ICLR 2026 Papers

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 13 LLMs and 10 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5× speedup while retaining > 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.

Federated Recommender Systems (FRS) preserve privacy by training decentralized models on client-specific user-item subgraphs without sharing raw data. However, FRS faces a unique challenge: subgraph structural imbalance, where drastic variations in subgraph scale (user/item counts) and connectivity (item degree) misalign client representations, making it challenging to train a robust model that respects each client’s unique structural characteristics. To address this, we propose a Low-pass Personalized Subgraph Federated recommender system (LPSFed). LPSFed leverages graph Fourier transforms and low-pass spectral filtering to extract low-frequency structural signals that remain stable across subgraphs of varying size and degree, allowing robust personalized parameter updates guided by similarity to a neutral structural anchor. Additionally, we leverage a localized popularity bias-aware margin that captures item-degree imbalance within each subgraph and incorporates it into a personalized bias correction term to mitigate recommendation bias. Supported by theoretical analysis and validated on five real-world datasets, LPSFed achieves superior recommendation accuracy and enhances model robustness.

Reinforcement Learning with Verifiable Rewards (RLVR) is a leading approach for tuning language models on mathematical reasoning tasks. However, it remains unclear whether RLVR's gains stem from genuine reasoning improvements or simply from steering the model toward answer formats that already appear in the reference distribution. Inspired by recent evidence \citep{zhao2025echo,yue2025does}, we study this question by optimizing only the first $k$ tokens (e.g. $k=32$) of each solution, generating the remainder of the response from the reference model. We study two methods for prefix optimization, using a naive algorithm that clusters prefixes and selects the best prefix (Prefix Clustering), and a method that optimizes the prefix by finetuning a lightweight adapter model with RL (Prefix-RL). We show that tuning only the first $k$ tokens can significantly improve the accuracy on math, suggesting that at least some of the gains from RL are due to upweighting a preferable solution strategy. Our results suggest that simple prefix optimization methods can provide an efficient alternative to RL, delivering substantial improvements across different models and benchmarks for a tiny fraction of the compute required for standard RL, and that these gains are robust across prefix lengths and random seeds.

Test-time adaptation (TTA) of Vision-Language Models (VLMs) has emerged as a technique for tackling distribution shifts during the test time. Recent research indicates that the test-time adaptation is intrinsically linked to the model's training history. However, existing TTA methods, such as Test-time Prompt Tuning, often design adaptation strategies in isolation from the models' training characteristics, which degrade their performance. This paper argues that the flatness acquired via sharpness-aware training is an efficient clue for the test-time adaptation of VLMs. Built on this insight, this paper proposes a novel Flatness-Guided Adaptation framework (FGA) for VLMs to cohesively unify training and test-time procedures. Its core idea is to leverage the alignment between the training minimum and test loss flat regions to guide the adaptation process. Specifically, our FGA consists of a prompt-tuning stage and a test-time adaptation stage. In the tuning stage, a Sharpness-Aware Prompt Tuning method is utilized to identify the training flat minimum, offering a geometric clue of flatness for subsequent adaptation. In the test stage, a Sharpness-based Test Sample Selection approach is proposed to ensure the alignment of flat minima between the training and each augmented test sample's loss landscape. In comparison to existing TTA methods, our FGA avoids the expensive prompt parameter updates during test time, and substantially reduces the computation overhead. Extensive experiments on both domain generalization and cross-dataset benchmarks demonstrate that our FGA achieves superior performance over prevalent TTA methods. Notably, FGA even surpasses SOTA performance by 4.55\% on ImageNet-A, when using a ViT-B/16 image encoder. Our code will be available soon.

