ICLR 2026 论文列表

Modern neural architectures are fundamentally constrained by their reliance on fixed activation functions, limiting their ability to adapt representations to task-specific structure and efficiently capture high-order interactions. We introduce deep low-rank separated neural networks (LRNNs), a novel architecture generalizing MLPs that achieves enhanced expressivity by learning adaptive, factorized activation functions. LRNNs generalize the core principles underpinning continuous low-rank function decomposition to the setting of deep learning, constructing complex, high-dimensional neuron activations through a multiplicative composition of simpler, learnable univariate transformations. This product structure inherently captures multiplicative interactions and allows each LRNN neuron to learn highly flexible, data-dependent activation functions. We provide a detailed theoretical analysis that establishes the universal approximation property of LRNNs and reveals why they are capable of excellent empirical performance. Specifically, we show that LRNNs can mitigate the curse of dimensionality for functions with low-rank structure. Moreover, the learnable product-structured activations enable LRNNs to adaptively control their spectral bias, crucial for signal representation tasks. These theoretical insights are validated through extensive experiments where LRNNs achieve state-of-the-art performance across diverse domains including image and audio representation, numerical solution of PDEs, sparse-view CT reconstruction, and supervised learning tasks. Our results demonstrate that LRNNs provide a powerful and versatile building block with a distinct inductive bias for learning compact yet expressive representations.

Vision–Language–Action (VLA) models show promise in embodied reasoning, yet remain far from true generalists—they often require task-specific fine-tuning, incur high compute costs, and generalize poorly to unseen tasks. We propose MetaVLA, a unified, backbone-agnostic post-training framework for efficient and scalable alignment. MetaVLA introduces Context-Aware Meta Co-Training, which consolidates diverse target tasks into a single fine-tuning stage while leveraging structurally diverse auxiliary tasks to improve in-domain generalization. Unlike naive multi-task SFT, MetaVLA integrates a lightweight meta-learning mechanism—derived from Attentive Neural Processes—to enable rapid adaptation from diverse contexts with minimal architectural change or inference overhead. On the LIBERO benchmark, MetaVLA with six auxiliary tasks outperforms OpenVLA by up to 8.0\% on long-horizon tasks, reduces training steps from 240K to 75K, and cuts GPU time by 76%. These results show that scalable, low-resource post-training is achievable—paving the way toward general-purpose embodied agents. Code will be available.

Converting pretrained attention modules such as *grouped-query attention* (GQA) into *multi-head latent attention* (MLA) can improve expressivity without increasing KV-cache cost, making it attractive for efficient inference. However, existing conversion methods typically apply naïve singular value decomposition (SVD). They focus on minimizing the difference between weight matrices rather than how those weights affect input activations, ignore the covariance structure of activations, and enforce a uniform rank across layers—causing activation drift and degraded attention fidelity. To address these issues, we propose **CARE** (**C**ovariance-**A**ware, **R**ank-**E**nhanced), a MLA conversion pipeline under a fixed KV width. CARE introduces three key steps: (i). **Activation-preserving factorization** — align the approximation with the actual input activations rather than just the weights. (ii). **Adjusted-rank allocation** — distribute a fixed KV budget across layers by giving more capacity to layers that need it most. (iii). **KV-parity mapping** — reparameterize the converted \(K\) and \(V\) to fit the MLA format while keeping the KV-cache size unchanged. Under a matched KV-cache budget, our method consistently outperforms a uniform-rank SVD baseline on Llama-3-8B, delivering up to **331%** relative gains in one-shot evaluation (higher accuracy, lower perplexity). With a brief post-SVD “healing” fine-tune, we fully recover the original model’s accuracy.

