ICLR 2026 Papers

On-device inference offers privacy, offline use, and instant response, but consumer hardware restricts large language models (LLMs) to low throughput and capability. To overcome this challenge, we present prima.cpp, a distributed on-device inference system that runs 30-70B LLMs on consumer home clusters with mixed CPUs/GPUs, insufficient RAM/VRAM, slow disks, Wi-Fi links, and heterogeneous OSs. We introduce pipelined-ring parallelism (PRP) to overlap disk I/O with compute and communication, and address the prefetch-release conflict in mmap-based offloading. We further propose Halda, a heterogeneity-aware scheduler that co-optimizes per-device CPU/GPU workloads and device selection under RAM/VRAM constraints. On four consumer home devices, a 70B model reaches 674 ms/token TPOT with <6% memory pressure, and a 32B model with speculative decoding achieves 26 tokens/s. Compared with llama.cpp, exo, and dllama, our proposed prima.cpp achieves 5-17× lower TPOT, supports fine-grained model sizes from 8B to 70B, ensures broader cross-OS and quantization compatibility, and remains OOM-free, while also being Wi-Fi tolerant, privacy-preserving, and hardware-independent. The code is available at https://gitee.com/zonghang-li/prima.cpp.

Low-Rank Adaptation (LoRA) is a widely adopted technique for parameter-efficient fine-tuning, but its slow convergence has spurred the development of numerous variants. Nevertheless, current approaches struggle to achieve simultaneous improvements in performance, memory footprint, and computational efficiency. To address this challenge, we revisit the causes of LoRA’s slow convergence and, based on these insights, propose \textbf{M}atr\textbf{i}x \textbf{S}hard \textbf{S}haring (MiSS) that shards the original weight matrix and updates by sharing a single trainable matrix $\boldsymbol{D}$ initialized to zero. To simultaneously ensure computational efficiency, low memory footprint, and scalable serving, we introduce MiSS$^e$. Through theoretical analyses and empirical results, our method reduces optimization complexity while maintaining strong performance, striking a favorable balance between performance, memory, and efficiency. Furthermore, we provide a comprehensive analysis of different PEFT methods with respect to memory usage, initialization time, and computational efficiency. By mapping the Pareto frontier, we show that MiSS achieves a favorable balance across these dimensions, integrating the strengths of prior approaches.

A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential probabilistic models. We first empirically demonstrate that a wide range of modern language models exhibit low-rank structure: in particular, matrices built from the model's logits for varying sets of prompts and responses have low approximate rank. We then show that this low-rank structure can be leveraged for generation --- in particular, we can generate a response to a target prompt using a linear combination of the model's outputs on unrelated, or even nonsensical prompts. On the theoretical front, we observe that studying the approximate rank of language models in the sense discussed above yields a simple universal abstraction whose theoretical predictions parallel our experiments. We then analyze the representation power of the abstraction and give provable learning guarantees.

Training Large Language Models (LLMs) faces severe memory constraints due to the increasing size of model parameters and optimizer states. The Muon optimizer, which is based on matrix orthogonalization, has recently demonstrated significant potential and offers considerable memory advantages over AdamW by utilizing only the first moment. However, how to apply memory-reduction techniques to further compress the optimizer states of Muon remains underexplored. Directly applying existing methods may encounter significant difficulties due to the orthogonalization process. In this work, we investigate the low-bit compression of Muon and systematically analyze the quantization error exacerbated by orthogonalization. We identify that the error primarily originates from the top singular subspace and the outlier patterns of moment matrix appearing across both dimensions. To address this, we propose 4-bit-Muon-GRASP (GRid And Subspace Preserving), which compresses the Muon optimizer states to 4 bits using grid quantization, while preserving the top singular subspace with minimal overhead. We evaluate 4-bit-Muon-GRASP through pre-training on LLaMA-130M, 350M, and 1.1B architectures and fine-tuning on 7B models for various reasoning tasks. Extensive experiment results show that our 4-bit-Muon-GRASP achieves accuracy comparable to full-precision counterparts while reducing training memory consumption by up to 28\%. Code will be made public upon acceptance.

