ICLR 2026 Papers

Model editing techniques, particularly task arithmetic with task vectors, offer an efficient alternative to full fine-tuning by enabling direct parameter updates through simple arithmetic operations. While this approach promises substantial computational savings, its impact on fairness has remained largely unexplored---despite growing concern over biased outcomes in high-stakes applications such as hate speech detection. In this work, we present the first systematic study of group fairness in task arithmetic within this binary text and image classification regime, comparing it against full fine-tuning (FFT) and Low-Rank Adaptation (LoRA). We evaluate across multiple language models and datasets using standard group fairness metrics, including Demographic Parity and Equalized Odds. Our analysis shows that task vectors can be tuned to achieve competitive accuracy while reducing disparities, and that merging subgroup-specific task vectors provides a practical mechanism for steering fairness outcomes. We further provide a theoretical bound linking task vector scaling to fairness metrics, offering insight into the observed trade-offs. Together, these findings establish task arithmetic not only as a cost-efficient editing method but also as a fairness-aware alternative to existing adaptation techniques, within the standard group-fair classification setting, laying the groundwork for responsible deployment of large language models.

Heavy-tailed noise in nonconvex stochastic optimization has garnered increasing research interest, as empirical studies, including those on training attention models, suggest it is a more realistic gradient noise condition. This paper studies first-order nonconvex stochastic optimization under heavy-tailed gradient noise in a decentralized setup, where each node can only communicate with its direct neighbors in a predefined graph. Specifically, we consider a class of heavy-tailed gradient noise that is zero-mean and has only $p$-th moment for $p \in (1, 2]$. We propose GT-NSGDm, Gradient Tracking based Normalized Stochastic Gradient Descent with momentum, that utilizes normalization, in conjunction with gradient tracking and momentum, to cope with heavy-tailed noise on distributed nodes. We show that, when the communication graph admits primitive and doubly stochastic weights, GT-NSGDm guarantees, for the \textit{first} time in the literature, that the expected gradient norm converges at an optimal non-asymptotic rate $O\big(1/T^{(p-1)/(3p-2)}\big)$, which matches the lower bound in the centralized setup. When tail index $p$ is unknown, GT-NSGDm attains a non-asymptotic rate $O\big( 1/T^{(p-1)/(2p)} \big)$ that is, for $p < 2$, topology independent and has a speedup factor $n^{1-1/p}$ in terms of the number of nodes $n$. Finally, experiments on nonconvex linear regression with tokenized synthetic data and decentralized training of language models on a real-world corpus demonstrate that GT-NSGDm is more robust and efficient than baselines.

Transformers are remarkably versatile and their design is largely consistent across a variety of applications. But are they optimal for any given task or dataset? The answer may be key for pushing AI beyond merely scaling current designs. **Method.** We present a method to optimize a transformer architecture for a given dataset, which we use as a tool to study optimal task-specific inductive biases. This method replaces the most important non-linearities (GeLUs,;softmax) with functions learned on held-out data. We then train the resulting architectures on other datasets, as a way to evaluate the compatibility between pairs of tasks. **Findings.** On algorithmic toy tasks, we identify new architectures with dramatic improvements in learning speed, in- and out-of-distribution generalization, and stability across seeds. The new designs prove very task-specific however, and indicate that these tasks require inductive biases very different from those of standard transformers. On code and language modeling datasets, we also find architectures with consistent, yet smaller improvements. These designs transfer much better across datasets and domains (English & computer code). **Implications.** Our results show that standard transformers are rarely a local optimum in the space of architectures. Simple alternatives can perform much better but sacrifice universality. This suggests that there may be room for improved architectures that better support multiple capabilities simultaneously, such as fluency and robust reasoning.

The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed metric is invariant to the sampling frequency of trajectories. It is also computationally efficient, supported by finite-sample convergence guarantees, and enables the computation of Fréchet means, providing interpolation between dynamical systems. Experiments on simulated and real-world datasets show that our approach consistently outperforms standard operator-based distances in machine learning applications, including dimensionality reduction and classification, and provides meaningful interpolation between dynamical systems.

