ICML 2026 Papers

Low-Rank Adaptation (LoRA) has emerged as a promising paradigm for Continual Learning. It independently updates its low-rank factors ($A$ and $B$), creating a composite update to the full weight matrix through their interaction. To prevent catastrophic forgetting, this update should remain orthogonal to the task-specific subspace that contains previously learned knowledge. However, we identify that this composite update systematically violates this orthogonality, reintroducing interference and undermining stability. Furthermore, naively enforcing this orthogonality compromises plasticity, disrupting the delicate stability-plasticity trade-off. To resolve these issues, we propose Janus-LoRA, a framework that restores this balance through two novel components. Specifically, we first introduce Gradient Rectification, a closed-form solution that mathematically decouples LoRA's factor updates, enforcing orthogonality against the historical knowledge subspace identified by an efficient Online Estimation. Next, to enhance plasticity, we introduce a Decoupled Margin Loss that promotes feature-level separation by pushing new feature representations away from old ones, thus creating distinct, low-interference regions for new learning. Comprehensive experiments on challenging benchmarks demonstrate that by harmonizing parameter-level orthogonality with feature-level separation, Janus-LoRA achieves a superior balance and establishes new state-of-the-art performance.

Long-context Large Language Models (LLMs) enable powerful applications but incur high memory costs due to the key-value states (KV-Cache). Recent studies attempt to share KV-Cache across layers, but these approaches either require expensive pretraining or rely on per-token cross-layer cosine similarity that is often limited in practice. We show, via Centered Kernel Alignment (CKA), that the dominant singular vectors of KV-Cache are well aligned across layers. Motivated by this observation, we propose xKV, a post-training compression method that jointly factorizes grouped-layer KV-Cache into a shared low-rank subspace, substantially reducing KV-Cache memory. Across widely used LLMs, xKV achieves up to 8× KV-Cache compression while preserving accuracy on long-context tasks and in multi-turn settings. To further improve efficiency, we introduce Selective Reconstruction (SR) at decode time. Combined with SR, xKV achieves up to 4.23× end-to-end speedup over the full attention baseline, and surpasses notable baselines with 30% higher throughput under a similar accuracy level. Overall, xKV provides a plug-and-play approach to reduce both memory and latency for long-context LLM inference. Our code is publicly available at: https://github.com/abdelfattah-lab/xKV.

We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text. Using singular value decomposition of weight matrices, we find that CPT leaves singular value spectra largely invariant, with adaptation driven mainly by changes in singular vectors. An analysis of attention-head projection matrices reveals strong, domain-dependent **head heterogeneity**, which we exploit to define a head importance criterion: up to **60%** of head updates can be removed without measurable quality loss. Selectively rewinding low-importance heads to their pre-trained state improves benchmark accuracy by up to **4%** versus the fully trained baseline. Finally, we identify **domain connectivity**—linear interpolation between CPT checkpoints yields smooth domain-quality interpolation without notable degradation on either domain—and release Diffract, an open-source toolkit for scalable spectral analysis of billion-parameter models.

Many advanced Large Language Model (LLM) applications require long-context processing, but the self-attention module becomes a bottleneck during the prefilling stage of inference due to its quadratic time complexity with respect to sequence length. Existing sparse attention methods accelerate attention computation by skipping less significant regions of the attention map. However, these approaches typically perform coarse-grained inspection of the attention map, resulting in their suboptimal performance. In this paper, we propose SALE, a fine-grained sparse attention method that accelerates the long-context prefilling stage of LLM with negligible loss in model accuracy. SALE achieves fast and accurate fine-grained attention map estimation using low-bit quantized query-key products to approximate attention weights, followed by the application of a novel Relative Attention Score metric to assess the importance of query-key pairs. This design enables us to accurately identify important regions in the attention map, thereby constructing a highly sparse attention mask. We implement a custom CUDA kernel in SALE optimized for hardware efficiency, reducing overhead to approximately 11% of the full attention latency. Notably, SALE requires no parameter training and can be seamlessly integrated into existing systems with trivial code modifications. Experiments on long-context benchmarks demonstrate that our method outperforms existing approaches in accuracy-efficiency trade-offs, achieving at least 3.36× speedups on Llama-3.1-8B for sequences longer than 64K while maintaining model quality.