While large language models (LLMs) achieve strong performance in recommendation, they face challenges in continual learning as users, items, and user preferences evolve over time. Existing LoRA-based continual methods primarily focus on preserving performance on previous tasks, but this overlooks the unique nature of recommendation: the goal is not to predict past preferences, and outdated preferences can even harm performance when current interests shift significantly. To address this, we propose PESO (Proximally rEgularized Single evolving lOra, a continual adaptation method for LoRA in recommendation. PESO introduces a proximal regularizer that anchors the current adapter to its most recent frozen state, enabling the model to flexibly balance adaptation and preservation, and to better capture recent user behaviors. Theoretically, we show that this proximal design provides data-aware, direction-wise guidance in the LoRA subspace. Empirically, PESO consistently outperforms existing LoRA-based continual learning methods.

Memory-efficient training of deep neural networks has become increasingly important as models grow larger while deployment environments impose strict resource constraints. We propose TraDy, a novel transfer learning scheme leveraging two key insights: layer importance for updates is architecture-dependent and determinable a priori, while dynamic stochastic channel selection provides superior gradient approximation compared to static approaches. We introduce a dynamic channel selection approach that stochastically resamples channels between epochs within preselected layers. Extensive experiments demonstrate TraDy achieves state-of-the-art performance across various downstream tasks and architectures while maintaining strict memory constraints, achieving up to 99\% activation sparsity, 95\% weight derivative sparsity, and 97\% reduction in FLOPs for weight derivative computation.

Featurizing odorants to enable robust prediction of their properties is difficult due to the complex activation patterns that odorants evoke in the olfactory system. Structurally similar odorants can elicit distinct activation patterns in both the sensory periphery (i.e., at the receptor level) and downstream brain circuits (i.e., at a perceptual level). Despite efforts to design or discover features for odorants to better predict how they activate the olfactory system, we lack a universally accepted way to featurize odorants. In this work, we demonstrate that feature-based approaches that rely on pre-trained foundation models $\textit{do not}$ significantly outperform classical hand-designed features, but that targeted foundation model fine-turning can increase model performance beyond these limits. To show this, we introduce a new model that creates olfaction-specific representations: $\textbf{L}$oRA-based $\textbf{O}$dorant-$\textbf{R}$eceptor $\textbf{A}$ffinity prediction with $\textbf{CROSS}$-attention ($\textbf{LORAX}$). We compare existing chemical foundation model representations to hand-designed physicochemical descriptors using feature-based methods and identify large information overlap between these representations, highlighting the necessity of fine-tuning to generate novel and superior odorant representations. We show that LORAX produces a feature space more closely aligned with olfactory neural representation, enabling it to outperform existing models on predictive tasks.

Fine-tuning large vision models (LVMs) and large language models (LLMs) under differentially private federated learning (DPFL) is hindered by a fundamental privacy-utility trade-off. Low-Rank Adaptation (LoRA), a promising parameter-efficient fine-tuning (PEFT) method, reduces computational and communication costs by introducing two trainable low-rank matrices while freezing pre-trained weights. However, directly applying LoRA in DPFL settings leads to performance degradation, especially in LVMs. Our analysis reveals three previously underexplored challenges: (1) gradient coupling caused by the simultaneous update of two asymmetric low-rank matrices, (2) compounded noise amplification under differential privacy, and (3) sharpness of the global aggregated model in the parameter space. To address these issues, we propose LA-LoRA (\textbf{L}ocal \textbf{A}lternating \textbf{LoRA}), a novel approach that decouples gradient interactions and aligns update directions across clients to enhance robustness under stringent privacy constraints. Theoretically, LA-LoRA strengthens convergence guarantees in noisy federated environments. Extensive experiments demonstrate that LA-LoRA achieves state-of-the-art (SOTA) performance on Swin Transformer and RoBERTa models, showcasing robustness to DP noise and broad applicability across both LVMs and LLMs. For example, when fine-tuning the Swin-B model on the Tiny-ImageNet dataset under a strict privacy budget ($\epsilon = 1$), LA-LoRA outperforms the best baseline, RoLoRA, by 16.83\% in test accuracy. Code is provided in the Appendix.

