empirical samples and integrates seamlessly with gradient-based training. Extensive experiments show that DistDF improves the performance diverse forecast models and achieves the state-of-the-art forecasting performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.

Incremental Object Detection (IOD) enables AI systems to continuously learn new object classes over time while retaining knowledge of previously learned categories. This capability is essential for adapting to dynamic environments without forgetting prior information. Although existing IOD methods have made progress in mitigating catastrophic forgetting, they usually lack explicit and quantitative modeling of information conflicts during knowledge preservation, making task boundaries ambiguous. Such conflicts often stem from the fact that a single image can contain objects belonging to previous, present, and future tasks, where unlabeled past and future objects are often mistakenly treated as background. In this paper, we propose a novel approach grounded in Elastic Weight Consolidation (EWC) to alleviate conflict knowledge preservation caused by task interference. Specifically, we introduce the Interference Knowledge Isolated Elastic Weight Consolidation (IKI-EWC) framework for IOD, which leverages the mispredictions of the old detector on new task data to estimate task conflicts and suppresses them at the parameter level. By reformulating the Bayesian posterior of model parameters, we derive a mathematical relationship between previously learned knowledge and interference knowledge, enabling targeted elimination of conflicts during model weight updates. In addition, we also propose a prototype-based knowledge calibration (PKC) mechanism to further preserve old knowledge during the training of the objector's classification head. This method employs a learnable projection layer to compensate semantic drift in old class prototypes, and then jointly trains the classification head using both calibrated prototypes and current task features, thereby mitigating forgetting caused by classifier updates. Extensive experiments on PASCAL VOC and MS-COCO benchmarks demonstrate the effectiveness of the proposed method, outperforming state-of-the-art approaches across various settings.

Catastrophic forgetting, the tendency of neural networks to forget previously learned knowledge when learning new tasks, has been a major challenge in continual learning (CL). To tackle this challenge, CL methods have been proposed and shown to reduce forgetting. Furthermore, CL models deployed in mission-critical settings can benefit from uncertainty awareness by calibrating their predictions to reliably assess their confidences. However, existing uncertainty-aware continual learning methods suffer from high computational overhead and incompatibility with mainstream replay methods. To address this, we propose idempotent experience replay (IDER), a novel approach based on the idempotent property where repeated function applications yield the same output. Specifically, we first adapt the training loss to make model idempotent on current data streams. In addition, we introduce an idempotence distillation loss. We feed the output of the current model back into the old checkpoint and then minimize the distance between this reprocessed output and the original output of the current model. This yields a simple and effective new baseline for building reliable continual learners, which can be seamlessly integrated with other CL approaches. Extensive experiments on different CL benchmarks demonstrate that IDER consistently improves prediction reliability while simultaneously boosting accuracy and reducing forgetting. Our results suggest the potential of idempotence as a promising principle for deploying efficient and trustworthy continual learning systems in real-world applications. Our code will be released upon publication.

Despite its recent successes, Deep Reinforcement Learning (DRL) is notoriously sample-inefficient. We argue that this inefficiency stems from the standard practice of optimizing policies directly in the high-dimensional and highly redundant parameter space $\\Theta$. This challenge is greatly compounded in multi-task settings. In this work, we develop a novel, unsupervised approach that compresses the policy parameter space $\\Theta$ into a low-dimensional latent space $\\mathcal Z$. We train a generative model $g:\\mathcal Z\\to\\Theta$ by optimizing a behavioral reconstruction loss, which ensures that the latent space is organized by functional similarity rather than proximity in parameterization. We conjecture that the inherent dimensionality of this manifold is a function of the environment's complexity, rather than the size of the policy network. We validate our approach in continuous control domains, showing that the parameterization of standard policy networks can be compressed up to five orders of magnitude while retaining most of its expressivity. As a byproduct, we show that the learned manifold enables task-specific adaptation via Policy Gradient operating in the latent space $\\mathcal{Z}$.

Unit testing is a core practice in programming, enabling systematic evaluation of programs produced by human developers or large language models (LLMs). Given the challenges in writing comprehensive unit tests, LLMs have been employed to automate unit test generation, yet methods for training LLMs to produce high-quality unit tests remain underexplored. In this work, we propose UTRL, a novel reinforcement learning (RL) framework that trains an LLM to generate high-quality unit test given a programming instruction. Our key idea is to iteratively train two LLMs, the unit test generator and the code generator, in an adversarial manner via RL: (1) the unit test generator is trained to maximize a discrimination reward, encouraging it to produce tests that reveal faults in the code generator’s solutions; and (2) the code generator is trained to maximize a code reward, encouraging it to produce solutions that pass the unit tests generated by the unit test generator. In our experiment, we demonstrate that unit tests generated by Qwen3-4B trained via UTRL show higher quality compared to unit tests generated by the same model trained via supervised fine-tuning on ground-truth unit tests, yielding code evaluations that more closely align with those induced by the ground-truth tests. Moreover, Qwen3-4B trained with UTRL outperforms frontier models like GPT-4.1 and GPT-4o in generating high-quality unit tests, highlighting the effectiveness of UTRL in training LLMs for the unit test generation.