Adapting large-scale pre-trained video generators for Video Super-Resolution (VSR) in novel domains remains computationally prohibitive. Methods that reformulate generation as direct Low-Quality to High-Quality mappings deviate from the original generative formulation, demanding extensive fine-tuning. ControlNet-style adapters lose their efficiency under modern Diffusion Transformers since the absence of encoder-decoder hierarchy forces duplication of the entire backbone. We observe that flow matching offers a principled alternative for cross-domain VSR adaptation. By predicting a constant velocity field across all timesteps, the adaptation task reduces to learning a fixed injection pattern rather than time-varying transformations. Building on this insight, we propose LiteVSR, a minimalist framework that performs VSR using a completely frozen Diffusion Transformer with a lightweight State-Aware Adapter. The adapter employs a dual-stream architecture that extracts static structural cues from the LQ input and dynamic cues from intermediate denoising states, aligning them through time-dependent cross-attention to enable adaptive transition from structural alignment to texture refinement as denoising proceeds. LiteVSR achieves competitive restoration quality with only 11.25% trainable parameters and 12 GPU-hours of training on a single A100, while maintaining fast sampling (down to a single step) compatibility.

Low-Rank Adaptation (LoRA) has become the de facto paradigm for parameter-efficient fine-tuning, with its effectiveness critically influenced by rank allocation across modules. However, existing approaches face a fundamental dilemma: uniform allocation ignores module heterogeneity, while adaptive methods introduce expensive training overhead or lack reusability across configurations. We propose CSPLoRA (Confidence-guided Structural Planning for LoRA), a decoupled framework that reweights probe samples by prediction uncertainty to obtain more discriminative module importance estimates. The key insight is that hard samples---those the model struggles with---provide more informative gradient signals for identifying critical modules than easy samples. For a fixed task-model pair, the resulting structural priors can be reused across compatible rank budgets and LoRA backends, supporting a practical "probe once, deploy everywhere" workflow. Experiments on GLUE, commonsense reasoning, and arithmetic tasks show that CSPLoRA improves over uniform LoRA on average (+1.25 points on LLaMA-2-7B commonsense reasoning) while maintaining comparable parameters, with the planned rank structure reusable across compatible LoRA variants.

Offline-to-online reinforcement learning (O2O RL) faces a central challenge between retaining offline conservatism and adapting to online feedback under distribution shift. This challenge arises because data behavior evolves during fine-tuning, rendering data origin a misleading basis for constraint handling and thereby leading to objective–data mismatch. We therefore propose Dynamic Alignment for RElaxation (DARE), a distribution-aware framework for sample-level constraint relaxation based on the behavioral consistency with a behavior model. To our knowledge, DARE is the first to condition constraint relaxation on behavioral consistency via a posterior-induced exchange mechanism, moving beyond a binary offline/online data distinction. Importantly, DARE requires only per-sample behavioral alignment, enabling instantiation on top of many offline algorithms with flexible choices of behavior models and fine-tuning objectives. We provide a theoretical analysis showing that behavior-based sample exchange consistently improves the distinction between offline-like and online-like subsets. Experiments on D4RL demonstrate that DARE consistently improves fine-tuning stability and achieves superior final performance over strong offline-to-online baselines. (The code is publicly available at \url{https://github.com/lpzu/DARE}.)

