ICLR 2026 Papers

Zero-Shot Super-Resolution Spatiotemporal Forecasting requires a deep learning model to be trained on low-resolution data and deployed for inference on high-resolution. Existing studies consider **maintaining** similar error across different resolutions as indicative of successful multi-resolution generalization performance. However, deep learning models serving as alternatives to numerical solvers should **reduce** error as resolution increases. The fundamental limitation is, the upper bound of physical law frequencies that low-resolution data can represent is constrained by its Nyquist frequency, making it difficult for models to process signals containing unseen frequency components during high-resolution inference. *This results in errors being anchored at low resolution, incorrectly interpreted as successful generalization.* We define this fundamental phenomenon as a new problem distinct from existing issues: **Scale Anchoring**. Therefore, we propose architecture-agnostic Frequency Representation Learning. It alleviates Scale Anchoring through resolution-aligned frequency representations and spectral consistency training: on grids with higher Nyquist frequencies, the frequency response in high-frequency bands of FRL-enhanced variants is more stable. This allows errors to decrease with resolution and significantly outperform baselines within our task and resolution range, while incurring only modest computational overhead.

We study the problem of recovering a low-tubal-rank tensor $\mathcal{X}\_\star\in \mathbb{R}^{n \times n \times k}$ from noisy linear measurements under the t-product framework. A widely adopted strategy involves factorizing the optimization variable as $\mathcal{U} * \mathcal{U}^\top$, where $\mathcal{U} \in \mathbb{R}^{n \times R \times k}$, followed by applying factorized gradient descent (FGD) to solve the resulting optimization problem. Since the tubal-rank $r$ of the underlying tensor $\mathcal{X}_\star$ is typically unknown, this method often assumes $r < R \le n$, a regime known as over-parameterization. However, when the measurements are corrupted by some dense noise (e.g., sub-Gaussian noise), FGD with the commonly used spectral initialization yields a recovery error that grows linearly with the over-estimated tubal-rank $R$. To address this issue, we show that using a small initialization enables FGD to achieve a nearly minimax optimal recovery error, even when the tubal-rank $R$ is significantly overestimated. Using a four-stage analytic framework, we analyze this phenomenon and establish the sharpest known error bound to date, which is independent of the overestimated tubal-rank $R$. Furthermore, we provide a theoretical guarantee showing that an easy-to-use early stopping strategy can achieve the best known result in practice. All these theoretical findings are validated through a series of simulations and real-data experiments.

Finetuning (pretrained) language models is a standard approach for updating their internal parametric knowledge and specializing them to new tasks and domains. However, the corresponding model weight changes ("weight diffs") are not generally interpretable. While inspecting the finetuning dataset can give a sense of how the model might have changed, these datasets are often not publicly available or are too large to work with directly. Towards the goal of broadly understanding model weight changes in natural language, we introduce Diff Interpretation Tuning (DIT), a method that trains models to describe their own finetuning-induced modifications. Our approach uses synthetic, labeled weight diffs to train an introspection adapter, which can be applied to a compatible finetuned model to make it self-describe the weight changes. We demonstrate in two proof-of-concept settings (reporting hidden behaviors and summarizing finetuned knowledge) that our method enables models to describe their finetuning-induced modifications using concise and accurate natural language descriptions.

The deployment of large language models (LLMs) for specialized tasks on resource-constrained edge devices like smartphones and sensors presents a significant scalability problem. To run on such hardware, these massive models must be compressed using techniques like \emph{quantization or pruning} to reduce their memory and computational footprint. Concurrently, foundational LLMs are periodically updated by their developers with new data, making their $\textit{internal parameters shift over time}$. While parameter-efficient methods like Low-Rank Adaptation (LoRA) streamline personalization by fine-tuning only a small fraction of parameters, the resulting adapters are $\textbf{brittle}$; a LoRA trained for one specific compression scheme is incompatible with another, and an adapter trained on an older base model performs poorly on an updated one. This forces a costly cycle of retraining for each unique device and every new model release. To address this, we introduce a novel framework that creates a single, universally portable adapter that is both $\textbf{\textit{(i)} compression-aware and \textit{(ii)} temporally robust}$. We achieve this by augmenting the training process with a variety of simulated compression techniques during a single run, utilizing a quantized forward pass to build resilience while maintaining a full-precision backward pass for stable gradient optimization. $\textit{This method yields a unified adapter robust to diverse compression artifacts and the subtle parameter shifts from model evolution}$. Extensive experiments on models such as $\texttt{Llama-2, Llama-3.1, Gemma-2}$, and $\texttt{Mistral}$ across reasoning benchmarks like $\textit{SQA, MATH, and GSM8K}$ demonstrate that our single adapter achieves performance comparable to specialized adapters ($\textit{e.g.}$, QLoRA) that are individually retrained for each compression scheme. Furthermore, we show this single adapter maintains its high performance when applied to future, evolved versions of the base model, eliminating the need for periodic retraining. Our work pioneers an efficient paradigm for edge AI, creating portable model patches that bridge the gap between cloud-based personalization, the diverse hardware ecosystem, and the lifecycle of evolving LLMs.

