ICML 2026 论文列表

Physics-informed neural networks (PINNs) can be unreliable on PDEs with oscillatory, multiscale, stiff, or long-time solutions, and these difficulties worsen in high dimensions where collocation-based training yields large numerical integration error and high-variance gradients. We propose Low-Rank Fourier Sums (LoRFS), representing the solution as a low-rank sum of separable Fourier expansions (products of one-dimensional Fourier series across coordinates). This makes high-frequency structure explicit and enables closed-form evaluation of common physics-based objectives and their gradients (e.g., $L^2$ residual and variational losses), replacing sampling-based collocation estimates with analytic loss evaluation and eliminating sampling noise. We further provide theoretical results that clarify why LoRFS is particularly well suited to high-dimensional regimes. Across canonical PINN failure-mode benchmarks and their high-dimensional extensions, LoRFS consistently outperforms strong PINN baselines and remains stable in regimes where competing methods degrade.

Optimal transport (OT) has emerged as a fundamental tool in modern machine learning, yet its computational cost remains a significant bottleneck for large-scale applications. While harnessing the massive parallelism of modern GPU hardware is critical for efficiency, the de facto standard Sinkhorn algorithm, despite its ease of parallelization, often suffers from slow convergence in challenging problems. More recently, the sparse-plus-low-rank quasi-Newton method offers a balance between convergence rate and per-iteration complexity; however, its efficiency on GPUs is severely hindered by the serial nature of sparse matrix symbolic analysis and irregular memory access patterns. To bridge this gap, we present cuRegOT, a high-performance GPU solver tailored for entropic-regularized OT. We introduce a suite of algorithmic and architectural optimizations, including an amortized symbolic analysis strategy to mitigate CPU bottlenecks, an asynchronous Sinkhorn iterates generation mechanism, and a fused kernel for bandwidth-efficient gradient evaluation. These strategies are backed by rigorous theoretical guarantees ensuring algorithmic convergence. Extensive numerical experiments demonstrate that cuRegOT achieves significant speedups over state-of-the-art GPU-based solvers across a variety of benchmark tasks.

Learning to rank can be cast as a probabilistic modeling problem over permutations, where the goal is to estimate the likelihood of an observed total ordering of items. This formulation naturally involves full-order probabilities of the form $\mathbb{P}(z_1 \leq \cdots \leq z_n)$, whose exact computation and optimization are intractable due to the factorial growth of the permutation space with respect to the list size. In this work, we introduce the *Full-Order Bound* (FOB), a tractable lower bound on the probability of an observed ordering, constructed from a subset of ordering constraints that factorizes across items while preserving full-order structure and order-reversal invariance. Under log-concave latent densities, the bound induces a convex inner tightening problem over latent cut points, which we solve efficiently during training using a *safe-region gradient ascent* (SRGA) procedure. Experiments on synthetic ranking tasks and large-scale learning-to-rank benchmarks show that FOB improves full-list ordering metrics and remains competitive on NDCG, while an optional metric-aligned variant recovers NDCG gains. Our code is available at https://github.com/tyxaaron/FOB.

The widespread availability of fine-tuned LoRA modules for open pre-trained models has led to an interest in methods that can adaptively merge LoRAs to improve performance. These methods typically include some way of selecting LoRAs from a pool and tune merging coefficients based on a task-specific dataset. While adaptive merging methods have demonstrated improvements in some settings, no past work has attempted to recycle LoRAs found ``in the wild'' on model repositories like the Hugging Face Hub. To address this gap, we consider recycling from a pool of nearly 1,000 user-contributed LoRAs trained from the Llama 3.1 8B-Instruct language model. Our empirical study includes a range of adaptive and non-adaptive merging methods in addition to a new method designed via a wide search over the methodological design space. We demonstrate that adaptive merging methods can improve performance over the base model but provide limited benefit over training a new LoRA on the same data used to set merging coefficients. We additionally find not only that the specific choice of LoRAs to merge has little importance, but that using LoRAs with randomly initialized parameter values yields similar performance. To better understand why past work has proven successful, we confirm that positive transfer is indeed possible when there are highly relevant LoRAs in the pool. We release the model checkpoints and code online at https://github.com/r-three/realistic-adaptive-merging.