Multi-target domain adaptation (MTDA) trains a model using a labeled source domain and several unlabeled target domains, aiming to enhance performance across all targets. However, existing methods lack a principled causal formulation and often rely on empirical domain-invariance enforcement, which can bias adaptation across targets. To fill this gap, we propose the **U**nbiased, **U**nconfounding, and **U**nified **C**ausal **F**ramework (**U$^3$CF**) for MTDA. To *unify* the alignment of multiple domains, we propose a prototype-driven alignment strategy that progressively updates prototypes by high-confidence target predictions, while the contrastive optimization objective jointly aligns target samples to semantic prototypes and preserves class discrimination. By formulating a structural causal model, we reveal that domain-invariant causal factors and domain-specific factors shape representations and labels, while the latter induce spurious label correlations across targets. Accordingly, U$^3$CF achieves *unbiased* prediction by disentangling representations into invariant causal components and domain-specific confounders and applying conditional intervention to *block confounding* effects while preserving invariant semantics. To ensure precise disentanglement, we leverage mutual information theory to derive a principled criterion for feature separation. Extensive experiments on four benchmarks demonstrate that U$^3$CF consistently outperforms leading methods.

The superficial alignment hypothesis (SAH) posits that large language models learn most of their knowledge during pre-training, and that post-training merely surfaces this knowledge. The SAH, however, lacks a precise definition, which has led to (i) different and seemingly orthogonal arguments supporting it, and (ii) important critiques to it. We propose a new metric called **task complexity**: the length of the shortest program that achieves a target performance on a task. In this framework, the SAH simply claims that pre-trained models drastically reduce the complexity of achieving high performance on many tasks. Our definition unifies prior arguments supporting the SAH, interpreting them as different strategies to find such short programs. Experimentally, we estimate the task complexity of mathematical reasoning, machine translation, and instruction following; we then show that these complexities can be remarkably low when conditioned on a pre-trained model. Further, we find that pre-training enables access to strong performances on our tasks, but it can require programs of gigabytes of length to access them. Post-training, on the other hand, collapses the complexity of reaching this same performance by several orders of magnitude. Overall, our results highlight that task adaptation often requires surprisingly little information---often just a few kilobytes

Parameter-efficient fine-tuning (PEFT) is a standard way to adapt multimodal large language models, yet extremely low-rank settings---especially rank-1 LoRA---are often unstable. We show that this instability is not solely due to limited capacity: in the rank-1 regime, optimization is highly sensitive to the update direction. Concretely, pretrained vision and text features form mismatched anisotropic regions, yielding a dominant "gap" direction that acts like a translation component and disproportionately steers early gradients under rank-1 constraints. Analyzing pretrained representations, we identify a modality-gap axis that dominates early gradient flow, while a random rank-1 initialization is unlikely to align with it, leading to weak gradients and training collapse. We propose Gap-Init, a geometry-aware initialization that aligns the rank-1 LoRA direction with an estimated modality-gap vector from a small calibration set, while keeping the initial LoRA update zero. Across multiple vision-language tasks and backbones, Gap-Init consistently stabilizes rank-1 training and can match or outperform strong rank-8 baselines. Our results suggest that at the extreme low-rank limit, initial alignment can matter as much as rank itself.

Low-rank adaptation (LoRA) is one of the most widely used parameter-efficient fine-tuning (PEFT) methods for adapting pre-trained large language models (LLMs) to downstream tasks. Although LoRA significantly reduces the number of trainable parameters and lowers fine-tuning costs, its performance is often limited by the inherent low-rank assumption. In this paper, we revisit the notion of rank for LoRA update matrices and show that the standard matrix rank fails to capture duplicated directions and redundancy in the update subspace. Motivated by this analysis, we argue that the Kruskal rank offers a more informative criterion for characterizing update diversity. We therefore propose Low Kruskal Rank Adaptation (LoKRA), a new PEFT algorithm with provable theoretical guarantees that mitigates the limitations of LoRA. We further introduce LoKRA$^+$, an enhanced variant that provides a tighter theoretical lower bound on the Kruskal rank and yields stronger empirical performance. Experiments on multiple LLMs show that our approach consistently outperforms LoRA and other baselines, establishing state-of-the-art performance across a range of benchmarks. The code can be viewed at https://github.com/AMD-AGI/LoKRA.