Deep reinforcement learning (RL) suffers from plasticity loss severely due to the nature of non-stationarity, which impairs the ability to adapt to new data and learn continually. Unfortunately, our understanding of how plasticity loss arises, dissipates, and can be dissolved remains limited to empirical findings, leaving the theoretical end underexplored. To address this gap, we study the plasticity loss problem from the theoretical perspective of network optimization. By formally characterizing the two culprit factors in online RL process: the non-stationarity of data distributions and the non-stationarity of targets induced by bootstrapping, our theory attributes the loss of plasticity to two mechanisms: the rank collapse of the Neural Tangent Kernel (NTK) Gram matrix and the Θ(1/k) decay of gradient magnitude. The first mechanism echoes prior empirical findings from the theoretical perspective and sheds light on the effects of existing methods, e.g., network reset, neuron recycle, and noise injection. Against this backdrop, we focus primarily on the second mechanism and aim to alleviate plasticity loss by addressing the gradient attenuation issue, which is orthogonal to existing methods. We propose Sample Weight Decay (SWD) --- a lightweight method to restore gradient magnitude, as a general remedy to plasticity loss for deep RL methods based on experience replay. In experiments, we evaluate the efficacy of SWD upon TD3, SAC with SimBa architecture in MuJoCo and DeepMind Control Suite tasks. The results demonstrate that SWD effectively alleviates plasticity loss and consistently improves learning performance across various configurations of deep RL algorithms, UTD, network architectures, and environments, achieving SOTA performance on challenging DMC Humanoid tasks.

Low-Rank Adaptation (LoRA) benefits from its plug-and-play nature, enabling large language models (LLMs) to achieve significant performance gains at low cost, has driven the development of LoRA-sharing platforms. However, the jailbreak and backdoor concerns associated with LoRA-sharing platforms remain underexplored. Existing LoRA-based attacks primarily focus on achieving high attack success rates, while neglecting the core reason why LoRA is adopted by user, i.e. to gain downstream task capabilities. However, achieving effective attacks while preserving strong multi-task performance remains challenging, as the largely unrelated objectives tend to interfere with each other during optimization. In this paper, we propose JailbreakLoRA, a multi-task jailbreak LoRA training method that balances task utility and attack capability, it resolves training interference by uncertainty-weighting losses and mitigating gradient conflicts. Additionally, JailbreakLoRA is designed to generate an affirmative prefix upon trigger activation, exploiting inference-time hallucinations to enhance the effectiveness of jailbreak. Experimental results demonstrate that our method outperforms SOTA LoRA-based attacks, achieving a 16.0\% improvement in attack success rate while also enhancing performance on multi-downstream tasks by 16.5\% in average.

We introduce and study the problem of consistent low-rank approximation, in which rows of an input matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ arrive sequentially and the goal is to provide a sequence of subspaces that well-approximate the optimal rank-$k$ approximation to the submatrix $\mathbf{A}^{(t)}$ that has arrived at each time $t$, while minimizing the recourse, i.e., the overall change in the sequence of solutions. We first show that when the goal is to achieve a low-rank cost within an additive $\varepsilon\cdot||\mathbf{A}^{(t)}||_F^2$ factor of the optimal cost, roughly $\mathcal{O}\left(\frac{k}{\varepsilon}\log(nd)\right)$ recourse is feasible. For the more challenging goal of achieving a relative $(1+\varepsilon)$-multiplicative approximation of the optimal rank-$k$ cost, we show that a simple upper bound in this setting is $\frac{k^2}{\varepsilon^2}\cdot\text{poly}\log(nd)$ recourse, which we further improve to $\frac{k^{3/2}}{\varepsilon^2}\cdot\text{poly}\log(nd)$ for integer-bounded matrices and $\frac{k}{\varepsilon^2}\cdot\text{poly}\log(nd)$ for data streams with polynomial online condition number. We also show that $\Omega\left(\frac{k}{\varepsilon}\log\frac{n}{k}\right)$ recourse is necessary for any algorithm that maintains a multiplicative $(1+\varepsilon)$-approximation to the optimal low-rank cost, even if the full input is known in advance. Finally, we perform a number of empirical evaluations to complement our theoretical guarantees, demonstrating the efficacy of our algorithms in practice.

