Low-Rank Compression

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12 papers in the last four weeks, with none the four weeks before. 0.1% of all new papers.

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Latest papers 58

Oct 4, 2026cs.AI

The Functional Structure of Post-Compression Recovery in Low-Rank LLMs

Different low-rank compression methods can produce compressed LLMs that respond differently to the same post-compression recovery procedure, and relative advantages observed between methods at the compression endpoint may shrink, grow, or even reverse after recovery. We ask whether this recovery heterogeneity reflects functional structure beyond scalar loss evolution, and how that structure evolves throughout recovery. Our results establish that this heterogeneity reflects a reproducible compression-induced functional structure, which we formalize as recovery pressure. To characterize this structure consistently throughout recovery, we develop a standardized functional characterization within each backbone that is applicable across heterogeneous low-rank methods. The primary backward characterization reveals reproducible module-wise structure across independent probes, while a complementary forward-only characterization recovers related structure without loss or backpropagation. We further find that recovery pressure measured at the endpoint is associated with subsequent recovery response; during recovery, its module-wise structure is reorganized non-uniformly, and localized updates induce distributed responses beyond directly updated modules. Further evidence indicates that tracking this evolving structure provides a complementary functional view of recovery progress alongside scalar loss.

Zishan Shao, Liang Tian, Georgiy Zemlevskiy +10

Duke University · Wake Forest University · Carnegie Mellon University +2

LLM Compression Low-Rank Compression LLM Post-Training

Sep 30, 2026cs.CL

Sequential Functional Structured Tucker Compression for Large Language Model Attentions

Post-training compression of LLM attention is often formulated as independent matrix approximation, ignoring both the shared structure among attention projections and the representation shift introduced by earlier compression. We propose FTC, a sequential structured compression framework that adapts the approximation to the current compressed model while jointly exploiting the native Q/K/V head structure under a fixed storage budget. The output projection is handled separately to account for the changed post-attention representation. FTC requires neither fine-tuning nor gradient-based recovery. Across seven decoder-only LLMs from 6B to 32B parameters, FTC achieves the lowest WikiText-2 perplexity among the compared methods at every tested keep ratio on five modern GQA models, with the largest gains under aggressive compression. The improvements transfer to downstream tasks and remain substantial at the 32B scale.

Jiangfeng Chen, Xinyu Wang, Tianshuo Yan +4

University of Manitoba · McGill University · Simpleway +2

LLM Compression Decoder-Only Language Models Tensor Decomposition Low-Rank Compression

Sep 30, 2026cs.LG

Learning Functional Subspaces for Neural Network Compression

Modern transformers pair impressive capabilities with substantial memory and compute demands. Low-rank weight factorization reduces both while keeping the matrices dense, and thus efficient on standard hardware. Existing methods, however, choose the subspace to remove from each weight matrix with local closed-form criteria: activation energy, layer-wise reconstruction error, or a quadratic approximation of the loss. These criteria ignore how errors propagate through the network, so at high compression the errors compound with depth and performance collapses. We introduce Learnable Subspace Projections (LSP), which instead learns the subspaces to discard end-to-end. Each linear layer, or tied group of layers that read the same activations, is assigned an orthogonal projector. All projectors are optimized jointly against a global objective--the KL divergence to the dense model's output distribution or the model's original training loss--while the pretrained weights remain frozen. Projectors are initialized from a whitened SVD truncation, and ranks are allocated by the output KL each projector induces per parameter saved. After training, the projectors merge into standard low-rank factors, with each tied group sharing one factor. In attention, this also lets the model cache one narrow latent in place of full keys and values. Across LLMs (OPT-125M/1.3B, Qwen3-4B, Llama-2-7B) and ViT-B/16, LSP outperforms baselines, and its advantage widens as compression increases. At -70% compression, LSP brings Llama-2-7B to 10.9 WikiText-2 perplexity and 42.2% mean zero-shot accuracy, versus 13.3 and 36.0% for the strongest baseline. The factorized model decodes up to 1.6x faster than the dense model at small batch sizes, and aching the shared latent shrinks the combined memory of weights and KV cache by 13.5x at a 128k-token context, versus at most 6.5x for untied baseline factorizations.

Massimo Bini, Anders Christensen, Stephan Alaniz +5

Helmholtz Munich · Technical University of Munich · MCML +6

LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Dimensionality Reduction Neural Network Compression

Sep 30, 2026cs.LG

Beyond Uniform Compression: Budgeted Transmission Allocation for Extreme Federated Learning

Federated learning faces severe communication bottlenecks when clients upload high-dimensional model updates. Existing methods often compress these updates uniformly across all layers. This uniform approach ignores the heterogeneous value of different parameter blocks and wastes limited bandwidth on insensitive layers. To address this issue, we propose Layer-wise Budgeted Adaptive Transmission (LBAT). LBAT reframes federated communication under extreme uplink budgets as a resource allocation problem. Our framework dynamically estimates the transmission value of different layers utilising local training signals. It then employs an exact byte dynamic programming allocator to determine optimal rank and bit configurations under strict budgets. We validate LBAT on highly heterogeneous federated tabular prediction and data generation tasks. Extensive experiments demonstrate that LBAT consistently outperforms uniform rank, uniform quantisation, and fixed compression baselines across various extreme budget regimes. Furthermore, it achieves significantly better communication and utility tradeoffs while preserving essential distributional fidelity.