Matrix denoising is a crucial component in machine learning, offering valuable insights into the behavior of learning algorithms (Bishop and Nasrabadi, 2006). This paper focuses on the rectangular matrix denoising problem, which involves estimating the left and right singular vectors of a rank-one matrix that is corrupted by additive noise. Traditional algorithms for this problem often exhibit high computational complexity, leading to the widespread use of gradient descent (GD)-based estimation methods with a quadratic cost function. However, the learning dynamics of these GD-based methods, particularly the analytical solutions that describe their exact trajectories, have been largely overlooked in existing literature. To fill this gap, we investigate the learning dynamics in detail, providing convergence proofs and asymptotic analysis. By leveraging tools from large random matrix theory, we derive a closed-form solution for the learning dynamics, characterized by the inner products of the estimates and the ground truth vectors. We rigorously prove the almost sure convergence of these dynamics as the signal dimensions tend to infinity. Additionally, we analyze the asymptotic behavior of the learning dynamics in the large-time limit, which aligns with the well-known Baik-Ben Arous-Péchée phase transition phenomenon n (Baik et al., 2005). Experimental results support our theoretical findings, demonstrating that when the signal-to-noise ratio (SNR) surpasses a critical threshold, learning converges rapidly from an initial value close to the stationary point. In contrast, estimation becomes infeasible when the ratio of the inner products between the initial left and right vectors and their corresponding ground truth vectors reaches a specific value, which depends on both the SNR and the data dimensions.

Unsupervised domain adaptation (UDA) is a statistical learning problem when the distribution of training (source) data is different from that of test (target) data. In this setting, one has access to labeled data only from the source domain and unlabeled data from the target domain. The central objective is to leverage the source data and the unlabeled target data to build models that generalize to the target domain. Despite its potential, existing UDA approaches often struggle in practice, particularly in scenarios where the target domain offers only limited unlabeled data or spurious correlations dominate the source domain. To address these challenges, we propose a novel distributionally robust learning framework that models uncertainty in both the covariate distribution and the conditional label distribution. Our approach is motivated by the multi-source domain adaptation setting but is also directly applicable to the single-source scenario, making it versatile in practice. We develop an efficient learning algorithm that can be seamlessly integrated with existing UDA methods. Extensive experiments under various distribution shift scenarios show that our method consistently outperforms strong baselines, especially when target data are extremely scarce.

Recently, there has been a growing interest in Long-term Time Series Forecasting (LTSF), which involves predicting long-term future values by analyzing a large amount of historical time-series data to identify patterns and trends. Significant challenges exist in LTSF due to its complex temporal dependencies and high computational demands. Although Transformer-based models offer high forecasting accuracy, they are often too compute-intensive to be deployed on devices with hardware constraints. In this paper, we propose MixLinear, which synergistically combines orthogonal segment-based trend extraction in the time domain with adaptive low-rank spectral filtering in the frequency domain. Our approach exploits the complementary structural sparsity of time series: local temporal patterns are efficiently captured through mathematically linear transformations that separate intra-segment and inter-segment correlations, while global trends are compressed into an ultra-low-dimensional frequency latent space through learnable rank-constrained filters. By reducing the parameter scale of a downsampled $n$-length input/output one-layer linear model from $O(n^2)$ to $O(n)$, MixLinear achieves efficient computation without sacrificing accuracy. Extensive evaluations show that MixLinear achieves forecasting performance comparable to, or surpasses, state-of-the-art models with significantly fewer parameters ($0.1K$), which makes it well suited for deployment on devices with limited computational capacity.

The demand for efficient deployment of large language models (LLMs) has driven interest in quantization, which reduces inference cost, and parameter-efficient fine-tuning (PEFT), which lowers training overhead. This motivated the development of quantization-aware PEFT to produce accurate yet efficient quantized models. In this setting, reducing quantization error prior to fine-tuning is crucial for achieving high model accuracy. However, existing methods that rely on low-rank adaptation suffer from limited representational capacity. Recent Fourier-related transform (FT)-based adapters offer greater representational power than low-rank adapters, but their direct integration into quantized models often results in ineffective error reduction and increased computational overhead. To overcome these limitations, we propose QWHA, a method that integrates FT-based adapters into quantized models by employing the Walsh-Hadamard Transform (WHT) as the transform kernel, together with a novel adapter initialization scheme incorporating adaptive parameter selection and value refinement. We demonstrate that QWHA effectively mitigates quantization errors while facilitating fine-tuning, and that its design substantially reduces computational cost. Experimental results show that QWHA consistently outperforms baselines in low-bit quantization accuracy and achieves significant training speedups over existing FT-based adapters.