Low-Rank Adaptation is a widely used finetuning method for large models. Its small memory footprint allows practitioners to adapt large models to specific tasks at a fraction of the cost of full finetuning. Different modifications have been proposed to enhance its efficiency by, for example, setting the learning rate, the rank, and the initialization. Another improvement axis is adapter placement strategy: when using LoRA, practitioners usually pick \emph{module types} to adapt with LoRA, such as Query and Key modules. Few works have studied the problem of adapter placement, with nonconclusive results: original LoRA paper suggested placing adapters in attention modules, while other works suggested placing them in the MLP modules. Through an intuitive theoretical analysis, we introduce PLoP (Precise LoRA Placement), a lightweight method that allows automatic identification of module types where LoRA adapters should be placed, given a pretrained model and a finetuning task. We demonstrate that PLoP consistently outperforms, and in the worst case competes, with commonly used placement strategies through comprehensive experiments on supervised finetuning and reinforcement learning for reasoning.

Microscaling data formats leverage per-block tensor quantization to enable aggressive model compression with limited loss in accuracy. Unlocking their potential for efficient training and inference necessitates hardware-friendly implementations that handle matrix multiplications in a native format and adopt efficient error-mitigation strategies. Herein, we reported the emergence of a surprising behavior associated with microscaling quantization, whereas the output of a quantized model degrades as block size is decreased below a given threshold. This behavior clashes with the expectation that a smaller block size should allow for a better representation of the tensor elements. We investigate this phenomenon both experimentally and theoretically, decoupling the sources of quantization error behind it. Experimentally, we analyze the distributions of several Large Language Models and identify the conditions driving the anomalous behavior. Theoretically, we lay down a framework showing remarkable agreement with experimental data from pretrained model distributions and ideal ones. Overall, we show that the anomaly is driven by the interplay between narrow tensor distributions and the limited dynamic range of the quantized scales. Based on these insights, we propose the use of FP8 unsigned E5M3 as a novel hardware-friendly format for the scales in FP4 microscaling data types. We demonstrate that UE5M3 achieves comparable performance to the conventional FP8 unsigned E4M3 scales while obviating the need of global scaling operations on weights and activations.

Effective LLM training relies on *consistency*, meaning that key quantities—such as final losses and optimal hyperparameters—scale predictably across model sizes. Qiu et al. (2025) recently showed that this consistency extends beyond scalars: whole training loss curves can *collapse* onto a universal trajectory after a simple normalization. What remains unclear is whether this phenomenon holds for LLM families trained under *practical scaling recipes*, where width, depth, learning rate, batch size, and weight decay are scaled jointly. We show that it does: loss curves collapse across scales precisely when optimization hyperparameters are set optimally for the given data budget, in accordance with recent empirical scaling laws. Collapse thus emerges as a signature of compute-efficient training. We demonstrate two applications at scale: (1) deviation-from-collapse provides a sensitive, early diagnostic of training pathologies, and (2) the predictability of collapsed curves enables early stopping in large-scale hyperparameter tuning. Finally, we train a competitive LLM family, *Celerity*, using these insights, highlighting collapse as an effective tool for developing efficient LLMs.

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive tasks. To address this limitation, we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. MoM serves as a general framework that can be seamlessly combined with diverse memory update mechanisms across linear models. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models.