Low-Rank Adaptation (LoRA) merging can efficiently combine diverse generative capabilities from multiple trained LoRAs for a diffusion model. However, existing LoRA merging techniques often suffer from severe parameter interference, causing destructive collisions in the shared parameter space. To address this, we propose Subspace Signal Routing (SSR), which resolves interference by routing internal signals instead of performing parameter-space merge. Specifically, SSR first constructs a unified subspace by concatenating candidate LoRAs along the rank dimension. Next, SSR employs an inverse correlation matrix to decorrelate mixed signals within this space. Finally, a directional guide matrix steers these purified signals into their respective task-specific subspaces. We provide a rigorous theoretical analysis proving that SSR aligns with the Ordinary Least Squares (OLS) solution, thereby ensuring mathematical optimality. We utilize the additivity of sufficient statistics to design a streaming algorithm. This enables on-the-fly updates that significantly reduce memory overhead and computation time. Extensive experiments validate that SSR significantly outperforms state-of-the-art methods while maintaining comparable efficiency. The source code will be made publicly available.

Federated Learning (FL) enables collaborative training across distributed clients while preserving data privacy. However, fine-tuning large-scale pre-trained models in FL is hindered by resource constraints and communication costs. Although introducing parameter-efficient fine-tuning strategies such as Low-Rank Adaptation (LoRA) effectively reduces trainable parameters, this low-rank constraint exacerbates noise sensitivity, leading to overfitting and aggregation bias. Existing robust federated fine-tuning methods rely on additional proxy data and treat low-rank adapters as generic weight vectors. In this paper, we investigate the structural properties of LoRA and reveal a robustness asymmetry. The down-projection matrix $A$ extracts stable general features, whereas the up-projection matrix $B$ is highly susceptible to fitting noise patterns. Based on this finding, we propose Federated Decoupled Robust LoRA (FedDR-LoRA), which employs a dual-branch mechanism to decouple robust feature learning from noise modeling and mitigates noise interference through noisy branch negative learning. During federated aggregation, we establish global consensus through aggregating $B$ while preserving local feature alignment in $A$. Extensive experiments demonstrate that FedDR-LoRA outperforms existing state-of-the-art methods across various noisy federated scenarios. Our code is available at: https://github.com/FangXiuwen/FedDR-LoRA.

Activation steering promises to be an extremely parameter-efficient form of adaptation, but its effectiveness depends on critical design choices---such as intervention location and parameterization---that currently rely on empirical heuristics rather than a principled foundation. We establish a first-order equivalence between activation-space interventions and weight-space updates, deriving the conditions under which activation steering can replicate fine-tuning behavior. This equivalence yields a \textbf{principled framework for steering design} and identifies the post-block output as a theoretically-backed and highly expressive intervention site. We explain why certain intervention locations outperform others and show that weight updates and activation updates play distinct, complementary functional roles. This analysis motivates a new approach---\textbf{joint adaptation}---that trains in both spaces simultaneously. Our post-block steering achieves accuracy within $0.2\%\text{--}0.9\%$ of full-parameter tuning, on average across tasks and models, while training only $0.04\%$ of model parameters. It consistently outperforms prior activation steering methods such as ReFT and PEFT approaches including LoRA, while using significantly fewer parameters. Finally, we show that joint adaptation often surpasses the performance ceilings of weight and activation updates in isolation, introducing a new paradigm for efficient model adaptation