This paper introduces *quasi-Monte Carlo latent variable models* (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard approaches, which rely on a learned encoder and variational lower bounds, QLVMs directly approximate the marginal likelihood by randomized quasi-Monte Carlo integration. While this brute force approach has drawbacks in higher-dimensional spaces, we find that it excels in fitting one, two, and three dimensional deep latent variable models. Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) and importance weighted autoencoders (IWAEs) with matched latent dimensionality. The resulting embeddings enable transparent visualization and *post hoc* analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial to validate in higher-dimensional spaces. While our approach is compute-intensive and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

Model merging has emerged as a promising approach for unifying independently fine-tuned models into an integrated framework, significantly enhancing computational efficiency in multi-task learning. Recently, several SVD-based techniques have been introduced to exploit low-rank structures for enhanced merging, but their reliance on heuristically designed rank selection often leads to inter-task interference and suboptimal performance. In this paper, we propose AdaRank, a model merging framework that replaces this heuristic selection by adaptively selecting the beneficial singular components of task vectors to merge multiple models. We first show empirically that (i) selecting only the top singular components of task vectors can cause critical interference with other tasks, and (ii) assigning fixed ranks does not align with the varying complexity of tasks and layers. AdaRank addresses both issues by adapting per-component masks, indicating the selection of the component, to the unlabeled test data with entropy minimization. Our experimental findings show that AdaRank consistently improves existing merging methods across diverse backbones from different modalities, largely narrowing the performance gap against individually fine-tuned models.

Loss curves are smooth during most of model training, so visible discontinuities stand out as possible conceptual breakthroughs. Studying these breakthroughs enables a deeper understanding of learning dynamics, but only when they are properly identified. This paper argues that similar breakthroughs occur frequently throughout training but they are obscured by a loss metric that collapses all variation into a single scalar. To find these hidden transitions, we introduce POLCA, a method for decomposing changes in loss along arbitrary bases of the low-rank training subspace. We use our method to identify clusters of samples that share similar changes in loss during training, disaggregating the overall loss into that of smaller groups of conceptually similar data. We validate our method on synthetic arithmetic and natural language tasks, showing that POLCA recovers clusters that represent interpretable breakthroughs in the model's capabilities. We demonstrate the promise of these hidden phase transitions as a tool for unsupervised interpretability.

Test-time adaptation (TTA) has been widely explored to prevent performance degradation when test data differ from the training distribution. However, fully leveraging the rich representations of large pretrained models with minimal parameter updates remains underexplored. In this paper, we propose a novel approach, Intrinsic Mixture of Spectral Experts (IMSE), that leverages the spectral experts inherently embedded in Vision Transformers. We decompose each linear layer via singular value decomposition (SVD) and adapt only the singular values, referring to each decomposed rank-1 component as a spectral expert while keeping the singular vectors fixed. We further identify a key limitation of entropy minimization in TTA: it often reduces feature variance, causing the model to rely on domain-specific cues rather than class-discriminative features. To address this, we propose a diversity maximization loss based on singular vector–input alignment, which maximizing diversity of response pattern. In the continual test-time adaptation (CTTA) scenario, beyond preserving pretrained knowledge, it is crucial to retain and reuse knowledge from previously observed domains. We introduce Domain-Aware Spectral Code Retrieval, which estimates input distributions to detect domain shifts, and retrieves adapted singular values for rapid adaptation. Extensive experiments show that our method achieves state-of-the-art performance on ImageNet-C/R/A under single-domain TTA. In CTTA, it improves accuracy by 3.4pp with 2,000$\times$ fewer trainable parameters.