Pengfei Li, Mohammad Khalil

Centre for the Science of Learning & Technology (SLATE), University of Bergen, Bergen, Norway

Communication-Efficient Distributed Training Low-Rank Compression Adaptive Rank Allocation Federated Learning

Sep 29, 2026cs.AI

KV-Kaizen: Learning Context-Adaptive Cache Compression Choices

As the context size of text processed with an LLM grows, the size of KV caches can outstrip the memory allocated for the original model weights. This impacts LLM throughput negatively, since decoding is memory-bound and decode cost grows with cache size. Recent work alleviates this bottleneck by discarding the least relevant tokens. Eviction introduces a tension, since a one-off decision to discard content may prove detrimental later. Instead, we focus on alternative choices that can lead to cache compression without evicting tokens. We achieve this by learning a selector that is able to produce, based on context, a per-layer cache configuration towards an overall compression budget. The selector operates along three axes: sharing one cache across layers (depth), caching at fewer bits (precision), or truncating the low-rank latent cache representations (rank). We call the resulting method KV-Kaizen, for the many small per-layer choices it compounds. We observe that these interventions taken independently and uniformly over all layers limit achievable compression because they degrade accuracy. Crucially, composing them locally and adaptively to the context can instead preserve accuracy while achieving large memory savings. At inference, the selector runs once, before pre-fill. In evaluations on instruction following and reasoning tasks, our selectors reach the Pareto frontier of accuracy against cache size, against learning-free and post-hoc baselines. On long-context tasks, KV-Kaizen improves on eviction and can be composed with it, reaching a 32x smaller decode-time cache on a 14B model while preserving accuracy. A 4x cache size reduction incurs no accuracy degradation from 7B parameters up, and a compressed model is more accurate than a smaller uncompressed one with the same cache size. Together, these findings support pre-training large models and compressing them only afterwards.

Joao Monteiro, Louis Béthune, Anastasiia Filippova +3

Apple

LLM Inference Acceleration Low-Rank Compression KV-Cache Compression KV-Cache Quantization

Sep 28, 2026cond-mat.dis-nn

Pre-registered tests of solid-state-physics-inspired LLM compression: a cluster-level negative result at small-language-model scale

We report a three-month autonomous research-agent program testing five solid-state-physics-inspired compression mappings on pretrained language models, with predictions committed to git before any pilot data and a 3-sigma gate deciding PASS or SHELVE. The common anchor -- area-law / Kohn-nearsighted decay of the one-particle density matrix -- has a distance face (P001 Wannier, P002 tight-binding) and a rank face (P003 DMRG-truncated MLPs, P005 Wilson-RG, P011 tensor-train embeddings). P005 was pre-empted at Phase 1; three of four Phase-3 pilots were falsified. On the attention face, GPT-2-medium attention-versus-distance is best fit by a stretched exponential in 12 of 16 median-layer heads once probe padding is excluded, and a tight-binding cutoff costs +96% perplexity (P002); on Pythia-160M the Wannier sparsity 0.054 +/- 0.004 is indistinguishable from PCA, random-Haar and identity baselines (P001). On the rank face, per-token tensor-train bond dimension does not track surprisal (r = 0.016 vs a pre-registered 0.65) and the format inflates rather than compresses (P011). P003 is mixed: its scaling claim shelved (r = -0.434), its MPO premise died at stage-0, and its cross-paper check, r = 0.523 as first written, collapses to 0.047 under the same correction, leaving both cross-paper checks null. The results invert the pre-registered prediction that most attention heads behave like Kohn-nearsighted insulators, pointing instead to critical, glassy or heavy-tailed regimes; the inversion is specific to the <= 350M scale tested, while the rank-face no-gain result held to 7-8B. We contribute the pre-registration + 3-sigma + cluster-framing + append-only-catalogue discipline -- including why our own enforcement gate was designed but not deployed -- four pre-registered negative results with full data release, and the inversion. The catalogue holds eighteen concluded studies, seventeen negative.

Jun-qiang Lu

Department of Physics, University of Puerto Rico, Mayagüez, PR 00680, USA

Tensor Networks LLM Compression Low-Rank Compression

Sep 24, 2026cs.CL

MILO: Efficient Many-shot In-Context Learning with Block-wise Low-rank Compression

Many-shot in-context learning (ICL) enables large language models (LLMs) to adapt to complex tasks by conditioning on thousands of demonstration examples, but this paradigm shifts the inference efficiency bottleneck to the key-value (KV) cache memory. Due to the linear scaling behavior of the KV cache, storing these intermediate tensors has become a paramount challenge for both online serving and on-device deployment. To address this issue, we propose a novel compression framework, termed MILO, that exploits the low-rank redundancy inherent in many-shot contexts. Specifically, MILO features a block-wise low-rank compression strategy that compresses the KV cache at the block granularity, where each block contains multiple many-shot examples. Furthermore, to handle the heterogeneous context density across different blocks, MILO dynamically allocates rank budgets based on the information entropy, preserving the fidelity of critical blocks while aggressively compressing redundant ones. Experimental results on Qwen2.5 models demonstrate that our method achieves up to 50% reduction in KV cache memory and 1.8x throughput improvement, with negligible performance degradation on classification and reasoning benchmarks, significantly outperforming prior baselines.