Large language models (LLMs) have achieved remarkable performance across diverse reasoning tasks, yet their deployment is hindered by prohibitive computational and memory costs. Quantization-aware training (QAT) enables ultra-low-bit compression (<4 bits per weight), but existing QAT methods often degrade reasoning capability, partly because complex knowledge structures are introduced during the post-training process in LLMs. In this paper, through a systematic investigation of how quantization affects different data domains, we find that its impact on pre-training and reasoning capabilities differs. Building on this insight, we propose a novel two-stage QAT pipeline specifically designed for reasoning LLMs. In the first stage, we quantize the model using mixed-domain calibration data to preserve essential capabilities across domains; in the second stage, we fine-tune the quantized model with a teacher-guided reward-rectification loss to restore reasoning capability. We first demonstrate that mixed-domain calibration outperforms single-domain calibration by up to 2.74% improvement on average over six tasks, including reasoning and pre-trained tasks. Following experiments on five reasoning benchmarks show that our 2-bit-quantized Qwen3-8B outperforms post-training quantization (PTQ) baselines by 50.45% on average. Moreover, compared to ultra-low-bit-specialized models such as BitNet-2B4T, our pipeline achieves about 2% higher mathematical-reasoning accuracy using only 40K training sequences.

The growing demand for high-quality 3D mesh models has fueled the need for efficient 3D mesh compression techniques. However, existing methods often exhibit suboptimal compression performance due to the inefficient representation of mesh data. To address this issue, we propose a novel neural mesh compression method based on Sparse Implicit Representation (SIR). Specifically, SIR records signed distance field (SDF) values only on regular grids near the surface, enabling high-resolution structured representation of arbitrary geometric data with a significantly lower memory cost, while still supporting precise surface recovery. Building on this representation, we construct a lightweight Sparse Neural Compression (SNC) network to extract compact embedded features from the SIR and encode them into a bitstream. Extensive experiments and ablation studies demonstrate that our method outperforms state-of-the-art mesh and point cloud compression approaches in both compression performance and computational efficiency across a variety of mesh models. The source code is available at https://github.com/yydlmzyz1/SIR-SNC.

While large language models (LLMs) demonstrate impressive performance across various tasks, their deployment in real-world scenarios is still constrained by high computational demands. Layer-wise pruning, a commonly employed strategy to mitigate inference costs, can partially address this challenge. However, existing approaches generally depend on static heuristic rules and fail to account for the interdependencies among layers, thereby limiting the effectiveness of the pruning process. To this end, this paper proposes a game-theoretic framework that formulates layer pruning as a cooperative game in which each layer acts as a player and model performance serves as the utility. As computing exact Shapley values is computationally infeasible for large language models (LLMs), we propose using a lightweight surrogate network to estimate layer-wise marginal contributions. This network can predict LLM performance for arbitrary layer combinations at a low computational cost. Additionally, we employ stratified Monte Carlo mask sampling to further reduce the cost of Sharpley value estimation. This approach captures inter-layer dependencies and dynamically identifies critical layers for pruning. Extensive experiments demonstrate the consistent superiority of our method in terms of perplexity and zero-shot accuracy, achieving more efficient and effective layer-wise pruning for large language models.

Federated bilevel optimization plays a crucial role in solving complex problems with nested optimization structures. However, its distributed nature makes it highly susceptible to faulty or Byzantine behaviors. Existing Byzantine-resilient approaches are either restricted to simple single-level optimization problems or rely on sub-loop updates that introduce significant computational and communication overhead. To address these limitations, we propose a family of Byzantine-resilient federated bilevel algorithms, which (i) operate within a single-loop structure, (ii) achieve optimal Byzantine resilience, and (iii) ensure computational and communication efficiency. The core of the proposed method, BR-FedBi, leverages an auxiliary variable that facilitates efficient hypergradient estimation while simultaneously solving the lower- and upper-level problems. Building on BR-FedBi, we further integrate the algorithm with Polyak’s momentum and the probabilistic gradient estimator (PAGE) (Li et al., 2021), resulting in provable optimal Byzantine resilience and optimal sample complexity. Both theoretical analysis and empirical results demonstrate the superior performance of the proposed algorithms.