Deploying ML systems with only a few real samples makes operational metrics (such as alert rates or mean scores) highly unstable. Existing uncertainty quantification (UQ) methods fail here: frequentist intervals ignore the deployed predictive rule, Bayesian posteriors assume continual refitting, and conformal methods offer per-example rather than long-run guarantees. We introduce a forecast-first UQ framework that blends the empirical distribution with a frozen pretrained generator using a unique Dirichlet schedule, ensuring time-consistent forecasts. Uncertainty is quantified via martingale posteriors: a lightweight, likelihood-free resampling method that simulates future forecasts under the deployed rule, yielding sharp, well-calibrated intervals for both current and long-run metrics without retraining or density evaluation. A single hyperparameter, set by a small-$n$ minimax criterion, balances sampling variance and model--data mismatch; for bounded scores, we provide finite-time drift guarantees. We also show how this framework informs optimal retraining decisions. Applicable off-the-shelf to frozen generators (flows, diffusion, autoregressive models, GANs) and linear metrics (means, tails, NLL), it outperforms bootstrap baselines across vision and language benchmarks (WikiText-2, CIFAR-10, and SVHN datasets); e.g., it achieves $\sim$90\% coverage on GPT-2 with 20 samples vs.\ 37\% for bootstrap. Importantly, our uncertainty estimates are operational under the deployed forecasting rule agnostic of the population parameters, affording practicable estimators for deployment in real world settings.

Fine-tuning large language models (LLMs) has achieved significant success in downstream tasks. However, as the model size continues to grow, traditional fine-tuning methods have become increasingly impractical due to their high computational and memory costs. This has motivated researchers to explore parameter-efficient and memory-friendly fine-tuning strategies to enable scalable approaches, with Low-Rank Adaptation (LoRA) standing out as a representative work. However, the LoRA update is restricted to a low-rank subspace, which results in suboptimal performance compared to the full-parameter update. Recent research has also explored memory-efficient fine-tuning LLMs using just forward passes while suffer from high variance in gradient estimation and low convergence speed. To address the issues above, we propose a new alternating optimization framework called LMAO (Low-rank and Memory-efficient Zeroth-Order Alternating Optimization), which combines the advantages of LoRA and MeZO. This method alternately updates the low-rank components and zeroth-order directions during training. By performing three forward propagations and one backward propagation, each update is full-rank, thereby reducing feature loss and enabling efficient fine-tuning under strict memory constraints. We provide theoretical guarantees on the convergence and convergence rate of this method. Empirical results demonstrate that, in experiments on multiple models (e.g., OPT, RoBERTa-large), LMAO achieves performance comparable to first-order methods. This presents a practical and scalable solution for fine-tuning large-scale models. Our source code is available at https://anonymous.4open.science/r/mlao-C2EC/.

Fine-tuning large foundation models is essential for building expert models tailored to specialized tasks and domains, but fully updating billions of parameters is computationally prohibitive. Reducing the number of trainable parameters using parameter-efficient fine-tuning is therefore crucial not only to reduce training costs but also to mitigate storage, caching, and serving overheads during deployment. Prior works, such as Singular Vectors-guided Fine-Tuning, have shown that exploiting the geometry of pre-trained weights can significantly improve parameter-efficiency, but they lack a solid theoretical foundation. In this paper, we introduce Parameter-efficient Fine-tuning with Column Space Projection (PiCa), a novel theoretically grounded PEFT method. We prove that projecting gradients onto the principal column space of pre-trained weights provides an effective inductive bias for adaptation and further enhance parameter efficiency through a novel weight-sharing strategy. Across diverse NLP and vision tasks, PiCa consistently outperforms state-of-the-art baselines under comparable or smaller parameter budgets, demonstrating both theoretical rigor and practical effectiveness.

Graph Domain Adaptation (GDA) aims to bridge distribution shifts between domains by transferring knowledge from well-labeled source graphs to given unlabeled target graphs. One promising recent approach addresses graph transfer by discretizing the adaptation process, typically through the construction of intermediate graphs or stepwise alignment procedures. However, such discrete strategies often fail in real-world scenarios, where graph structures evolve continuously and nonlinearly, making it difficult for fixed-step alignment to approximate the actual transformation process. To address these limitations, we propose \textbf{DiffGDA}, a \textbf{Diff}usion-based \textbf{GDA} method that models the domain adaptation process as a continuous-time generative process. We formulate the evolution from source to target graphs using stochastic differential equations (SDEs), enabling the joint modeling of structural and semantic transitions. To guide this evolution, a domain-aware network is introduced to steer the generative process toward the target domain, encouraging the diffusion trajectory to follow an optimal adaptation path. We theoretically show that the diffusion process converges to the optimal solution bridging the source and target domains in the latent space. Extensive experiments on 14 graph transfer tasks across 8 real-world datasets demonstrate DiffGDA consistently outperforms state-of-the-art baselines.