Federated fine-tuning is critical for improving the performance of large language models (LLMs) in handling domain-specific tasks while keeping training data decentralized and private. However, prior work has shown that clients' private data can actually be recovered via gradient inversion attacks. Existing privacy preservation techniques against such attacks typically entail performance degradation and high costs, making them ill-suited for clients with heterogeneous data distributions and device capabilities. In this paper, we propose SHE-LoRA, which integrates selective homomorphic encryption (SHE) and low-rank adaptation (LoRA) to enable efficient and privacy-preserving federated tuning of LLMs in cross-device environments. Based on model parameter sensitivity assessment, heterogeneous clients adaptively negotiate and select a subset of model parameters for homomorphic encryption. To ensure accurate model aggregation, we design a column-aware secure aggregation method and customized reparameterization techniques to align the aggregation results with the heterogeneous device capabilities of clients. Extensive experiments demonstrate that SHE-LoRA maintains performance comparable to non-private baselines, achieves strong resistance to state-of-the-art attacks, and significantly reduces communication overhead by 99.71\% and encryption time by 99.87\%, compared to HE baselines.

As API access becomes a primary interface to large language models (LLMs), users often interact with black-box systems that offer little transparency into the deployed model. To reduce costs or maliciously alter model behaviors, API providers may discreetly serve quantized or fine-tuned variants, which can degrade performance and compromise safety. Detecting such substitutions is difficult, as users lack access to model weights and, in most cases, even output logits. To tackle this problem, we propose a rank-based uniformity test (RUT) that can verify the behavioral equality of a black-box LLM to a locally deployed authentic model. Our method is accurate, query-efficient, and avoids detectable query patterns, making it robust to adversarial providers that reroute or mix responses upon the detection of testing attempts. We evaluate the approach across diverse query domains and threat scenarios, including quantization, harmful fine-tuning, jailbreak prompts, full model substitution, showing that it consistently achieves superior detection power over prior methods under constrained query budgets.

Deep learning has advanced at an unprecedented pace. This progress has led to a significant increase in its complexity. However, despite extensive research on accelerating inference, training deep models directly within a resource-constrained budget remains a considerable challenge due to its high computational and memory requirements. In this paper, we introduce INSTANT (compressIng gradieNtS and acTivAtions for resource-efficieNt Training), a method designed to address both the computational and the memory bottlenecks when training. INSTANT reduces resource demands during backpropagation by projecting gradients and activations into a low-rank subspace and performing computation within that compressed representation. Experimental results demonstrate that INSTANT achieves a $15\times$ reduction in computational cost and $32\times$ reduction in activation memory with negligible impact on model performance. The code will be made publicly available upon the paper's acceptance.

How cost-effectively can strong reasoning abilities be achieved in language models? Driven by this question, we present Tina, a family of tiny reasoning models achieved with high cost-efficiency. Tina shows that substantial reasoning performance can be developed using only minimal resources, by applying low-rank adaptation (LoRA) during reinforcement learning (RL), to an already tiny 1.5B parameter base model. This minimalist approach produces models that are competitive with, and sometimes surpass, SOTA RL reasoning models built upon the same base model. Crucially, this is achieved at a tiny fraction of the computational cost employed by existing models. In fact, the best Tina model achieves a >20\% reasoning performance increase and 43.33\% zero-shot Pass@1 accuracy on AIME24, at only \$9 USD cost (i.e., an estimated 260x reduction). Our work reveals the surprising effectiveness of efficient RL reasoning via LoRA. We validate this across multiple open-source reasoning datasets and various ablation settings starting with a single, fixed set of hyperparameters. Furthermore, we explore the hypothesis that this effectiveness and efficiency stem from LoRA rapidly adapting the model to the structural format of reasoning rewarded by RL, while largely preserving the base model's underlying knowledge. In service of accessibility and open research, we fully open-source all code, training logs, model weights, and checkpoints.