Low-rank adaptation (LoRA) is a parameter-efficient fine-tuning (PEFT) method widely used in large language models (LLMs). It approximates the update of a pretrained weight matrix $W\in\mathbb{R}^{m\times n}$ by the product of two low-rank matrices, $BA$, where $A \in\mathbb{R}^{r\times n}$ and $B\in\mathbb{R}^{m\times r} (r\ll\min\{m,n\})$. Increasing the dimension $r$ can raise the rank of LoRA weights (i.e., $BA$), which typically improves fine-tuning performance but also significantly increases the number of trainable parameters. In this paper, we propose **Block Diversified Low-Rank Adaptation (BoRA)**, which improves the rank of LoRA weights with a small number of additional parameters. Specifically, BoRA treats the product $BA$ as a block matrix multiplication, where $A$ and $B$ are partitioned into $b$ blocks along the columns and rows, respectively (i.e., $A=[A_1,\dots,A_b]$ and $B=[B_1,\dots,B_b]^\top$). Consequently, the product $BA$ becomes the concatenation of the block products $B_iA_j$ for $i,j\in[b]$. To enhance the diversity of different block products, BoRA introduces a unique diagonal matrix $\Sigma_{i,j} \in \mathbb{R}^{r\times r}$ for each block multiplication, resulting in $B_i \Sigma_{i,j} A_j$. By leveraging these block-wise diagonal matrices, BoRA increases the rank of LoRA weights by a factor of $b$ while only requiring $b^2r$ additional parameters. Extensive experiments across multiple datasets and models demonstrate the superiority of BoRA, and ablation studies further validate its scalability. The code is available at \url{https://anonymous.4open.science/r/BoRA}.

Reinforcement learning with verifiable rewards (RLVR) has become a trending paradigm for training reasoning large language models (LLMs). However, due to the autoregressive decoding nature of LLMs, the rollout process becomes the efficiency bottleneck of RL training, consisting of up to 70\% of the total training time. In this work, we propose Quantized Reinforcement Learning (QuRL) that uses a quantized actor for accelerating the rollout. We address two challenges in QuRL. First, we propose Adaptive Clipping Range (ACR) that dynamically adjusts the clipping ratio based on the policy ratio between the full-precision actor and the quantized actor, which is essential for mitigating long-term training collapse. Second, we identify the weight update problem, where weight changes between RL steps are extremely small, making it difficult for the quantization operation to capture them effectively. We mitigate this problem through the invariant scaling technique that reduces quantization noise and increases weight update. We evaluate our method with INT8 and FP8 quantization experiments on DeepScaleR and DAPO, and achieve 20% to 80% faster rollout during training.

While recent advances in machine learning have equipped Weather Foundation Models (WFMs) with substantial generalization capabilities across diverse downstream tasks, the escalating computational requirements associated with their expanding scale increasingly hinder practical deployment. Current Parameter-Efficient Fine-Tuning (PEFT) methods, designed for vision or language tasks, fail to address the unique challenges of weather downstream tasks, such as variable heterogeneity, resolution diversity, and spatiotemporal coverage variations, leading to suboptimal performance when applied to WFMs. To bridge this gap, we introduce WeatherPEFT, a novel PEFT framework for WFMs incorporating two synergistic innovations. First, during the forward pass, Task-Adaptive Dynamic Prompting (TADP) dynamically injects the embedding weights within the encoder to the input tokens of the pre-trained backbone via internal and external pattern extraction, enabling context-aware feature recalibration for specific downstream tasks. Furthermore, during backpropagation, Stochastic Fisher-Guided Adaptive Selection (SFAS) not only leverages Fisher information to identify and update the most task-critical parameters, thereby preserving invariant pre-trained knowledge, but also introduces randomness to stabilize the selection. We demonstrate the effectiveness and efficiency of WeatherPEFT on three downstream tasks, where existing PEFT methods show significant gaps versus Full-Tuning, and WeatherPEFT achieves performance parity with Full-Tuning using fewer trainable parameters. The code of this work is available at https://anonymous.4open.science/r/WeatherPEFT-A068.

