ICML 2026 Papers

While prompt-based parameter-efficient continual learning mitigates catastrophic forgetting by isolating task-specific prompts, this isolation also limits later tasks from improving earlier ones, leaving backward knowledge transfer underexplored. We address this limitation by proposing Selective bAckward refinement for positive Backward knowledge transfER (SABER), a replay-free framework that enables controlled backward transfer in prompt-based continual learning. SABER determines when backward refinement is beneficial using complementary task-correlation criteria based on prompt-gradient geometry and loss-distribution similarity, and how to perform refinement safely by restricting updates to non-interfering directions in the prompt parameter space. Extensive experiments across multiple continual learning benchmarks, and diverse pretrained backbones, including T5-Large, LLaMA, and Qwen, demonstrate that SABER consistently achieves positive backward transfer while maintaining strong overall average performance.

Large language models are typically optimized for accuracy and, therefore, will guess even when uncertain about their predictions. This problem becomes especially pronounced when the model is fine-tuned on small datasets, which often causes overfitting and results in a tendency toward miscalibration. In this work, we introduce Bayesian-LoRA, which reformulates the deterministic LoRA update as a probabilistic low-rank representation inspired by Sparse Gaussian Processes (SGP). We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning, language modeling, and mathematical reasoning benchmarks. With only approximately 0.42M additional parameters and ${\approx}1.2{\times}$ training cost relative to standard LoRA, Bayesian-LoRA significantly improves calibration across models from 7B up to 30B, achieving up to 84\% Expected Calibration Error (ECE) and 76\% Negative Log-Likelihood (NLL) reduction while maintaining competitive accuracy for both in-distribution and out-of-distribution (OoD) evaluations.

Adaptive Moment Estimation (Adam) is one of the most popular and often the default stochastic optimizers for deep neural network training. Using first- and second-moment estimation, Adam provides adaptive learning rates for each parameter, significantly outperforming Stochastic Gradient Descent (SGD). However, as deep neural networks become larger, estimating the first and second moments consumes substantial memory. It motivates various methods to reduce memory usage for adaptive optimizers. In this paper, we propose to rethink the first and second moment estimation from a gradient computation perspective. The gradient of the weight matrix is the multiplication of the input and the gradient of the output. Instead of finding low-rank approximations of the first and second moments, as in previous work, we propose tracking the input and output gradients to efficiently estimate moments. We provide analyses of the similarities and differences between our proposed method, the widely used Adam optimizer, and previous memory-efficient optimizers designed to reduce memory usage. We conduct experiments to verify the effectiveness of our method, which reduces memory usage by up to $30$% while preserving similar performance or even improving the performance of Adam.

Merging multiple low-rank adapters (LoRA) provides a practical route to scaling multi-task learning and deployment more efficiently than full-model weight merging, while avoiding reliance on task-specific training data. However, most existing approaches either treat LoRA updates as dense weight deltas or depend on expensive subspace factorizations, making the merge step a primary latency bottleneck. To address this issue, this paper establishes a theoretically positive relationship between merging quality and the effective rank of the matrices being merged. Motivated by this insight, we propose **CircuMerge**, a sketch-based framework for low-rank model merging built on shared circulant transforms. Especially, this approach treats each adapter as a pair of low-rank matrices and applies a shared circulant transform to align all tasks in a common coordinate system. This alignment enables more efficient sampling, allowing us to generate compact sketches that effectively summarize the interactions between tasks. These compact sketches enable applying the merging rules directly to them and reconstructing a standard low-rank adapter, preserving the essential information while significantly reducing computational overhead. Across a broad multi-task LoRA benchmarks covering both vision and language settings, extensive empirical results demonstrate that CircuMerge reduces the overall merging time by at least 44\% compared to the state-of-the-art approaches, with accuracy matching or exceeding the optimal level.