Large Language Models have demonstrated strong performance across a wide range of tasks, but adapting them efficiently to new domains remains a key challenge. Parameter-Efficient Fine-Tuning (PEFT) methods address this by introducing lightweight, trainable modules while keeping most pre-trained weights fixed. The prevailing approach, LoRA, models updates using a low-rank decomposition, but its expressivity is inherently constrained by the rank. Recent methods like HiRA aim to increase expressivity by incorporating a Hadamard product with the frozen weights, but still rely on the structure of the pre-trained model. We introduce ABBA, a new PEFT architecture that reparameterizes the update as a Hadamard product of two independently learnable low-rank matrices. In contrast to prior work, ABBA fully decouples the update from the pre-trained weights, enabling both components to be optimized freely. This leads to significantly higher expressivity under the same parameter budget, a property we validate through matrix reconstruction experiments. Empirically, ABBA achieves state-of-the-art results on arithmetic and commonsense reasoning benchmarks, consistently outperforming existing PEFT methods by a significant margin across multiple models. Our code is publicly available at: https://github.com/CERT-Lab/abba.

We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior theory largely focuses on shallow (depth-2) models and does not fully explain the implicit low-rank bias observed in deeper networks. We identify coupled dynamics as a key mechanism behind this bias and show that it intensifies with increasing depth. Focusing on gradient flow under diagonal observations, we prove: (a) networks of depth $\geq 3$ exhibit coupling unless initialized diagonally, and (b) convergence to rank-1 occurs if and only if the dynamics is coupled—resolving an open question by Menon (2024) for a family of initializations. We also revisit the loss of plasticity phenomenon in matrix completion (Kleinman et al., 2024), where pre-training on few observations and resuming with more degrades performance. We show that deep models avoid plasticity loss due to their low-rank bias, whereas depth-2 networks pre-trained under decoupled dynamics fail to converge to low-rank, even when resumed training (with additional data) satisfies the coupling condition—shedding light on the mechanism behind this phenomenon.

We propose \textbf{ABSignSGD}, a block‑coordinate variant of sign-based descent with flexible block selection that enables memory‑ and runtime‑efficient full‑parameter fine‑tuning of large language models. We present a unified convergence analysis under mild conditions, covering both the base method and a \textit{majority‑vote} extension for distributed training. The latter improves communication efficiency by aggregating only gradient signs rather than averaging full gradients. Experiments on \textcolor{blue}{Qwen3‑8B, Llama3-8B, and Qwen3-32B}, spanning mathematical reasoning and general instruction‑following tasks, show that ABSignSGD converges faster per iteration and delivers superior downstream performance while reducing both runtime and memory usage compared to existing methods. Ablation studies further indicate that the memoryless sign-based update naturally complements block‑wise updates, explaining the method’s strong empirical performance.

Studies have shown that catastrophic forgetting primarily stems from the difficulty of reactivating old memories; although parameter-efficient fine-tuning can mitigate forgetting while keeping most model parameters frozen, it still falls short in fully reawakening knowledge of prior tasks. In contrast, humans can efficiently retrieve and flexibly integrate existing experiences when learning new tasks, thereby maintaining stable performance on earlier ones. During cognition, the hippocampal EC–DG–CA3–CA1 circuit engages in multiple rounds of associative recall, and its pattern-separation and memory-completion mechanisms excel at activating historical information. Inspired by this mechanism, we propose HippoTune, a latent-space iterative retrieval strategy that embeds a query–retrieve–feedback loop within each Transformer layer. Starting from the hidden state as an initial query, the model performs a few rounds of soft key–value retrieval, projects the retrieved signals back into the query, and updates it iteratively until convergence or a preset iteration limit. Theoretically, we show this process implements a Krylov-style polynomial approximation, equivalent to a differentiable second-order preconditioner, thereby deepening retrieval in a principled way. Empirically, HippoTune outperforms classical buffer-free PEFT-CL methods by 5–8% in accuracy across three vision benchmarks, while reducing training FLOPs by 50%, effectively mitigating forgetting under tight compute constraints. Code is available at: https://anonymous.4open.science/r/HippoTune-1DF2.

