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LeSTD: LLM Compression via Learning-based Sparse Tensor Decomposition

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.5Download Report PDF
LLM CompressionPost-training CompressionTucker DecompositionSparsity
Abstract:

Large Language Models (LLMs) achieve remarkable success, but their massive parameter counts present significant deployment challenges. Post-training tensor decomposition offers a promising, data-free compression strategy by exploiting structural redundancies within the model weights. However, existing tensor methods face a critical limitation: the dense core tensor bottleneck. While these methods find a shared low-rank basis, the resulting dense core tensor grows polynomially with the chosen ranks, becoming a new storage bottleneck and capping the maximum achievable compression. To overcome this fundamental barrier, we introduce LeSTD (\textbf{Le}arning-based \textbf{S}parse \textbf{T}ensor \textbf{D}ecomposition), a novel two-stage framework for the high-ratio compression of Multi-Head Attention (MHA) blocks. LeSTD first employs an iterative algorithm to identify a high-quality, and shared orthogonal basis that jointly represents all attention heads. Subsequently, it introduces a principled, importance-based pruning algorithm that learns an ultra-sparse core tensor by systematically removing the least salient elements and refitting the remaining ones to preserve model fidelity. By decoupling basis optimization from core sparsification, LeSTD breaks the compression ceiling imposed by the dense core, enabling significantly higher compression ratios than prior methods.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces LeSTD, a two-stage framework for compressing Multi-Head Attention blocks via sparse tensor decomposition. It resides in the 'Tensor Decomposition with Sparsity' leaf, which contains three papers total, suggesting a moderately sparse research direction within the broader hybrid compression landscape. The taxonomy tree reveals that while tensor decomposition methods are well-explored (six subcategories under 'Tensor Decomposition Methods'), the specific integration of sparsity into tensor factorizations remains less crowded, with LeSTD positioned alongside only two sibling works focused on augmenting tensor decompositions with sparse constraints.

The taxonomy structure shows that LeSTD's leaf sits within 'Hybrid Low-Rank and Sparse Methods', which itself contains four subcategories addressing different combinations of rank reduction and sparsity. Neighboring leaves include 'Joint Low-Rank and Sparse Approximation' (matrix-level methods like LoSparse) and 'Activation-Aware Sparse Low-Rank Decomposition', both of which operate on matrix factorizations rather than higher-order tensors. The exclude notes clarify that LeSTD's tensor-based approach distinguishes it from these matrix-centric hybrid methods, while its sparsity focus separates it from pure tensor decomposition branches like 'Tucker and Block-Term Tensor Decomposition' or 'Tensor Train and Tensor Ring Decomposition'.

Among twenty candidates examined, the contribution-level analysis reveals mixed novelty signals. The two-stage compression design (Contribution 1) shows no clear refutation across nine candidates, suggesting relative novelty in the overall framework architecture. However, the closed-form importance score for core tensor pruning (Contribution 2) and direct inference without reconstruction (Contribution 3) each face one refutable candidate among limited samples. The scale of this search—twenty papers from semantic matching—means these findings indicate potential overlaps within a focused neighborhood rather than definitive verdicts across the entire field.

Given the limited search scope, LeSTD appears to occupy a moderately novel position within a less saturated hybrid compression direction. The framework-level design shows stronger novelty signals than individual technical components, which face some prior work overlap in the examined candidate set. The taxonomy context suggests that while tensor-sparsity hybrids remain an active but not overcrowded area, the specific techniques for pruning and inference may draw on established principles from neighboring matrix-based hybrid methods.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
20
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: LLM compression via sparse tensor decomposition. The field organizes around several complementary strategies for reducing the memory and computational footprint of large language models. Low-Rank Decomposition Methods such as ASVD[1] and SVD-LLM[3] factorize weight matrices into smaller components, while Tensor Decomposition Methods like Tensorized Transformer[18] and TT-LoRA[49] exploit higher-order structure to achieve more aggressive compression. Hybrid Low-Rank and Sparse Methods combine both paradigms, and Sparsity-Based Compression Methods focus on pruning or structured sparsity patterns. Meanwhile, KV Cache Compression Methods target inference-time memory bottlenecks, Hardware-Aware and Deployment-Oriented Methods optimize for specific accelerators, and Theoretical and Methodological Frameworks provide foundational analysis. Together, these branches reflect a spectrum from purely algebraic factorizations to hardware-conscious implementations, with hybrid approaches bridging the gap between rank reduction and sparsity. Recent work has intensified around hybrid strategies that merge low-rank factorization with sparsity constraints, aiming to capture the benefits of both worlds. For instance, methods like LoSparse[20] and LOST[21] integrate sparse patterns into low-rank updates, while DOTA[5] and SVD-LLM V2[4] refine decomposition techniques with adaptive rank selection. Within this landscape, LeSTD[0] sits squarely in the Tensor Decomposition with Sparsity cluster, emphasizing the use of sparse tensor factorizations to compress model parameters. Compared to neighbors like Sparse Low Rank[11] and Parameter Sharing Tensor[27], LeSTD[0] places greater emphasis on leveraging tensor structure rather than simple matrix factorization, potentially offering more compact representations at the cost of increased algorithmic complexity. The central trade-off across these hybrid methods remains balancing compression ratio, accuracy retention, and computational overhead during both training and inference.

Claimed Contributions

LeSTD framework with two-stage compression design

The authors propose LeSTD, a novel two-stage post-training compression framework that first learns a shared orthonormal subspace for all attention heads via iterative Tucker decomposition (Stage I), then applies importance-based pruning to create an ultra-sparse core tensor (Stage II), thereby breaking the dense core bottleneck of existing tensor decomposition methods.

9 retrieved papers
Closed-form importance score for core tensor pruning

The authors derive a theoretically grounded, closed-form importance metric that quantifies how each core tensor element affects reconstruction error. This enables principled magnitude-based pruning in the orthonormal latent space rather than relying on heuristics.

1 retrieved paper
Can Refute
Direct inference in compressed domain without reconstruction

The authors develop an inference procedure that executes all multi-head attention computations directly using the shared factor matrices and sparse core tensor, eliminating the need to materialize the original dense weight matrices and thereby reducing both storage and computational costs.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

LeSTD framework with two-stage compression design

The authors propose LeSTD, a novel two-stage post-training compression framework that first learns a shared orthonormal subspace for all attention heads via iterative Tucker decomposition (Stage I), then applies importance-based pruning to create an ultra-sparse core tensor (Stage II), thereby breaking the dense core bottleneck of existing tensor decomposition methods.

Contribution

Closed-form importance score for core tensor pruning

The authors derive a theoretically grounded, closed-form importance metric that quantifies how each core tensor element affects reconstruction error. This enables principled magnitude-based pruning in the orthonormal latent space rather than relying on heuristics.

Contribution

Direct inference in compressed domain without reconstruction

The authors develop an inference procedure that executes all multi-head attention computations directly using the shared factor matrices and sparse core tensor, eliminating the need to materialize the original dense weight matrices and thereby reducing both storage and computational costs.

Table of Contents