Youpeng Zhao, Tian Tan, Liqian Peng +2

Google · University of Central Florida

Memory-Efficient Inference LLM Inference Acceleration In-Context Learning Low-Rank Compression KV-Cache Compression

Sep 24, 2026stat.ML

Low-Rank Friction for Memory-Efficient Transformer Pretraining

iKFAD is a recently proposed optimiser that replaces adaptive learning rates with adaptive friction in the momentum dynamics, yet performs as well as Adam. Its limitation is that the full friction tensor

ξ\in\mathbb{R}^{m\times n}

carries the same

\mathcal{O}(mn)

memory overhead per layer as Adam's second-moment buffer. Here we replace iKFAD's friction tensor

ξ

with a rank-1 outer-product factorisation built from row and column momentum statistics, resulting in Rank-1 iKFAD (R-iKFAD). This reduces the friction memory footprint from

\mathcal{O}(mn)

to

\mathcal{O}(m+n)

per layer, which approximately halves iKFAD's total optimiser state. Despite this reduction, R-iKFAD maintains parity in performance with iKFAD: experiments on GPT2-Nano, TinyViT, DistilBERT and GPT2-S confirm that it matches or exceeds iKFAD while nearly halving the memory footprint and remaining comparably robust to hyperparameters. We analyse the continuous-time dynamics in two damping regimes. For linear damping (

γ>0

) we prove exponential convergence under strong convexity. For

γ=0

, the preferred option in our experiments, the friction is generated entirely from past momentum and switches off as the momentum vanishes, so geometric convergence cannot be shown. We nonetheless prove convergence to the minimiser, together with matching upper and lower bounds on the energy: of order

t^{-1}

when the regularisation scale

ε_{\mathrm{stab}}

is zero, and of order

t^{-1/2}

when it is positive. To our knowledge this is the first convergence rate for a rank-1 factored optimiser in continuous time, and the first such result that does not require positive damping.

Rajit Rajpal, Benedict Leimkuhler

School of Mathematics University of Edinburgh Edinburgh, UK EH9 3FD

Deep Learning Optimization Low-Rank Compression Memory-Efficient Training

Sep 22, 2026cs.LG

GeoPair: Geometry-Preserving Cross-Layer Factorization for Training-Free Transformer Compression

Transformer architectures exhibit cross-layer redundancies, yet post-training compression pipelines typically optimize layers in isolation or rely on heuristic grouping strategies that disregard layer-specific activation geometries. We introduce a principled, training-free framework that sequentially optimizes cross-layer weight pairings and shared-dictionary factorizations. Rather than forcing weights of adjacent layers to share a basis or heuristically merging activation statistics, our approach identifies structurally compatible projections and learns a shared representation that better preserves each layer's distinct calibration geometry. Coupled with structured sparsity, this yields highly efficient weight decompositions without sacrificing functional fidelity. Across diverse architectures, scales, and modalities, our method achieves state-of-the-art results, consistently outperforming independent structured weight decompositions and alternative pairwise weight factorizations, which operate under heuristic grouping strategies. By replacing heuristic engineering strategies with a convergent, optimization-driven pipeline, we establish a theoretically grounded foundation for scalable, transformer compression across different modalities.

Baher Mohammad, Ammar Ali, Stamatios Lefkimmiatis

MWS AI, ITMO University · MWS AI

Model Compression Low-Rank Compression Neural Network Compression

Sep 21, 2026cs.LG

KV-COBRA: KV Cache Compression via Co-Optimized Bit-Rank Allocation

What limits KV-cache compression at extreme bit-rates? We argue that it is not the choice of compression scheme, but how its budget is allocated across attention heads. Existing methods apply rank and bit-width uniformly, ignoring that each head has a different optimal mix of rank truncation and quantization. We show that co-optimizing rank and bit-width per head, using only standard low-rank projection and scalar quantization, dominates uniform allocation, with the largest gains at low bit-rates. Our method, KV-COBRA (Co-Optimized Bit-Rank Allocation), formalizes this as a resource-allocation problem: it balances rank-truncation loss against quantization loss within each head, then redistributes budget across heads to minimize total distortion. A fused Hadamard rotation equalizes per-channel variance, and reordering the SVD basis by attention-KL importance makes the solver query-aware. The same allocator extends to joint

K{+}V

compression. On perplexity, zero-shot, and long-context benchmarks from

0.5

to

4

bits per dimension (bpd), KV-COBRA shows the smallest accuracy degradation among evaluated methods at low bpd, with no per-token overhead.

Sihyeon Ha, Jaeho Lee, Yo-Seb Jeon

Pohang University of Science and Technology (POSTECH)

Low-Rank Compression KV-Cache Compression KV-Cache Quantization

Sep 14, 2026cs.LG

Per-Matrix Optimality Is Not Enough: Three-Level Optimization for Low-Rank LLM Compression

Per-matrix singular value decomposition (SVD) truncation is Eckart-Young optimal in the whitened Frobenius norm, but errors from independently compressed matrices compound through the block's nonlinear forward pass. Inspired in part by hierarchical variational optimization in quantum many-body methods, we introduce a three-level chain that widens optimization scope from individual matrices to Transformer blocks to the full model: whitened SVD~(L1), block-level joint optimization~(L2), and end-to-end language-modeling loss refinement~(L3), all from 256 calibration sequences, with no instruction or recovery data. On LLaMA-7B at 60% compression, the chain reduces WikiText-2 perplexity from 42.1 to 19.1 to 11.4. The block-level stage acts as a regularizer: skipping it worsens Penn Treebank (PTB) perplexity by 24 points, a gap that additional end-to-end training did not close in our experiments. Perplexity gains hold across 20-80% compression, five architectures up to 13B parameters, and both in-distribution and out-of-distribution benchmarks, though the cross-architecture rows use architecture-specific configurations and the ratio sweep was not run under one common protocol. With more calibration data, skipping the block-level stage becomes competitive, revealing an offline compute--data trade-off. We therefore claim improvements only in perplexity and compression fidelity; downstream accuracy remains well below the dense model.