Vector Quantization (VQ) underpins modern discrete visual tokenization. However, training quantization modules for state-of-the-art VQ-based models requires significant computational resources which, in practice, all but prevents the development of novel, cutting-edge VQ techniques under resource constraints. To address this limitation, we propose VQ-Transplant, a simple framework that enables plug-and-play integration of new VQ modules into frozen, pre-trained tokenizers by replacing their native VQ modules. Crucially, the proposed transplantation process preserves all encoder-decoder parameters, obviating the need for costly end-to-end retraining when modifying the quantization method. To mitigate decoder-quantization mismatch, we introduce a lightweight decoder adaptation strategy (trained for only 5 epochs on ImageNet-1k) to align feature priors with the new quantization space. In our empirical evaluation, we find that VQ-Transplant allows obtaining near state-of-the-art reconstruction fidelity for industry-level models like VAR while reducing the training cost by 95%. VQ-Transplant democratizes quantization research by enabling resource-efficient integration of novel VQ techniques while matching industry-level reconstruction performance.

State Space Models (SSMs) have emerged as powerful alternatives to attention-based Transformers, with Mamba demonstrating impressive efficiency and scalability. As these models grow increasingly larger, the need for Parameter-Efficient Fine-Tuning (PEFT) methods becomes critical to adapt pre-trained Mamba to downstream tasks without prohibitive computational costs. However, previous approaches simply apply traditional Transformer-tailored PEFT methods without addressing the unique temporal processing dynamics of SSMs. To address this limitation, we propose ***Memba***, a membrane-driven PEFT approach specifically designed for Mamba. ***Memba*** introduces Leaky Integrate Membrane (LIM) neurons as bio-inspired gating mechanisms that naturally accumulate membrane potentials over time, enhancing selective information retention. By strategically combining LIM neurons with Low-Rank Adaptations (LoRA) and cross-layer membrane transfer, our approach significantly improves Mamba's temporal modeling capabilities. Extensive experiments across language and vision tasks demonstrate that ***Memba*** achieves substantial improvements over existing PEFT methods.

In Diffusion Transformer (DiT) models, particularly for video generation, attention latency is a major bottleneck due to the long sequence length and the quadratic complexity. Interestingly, we find that attention weights can be decoupled into two matrices: a small fraction of large weights with high rank and the remaining weights with very low rank. This naturally suggests applying sparse acceleration to the first part and low-rank acceleration to the second. Based on this finding, we propose SLA (**S**parse-**L**inear **A**ttention), a trainable attention method that fuses sparse and linear attention to accelerate diffusion models. SLA classifies attention weights into critical, marginal, and negligible, applying $\mathcal{O}(N^2)$ attention to critical weights, $\mathcal{O}(N)$ attention to marginal weights, and skipping negligible ones. SLA combines these computations into a single GPU kernel and supports both forward and backward passes. With only a few fine-tuning steps using SLA, DiT models achieve a $\textbf{20x}$ reduction in attention computation, resulting in significant acceleration without loss of generation quality. Experiments show that SLA reduces attention computation by $\textbf{95}$\% without degrading end-to-end generation quality, outperforming baseline methods. In addition, we implement an efficient GPU kernel for SLA, which yields a $\textbf{13.7x}$ speedup in attention computation and a $\textbf{2.2x}$ end-to-end speedup in video generation on Wan2.1-1.3B.

Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE, even without hyperparameter tuning required by TE, to accurately select high-confidence views and seamlessly integrate with label adjustment strategy to enhance adaptation. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://anonymous.4open.science/r/TTA-Entropy.