Facial expression recognition (FER) models are employed in many video-based affective computing applications, such as human-computer interaction and healthcare monitoring. However, deep FER models often struggle with subtle expressions and high inter-subject variability, limiting their performance in real-world applications. To improve their performance, source-free domain adaptation (SFDA) methods have been proposed to personalize a pretrained source model using only unlabeled target domain data, thereby avoiding data privacy, storage, and transmission constraints. This paper addresses a challenging scenario, where source data is unavailable for adaptation, and only unlabeled target data consisting solely of neutral expressions is available. SFDA methods are not typically designed to adapt using target data from only a single class. Further, using models to generate facial images with non-neutral expressions can be unstable and computationally intensive. In this paper, personalized feature translation (PFT) is proposed for SFDA. Unlike current image translation methods for SFDA, our lightweight method operates in the latent space. We first pre-train the translator on the source domain data to transform the subject-specific style features from one source subject into another. Expression information is preserved by optimizing a combination of expression consistency and style-aware objectives. Then, the translator is adapted on neutral target data, without using source data or image synthesis. By translating in the latent space, PFT avoids the complexity and noise of face expression generation, producing discriminative embeddings optimized for classification. Using PFT eliminates the need for image synthesis, reduces computational overhead (using a lightweight translator), and only adapts part of the model, making the method efficient compared to image-based translation. Extensive experiments on four challenging video FER benchmark datasets, BioVid, StressID, BAH, and AffWild2, show that PFT consistently outperforms state-of-the-art SFDA methods, providing a cost-effective approach that is suitable for real-world, privacy-sensitive FER applications.

As AI increasingly shapes daily life, energy consumption and data privacy have become pressing concerns. On-device learning trains models directly on edge devices, cutting energy consumption and safeguarding data privacy. However, the expanding scale of modern neural networks creates a major obstacle for on-device training. Although prior work has concentrated on compact convolutional architectures, we instead apply subspace-based training to transformer models. Motivated by the idea that a model's essential information lies in a fixed subspace, we introduce Weight-Activation Subspace Iteration (WASI), a method that mitigates the memory bottleneck of backpropagation and boosts inference efficiency in transformer models by restricting training to this subspace. Our results demonstrate that WASI maintains accuracy comparable to vanilla training while reducing memory usage by up to $62\times$ and computational cost (FLOPs) by up to $2\times$. On a Raspberry Pi 5, WASI achieves roughly $1.4\times$ faster training and inference than vanilla training. The code is available at https://github.com/Le-TrungNguyen/ICLR2026-WASI.git.

The pursuit of computational efficiency has driven the adoption of low-precision formats for training transformer models. However, this progress is often hindered by notorious training instabilities. This paper provides the first mechanistic explanation for a long-standing and unresolved failure case where training with flash attention in low-precision settings leads to catastrophic loss explosions. Our in-depth analysis reveals that the failure is not a random artifact but caused by two intertwined phenomena: the emergence of similar low-rank representations within the attention mechanism and the compounding effect of biased rounding errors inherent in low-precision arithmetic. We demonstrate how these factors create a vicious cycle of error accumulation that corrupts weight updates, ultimately derailing the training dynamics. To validate our findings, we introduce a minimal modification to the flash attention that mitigates the bias in rounding errors. This simple change stabilizes the training process, confirming our analysis and offering a practical solution to this persistent problem. Code is available at https://anonymous.4open.science/r/why-low-precision-training-fails.

Aligning Large Language Models with human preferences typically requires computationally intensive training or complex reward architectures. We introduce PALC (Preference Alignment via Logit Calibration), a parameter-efficient framework that achieves test-time alignment through a novel intervention strategy: direct calibration in vocabulary space. Unlike existing methods that manipulate entangled hidden representations or rely on external reward models, PALC operates at the logit layer where each dimension corresponds to a distinct token, providing interpretable and efficient control. Our approach employs a bottleneck architecture that learns to compress the base model's hidden states and generate position-dependent calibration vectors, requiring only a fraction of the base model's parameters. Through this design, PALC sidesteps the superposition problem inherent in representation engineering while eliminating the computational overhead of guided decoding methods. A single scaling factor enables runtime adjustment of alignment strength without retraining, allowing practitioners to balance between preserving model capabilities and enforcing preferences. Experiments demonstrate that PALC outperforms most test-time alignment methods while maintaining near-baseline inference speed. Our ablations reveal that human preferences concentrate on surprisingly low-dimensional manifolds, validating our architectural choices. By establishing vocabulary-space intervention as an effective alignment paradigm, PALC makes preference alignment accessible for resource-constrained deployments where traditional methods are infeasible, opening new avenues for scalable and adaptive AI alignment.