The training of neural networks has been extensively studied from both algorithmic and complexity-theoretic perspectives, yet recent results in this direction almost exclusively concern real-valued networks. In contrast, advances in machine learning practice highlight the benefits of quantization, where network parameters and data are restricted to finite integer domains, yielding significant improvements in speed and energy efficiency. Motivated by this gap, we initiate a systematic complexity-theoretic study of ReLU Neural Network Training in the full quantization mode. We establish strong lower bounds by showing that hardness already arises in the binary setting and under highly restrictive structural assumptions on the architecture, thereby excluding parameterized tractability for natural measures such as depth and width. On the positive side, we identify nontrivial fixed-parameter tractable cases when parameterizing by input dimensionality in combination with width and either output dimensionality or error bound, and further strengthen these results by replacing width with the more general treewidth.

When a deep ReLU network is initialized with small weights, gradient descent (GD) is at first dominated by the saddle at the origin in parameter space. We study the so-called escape directions along which GD leaves the origin, which play a similar role as the eigenvectors of the Hessian for strict saddles. We show that the optimal escape direction features a \textit{low-rank bias} in its deeper layers: the first singular value of the $\ell$-th layer weight matrix is at least $\ell^{\frac{1}{4}}$ larger than any other singular value. We also prove a number of related results about these escape directions. We suggest that deep ReLU networks exhibit saddle-to-saddle dynamics, with GD visiting a sequence of saddles with increasing bottleneck rank.

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

Outliers have emerged as a fundamental bottleneck in preserving accuracy for low-precision large models, particularly within Mixture-of-Experts (MoE) architectures that are increasingly central to large-scale language modeling. Under post-training quantization (PTQ), these outliers induce substantial quantization errors, leading to severe accuracy degradation. While recent rotation-based smoothing techniques alleviate the problem by redistributing outlier magnitudes, residual errors remain and continue to impede reliable low-precision deployment. In this work, we tackle this challenge by introducing a unified quantization-and-clustering scheme that contains smoothing activation outliers via learnable rotation and absorbing weight outliers into fine-tuned cluster centroids for MoE. This design reduces the influence of extreme values by fitting them within cluster centroids, thereby lowering quantization error while maintaining expressive capacity. We introduce~\textit{CodeQuant}, a unified quantization-and-clustering framework tailored for MoEs. Coupled with a dedicated kernel design for GPU and CPU, CodeQuant achieves up to $4.15\times$ speedup while delivering significantly higher accuracy than state-of-the-art quantization approaches across diverse MoE models. Our results highlight CodeQuant as a promising direction for efficient and accurate deployment of MoE-based large language models under low-precision constraints.

Although Direct Feedback Alignment (DFA) has demonstrated potential by enabling efficient and parallel updates of weight parameters through direct propagation of the network's output error, its usage has been primarily restricted to training networks from scratch. In this paper, we introduce feedback-weight matching, a first method that enables reliable fine-tuning of fully connected neural networks using DFA. We provide an analysis showing that existing standard DFA struggles to fine-tune networks that are pre-trained via back-propagation. Through a thorough analysis of weight alignment (WA) and gradient alignment (GA), we demonstrate that the proposed feedback-weight matching enhances DFA's ability and stability in fine-tuning, which provides useful insights into DFA's behavior and characteristics when applied to fine-tuning. In addition, we prove that feedback-weight matching, when combined with weight decay, not only mitigates over-fitting but also further reduces the network output error, leading to improved learning performance during DFA-based fine-tuning. Experimental results show that feedback-weight matching, for the first time, enables reliable fine-tuning across various fine-tuning tasks, compared to existing standard DFA, e.g., achieving 7.97% accuracy improvement on image classification tasks (82.67% vs. 74.70%) and 0.66 higher correlation score on NLP tasks (0.76 vs. 0.10). The code is available on an anonymous GitHub.