We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.e., $\mathbb{R}^3$ as representation space. This allows us to track how a neural network changes low-dimensional topological invariants through its layers. Just about any topological structure may be simplified or even trivialized by simply increasing dimension; e.g., any knot is equivalent to an unknot in $\mathbb{R}^4$. By restricting to $\mathbb{R}^3$, we not only isolate the effects of activation and depth from that of width, we work in a space that lends itself to easy visualization. We focus on linking number here, deferring other invariants like link groups, Milnor's $\bar{\mu}$-invariants, knot types, ambient cobordisms, to a sequel. We provide full proofs and empirical experiments to justify the following insights: When measured by their power to effect changes in linking numbers, the layer-skipping feature in ResNets is as powerful as the attention mechanism in transformers; both ResNets and transformers are strictly more powerful than feedforward neural networks with monotonic activations, which are in turn more powerful than invertible and flow-based models; but replacing monotonic activation with a nonmonotonic one elevates a feedforward network into the same expressivity class as ResNets and transformers. These results suggest that low-dimensional topology can be a useful tool to guide designs of AI architectures. We also generalize our results from $d = 3$ to arbitrary $d > 3$.

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs associated with generating large-scale, high-quality datasets and training models. In this work, inspired by studies on the structure of Green's functions for elliptic PDEs, we introduce Neural-HSS, a parameter-efficient architecture built upon the Hierarchical Semi-Separable (HSS) matrix structure that is provably data-efficient for a broad class of PDEs. We theoretically analyze the proposed architecture, proving that it satisfies exactness properties even in very low-data regimes. We also investigate its connections with other architectural primitives, such as the Fourier neural operator layer and convolutional layers. We experimentally validate the data efficiency of Neural-HSS on the three-dimensional Poisson equation over a grid of two million points, demonstrating its superior ability to learn from data generated by elliptic PDEs in the low-data regime while outperforming baseline methods. Finally, we demonstrate its capability to learn from data arising from a broad class of PDEs in diverse domains, including electromagnetism, fluid dynamics, and biology.

Low-rank approximation has emerged as a cornerstone technique for model compression and parameter-efficient fine-tuning, enabling substantial reductions in computation and memory without altering model architectures. However, existing approaches often overlook the shifts in feature distributions induced by the approximation process, which can lead to error amplification and unstable inference. We propose a distribution-aware whitening framework that dynamically whitens layer inputs based on the evolving feature distributions, ensuring second-order isotropy of input features. This allows that the discarded components in the low-rank approximation are those with minimal impact on model outputs, thereby minimizing cumulative approximation errors across layers. We theoretically analyze how distribution misalignment leads to error propagation and demonstrate that our approach achieves tighter control over layerwise distortion. Extensive experiments across various large language models demonstrate the superiority of our method in post-training compression. Moreover, our method can also serve as an effective initialization for LoRA-style parameter-efficient fine-tuning. Our findings highlight the importance of considering feature distributions in low-rank approximations, paving the way for reliable and effective model compression strategies.

Adapting large language models (LLMs) to low-resource domains remains challenging due to the scarcity of domain-specific data. While in-domain data is limited, there exists a vast amount of general-domain data that shares similar question–answer formats and reasoning patterns with domain tasks. This observation raises an important question: can useful general-domain data be mined to improve low-resource domain adaptation? Our initial findings show that general-domain chain-of-thought data contains useful auxiliary signals for domain adaptation, even without careful selection. This observation motivates a new paradigm for domain adaptation beyond exclusive reliance on domain-specific data. To systematically identify the most beneficial general-domain samples, we propose NTK-Selector, motivated by the Neural Tangent Kernel’s ability to capture alignment in training dynamics. Since directly applying NTK to pretrained LLMs is impractical, we introduce a Jacobian-free NTK approximation and empirically demonstrate stable NTK-like behavior during fine-tuning. Extensive experiments across medical, financial, legal, and psychological domains demonstrate that NTK-Selector consistently outperforms domain-only fine-tuning and existing data selection baselines. In particular, NTK-Selector achieves gains of +8.7 and +5.1 points on Llama3-8B-Instruct and Qwen3-8B, respectively, compared to only +0.8 and +0.9 points from domain-only fine-tuning.

Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. Whereas most previous low-discrepancy constructions rely on abstract algebra and number theory, Message-Passing Monte Carlo (MPMC) was recently introduced to exploit machine learning methods for generating point sets with lower discrepancy than previously possible. However, MPMC is limited to generating point sets and cannot be extended to low-discrepancy sequences (LDS), i.e., sequences of points in which every prefix has low discrepancy, a property essential for many applications. To address this limitation, we introduce Neural Low-Discrepancy Sequences (*NeuroLDS*), the first machine learning-based framework for generating finite LDS. Drawing inspiration from classical LDS, we train a neural network to map indices to points such that the resulting sequences exhibit minimal discrepancy across all prefixes. To this end, we deploy a two-stage learning process: supervised approximation of classical constructions followed by unsupervised fine-tuning to minimize prefix discrepancies. We demonstrate that *NeuroLDS* outperforms all previous LDS constructions by a significant margin with respect to discrepancy measures. Moreover, we demonstrate the effectiveness of *NeuroLDS* across diverse applications, including numerical integration, robot motion planning, and scientific machine learning. These results highlight the promise and broad significance of Neural Low-Discrepancy Sequences.

Many decision-making problems require ranking individuals by their treatment effects rather than estimating the exact effect magnitudes. Examples include prioritizing patients for preventive care interventions, or ranking customers by the expected incremental impact of an advertisement. Surprisingly, while causal effect estimation has received substantial attention in the literature, the problem of directly learning *rankings of treatment effects* has largely remained unexplored. In this paper, we introduce *Rank-Learner*, a novel two-stage learner that directly learns the ranking of treatment effects from observational data. We first show that naive approaches based on precise treatment effect estimation solve a harder problem than necessary for ranking, while our *Rank-Learner* optimizes a pairwise learning objective that recovers the true treatment effect ordering, without explicit CATE estimation. We further show that our *Rank-Learner* is Neyman-orthogonal and thus comes with strong theoretical guarantees, including robustness to estimation errors in the nuisance functions. In addition, our *Rank-Learner* is model-agnostic, and can be instantiated with arbitrary machine learning models (e.g., neural networks). We demonstrate the effectiveness of our method through extensive experiments where *Rank-Learner* consistently outperforms standard CATE estimators and non-orthogonal ranking methods. Overall, we provide practitioners with a new, orthogonal two-stage learner for ranking individuals by their treatment effects.

Fine-tuning large pre-trained models on a target distribution often improves in-distribution (ID) accuracy, but at the cost of out-of-distribution (OOD) robustness as representations specialize to the fine-tuning data. Weight-space ensembling methods, such as Model Soups, mitigate this effect by averaging multiple checkpoints, but they are computationally prohibitive, requiring the training and storage of dozens of fine-tuned models. In this paper, we introduce MonoSoup, a simple, data-free, hyperparameter-free, post-hoc method that achieves a strong ID–OOD balance using _only a single_ checkpoint. Our method applies Singular Value Decomposition (SVD) to each layer’s update and decomposes it into high-energy directions that capture task-specific adaptation and low-energy directions that introduce noise but may still encode residual signals useful for robustness. MonoSoup then uses entropy-based effective rank to automatically re-weigh these components with layer-wise coefficients that account for the spectral and geometric structure of the model. Experiments on CLIP models fine-tuned on ImageNet and evaluated under natural distribution shifts, as well as on Qwen language models tested on mathematical reasoning and multiple-choice benchmarks, show that this plug-and-play approach is a practical and effective alternative to multi-checkpoint methods, retaining much of their benefits without their computational overhead.