Low-Rank Adaptation (LoRA) is a widely used parameter-efficient fine-tuning technique, and previous works have studied the update dynamics of LoRA, showing that updating via the low-rank matrix $\mathbf{A}$ can be viewed as a process within the compressed subspace spanned by $\mathbf{A}^{\top} \mathbf{A}$ of the gradient $\nabla f\left(\mathbf{W} \right)$. However, few works analyze how the properties of the low-rank matrices affect the performance of LoRA, since existing methods heuristically initialize the low-rank matrices as Gaussian matrices. In this paper, we provide a theoretical understanding of the update dynamics of LoRA. We reveal that the update dynamics can be viewed as a process within the subspace spanned by $\mathbf{A}^{\top} (\mathbf{A} \mathbf{A}^{\top})^{\dagger} \mathbf{A}$, and prove that when the gradient $\nabla f\left(\mathbf{W} \right)$ is unavailable, if $\mathbf{A}$ is an Equiangular Tight Frame (ETF), $\mathbf{A}^{\top} \mathbf{A}$ and $\mathbf{A}^{\top} (\mathbf{A} \mathbf{A}^{\top})^{\dagger} \mathbf{A}$ can preserve the maximum information from the gradient $\nabla f\left(\mathbf{W} \right)$. Thus, initializing $\mathbf{A}$ as an ETF is the optimal solution for low-rank adaptation when the gradient $\nabla f\left(\mathbf{W} \right)$ is unavailable. Furthermore, we establish the convergence of Low-Rank Adaptation with a rate of $\mathcal{O}\left(\frac{1}{T}\right)$ when $\mathbf{A}$ is an ETF. Extensive experiments show that initializing the low-rank matrices as ETFs significantly outperforms the commonly used Gaussian initialization for existing primary LoRA variants.

The persistent storage requirements for high-resolution, spatiotemporally evolving fields governed by large-scale and high-dimensional partial differential equations (PDEs) have reached the petabyte-to-exabyte scale. Transient simulations modeling Navier-Stokes equations, magnetohydrodynamics, plasma physics, or binary black hole mergers generate data volumes that are prohibitive for modern high-performance computing (HPC) infrastructures. To address this bottleneck, we introduce ANTIC (Adaptive Neural Temporal in situ Compressor), an end-to-end in situ compression pipeline. ANTIC consists of an adaptive temporal selector tailored to high-dimensional physics that identifies and filters informative snapshots at simulation time, combined with a spatial neural compression module based on continual fine-tuning that learns residual updates between adjacent snapshots using neural fields. By operating in a single streaming pass, ANTIC enables a combined compression of temporal and spatial components and effectively alleviates the need for explicit on-disk storage of entire time-evolved trajectories. Experimental results demonstrate that ANTIC achieves storage reductions of approximately $\sim 400\times$ for 2D Kolmogorov flow simulations and $\sim 7000\times$ for large-scale physics simulations such as binary black hole mergers.

We develop a continual learning method for pretrained models that \emph{requires no access to old-task data}, addressing a practical barrier in foundation model adaptation where pretraining distributions are often unavailable. Our key observation is that pretrained networks exhibit substantial \emph{geometric redundancy}, and that this redundancy can be exploited in two complementary ways. First, redundant neurons provide a proxy for dominant pretraining-era feature directions, enabling the construction of approximately protected update subspaces directly from pretrained weights. Second, redundancy offers a natural bias for \emph{where} to place plasticity: by restricting updates to a subset of redundant neurons and constraining the remaining degrees of freedom, we obtain update families with reduced functional drift on the old-data distribution and improved worst-case retention guarantees. These insights lead to \textsc{PLATE} (\textbf{Pla}sticity-\textbf{T}unable \textbf{E}fficient Adapters), a continual learning method requiring no past-task data that provides explicit control over the plasticity-retention trade-off. PLATE parameterizes each layer with a structured low-rank update $\Delta W = B A Q^\top$, where $B$ and $Q$ are computed once from pretrained weights and kept frozen, and only $A$ is trained on the new task. Code is available at https://github.com/SalesforceAIResearch/PLATE.

Test-time adaptation (TTA) aims to adapt models to maintain reliable performance on non-stationary test streams without requiring labeled data. Despite its empirical success, the learnability of TTA under non-stationary streams remains unexplored. A key challenge is the lack of a principled theoretical framework that simultaneously aligns with the TTA objective and captures both continuously evolving distribution shifts and intrinsic information constraints. To address this gap, we propose the first theoretical framework for studying the learnability of TTA and introduce $(\epsilon,\delta)$-Recovery Complexity and $(\epsilon,\rho)$-TTA Learnability. Recovery complexity measures the post-shift time needed to maintain excess risk below a target level with high probability, and is further extended to TTA learnability, which measures the long-term reliability of TTA. Within this framework, we introduce a novel discrete surrogate for non-stationary test streams, enabling a unified and tractable analysis of both gradual and abrupt shifts. We derive order-wise matching lower and upper bounds on recovery complexity, revealing fundamental limits of TTA and an intrinsic adaptivity-information trade-off. These results provide unified learnability guarantees for TTA that complement regret-based analyses.