Huicheng Zhang, Xiyao Feng, Ze-Tong Li +6

Hong Kong University of Science and Technology (Guangzhou), Guangdong 511453, China · QudeLeap Research, Shanghai 200030, China

Model Compression LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Singular Value Decomposition

Sep 7, 2026cs.CV

Mind the Approximation: Fisher-Weighted SVD Compression for ViTs

Model compression is key to mitigate deployment challenges of ever growing machine learning models. In this area of research, singular value decomposition (SVD)-based compression offers a compelling trade-off between computational efficiency and model accuracy. Fisher-weighted SVD in particular provides principled, loss-aware compression. However, we find that improving the fidelity of Fisher approximation used in the compression is poorly predictive of post-compression accuracy for Vision Transformers (ViTs). Motivated by this observation, we propose FACTS, a structured Fisher Approximation tailored to Compressing ViTs with Fisher-weighted SVD, which enforces token-local aggregation while preserving within-token activation-gradient dependence. Additionally, we introduce a fast Constrained Rank Search (CoRS), that optimizes layer-wise rank allocation while adhering to a fixed floating point operation (FLOP) constraint. Extensive experiments across ViTs and hybrid architectures demonstrate that FACTS consistently improves accuracy-efficiency trade-offs without requiring finetuning. Notably, it outperforms the strongest SVD baseline by up to +5.8 percentage points (p.p.) Top-1 on Swin-B, with further gains driven by our search method. Code is available at https://github.com/MoritzTho/FACTS.

Moritz Thoma, Maximilian Groezinger, Maximilian Forstenhäusler +7

Technical University of Munich, DE · BMW Group, DE · University of Glasgow, GB +1

Efficient ViTs Low-Rank Compression Singular Value Decomposition Neural Network Compression

Aug 9, 2026cs.AI

Understanding Calibration and Truncation Error Propagation in Training-Free Low-Rank Compression for LLMs

Training-free low-rank compression frameworks have been gaining prominence for LLM compression given their effectiveness in reducing model parameter count while maintaining task-level accuracy. However, existing SOTA frameworks share two key limitations: (1) residual errors in calibration data activations accumulate across layers during compression, causing misalignment between representations simulated at compression time and those experienced at inference; (2) the assumption that layer importance distribution is preserved post-compression does not hold. Together, these two effects introduce misalignment in the compression process in relation to the deployed model. We study these effects and propose a simple, training-free methodology compatible with existing frameworks to mitigate them, comprising: (1) Layer-by-Layer Compression with Calibration Correction; (2) Iterative Compression with Rank Allocation Correction. Implemented atop an existing SOTA decomposition framework, and evaluated on Llama and Qwen3 models across various benchmarks and compression rates, our approach demonstrates up to ~1-2.5 accuracy point improvements over per-weight and joint decomposition baselines on zero-shot tasks.

Mohanad Odema, Gabrielle De Micheli, Dayin Gou +3

LG Electronics, North America

Model Compression LLM Compression Low-Rank Compression Adaptive Rank Allocation

Aug 7, 2026cs.LG

Shape Mutating Expert Compression:LorExperts and BTExperts

Mixture-of-Experts (MoE) language models deliver high capacity at low per-token compute, but deploying them cheaply requires compressing their many expert weight matrices. Expert pruning (e.g., REAP) and merging reduce cost but sacrifice accuracy and require retraining the router; low-rank delta decomposition of experts (e.g., D^2-MoE) preserves all experts and the router, but degrades sharply as the expert count grows because a single shared component cannot approximate many near-orthogonal experts. Because MoE expert weights are near-orthogonal, a single shared component (as in prior delta decomposition) scales poorly with the expert count; we show that experts nonetheless organize into functional co-activation communities that are decoupled from weight similarity. Building on this, we introduce LorExperts, a router-preserving compression method that clusters experts, keeps one full-precision dominant per cluster, and represents the remaining members as low-rank corrections to their local dominant. LorExperts retains all experts and the original router (no router retraining). At ~50% expert compression on Qwen3-30B-A3B and Gemma-4-26B-A4B, LorExperts preserves downstream accuracy and perplexity better than the baselines on most of the tasks; the margin over D^2-MoE grows with expert count E. We further give a reconstruction fine-tuning procedure for LorExperts, and BTExperts, a tree organization of dominants and corrections that enables inference-time amortization of shared computation.

Inesh Chakrabarti, Sourjya Roy, Bowen Bao +3

Advanced Micro Devices

Mixture-of-Experts Language Models Low-Rank Matrix Decomposition Mixture-of-Experts Inference Low-Rank Compression Matrix Factorization

Aug 4, 2026cs.AI

FraQ: Efficient Coordinate-Space Recompression for Federated Low-Rank Adaptation

Federated fine-tuning with Low-Rank Adaptation (LoRA) enables efficient collaborative adaptation of Large Language Models (LLMs) without centralizing private data. However, LoRA's two-factor parameterization creates an aggregation mismatch across clients: naively averaging the factors does not recover the average of their induced updates. This mismatch can be avoided by forming the exact aggregate in the full weight space and then recompressing it, but decomposing the resulting dense matrix is computationally expensive and memory-intensive. We propose FraQ, an efficient coordinate-space recompression method for federated LoRA. Starting from stacked factors that exactly represent the aggregate, FraQ factorizes it into an orthonormal basis and a compact coordinate matrix. It then recovers the singular spectrum from a small Gram matrix, selects the smallest rank satisfying a prescribed energy threshold, and maps the selected coordinate subspace back through the basis to construct the global adapter. Experiments on text classification and commonsense reasoning benchmarks show that FraQ achieves accuracy close to uncompressed baselines while substantially reducing downlink communication with low server-side recompression overhead.