Source-Free Domain Adaptation (SFDA) enables model adaptation under distribution shifts without access to source data, providing a practical solution for privacy-sensitive applications and having shown substantial progress in classification. In contrast, regression involves ordered and continuous target variables, posing unique challenges for representation adaptation and pseudo-label refinement in the SFDA setting. To address this gap, we propose a novel algorithm for continuous label prediction in SFDA that leverages instance-dependent, discretized density–informed supervisory signals to refine pseudo-labels within an uncertainty-aware paradigm. By incorporating auxiliary discretized distribution learning, our method also promotes more compact and structured feature representations, mitigating the inherent difficulties of adapting regression models under distribution shift. We theoretically demonstrate that the resulting density structure is robust to potential perturbations, supporting reliable SFDA for regression. Extensive experiments across multiple benchmarks validate the effectiveness of the proposed approach.

Continual Learning (CL) requires models to sequentially adapt to new tasks without forgetting old knowledge. Recently, Low-Rank Adaptation (LoRA), a representative Parameter-Efficient Fine-Tuning (PEFT) method, has gained increasing attention in CL. Several LoRA-based CL methods reduce interference across tasks by separating their update spaces, typically building the new space from the estimated null space of past tasks. However, they (i) overlook task-shared directions, which suppresses knowledge transfer, and (ii) fail to capture truly effective task-specific directions since these ``null bases" of old tasks can remain nearly inactive for new task under correlated tasks. To address this, we study LoRA learning capability from a projection energy perspective, and propose Low-rank Decomposition and Adaptation (LoDA). It performs a task-driven decomposition to build general and truly task-specific LoRA subspaces by solving two energy-based objectives, decoupling directions for knowledge sharing and isolation. LoDA fixes LoRA down-projections on two subspaces and learns robust up-projections via a Gradient-Aligned Optimization (GAO) approach. After each task, before integrating the LoRA updates into the backbone, LoDA derives a closed-form recalibration for the general update, approximating a feature-level joint optimum along this task-shared direction. Experiments indicate that LoDA outperforms existing CL methods.

Magnitude-based stability proxies such as parameter drift are widely used in narrow-task fine-tuning, yet they do not reliably indicate degradation of broad capabilities. We identify trajectory lock-in: under fixed training conditions for narrow adaptation, the joint evolution of task loss and broad generalization collapses onto a shared low-dimensional degradation curve, so many stabilizers primarily change the rate of progress along this curve rather than altering the curve itself. This yields a drift paradox, in which comparable Euclidean displacement can still correspond to divergent generalization outcomes. To diagnose the underlying structure, we introduce objective-agnostic geometric probes that track the effective update subspace, together with an online harm signal that reflects curvature-dominated channeling toward directions associated with broad degradation. Finally, we show that escaping lock-in requires a spectral bifurcation, namely a qualitative reorientation of the update subspace toward softer curvature modes, thereby improving broad generalization while maintaining matched training performance. We validate these findings across model scales and modalities in narrow-task settings, and report practical deployment procedures and overhead measurements.

Biomedical regression tasks require predicting continuous targets from heterogeneous and unstructured evidence. While Large Language Models (LLMs) provide a robust interface for reasoning over mixed modalities, they are inherently limited by their discrete tokenization and cross-entropy objectives, which lack awareness of numerical proximity. To bridge this gap, we present \textbf{SPR-RAFT}, a parameter-efficient and regression-aware framework that adapts frozen LLMs for high-precision regression. SPR-RAFT introduces a dual-module architecture: a learnable soft prompt that conditions the LLM to route numerical reasoning into a specific latent state, and a lightweight regression head anchored on a dedicated readout token for numerical reasoning consolidation. Crucially, we align these two modalities via a hybrid objective that combines distribution-based text generation with representation-based robust regression. This ensures the model remains both semantically coherent and numerically calibrated. With only about 1.6M trainable parameters ($\sim$0.04\% of a 4B-parameter backbone), SPR-RAFT consistently outperforms prompting strategies, standard fine-tuning, and non-LLM baselines across diverse biomedical benchmarks, including clinical trial duration, biological age estimation, and molecular property prediction.