The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable \citep{wu2023expected}, and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal \citep{pmlr-v247-wu24a}. This paper takes a significant step towards achieving statistical optimality and computational efficiency \emph{simultaneously} in the Hybrid Learning setting. To do so, we consider a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions $\mathcal{R}$. Our main result is a new learning algorithm, which runs efficiently given an ERM oracle and obtains regret scaling with the Rademacher complexity of a class derived from the Learner's hypothesis class $\mathcal{H}$ and the Adversary's label class $\mathcal{R}$. As a key corollary, we give an oracle-efficient algorithm for computing equilibria in stochastic zero-sum games when action sets may be high-dimensional but the payoff function exhibits a type of low-dimensional structure. Technically, we develop a number of novel tools for the design and analysis of our learning algorithm, including a novel Frank-Wolfe reduction with "truncated entropy regularizer" and a new tail bound for sums of "hybrid'' martingale difference sequences.

Modern optimizers like Adam and Muon are central to training large language models, but their reliance on first- and second-order momenta introduces significant memory overhead, which constrains scalability and computational efficiency. In this work, we re-frame the exponential moving average (EMA) used in these momenta as the training of a linear regressor via online gradient flow. Building on this equivalence, we introduce LoRA-Pre, a novel low-rank optimizer designed for efficient pre-training. Specifically, LoRA-Pre reduces the optimizer's memory footprint by decomposing the full momentum matrix into a compact low-rank subspace within the online linear learner, thereby maintaining optimization performance while improving memory efficiency. We empirically validate LoRA-Pre's efficacy by pre-training models from the Llama architecture family, scaling from 60M to 1B parameters. LoRA-Pre achieves the highest performance across all model sizes. Notably, LoRA-Pre demonstrates remarkable rank efficiency, achieving comparable or superior results using only 1/8 the rank of baseline methods. Beyond pre-training, we evaluate LoRA-Pre's effectiveness in fine-tuning scenarios. With the same rank, LoRA-Pre consistently outperforms all efficient fine-tuning baselines. Specifically, compared to standard LoRA, LoRA-Pre achieves substantial improvements of 3.14 points on Llama-3.1-8B and 6.17 points on Llama-2-7B, validating our approach's effectiveness across both pre-training and fine-tuning paradigms.

As increasingly large pre-trained models are released, deploying them on edge devices for privacy-preserving applications requires effective compression. Recent works combine quantization with the fine-tuning of high-precision LoRA adapters, which can substantially reduce model size while mitigating the accuracy loss from quantization. However, edge devices have inherently heterogeneous capabilities, while performing configuration-wise fine-tuning for every quantization setting is computationally prohibitive. In this paper, we propose CoA-LoRA, a method that dynamically adjusts the LoRA adapter to arbitrary quantization configurations (i.e., the per-layer bit-width choices of a pre-trained model) without requiring repeated fine-tuning. This is accomplished via a configuration-aware model that maps each configuration to its low-rank adjustments. The effectiveness of this model critically depends on the training configuration set, a collection of configurations chosen to cover different total bit-width budgets. However, constructing a high-quality configuration set is non-trivial. We therefore design a Pareto-based configuration search that iteratively optimizes the training configuration set, yielding more precise low-rank adjustments. Our experiments demonstrate that, unlike the state-of-the-art methods that require fine-tuning a separate LoRA adapter for each configuration, CoA-LoRA incurs no additional time cost while achieving comparable or even superior performance to those methods.