Fluorescence microscopy (FM) imaging is a fundamental technique for observing live cell division—one of the most essential processes in the cycle of life and death. Observing 3D live cells requires scanning through the cell volume while minimizing lethal phototoxicity. That limits acquisition time and results in sparsely sampled volumes with anisotropic resolution and high noise. Existing image restoration methods, primarily based on inverse problem modeling, assume known and stable degradation processes and struggle under such conditions, especially in the absence of high-quality reference volumes. In this paper, from a new perspective, we propose a novel tensor completion framework tailored to the nature of FM imaging, which inherently involves nonlinear signal degradation and incomplete observations. Specifically, FM imaging with equidistant Z-axis sampling is essentially a tensor completion task under a uniformly random sampling condition. On one hand, we derive the theoretical lower bound for exact cell tensor completion, validating the feasibility of accurately recovering 3D cell tensor. On the other hand, we reformulate the tensor completion problem as a mathematically equivalent score-based generative model. By incorporating structural consistency priors, the generative trajectory is effectively guided toward denoised and geometrically coherent reconstructions. Our method demonstrates state-of-the-art performance on SR-CACO-2 and four real \textit{in vivo} cellular datasets, showing substantial improvements in both signal-to-noise ratio and structural fidelity.

Open world image segmentation aims to achieve precise segmentation and semantic understanding of targets within images by addressing the infinitely open set of object categories encountered in the real world. However, traditional closed-set segmentation approaches struggle to adapt to complex open world scenarios, while foundation segmentation models such as SAM exhibit notable discrepancies between their strong segmentation capabilities and relatively weaker semantic understanding. To bridge discrepancies, we propose WOW-Seg, a Word-free Open World Segmentation model for segmenting and recognizing objects from open-set categories. Specifically, WOW-Seg introduces a novel visual prompt module, Mask2Token, which transforms image masks into visual tokens and ensures their alignment with the VLLM feature space. Moreover, We introduce the Cascade Attention Mask to decouple information across different instances. This approach mitigates inter-instance interference, leading to a significant improvement in model performance. We further construct an open world region recognition test benchmark: the Region Recognition Dataset (RR-7K). With 7,662 classes, it represents the most extensive category-rich region recognition dataset to date. WOW-Seg attains strong results on the LVIS dataset, achieving a semantic similarity of 89.7 and a semantic IoU of 82.4. This performance surpasses the previous SOTA while using only one-eighth the parameter count. These results underscore the strong open world generalization capabilities of WOW-Seg. The code and related resources are available at https://anonymous.4open.science/r/WOW-Seg-4C5E.

While Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in image and video understanding, their ability to comprehend the physical world has become an increasingly important research focus. Despite their improvements, current MLLMs struggle significantly with high-level physics reasoning. In this work, we investigate the first step of physical reasoning, i.e., **intuitive physics understanding**, revealing substantial limitations in understanding the dynamics of continuum objects. To isolate and evaluate this specific capability, we introduce two fundamental benchmark tasks: Next Frame Selection (NFS) and Temporal Coherence Verification (TCV). Our experiments demonstrate that even state-of-the-art MLLMs perform poorly on these foundational tasks. To address this limitation, we propose Scene Dynamic Field (SDF), a concise approach that leverages physics simulators within a multi-task fine-tuning framework. SDF substantially improves performance, achieving up to $20.7\%$ gains on fluid tasks while showing strong generalization to unseen physical domains. This work not only highlights a critical gap in current MLLMs but also presents a promising cost-efficient approach for developing more physically grounded MLLMs. Our code and data will be publicly available.

Tokenizer is a crucial component for both visual understanding and generation. To advance toward the ultimate goal of universal modeling, recent research has focused on developing a unified tokenizer. However, existing tokenizers face a significant performance trade-off between understanding and generation, stemming from the inherent conflict between high-level semantic abstraction and low-level pixel reconstruction. To tackle this challenge, we propose a generic and unified tokenizer, namely $\textbf{UniFlow}$, by flexibly adapting any visual encoder with a concise reconstruction decoder. Specifically, we introduce $\textit{layer-wise adaptive self-distillation}$ applied to the well-pretrained visual encoders, which enables UniFlow to simultaneously inherit the strong semantic features for visual understanding and flexibly adapt to model fine-grained details for visual generation. Moreover, we propose a lightweight $\textit{patch-wise pixel flow decoder}$, which efficiently achieves high-fidelity pixel reconstruction by modeling a conditional flow from the noisy state back to the patch-wise pixel domain. By leveraging the semantic features as visual conditions for the decoder, we effectively alleviate the training conflicts between understanding and generation. Furthermore, the patch-wise learning strategy simplifies the data distribution, thereby improving training efficiency. For instance, our 7B UniFlow-XL not only surpasses the 14B TokenFlow-XL by 6.05\% on average understanding benchmarks, but also achieves a competitive results in both visual reconstruction and generation, surpassing UniTok by 0.15 in rFID and 0.09 in gFID (without guidance), respectively.