Shenghui Li, Thiemo Voigt

Uppsala University, Uppsala, Sweden · Research Institutes of Sweden, Stockholm, Sweden

Federated Learning Aggregation Communication-Efficient Distributed Training Low-Rank Matrix Decomposition Low-Rank Adaptation Low-Rank Compression Federated Fine-Tuning+1

Aug 4, 2026cs.LG

Pin Once, Swap Light: Subspace-Aligned Centroid-Residual Training for Efficient Ultra-LoRA Serving

Modern multi-tenant Low-Rank Adapters (LoRAs) serving systems concurrently host tens to hundreds of LoRA adapters. Though powerful, this introduces a critical system dilemma between serving efficiency and task performance: higher-rank adapters generally achieve better downstream task performance, but their GPU VRAM footprint and Host-to-Device PCIe swapping overhead severely constrain scalability. Conversely, ultra-low-rank adapters (

r \le 2

) minimize both VRAM footprint and PCIe transfer overhead, but suffer from downstream task performance degradation. To solve this problem, we propose Subspace-Aligned LoRA Training (SALT), a serving efficiency-aware hierarchical fine-tuning framework. Our solution operates in three phases. First, a provider jointly trains high-capacity domain centroids on public data within the domain using a novel alignment regularizer that coheres in-domain task subspaces into a unified basis. Next, users fine-tune ultra-low-rank task residual adapters on private data atop those frozen centroids. Finally, during inference, the provider pins the centroid in GPU VRAM and dynamically swaps in each user's task residual on demand. Across LLMs of varying scales, SALT recovers high-rank accuracy using

r \le 2

residuals, achieving up to 18.5% absolute accuracy gains over state-of-the-art compression baselines and reducing per-adapter memory by up to 16x. When integrated into vLLM, SALT improves serving throughput by up to 51% under PCIe bandwidth pressure and 28% under GPU VRAM constraints for Llama-3.2-3B.

Xiang Li, Pengcheng Wang, Huazheng Wang +1

1Purdue University · 2Oregon State University

LLM Inference Efficiency LLM Serving Memory-Efficient Fine-Tuning Low-Rank Adaptation Low-Rank Compression Parameter-Efficient Fine-Tuning

Aug 4, 2026cs.LG

SAKI: Score-Aware Low-Rank Key Indexing with Random-Matrix Noise Correction for KV Retrieval

Existing low rank KV cache methods preserve either model weights or key variance, neither of which directly reflects the attention scores used during inference. We derive the expected attention score distortion caused by rank r key compression and show that it yields a covariance weighted low rank objective. Under a margin condition, controlling this distortion also improves top k recall. The optimal rank r solution has a closed form asymmetric factorization obtained from the SVD of the covariance weighted query key operator. This motivates SAKI, a training free KV cache index that directly preserves attention scores rather than key reconstruction quality. Across LLaMA 3.1 8B, Qwen 2.5 7B, Mistral 7B v0.1, and Llama 3.2 3B, SAKI outperforms key PCA at every tested rank. At rank 32, it removes 13 to 30 percent of PCA's remaining top 64 recall error, including improvements from 0.748 to 0.799 on LLaMA 3.1 8B and from 0.786 to 0.850 on Qwen 2.5 7B. It improves 68 to 89 percent of attention heads per model, with the largest gains in deeper layers. Predicted score MSE reductions closely match empirical measurements, with a Pearson correlation of 0.997, while ablation studies confirm that the gains arise from optimizing the attention score objective rather than covariance weighting alone. Analysis of the scoring operator further explains why weight only, invariant subspace, and key reconstruction methods can be suboptimal. SAKI uses random-matrix theory to separate genuine covariance signal from autocorrelated sampling noise, matching PCA with only 512 calibration tokens and adding value exactly where PCA sees no reliable signal.

Lin Zhang

Data Science and Platform, Cotality

Low-Rank Attention KV Caching Low-Rank Matrix Decomposition Low-Rank Compression Low-Rank Approximation KV-Cache Compression

Aug 3, 2026cs.CL

ARCHead: Activation-Metric Residual Correction for Large Language Model Output Heads

Weight-only quantization substantially reduces the storage of large language model (LLM) transformer blocks, but practical backends often retain the final language-modeling head (LM-head) in BF16 or FP16. Quantizing this projection naively can strongly perturb the vocabulary-logit distribution. We present ARCHead, a packed LM-head compressor that combines a quantized low-rank core, group-wise INT4 residuals, and a low-rank correction fitted in an activation-derived metric. ARCHead stores no dense BF16 head and reduces persistent LM-head storage by 3.7-3.9x. On Qwen3-8B-Base, it uses 25.6% of BF16 head storage while attaining 1.007 relative perplexity; storage-matched naive INT4 yields 1.14-1.16. Replacing the BF16 head left by AWQ or bitsandbytes adds only 0.006-0.007 cross-entropy, with less than 2% throughput change in our measurements. ARCHead therefore complements block quantizers by compressing the large output projection they can leave untouched. Code is available at https://github.com/suayptalha/archead.

Şuayp Talha Kocabay, Talha Rüzgar Akkuş, Kamer Ali Yuksel

Independent Researcher · aiXplain, Inc.