Sparse-reward reinforcement learning typically focuses on exploration, but we ask: can structural assumptions about reward functions themselves accelerate learning? We introduce Policy-Aware Matrix Completion (PAMC), which exploits low-rank structure in reward matrices while correcting for policy-induced sampling bias. PAMC combines three key components: a low-rank plus sparse reward model, inverse propensity weighting to handle Missing-Not-At-Random (MNAR) data, and confidence-gated abstention that falls back to intrinsic exploration when uncertain. We provide finite-sample theory showing that completion error scales as $O(\sigma\sqrt{r(|\mathcal{S}|+|\mathcal{A}|)/\text{ESS}})$ where ESS is the effective sample size under policy overlap $\kappa$. PAMC achieves strong empirical results at 10M steps (a sample-efficiency comparison): 4100$\pm$250 return vs. 200$\pm$50 for DrQ-v2 on Montezuma's Revenge, 78\% vs. 65\% success rate on MetaWorld-50, and 15\% improvement over CQL on D4RL datasets. The method maintains 8\% computational overhead while providing calibrated confidence intervals (95\% empirical coverage). When structural assumptions are violated, PAMC gracefully degrades through increased abstention rather than catastrophic failure. Our approach demonstrates that reward structure exploitation can complement traditional exploration methods in sparse-reward domains.

Recent advances in large-scale diffusion models have intensified concerns about their potential misuse, particularly in generating realistic yet harmful or socially disruptive content. This challenge has spurred growing interest in effective machine unlearning, the process of selectively removing specific knowledge or concepts from a model without compromising its overall generative capabilities. Among various approaches, Low-Rank Adaptation (LoRA) has emerged as an effective and efficient method for fine-tuning models toward targeted unlearning. However, LoRA-based methods often exhibit limited adaptability to concept semantics and struggle to balance removing closely related concepts with maintaining generalization across broader meanings. Moreover, these methods face scalability challenges when multiple concepts must be erased simultaneously. To address these limitations, we introduce UnHype, a framework that incorporates hypernetworks into single- and multi-concept LoRA training. The proposed architecture can be directly plugged into Stable Diffusion as well as modern flow-based text-to-image models, where it demonstrates stable training behavior and effective concept control. During inference, the hypernetwork dynamically generates adaptive LoRA weights based on the CLIP embedding, enabling more context-aware, scalable unlearning. We evaluate UnHype across several challenging tasks, including object erasure, celebrity erasure, and explicit content removal, demonstrating its effectiveness and versatility.

While low-rank decomposition offers potential for reducing LLM parameters, maintaining the original capabilities remains a significant challenge. In this work, we identify and formalize a key overlooked issue in LLM decomposition: \textit{representation drift}. We show that approximation errors introduced by decomposition propagate and amplify non-linearly through the deep layers of the transformer architecture, progressively distorting internal representations and degrading downstream performance. To mitigate this, we introduce a conceptually simple but principled compensation mechanism, named ``Decomper'', that operates by suppressing error at its source. By learning to align the output distribution of decomposed transformer blocks with their original counterparts, our method effectively counteracts representation drift, achieving notable performance recovery with near-zero inference overhead. Extensive experiments in OPT, LLaMA-2/3, and Qwen exhibit remarkable improvements. For instance, on LLaMA-3-8B and OPT-13B at 40\% compression, perplexity is reduced by more than 70\% while reasoning task accuracy improves by over 10\%. Our code is available at this \href{https://github.com/xinhaoH/SVD-Compen}{URL}.