Post-Training Quantization (PTQ) and Low-Rank Adaptation (LoRA) constitute the standard pipeline for efficient Large Language Model (LLM) deployment. However, applying them sequentially poses a problem: PTQ often leaves behind random noise that is spread out (across the model's weights) in a way LoRA can't easily fix, meaning that LoRA ends up wasting its limited capacity trying to fix uncorrectable noise instead of improving task performance. In this paper, we propose \textbf{ProjQ}, a novel framework for constraining quantization noise to the low-rank manifold via orthogonal subspace projection. We derive an efficient alternating algorithm that shapes the quantization noise into a low-rank structure, effectively offloading dominant error components to the subsequent adapter while minimizing the residual error in the orthogonal "uncorrectable" subspace. Our theoretical analysis demonstrates that ProjQ preserves strictly greater model plasticity for downstream tasks compared to standard PTQ. Extensive experiments on LLaMA-2, Qwen2.5 and Qwen3 confirm that ProjQ consistently outperforms existing methods in both quantization error compensation and downstream task fine-tuning, achieving up to $2\times$ lower evaluation loss for compensation and matching the performance of standard 4-bit baselines on language modeling tasks with only 3 bits. The code is available on \url{https://github.com/yy9301/ProjQ}.

Personalized federated learning has emerged as a popular approach to training on devices holding statistically heterogeneous data, known as clients. However, most existing approaches require a client to have labeled data for training or finetuning in order to obtain their own personalized model. In this paper we address this by proposing FLowDUP, a novel method that is able to generate a personalized model using only a forward pass with unlabeled data. The generated model parameters reside in a low-dimensional subspace, enabling efficient communication and computation. FLowDUP's learning objective is theoretically motivated by our new transductive multi-task PAC-Bayesian generalization bound, that provides performance guarantees for unlabeled clients. The objective is structured in such a way that it allows both clients with labeled data and clients with only unlabeled data to contribute to the training process. To supplement our theoretical results we carry out a thorough experimental evaluation of FLowDUP, demonstrating strong empirical performance on a range of datasets with differing sorts of statistically heterogeneous clients. Through numerous ablation studies, we test the efficacy of the individual components of the method.

Hyperspectral image change detection (HSI-CD) suffers from severe annotation scarcity and complex change patterns, which fundamentally limit the effectiveness of directly fine-tuning pre-trained foundation models. Although semi-supervised learning provides a promising direction, existing approaches mainly rely on confidence-based pseudo-label selection, leading to limited data diversity or severe error propagation. In this paper, we propose Influence-Aware Semi-supervised Fine-tuning (IA-SFT), a novel framework that evaluates the influence of pseudo-labels on model decision behavior to identify truly valuable supervision signals. Instead of confidence-based selection, IA-SFT evaluates each low-confidence pseudo-label by measuring its impact on labeled data, enabling reliable filtering of high-value pseudo-labels with minimal noise. To further adapt foundation models to HSI-CD, we design an Adaptive Fusion Change Decoder (AFCD) that jointly models global semantic consistency and local change details. Extensive experiments on three benchmark datasets demonstrate that IA-SFT consistently improves pseudo-label quality and detection performance, achieving superior accuracy compared to state-of-the-art methods. Additional analyses validate the transferability of IA-SFT when integrated into different frameworks in a plug-and-play manner. Code will be released.

Due to limited resources and public safety concerns, deep reinforcement learning (RL) agents for many cyber-physical systems (e.g., autonomous vehicles) are first trained in simulators. However, when deployed in real world environments, they often suffer from performance degradation or safety violations because of the inevitable Sim2Real gap. Existing zero-shot approaches, such as robust safe RL and domain randomization, mitigate this issue but typically at the cost of degraded performance or residual safety risks when experiencing unmodeled system dynamics. To address these limitations, we propose a novel reinforcement learning framework that enables safe and efficient policy transfer via probabilistic latent embeddings and dynamic policy adaptation. We consider a family of Constrained Markov Decision Processes (CMDPs) under different environment contexts. By leveraging latent context variable in meta-RL, the proposed framework infers the latent representation of the environment from simulated experiences. Furthermore, it incorporates a distributional RL formulation, which allows risk levels of the deployed policy to be adjusted dynamically, based on the estimation accuracy of the latent context variable. This strategy promotes safety at the early deployment stage and improves efficiency through fast policy adaptation under the Sim2Real gap.

