# LaMoC: Loss-Aware Modular Compression for LLMs

arXiv: https://arxiv.org/abs/2608.30226 · HTML: https://mlsanity.com/paper/2608.30226/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [You Only Prune Once: Designing Calibration-Free Model Compression With Policy Learning](https://mlsanity.com/paper/2501.15296/) (2025)
- [SAES-SVD: Self-Adaptive Suppression of Accumulated and Local Errors for SVD-based LLM Compression](https://mlsanity.com/paper/2602.03051/) (2026)
- [A3 : an Analytical Low-Rank Approximation Framework for Attention](https://mlsanity.com/paper/2505.12942/) (2025)
- [LatentLLM: Attention-Aware Joint Tensor Compression](https://mlsanity.com/paper/2505.18413/) (2025)
- [DuoGPT: Training-free Dual Sparsity through Activation-aware Pruning in LLMs](https://mlsanity.com/paper/2506.20194/) (2025)
- [UniQL: Unified Quantization and Low-rank Compression for Adaptive Edge LLMs](https://mlsanity.com/paper/2512.03383/) (2025)
- [Understanding Calibration and Truncation Error Propagation in Training-Free Low-Rank Compression for LLMs](https://mlsanity.com/paper/2608.08506/) (2026)

## Abstract (arXiv)

Modular compression has enabled considerable parameter reduction in LLMs while preserving strong language understanding and downstream task accuracy. However, existing joint modular compression methods primarily rely on activation statistics, leaving loss-sensitivity information and its module-level characterization underexplored. We investigate addressing this gap with LaMoC, a loss-aware modular compression methodology that blends activation and Empirical Fisher statistics through gradient-error alignment. LaMoC improves joint compression by selecting compression statistics that better align local module reconstruction error with the downstream loss. Our contributions are three-fold: (1) We characterize the Empirical Fisher as a module-level loss-aware proxy that can be blended with the activation statistics required for compression. (2) We reformulate joint modular compression as a two-tiered optimization problem that minimizes module reconstruction error while tuning the activation and gradient information blending rate. (3) We implement an empirically driven methodology with statistical validation to solve the resulting compression problem. We evaluate LaMoC across four model families spanning eight models. On the 4-8B models, LaMoC achieves an average 2.5% reduction in perplexity and a 1% relative improvement in task accuracy over state-of-the-art modular compression methods.