Modern large language models are increasingly deployed under compute and memory constraints, making flexible control of model capacity a central challenge. While sparse and low-rank structures naturally trade off capacity and performance, existing approaches often rely on heuristic designs that ignore layer and matrix heterogeneity or require model-specific architectural modifications. We propose SALAAD, a plug-and-play framework applicable to different model architectures that induces sparse and low-rank structures during training. By formulating structured weight learning under an augmented Lagrangian framework and introducing an adaptive controller that dynamically balances the training loss and structural constraints, SALAAD preserves the stability of standard training dynamics while enabling explicit control over the evolution of effective model capacity during training. Experiments across model scales show that SALAAD substantially reduces memory consumption during deployment while achieving performance comparable to ad-hoc methods. Moreover, a single training run yields a continuous spectrum of model capacities, enabling smooth and elastic deployment across diverse memory budgets without the need for retraining.

Distributed training of foundation models via $\texttt{DDP}$ is limited by interconnect bandwidth. While infrequent communication strategies reduce synchronization frequency, they remain bottlenecked by the memory and communication requirements of optimizer states. Low-rank optimizers can alleviate these constraints; however, in the local-update regime, workers lack access to the full-batch gradients required to compute low-rank projections, which degrades performance. We propose $\texttt{LoRDO}$, a principled framework unifying low-rank optimization with infrequent synchronization. We first demonstrate that, while global projections based on pseudo-gradients are theoretically superior, they permanently restrict the optimization trajectory to a low-rank subspace. To restore subspace exploration, we introduce a full-rank quasi-hyperbolic update. $\texttt{LoRDO}$ achieves near-parity with low-rank $\texttt{DDP}$ in language modeling and downstream tasks at model scales of $125$M--$720$M, while reducing communication by $\approx10\times$. Finally, we show that $\texttt{LoRDO}$ improves performance even more in very low-memory settings with small rank/batch size.

Custom diffusion models (CDMs) have demonstrated impressive success in visual personalization tasks by enabling the generation of user-specific concepts. However, existing CDMs typically assume that personalized concepts are static and rely on costly model merging or sequential updates that are prone to catastrophic forgetting as new concepts are introduced. To address these limitations, we propose a Submodular Concept Neuron Selection method (SCNS), to solve CDMs with continual personalized concepts, which formulates continual personalization as a constrained submodular optimization problem to select a minimal yet sufficient set of concept-specific neurons under diminishing returns. SCNS combines a Facility Location-based coverage objective to suppress semantic redundancy, a Fisher-weighted risk proxy to protect previously learned concepts, and a cost-aware greedy rule to balance stability and plasticity with extreme sparsity. Extensive experiments demonstrate that SCNS achieves state-of-the-art performance in image alignment and anti-forgetting, while enabling fusion-free continual personalization by modifying only 0.41% of the total parameters for each concept on average. Our implementation is available at SCNS.

We consider imitation learning in the low-data regime, where only a limited number of expert demonstrations are available. In this setting, methods that rely on large-scale pretraining or high-capacity architectures can be difficult to apply, and efficiency with respect to demonstration data becomes critical. We introduce Noise-Guided Transport (NGT), a lightweight off-policy method that casts imitation as an optimal transport problem solved via adversarial training. NGT requires no pretraining or specialized architectures, incorporates uncertainty estimation by design, and is easy to implement and tune. Despite its simplicity, NGT achieves strong performance on challenging continuous control tasks, including high-dimensional Humanoid tasks, under ultra-low data regimes with as few as 20 transitions.