Low-Rank Adaptation (LoRA) achieves parameter-efficient fine-tuning by constraining model updates to a low-rank subspace and has been widely used in practice. However, LoRA typically employs a shared low-rank update across tokens, which limits its ability to fully exploit the adaptation subspace for tokens from different sequences. To address this issue, we propose an adaptive utilization of Low-Rank Adaptation (U-LoRA), which employs conditioned gating to explicitly learn effective token-level utilization of the limited low-rank adaptation subspace. Specifically, U-LoRA generates utilization coefficients along low-rank directions for each token and jointly coordinates and constrains them using sequence-level contextual information, thereby inducing more consistent adaptive patterns within a sentence. To further enhance training stability, we introduce a bias-corrected exponential moving average (EMA) historical prior that calibrates utilization signals across optimization steps, suppressing noise caused by batch-to-batch fluctuations. The effectiveness of our method arises from a better utilization of the existing low-rank subspace via input-conditioned strategies, rather than from expanding the subspace. Experiments on mathematical reasoning and natural language understanding benchmarks demonstrate that U-LoRA achieves competitive performance under comparable parameter budgets when with strong LoRA baselines and recent variants.

Model merging in the pretrain-finetune paradigm has proven effective by combining multiple finetuned models into one with multi-task capabilities. However, existing methods rely on fix or manually tuned merging coefficients, making the unified model sensitive to the initial merging strategy and suboptimal for downstream adaptation. Thus, this paper proposed an innovative model merging framework called MetaMerging, a novel meta-learning algorithm to adaptively optimize the merging coefficients to construct a unified model tailored for task-specific adapter training. By simulating adapter updates in an inner loop and meta-optimizing merging coefficients in an outer loop, MetaMerging produces more balanced and generalizable unified models. Extensive experiments on CV and NLP fields show strong performance of MetaMerging on various downstream tasks and demonstrate the effectiveness of meta-learning in our method compared to other parameter merging methods. Our code is available at https://github.com/cjcj46262/MetaMerging.

We propose Log-Normal Multiplicative Dynamics (LMD), a new algorithm to stabilize low-precision deep learning. LMD is motivated by the robustness of biological neural networks where synaptic spine sizes follow a log-normal distribution and fluctuate via noisy multiplicative dynamics. So far, no algorithm has successfully incorporated all these synaptic properties to train large models. LMD incorporates these properties through a variational Bayesian formulation that uses a log-normal posterior over weights. We evaluate LMD with low-precision forward-pass matrix multiplications, including training a Vision Transformer and GPT-2 from scratch. Our findings demonstrate the utility of biologically inspired approaches for designing energy-efficient algorithms for stable low-precision deep learning.

Action-values are foundational to many control algorithms such as Q-learning. Therefore learning action-values efficiently is central to reinforcement learning (RL). However, learning them can be slow, requiring many updates to move values from their initialization, typically near zero, to their true values, which may be far from zero. Moreover, action-value learning algorithms typically update each state–action pair independently, without learning shared value structure across actions within a state. In this paper, we address these inefficiencies by introducing the mean-expansion layer, which accelerates action-value learning by sharing values across actions within a state and by changing the problem from directly learning potentially large action-values to learning a lower-norm representation of them. In deep RL, this layer can be applied as a parameter-free addition to Q-network architectures without altering the underlying algorithm. Applied to deep Q-networks and implicit quantile networks, it improves aggregate performance across 57 Atari games while increasing action gaps and dramatically reducing value overestimation.

Sequential recommendation models, while powerful, have limited flexibility in responding to immediate user requests, making it difficult to adapt their recommendations to the user's timely interests. Unfortunately, existing user request adaptation methods often incur high computational overhead due to either 1) retraining the entire backbone network or 2) leveraging the inference ability of large language models (a.k.a. prompt engineering), limiting their applicability in large-scale recommendation services. This paper presents **C**ontrol via **R**equest-**A**ware **M**asking for **E**diting **R**ecommenders (**CRAMER**), a framework that takes users' natural-language requests to immediately change sequential recommendation models' behavior. Specifically, inspired by the model control theory, CRAMER treats user requests as control signals to modulate frozen backbone parameters through masking, achieving instant adaptation to diverse requests while avoiding costly retraining. Experiments on multiple large-scale benchmark datasets show that CRAMER outperforms four state-of-the-art request-aware baselines across multiple recommendation metrics while achieving minimal overhead. Moreover, the proposed framework exhibits enhanced controllability and cross-domain adaptability, establishing a new paradigm for request-aware sequential recommendation.