Simulating the long-timescale dynamics of biomolecules is a central challenge in computational science. While enhanced sampling methods can accelerate these simulations, they rely on pre-defined collective variables that are often difficult to identify, restricting their ability to model complex switching mechanisms between metastable states. A recent generative model, LD-FPG, demonstrated that this problem could be bypassed by learning to sample the static equilibrium ensemble as all-atom deformations from a reference structure, establishing a powerful method for all-atom ensemble generation. However, while this approach successfully captures a system's probable conformations, it does not model the temporal evolution between them. We introduce the Graph Latent Dynamics Propagator (GLDP), a modular component for simulating dynamics within the learned latent space of LD-FPG. We then compare three classes of propagators: (i) score-guided Langevin dynamics, (ii) Koopman-based linear operators, and (iii) autoregressive neural networks. Within a unified encoder–propagator–decoder framework, we evaluate long-horizon stability, backbone and side-chain ensemble fidelity, and temporal kinetics via TICA. Benchmarks on systems ranging from small peptides to mixed-topology proteins and large GPCRs reveal that autoregressive neural networks deliver the most robust long rollouts and coherent physical timescales; score-guided Langevin best recovers side-chain thermodynamics when the score is well learned; and Koopman provides an interpretable, lightweight baseline that tends to damp fluctuations. These results clarify the trade-offs among propagators and offer practical guidance for latent-space simulators of all-atom protein dynamics.

Model merging, which combines multiple domain-specialized experts into a single model, offers a practical path to endow Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) with broad capabilities without the cost of joint training or serving many models. However, training-free methods rely on hand-tuned coefficients, whereas training-based methods primarily align parameters rather than downstream task behavior and typically treat all layers uniformly, ignoring inter-layer heterogeneity. We introduce Expert Merging, a training-light method that learns a small set of layer-wise coefficients using only unlabeled calibration data. The coefficients are optimized to explicitly align the merged model’s hidden states and logits with those of the corresponding experts, with a coefficient regularizer for stability and task-weighted losses for controllable trade-offs. To capture inter-layer variation, Expert Merging++ augments this design with importance-guided chunking: a normalized layer-importance metric, derived from learned coefficients, task-vector magnitudes, and parameter counts, allocates more chunk-wise coefficients to high-importance layers while keeping low-importance layers lightweight. The result is a label-free, parameter-efficient, and scalable approach to multi-expert model merging across LLMs and MLLMs. Across MLLM backbones (InternVL and Qwen2-VL) and the LLM backbone (Mistral), our method surpasses strong training-free and training-based merging baselines, with Expert Merging++ delivering further gains and, in some cases, even exceeding supervised Mixture Training. Our code is available at https://anonymous.4open.science/r/ExpertMeging and in the supplementary materials.

Handcrafted optimizers become prohibitively inefficient for complex black-box optimization (BBO) tasks. MetaBBO addresses this challenge by meta-learning to automatically configure optimizers for low-level BBO tasks, thereby eliminating heuristic dependencies. However, existing methods typically require extensive handcrafted training tasks to learn meta-strategies that generalize to target tasks, which poses a critical limitation for realistic applications with unknown task distributions. To overcome the issue, we propose the Adaptive meta Black-box Optimization Model (ABOM), which performs online parameter adaptation using solely optimization data from the target task, obviating the need for predefined task distributions. Unlike conventional metaBBO frameworks that decouple meta-training and optimization phases, ABOM introduces a closed-loop adaptive parameter learning mechanism, where parameterized evolutionary operators continuously self-update by leveraging generated populations during optimization. This paradigm shift enables zero-shot optimization: ABOM achieves competitive performance on synthetic BBO benchmarks and realistic unmanned aerial vehicle path planning problems without any handcrafted training tasks. Visualization studies reveal that parameterized evolutionary operators exhibit statistically significant search patterns, including natural selection and genetic recombination.