LLM Quantization LLM Compression Low-Rank Compression Weight-Only Quantization

Aug 1, 2026cs.CL

S $^4$ R: Selective Sampling, Subspaces, and Sparse Reconstruction for Compressed Long-Context KV Caching

The growth of context window lengths in Large Language Models (LLMs) significantly enhances their long-context capabilities but incurs prohibitive memory costs due to the Key-Value (KV) cache. Although low-rank compression of KV cache is a promising remedy, existing methods face a dilemma: offline approaches depend on external calibration data, whereas online approaches incur substantial compute for full-prompt decomposition and reconstruction. In this paper, we propose S

^4

R, which builds low-rank subspaces from selectively sampled tokens and computes attention over a sparsely reconstructed KV representation. S

^4

R uses prompt-aware initialization to build initial key/value bases from a representative prompt subset, trading off calibration-data dependence against prefilling cost. Because fully reconstructing the cache at every decoding step is prohibitively expensive and hurts throughput, we further adopt sparse reconstruction to retain only informative positions during decoding. Extensive experiments on LongBench and RULER with Llama and Qwen model families show that S

^4

R achieves up to 5

\times

KV compression with near full-cache accuracy, combining the efficiency of fixed compression with the adaptability of prompt-dependent methods.

Jialong Han, You Wu, Kewei Tu

School of Information Science and Technology, ShanghaiTech University · Shanghai Engineering Research Center of Intelligent Vision and Imaging

KV Caching Long-Context Language Model Inference Low-Rank Compression KV-Cache Compression

Jul 30, 2026cs.CL

Fidelity Is Not Safety: Gently-Compressed LLMs Pass Every Data-Free Quality Guard Yet Invent Procedure Steps in Agentic Execution

Practitioners accept a compressed language model once it clears a stack of data-cheap quality guards: perplexity within a small factor of the original, downstream accuracy (for example MMLU) inside a confidence interval, and data-free output-fidelity signals that compare the compressed and original network's internal representations under random probe inputs. This stack has a blind spot. Across three model families, gently-compressed models clear every guard and then invent procedure steps that were never in the instructions when they run a standard operating procedure (SOP) as an agent. The effect is operator-specific: coherent low-rank (SVD) truncation induces it, and magnitude pruning matched to the same perplexity does not. One dissociation isolates the cause. The same compressed weights that CI-win a paired output-fidelity test CI-fail the invented-step canary. The governing axis is the coherence of the compression error times its rate; the magnitude of the damage does not predict it. The data-free fidelity probe is a fidelity oracle by construction, so it cannot see this axis. We characterize the blindspot and dissociation with paired confidence intervals on a pre-registered, powered canary across three architectures. Operator-specificity replicates on all three, and the perplexity-guard evasion appears where the model admits in-guard low-rank headroom. We then give a data-free screen: a two-axis statistic of the compression error (coherent-fraction and error-rate) that flags the failing builds with fixed thresholds across architectures and matches the coherence-times-rate mechanism. Perplexity, MMLU, and fidelity acceptance do not certify agent safety. Screen gently-compressed low-rank builds before agentic deployment

I. Kennedy, T. Kennedy

Model Compression AI Agent Reliability LLM Compression Language Model Safety Evaluation LLM Agent Verification Low-Rank Compression+2

Jul 14, 2026cs.LG

A JoLT for the KV cache: Near-Lossless KV Cache Compression via Joint Rank-bit Allocation

The key-value (KV) cache is the dominant memory bottleneck in long-context language model inference. Existing compression methods apply low-rank factorization or quantization independently, without jointly allocating rank and precision under a shared storage budget. We introduce JoLT, a training-free compressor that treats grouped prefill caches as fourth-order tensors and applies partial Tucker decomposition along the token and feature modes, the two axes that carry low-rank structure, while leaving the head and layer modes intact. A rotated low-bit quantizer captures the truncation residual, and a single Lagrangian dual allocates per-group Tucker ranks and residual bit-widths under a global byte constraint. FlashJoLT replaces the exact token-mode SVD with a randomized approximation that matches JoLT within the free zone at a fraction of the compression cost, and a fused Triton decode kernel evaluates attention directly over the stored factors without materializing dense KV tensors. Across five models from four architecture families, covering multi-head attention, grouped-query attention, and mixture-of-experts architecture, JoLT achieves 2 - 3x compression with less than 0.2% perplexity degradation, without retraining. On RULER at 64K context with LLaMA-3.1-8B, retrieval accuracy remains near-lossless through 3x and declines by only 0.90 and 2.40pp at 4x and 5x, respectively. JoLT demonstrates that tensor-aware low-rank decomposition and quantized residuals, unified under a single storage budget, achieve near-lossless KV-cache compression across diverse model architectures without retraining.

Rahul Krishnan, Volker Schulz

Universität Trier · Fachbereich IV, Mathematik, Universität Trier

KV Caching Low-Rank Matrix Decomposition Tensor Decomposition Low-Rank Compression Low-Rank Approximation KV-Cache Compression+1

Jul 11, 2026cs.LG

CARE-LoRA: Compressed Activation REconstruction for Memory-Efficient LoRA

As the scale of large pre-trained models continues to grow, fine-tuning them under limited memory budgets has become increasingly challenging. Low-Rank Adaptation (LoRA), currently one of the most widely adopted parameter-efficient fine-tuning (PEFT) methods, mitigates this challenge by optimizing only low-rank adaptation matrices, thereby greatly reducing the number of trainable parameters. With the parameter overhead substantially reduced, the activations retained for backpropagation have emerged as the primary remaining memory bottleneck during LoRA fine-tuning. To address this, we propose CARE-LoRA, a data-aware Compressed Activation REconstruction framework. By exploiting the inherent projection structure of LoRA, CARE-LoRA replaces the full input activation with the low-rank compressed activation naturally produced by the LoRA branch. It further computes a lightweight reconstruction matrix during the forward pass with negligible additional computation cost, which is used during backpropagation to reconstruct the gradient signal, thereby keeping LoRA matrices fully trainable. Extensive experiments across diverse models and downstream tasks demonstrate that, while substantially reducing the overall memory footprint, CARE-LoRA achieves competitive or even superior performance compared with standard LoRA and representative LoRA variants. Our code is publicly available at https://github.com/fishandyu/CARE-LoRA .