Multiview subspace clustering (MvSC) has shown remarkable potential in exploring underlying structures of high-dimensional data. However, existing MvSC methods still suffer from two shortcomings: (1) the commonly use of convex low-rank approximations inadequately capture high-order correlations across views, while sensitivity to noise and outliers degrades clustering performance, and (2) they lack the ability to preserve global correlations and local geometric patterns simultaneously. To address these issues, we propose a novel nonconvex regularized MvSC model with deep prior, which not only accurately characterizes the intrinsic low-rank structure and suppresses the effect of outliers, but also preserves local structural properties through deep networks. By mathematically analyzing the optimal solution of the optimization problem in our proposed model, we develop an efficient ADMM-based algorithm with provable convergence guarantees to solve it. Extensive experiments on various datasets demonstrate the superiority of the proposed model.

As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent positions" are often estimated via embeddings, whereby the nodes of a network are mapped to points in Euclidean space so that "similar" nodes are mapped to nearby points. Under certain model assumptions, these embeddings are consistent estimates of the latent positions, but most such results require the embedding dimension to be chosen correctly. Methods for choosing the embedding dimension have been studied extensively, but little is known about the behavior of embeddings when the dimension is misspecified. In this work, we provide a theoretical description of the effects of dimension misspecification under the random dot product graph, a class of latent space network models that includes several widely-used network models, most notably the stochastic blockmodel, as special cases. We show that when the dimension is chosen too large, consistent estimation still holds, albeit at a slower rate than when the embedding dimension is chosen correctly. On the other hand, when the dimension is chosen too small, there is a fundamental estimation error lower bound that need not go to zero in the large-network limit. A range of synthetic data experiments support our theoretical results. Our main technical result, which may be of independent interest, is a generalization of earlier work in random matrix theory showing that all non-signal eigenvectors of a low-rank matrix subject to additive noise are delocalized.

End-to-end deep learning has achieved impressive results but often relies on large labeled datasets, exhibits limited generalization to unseen scenarios, and incurs substantial computational cost. Classical optimization methods, in contrast, are more data-efficient and lightweight but frequently suffer from slow convergence. Learned optimizers aim to bridge this gap, yet existing approaches have focused primarily on first-order methods, while learned second-order optimization has received much less attention. We introduce L-SR1, a learned second-order optimizer inspired by the classical Symmetric Rank-One (SR1) method. At its core, L-SR1 employs a Projection-Guided Secant Mechanism (PGSM) that generates positive semi-definite preconditioners and biases meta-training toward the quasi-Newton secant relation. Through controlled analytic benchmarks, we study stability, generalization across problem dimensions, and search direction quality, and further evaluate L-SR1 on Monocular Human Mesh Recovery (HMR), where it outperforms both classical and learned optimization-based baselines. With a compact model and no reliance on task-specific fine-tuning or annotated data, L-SR1 demonstrates strong generalization and can be integrated into a broad range of iterative optimization problems to accelerate convergence and reduce the required number of iterations.

Multi-label recognition with frozen Vision-Language Models (VLMs) is brittle under distribution shift: standard zero-shot inference scores labels independently, ignoring co-occurrence structure and producing incoherent label sets where dominant concepts suppress weaker but compatible labels. We introduce Bayesian Conditional Priors (BCP) Estimation, a gradient-free test-time adaptation method that injects label dependency without tuning the backbone. BCP views zero-shot logits as a proxy for marginal posteriors under a fixed image-text likelihood and attributes shift-induced errors mainly to a mismatched label prior. For each test image, it selects a high-confidence anchor label and applies an anchor-conditioned Bayesian refinement. This update is closed-form in logit space and admits a pointwise mutual information (PMI) interpretation, explicitly promoting compatible labels and suppressing incompatible ones. BCP operates without target annotations by estimating anchor-conditioned priors online from the unlabeled test stream via lightweight second-order co-occurrence statistics, adding negligible overhead beyond a single forward pass. Across standard multi-label benchmarks and multiple CLIP backbones, BCP consistently outperforms strong TTA baselines, e.g., improving RN50 average mAP from 57.31 to 69.22 and ViT-B/16 from 62.61 to 71.79.