This paper studies online bidding subject to simultaneous budget and return-on-investment (ROI) constraints, which encodes the goal of balancing high volume and profitability. We formulate the problem as a general constrained online learning problem that can be applied to diverse bidding settings (e.g., first-price or second-price auctions) and feedback regimes (e.g., full or partial information), among others. We introduce L2FOB, a Look-ahead Lyapunov Framework for Online Bidding with strong empirical and theoretical performance. By combining optimistic reward and pessimistic cost estimation with the look-ahead virtual queue mechanism, L2FOB delivers safe and optimal bidding decisions. We provide adaptive guarantees: L2FOB achieves $O (\mathcal{E}\_r(T,p)+(\nu^* / \rho) \mathcal{E}\_c(T,p))$ regret and $O (\mathcal{E}\_r(T,p)+\mathcal{E}\_c(T,p))$ anytime ROI constraint violation, where $\mathcal{E}_r(T,p)$ and $\mathcal{E}_c(T,p)$ are cumulative estimation errors over $T$ rounds, $\rho$ is the average per-round budget, and $\nu^*$ is the offline optimal average reward. We instantiate L2FOB in several online bidding settings, demonstrating guarantees that match or improve upon the best-known results. These results are derived from the novel look-ahead design and Lyapunov stability analysis. Numerical experiments further validate our theoretical guarantees.

Flow matching models have emerged as a strong alternative to diffusion models, but existing inversion and editing methods designed for diffusion are often ineffective or inapplicable to them. The straight-line, non-crossing trajectories of flow models pose challenges for diffusion-based approaches but also open avenues for novel solutions. In this paper, we introduce a predictor-corrector-based framework for inversion and editing in flow models. First, we propose Uni-Inv, an effective inversion method designed for accurate reconstruction. Building on this, we extend the concept of delayed injection to flow models and introduce Uni-Edit, a region-aware, robust image editing approach. Our methodology is tuning-free, model-agnostic, efficient, and effective, enabling diverse edits while ensuring strong preservation of edit-irrelevant regions. Extensive experiments across various generative models demonstrate the superiority and generalizability of Uni-Inv and Uni-Edit, even under low-cost settings.

As everyday use cases of large language model (LLM) AI assistants have expanded, it is becoming increasingly important to personalize responses to align to different users' preferences and goals. While reinforcement learning from human feedback (RLHF) is effective at improving LLMs to be generally more helpful and fluent, it does not account for variability across users, as it models the entire user population with a single reward model, meaning it assumes that everyone's preferences are the same. We present a novel framework, **P**reference **L**earning **U**sing **S**ummarization (**PLUS**), that uses reinforcement learning (RL) to learn to produce text-based summaries of each user's preferences, characteristics, and past conversations. These summaries condition the reward model, enabling it to make personalized predictions about the types of responses valued by each user. Both the user-summarization model and reward model are trained simultaneously, creating an online co-adaptation loop. We show that in contrast to the standard Bradley–Terry model, summaries produced by PLUS capture diverse aspects of user preferences, achieving a 11–77\% improvement in reward model accuracy. Key strengths of PLUS are: (1) robust performance with new users and conversation topics, achieving a 25\% improvement over the best personalized reward model technique used for RLHF; (2) zero-shot personalization with state-of-the-art proprietary models like GPT-4 (e.g., PLUS-summary-conditioned responses achieved a 72\% win rate compared to 28\% for default GPT-4o); (3) learning from flexible user contexts beyond preference labels, and (4) interpretable representation of users, enabling greater transparency and user control in pluralistic LLM alignment.

Temperature is a crucial hyperparameter in large language models (LLMs), controlling the trade-off between exploration and exploitation during text generation. High temperatures encourage diverse but noisy outputs, while low temperatures produce focused outputs but may cause premature convergence. Yet static or heuristic temperature schedules fail to adapt to the dynamic demands of reinforcement learning (RL) throughout training, often limiting policy improvement. We propose Temperature Adaptive Meta Policy Optimization (TAMPO), a new framework that recasts temperature control as a learnable meta-policy. TAMPO operates through a hierarchical two-loop process. In the inner loop, the LLM policy is updated (e.g., using GRPO) with trajectories sampled at the temperature selected by the meta-policy. In the outer loop, meta-policy updates the distribution over candidate temperatures by rewarding those that maximize the likelihood of high-advantage trajectories. This trajectory-guided, reward-driven mechanism enables online adaptation without additional rollouts, directly aligning exploration with policy improvement. On five mathematical reasoning benchmarks, TAMPO outperforms baselines using fixed or heuristic temperatures, establishing temperature as an effective learnable meta-policy for adaptive exploration in LLM reinforcement learning.