Gengyu Zhang, Haiyin Ran, Zhengbao He +4

Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai 200240, China

Fine-Tuning Memory-Efficient Fine-Tuning LLM Fine-Tuning Low-Rank Adaptation Low-Rank Compression Neural Network Compression+1

Jul 9, 2026cs.LG

SLORR: Simple and Efficient In-Training Low-Rank Regularization

Low-rank factorization is widely used to compress neural networks, but modern models are often not naturally amenable to aggressive factorization without significant accuracy loss. Existing training-time low-rank regularizers can improve compressibility, but they often require SVDs of large weight matrices, modify the model architecture (introducing additional trainable parameters), or rely on stateful cached quantities. To address these limitations, we introduce SLORR, a simple, stateless, and architecture-preserving framework for in-training low-rank regularization, instantiated with two main variants based on the Hoyer sparsity metric and the nuclear norm. SLORR directly regularizes the original weight matrices using GPU-friendly approximations for the forward and backward passes of the regularizers, for which we provide approximation guarantees. We first evaluate SLORR on ImageNet-1K across short-horizon continued training of ResNet-50, ViT-B/16, and ViT-L/16, and pretraining of ResNet-18, where SLORR induces compressibility while introducing less than 8% training overhead. We further evaluate SLORR-Hoyer in LLM pretraining at 135M and 560M scales: SLORR-trained compressed models preserve performance substantially better than unregularized models while adding less than 1% average training overhead.

David González-Martínez, Shiwei Liu

Max Planck Institute for Intelligent Systems · University of Tübingen · ELLIS Institute Tübingen +1

LLM Compression Low-Rank Matrix Decomposition Nuclear Norm Minimization Low-Rank Compression Low-Rank Approximation Neural Network Compression

Jul 7, 2026cs.AI

DepthWeave-KV: Token-Adaptive Cross-Layer Residual Factorization for Long-Context KV Cache Compression

Long-context language model inference is increasingly limited by the memory bandwidth and capacity required to store key-value caches, yet existing compression methods often apply uniform budgets across layers or tokens and degrade retrieval when lexical cues and semantic states require different preservation. We introduce DepthWeave-KV, a token-adaptive cache compression method that factorizes key and value states across neighboring transformer layers using shared low-rank channel bases while retaining lightweight token-specific residuals where attention behavior is sensitive. DepthWeave-KV combines cross-depth residual factorization with a token-conditional depth router that allocates higher reconstruction rank to instruction-bearing and retrieval-critical tokens, and uses calibration-free online error tracking from attention-output probes to adapt compression during generation without retraining the base model. A fused CUDA implementation jointly performs basis lookup, residual dequantization, and attention projection to reduce decode-time memory traffic. Across LongBench, Needle-in-a-Haystack, L-Eval, and long-form QA and summarization benchmarks, DepthWeave-KV achieves near-full-cache task quality with substantially lower memory use, improving average score and retrieval accuracy over prior compressed caches while reaching 8.3x KV memory reduction and 72.8 tokens per second at 64K context.

Anna Cordoba, Adam Puente Tercero, Nerea Angulo Hijo +4

Instituto de Investigación en Visión Artificial

KV Caching Long-Context Language Model Inference Memory-Efficient Optimization LLM Inference Acceleration Low-Rank Compression KV-Cache Compression

Jul 5, 2026cs.LG

SAD-LoRA: Spectral Alignment for Low-Rank Knowledge Distillation

Distilling a fine-tuned teacher into a LoRA-adapted student is a standard recipe for parameter-efficient compression, but output-level KD does not explicitly control which rank-

r

weight subspace the adapter occupies. We propose \textbf{SAD-LoRA} (\textbf{S}pectral \textbf{A}lignment \textbf{D}istillation), which selects this subspace from the data-weighted student-space reference update

\DWT\Sigx^{1/2}

and maintains it during training via a differentiable principal-angle loss on

\colspan(B)

. We show that the data-weighted distillation error decomposes exactly into subspace misalignment, within-subspace coefficient mismatch, and irreducible rank residual; standard KD can affect the first term only indirectly through output gradients. On controlled synthetic problems with a flat teacher spectrum, SAD-LoRA reduces the subspace-misalignment term from

51\%

to nearly zero and lifts final subspace alignment from

0.49

to

1.00

. On RoBERTa-large to RoBERTa-base distillation across six GLUE tasks, SAD-LoRA improves rank efficiency: at

r{=}4

, it matches or beats the strongest included spectral baseline on five of six tasks, and at

r{=}8

it gives the best result on SST-2 and CoLA. Ablations identify subspace alignment as the load-bearing component, while coefficient matching is auxiliary.

Omer Tariq, Syed Muhammad Raza, Jeongbae Son

Neubility Inc, Seoul, South Korea

Low-Rank Adaptation Low-Rank Compression Language Model Distillation Knowledge Distillation

Jul 3, 2026cs.LG

LACE-SVD: Loss-Aware SVD with Cumulative Error Correction for LLM Compression

The rapid growth in the parameter scale of large language models (LLMs) has created a strong demand for efficient compression techniques. As a hardware-agnostic and highly compatible approach, low-rank compression has been widely adopted to reduce both memory footprint and computational cost. However, existing SVD-based methods are still largely driven by local reconstruction objectives, overlooking two critical limitations: rank budgets are often allocated without explicitly considering layer-wise loss sensitivity, and local approximation errors can propagate and accumulate through the residual stream, leading to amplified global deviations from the original model. To address these issues, we propose LACE-SVD, a Loss-Aware SVD framework with Cumulative Error correction for LLM compression. LACE-SVD first estimates the calibration negative-log-likelihood increase induced by candidate layer-wise compression ratios and solves a budget-constrained allocation problem to assign rank budgets. It then refines the compressed model with closed-form local updates and introduces a propagation-aware correction for residual-stream output modules, reducing layer-output discrepancy as a proxy for cumulative error propagation. Experimental results demonstrate that at a high compression ratio (0.6), the WikiText-2 PPL of our method on LLaMA-7B (32.57) is significantly better than that of Dobi-SVD (46.18).