As large language models (LLMs) scale to billions of parameters, full-parameter fine-tuning becomes compute- and memory-prohibitive. Parameter-efficient fine-tuning (PEFT) mitigates this issue by updating only a small set of task-specific parameters while keeping the base model frozen. Among PEFT approaches, low-rank adaptation (LoRA) is widely adopted; however, it enforces a uniform rank across layers despite substantial variation in layer importance, motivating layerwise rank allocation. Recent adaptive-rank variants (e.g., AdaLoRA) allocate ranks based on importance scores, yet typically rely on instantaneous gradients that capture only local sensitivity, overlooking non-local, pathwise effects within the same layer, which yields unstable and biased scores. To address this limitation, we introduce IGU-LoRA, an adaptive-rank LoRA that (i) computes within-layer Integrated Gradients (IG) sensitivities and aggregates them into a layer-level score for rank allocation, and (ii) applies an uncertainty-aware scheme using exponential moving averages with deviation tracking to suppress noisy updates and calibrate rank selection. Theoretically, we prove an upper bound on the composite trapezoidal rule approximation error for parameter-space IG under a pathwise Hessian-Lipschitz condition, which informs the quadrature budget. Across diverse tasks and architectures, IGU-LoRA consistently outperforms strong PEFT baselines at matched parameter budgets, improving downstream accuracy and robustness. Ablations confirm the contributions of pathwise within-layer sensitivity estimates and uncertainty-aware selection to effective rank allocation.

Personalization has become a pivotal field of study in contemporary intelligent systems. While large language models (LLMs) excel at general knowledge tasks, they often struggle with personalization, i.e., adapting their outputs to individual user expectations. Existing approaches that steer LLM behavior to meet users’ implicit preferences and behavior patterns, primarily relying on tune-free methods (e.g., RAG, PAG) or parameter fine-tuning methods (e.g., LoRA), face challenges in effectively balancing effectiveness and efficiency. Moreover, the mechanisms underlying personalized preferences remain underexplored. To address these challenges, we first uncover key patterns of user-specific information embedded in the representation space. Specifically, we find that (1) personalized information lies within a low-rank subspace represented by vectors, and (2) these vectors demonstrate both a collective shift shared across users and a personalized shift unique to each individual user. Building on these insights, we introduce PerFit, a novel two-stage solution that directly fine-tunes interventions in the hidden representation space by addressing both collective and user-specific shifts, thereby achieving precise steering of LLM with minimal parameter overhead. Experimental results demonstrate that \perfit delivers strong performance across six datasets while \cutting the number of parameters by an average of 92.3% compared to the state-of-the-art method.

Parameter-Efficient Fine-Tuning (PEFT) methods have become crucial for rapidly adapting large language models (LLMs) to downstream tasks. Prefix-Tuning, an early and effective PEFT technique, demonstrated the ability to achieve performance comparable to full fine-tuning with significantly reduced computational and memory overhead. However, despite its earlier success, its effectiveness in training modern state-of-the-art LLMs has been very limited. In this work, we demonstrate empirically that Prefix-Tuning underperforms on LLMs because of an inherent tradeoff between the contribution of input prompt and parameterized prefix within the attention head. This motivates us to introduce PrefixMemory-Tuning, an architecture that generalizes the principles of Prefix-Tuning while addressing its shortcomings by shifting the prefix module out of the attention head itself and improving its expressiveness. Our experiments show that, across diverse benchmarks, PrefixMemory-Tuning consistently outperforms existing Prefix-Tuning methods. Notably, it achieves competitive performance with modern PEFTs on several general benchmarks, highlighting a potential extension of Prefix-Tuning approaches to become state-of-the-art. Our findings suggest that by overcoming its inherent limitations, Prefix-Tuning can remain a competitive and relevant research direction in the landscape of parameter-efficient LLM adaptation.