Concept Bottleneck Models (CBMs) achieve interpretability by interposing a human-understandable concept layer between perception and label prediction. The foundation of CBMs lies in the many-to-many mapping that translates high-dimensional visual features to a set of discrete concepts. However, we identify a critical and pervasive challenge that undermines this process: \emph{representational collapse}, where visual patch features degenerate into a low-rank subspace during training, severely degrading the quality of learned concept activation vectors, thus hindering both model interpretability and downstream performance. To address these issues, we propose Implicit Vector Quantization (IVQ), a lightweight regularizer that maintains high-rank, diverse representations throughout training. Rather than imposing a hard bottleneck via direct quantization, IVQ learns a codebook prior that anchors semantic information in visual features, allowing it to act as a proxy objective. To further exploit these high-rank concept-aware features, we propose Magnet Attention, which dynamically aggregates patch-level features into visual concept prototypes, explicitly modeling the many-to-many vision–concept correspondence. Extensive experimental results show that our approach effectively prevents representational collapse and achieves state-of-the-art performance on eight diverse benchmarks. Our experiments further probe the low-rank phenomenon in representational collapse, finding that IVQ mitigates the information bottleneck and yields cross-modal representations with clearer, more interpretable consistency.

We propose Low-Rank Sparse Attention (Lorsa), a sparse replacement model of Transformer attention layers to disentangle original Multi Head Self Attention (MHSA) into individually comprehensible components. Lorsa is designed to address the challenge of \textit{attention superposition} to understand attention-mediated interaction between features in different token positions. Lorsa helps find cleaner and finer-grained versions of previously discovered MHSA behaviors like induction heads, successor heads, attention sink, and a comprehensive family of arithmetic-specific Lorsa heads. Interestingly, we identify a novel head type called \emph{subtoken induction heads} that function at character level rather than token level. Automated interpretability analysis indicates that Lorsa achieves parity with SAE in interpretability while Lorsa exhibits superior circuit discovery properties. We also conduct extensive experiments on architectural design ablation, correlation to original MHSA heads and error analysis. Our early attempt to fully sparsify a toy Transformer succeeds to reveal clean global circuits. Eventually, we hope Lorsa would help us greatly understand attention computation and enable full sparsification of model computation along with its MLP counterparts. Lorsa is open-sourced at https://anonymous.4open.science/r/Lorsa-5686/.

Universal Test-Time Adaptation (UTTA) tackles the challenge of handling both class and domain shifts in unsupervised settings with stream testing data. Currently, most UTTA methods can only deal with minor shifts and heavily rely on heuristic approaches. To advance UTTA under dual shifts, we propose a novel Active Universal Test-Time Adaptation (AUTTA) framework, Exposing Mixture and Annotating Confusion (EMAC), which incorporates active human annotation into the UTTA setting. To select appropriate samples for annotation in AUTTA, we first identify the mixed regions of target domain samples under dual shifts, highlighting potential candidate samples. We then design a reward-guided active selection strategy to prioritize annotating the most representative samples within this set, maximizing annotation effectiveness. Additionally, to balance the use of pseudo-labels with the limited number of annotations, we propose an adaptation objective designed to address the adaptation imbalance caused by annotation scarcity. Extensive experiments show that the proposed AUTTA approach significantly improves performance and achieves state-of-the-art.

Large language models (LLMs) have achieved remarkable success in diverse tasks, yet their safety alignment remains fragile during adaptation. Even when fine-tuning on benign data or with low-rank adaptation, pre-trained safety behaviors are easily degraded, leading to harmful responses in the fine-tuned models. To address this challenge, we propose GuardSpace, a guardrail framework for preserving safety alignment throughout fine-tuning, composed of two key components: a safety-sensitive subspace and a harmful-resistant null space. First, we explicitly decompose pre-trained weights into safety-relevant and safety-irrelevant components using covariance-preconditioned singular value decomposition, and initialize low-rank adapters from the safety-irrelevant ones, while freezing safety-relevant components to preserve their associated safety mechanism. Second, we construct a null space projector that restricts adapter updates from altering safe outputs on harmful prompts, thereby maintaining the original refusal behavior. Experiments with various pre-trained models on multiple downstream tasks demonstrate that GuardSpace achieves superior performance over existing methods. Notably, for Llama-2-7B-Chat fine-tuned on GSM8K, GuardSpace outperforms the state-of-the-art method AsFT, reducing the average harmful score from 14.4\% to 3.6\%, while improving the accuracy from from 26.0\% to 28.0\%.