Zhuowen Liu, Longkun Hao, Shiyu Feng +3

Zhuowen Liu1 · Longkun Hao2 · Shiyu Feng3 +3

Model Compression LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Low-Rank Approximation Singular Value Decomposition

Jun 27, 2026cs.LG

DLR: Zero-Inference-Cost Latent Residuals for Low-Rank Pre-Training

Large language models have driven recent progress in language and multimodal AI, yet pre-training them at scale is prohibitively expensive. Low-rank pre-training, which factorizes each weight matrix into a rank-r product to reduce both parameters and FLOPs, is a promising response but typically lags full-rank training in quality. We propose Duplicated Latent Residual (DLR), a training-only, parameter-free, foldable plug-in for low-rank pre-training. DLR augments the standard low-rank output Bz with a fixed structured residual alpha/sqrt(K) * Expand_K(z) that replicates each latent coordinate K = ceil(d_out/r) times across the output. With alpha fixed, DLR adds zero learnable parameters per layer; after training, it is absorbed into the up-projection in closed form, B* = B + alpha/sqrt(K) R^T, so deployment parameter count, FLOPs and memory match the underlying low-rank backbone exactly. Across LLaMA models from 60M to 7B parameters, DLR strengthens low-rank pre-training on C4 validation perplexity in most settings, with the clearest gains at 130M and above; folded checkpoints transfer cleanly to supervised fine-tuning on standard benchmarks.

Dong Wang, Wenwu Tang, Yun Cheng +1

Graz University of Technology, Austria · Swiss Data Science Center, Switzerland

Language Model Pretraining LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Matrix Factorization

Jun 22, 2026cs.LG

SVD-Surgeon: Optimal Singular-Value Surgery for Large Language Model Compression

Large language models (LLMs) achieve remarkable performance across a wide range of tasks, but their deployment is constrained by substantial memory and compute requirements. Low-rank compression via singular value decomposition (SVD) is an effective remedy, but existing methods focus on how to factorize and which components to keep. We introduce SVD-Surgeon, a training-free method that brings the Optimal Brain Surgeon (OBS) framework to the singular-value basis. Treating each singular value as a parameter, it computes a closed-form update of the retained singular values that compensates, to second order in the model loss, for those removed by truncation. The same analysis yields a saliency for choosing which values to prune. As it operates directly on the singular-value factorization, SVD-Surgeon can be layered on top of existing SVD compressors. Applied to SVD-LLM, a leading SVD-based method, it improves the perplexity-compression trade-off on the OPT family and LLaMA 2-7B without any retraining.

Mahmoud Safari, Frank Hutter

University of Freiburg · Prior Labs · ELLIS Institute Tübingen

LLM Pruning LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Low-Rank Approximation Singular Value Decomposition+1

Jun 20, 2026cs.LG

UniRank: Unified Rank Allocation for Low-Rank LLM Compression

Low-rank decomposition is a promising compression paradigm for large language models (LLMs), yet its effectiveness hinges on rank budget allocation across weight matrices: uniform or hand-crafted rules ignore module-wise importance, while learning-based allocation incurs substantial training overhead. We formulate rank allocation as a global sorting-and-truncation pipeline that scores every singular component by combining local singular energy with global functional importance, estimated via layer-wise input--output cosine similarity on a tiny calibration set. We show, both geometrically and empirically, that high input--output cosine similarity implies low effective rank. We further propose rank-preserving fine-tuning (RPFT), which adapts only a small subset of retained singular components so that the allocated rank stays bounded without re-decomposition. Experimental results show that UniRank cuts zero-shot perplexity by up to 50%, improves average reasoning accuracy by 3.0% over LoRAP at 25% sparsity, and boosts four SVD-based decomposition methods as a plug-and-play module.

Chao Han, Yongjie Du, Junjie Tan +1

Ningbo Institute of Digital Twin, Eastern Institute of Technology, Ningbo

LLM Compression Low-Rank Matrix Decomposition Low-Rank Compression Low-Rank Approximation Adaptive Rank Allocation

Jun 18, 2026cs.LG

Activation- and Influence-Aware Ranks (AIR): Function-Preserving SVD Compression for LLMs

We present Activation- and Influence-Aware Ranks (AIR), an SVD-based LLM compression framework that guides each weight matrix's low-rank approximation with a backward-signal influence metric. Starting from the activation-aware optimum of SVD-LLM(W), AIR runs a single closed-form alternating least squares (ALS) sweep that integrates influence element-wise under a monotone-descent guarantee. AIR is layer-local and composes orthogonally with end-to-end methods: alone it exceeds ACIP, and AIR+LoRA outperforms it further. AIR improves perplexity over SVD-LLM(W) by >18% at <=60% parameter retention, matches its quality with ~90% less calibration data, and turns parameter savings into FLOP, peak-memory, and per-token latency gains.

Nico Harder, Daniel Becking, Karsten Mueller +1

Fraunhofer HHI, Berlin, Germany

LLM Compression Low-Rank Matrix Decomposition LLM Inference Acceleration Low-Rank Compression Low-Rank Approximation Neural Network Compression