Instruction fine-tuning is a key technique for enhancing the performance of large language models (LLMs), but low-quality and redundant data often hinder its effectiveness. Recent studies suggest that filtering a small amount of high-quality data for instruction fine-tuning can achieve faster and more efficient training performance. However, existing data filtering approaches predominantly depend on predefined evaluation models or manually designed metrics, without leveraging information from the target LLM itself. This limitation may result in a mismatch between the filtering criteria and the actual requirements of the LLM being fine-tuned, thereby reducing the effectiveness of the fine-tuning process. To address these issues, we propose a novel perspective: the hidden states of LLMs implicitly reflect the quality of the training data. Based on this insight, we propose a novel data filtering method that extracts the hidden states that reflect the target LLM’s perception of the data as representative features, and builds a data classification model upon them, which outputs the Contrastive Perception Quality Score (CPQS) for dataset filtering. Our experiments are conducted in both general and downstream domains. (1) In the general domain, our experiments show that training on under 10\% of the data from both the Alpaca\_GPT4 and DeepSeek-R1 synthesized reasoning datasets enables our method to outperform models trained on the complete datasets. Moreover, it surpasses the performance of current state-of-the-art data-selection techniques. (2) In downstream tasks, our approach delivers an average performance gain exceeding 3.6\% over leading data-selection algorithms across multiple benchmarks, including GSM8K, HumanEval, and HumanEval-Plus.

Fine-tuning is a critical step for adapting large language models (LLMs) to domain-specific downstream tasks. To mitigate the substantial computational and memory costs of full-model fine-tuning, Parameter-Efficient Fine-Tuning (PEFT) methods have been proposed to update only a small subset of model parameters. However, performance gaps between PEFT approaches and full-model fine-tuning still exist. In this work, we present *DiaBlo*, a simple yet effective PEFT approach that updates only the diagonal blocks of selected model weight matrices. Unlike Low-Rank Adaptation (LoRA) and its variants, DiaBlo eliminates the need for low-rank matrix products, thereby avoiding the reliance on auxiliary initialization schemes or customized optimization strategies to improve convergence. This design leads to stable and robust convergence while maintaining comparable memory efficiency and training speed to LoRA. Moreover, we provide theoretical guarantees showing that, under mild low-rank conditions, DiaBlo is more expressive than LoRA in the linear problem and converges to a stationary point of the general nonlinear full fine-tuning. Through extensive experiments across a range of tasks—including commonsense reasoning, arithmetic reasoning, code generation, and safety alignment—we show that fine-tuning only diagonal blocks is sufficient for strong and consistent performance. DiaBlo not only achieves competitive accuracy but also preserves high memory efficiency and fast fine-tuning speed.

We introduce SeerAttention-R, a sparse attention framework specifically tailored for the long decoding of reasoning models. Extended from SeerAttention, SeerAttention-R retains the design of learning attention sparsity through a self-distilled gating mechanism, while removing query pooling to accommodate auto-regressive decoding. With a lightweight plug-in gating, SeerAttention-R is flexible and can be easily integrated into existing pretrained model without modifying the original parameters. We demonstrate that SeerAttention-R, trained on just 0.4B tokens, maintains near-lossless reasoning accuracy with 4K token budget in AIME benchmark under large sparse attention block sizes (64/128). Using TileLang, we develop a highly optimized sparse decoding kernel that achieves near-theoretical speedups of up to 9x over FlashAttention-3 on H100 GPU at 90\% sparsity.

Fine-tuning Large Language Models (LLMs) with downstream data is often considered time-consuming and expensive. Structured pruning methods are primarily employed to improve the inference efficiency of pre-trained models. Meanwhile, they often require additional time and memory for training, knowledge distillation, structure search, and other strategies, making efficient model fine-tuning challenging to achieve. To simultaneously enhance the training and inference efficiency of downstream task fine-tuning, we introduce GradPruner, which can prune layers of LLMs guided by gradients in the early stages of fine-tuning. GradPruner uses the cumulative gradients of each parameter during the initial phase of fine-tuning to compute the Initial Gradient Information Accumulation Matrix (IGIA-Matrix) to assess the importance of layers and perform pruning. We sparsify the pruned layers based on the IGIA-Matrix and merge them with the remaining layers. Only elements with the same sign are merged to reduce interference from sign variations. We conducted extensive experiments on two LLMs across eight well-known datasets in downstream tasks. Including medical, financial, and general benchmark tasks. The results demonstrate that GradPruner has achieved a parameter reduction of 40% with only a 0.99% decrease in accuracy. Our code is available at https://anonymous.4open.science/r/LLM-GradPrune-436D.