# AlphaPruning: Using Heavy-Tailed Self Regularization Theory for Improved Layer-wise Pruning of Large Language Models

arXiv: https://arxiv.org/abs/2410.10912 · HTML: https://mlsanity.com/paper/2410.10912/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 79 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 30 of 63)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)

## Built on by (most cited first, 30 of 36)

- [The Curse of Depth in Large Language Models](https://mlsanity.com/paper/2502.05795/) (2025)
- [Flow caching for autoregressive video generation](https://mlsanity.com/paper/2602.10825/) (2026)
- [Demystifying the Roles of LLM Layers in Retrieval, Knowledge, and Reasoning](https://mlsanity.com/paper/2510.02091/) (2025)
- [When Reasoning Meets Compression: Understanding the Effects of LLMs Compression on Large Reasoning Models](https://mlsanity.com/paper/2504.02010/) (2025)
- [AlphaDecay: Module-wise Weight Decay for Heavy-Tailed Balancing in LLMs](https://mlsanity.com/paper/2506.14562/) (2025)
- [LayerIF: Estimating Layer Quality for Large Language Models using Influence Functions](https://mlsanity.com/paper/2505.23811/) (2025)
- [ProxSparse: Regularized Learning of Semi-Structured Sparsity Masks for Pretrained LLMs](https://mlsanity.com/paper/2502.00258/) (2025)
- [Models of Heavy-Tailed Mechanistic Universality](https://mlsanity.com/paper/2506.03470/) (2025)
- [EvoESAP: Non-Uniform Expert Pruning for Sparse MoE](https://mlsanity.com/paper/2603.06003/) (2026)
- [AbbIE: Autoregressive Block-Based Iterative Encoder for Efficient Sequence Modeling](https://mlsanity.com/paper/2507.08567/) (2025)
- [DLP: Dynamic Layerwise Pruning in Large Language Models](https://mlsanity.com/paper/2505.23807/) (2025)
- [Pivoting Factorization: A Compact Meta Low-Rank Representation of Sparsity for Efficient Inference in Large Language Models](https://mlsanity.com/paper/2501.19090/) (2025)
- [Dynamic Sparse Training of Diagonally Sparse Networks](https://mlsanity.com/paper/2506.11449/) (2025)
- [PATCH: Learnable Tile-level Hybrid Sparsity for LLMs](https://mlsanity.com/paper/2509.23410/) (2025)
- [ARA: Adaptive Rank Allocation for Efficient Large Language Model SVD Compression](https://mlsanity.com/paper/2510.19389/) (2025)
- [One LR Doesn't Fit All: Heavy-Tail Guided Layerwise Learning Rates for LLMs](https://mlsanity.com/paper/2605.22297/) (2026)
- [Emergent Specialization: Rare Token Neurons in Language Models](https://mlsanity.com/paper/2505.12822/) (2025)
- [Leave it to the Specialist: Repair Sparse LLMs with Sparse Fine-Tuning via Sparsity Evolution](https://mlsanity.com/paper/2505.24037/) (2025)
- [RCPU: Rotation-Constrained Error Compensation for Structured Pruning of Large Language Models](https://mlsanity.com/paper/2510.07782/) (2025)
- [Layer Collapse in Diffusion Language Models](https://mlsanity.com/paper/2605.06366/) (2026)
- [TRIM: Achieving Extreme Sparsity with Targeted Row-wise Iterative Metric-driven Pruning](https://mlsanity.com/paper/2505.16743/) (2025)
- [Distributed Specialization: Rare-Token Neurons in Large Language Models](https://mlsanity.com/paper/2509.21163/) (2025)
- [ActTail: Global Activation Sparsity in Large Language Models](https://mlsanity.com/paper/2603.12272/) (2026)
- [Adaptive Pruning for Large Language Models with Structural Importance Awareness](https://mlsanity.com/paper/2412.15127/) (2024)
- [EGGS-PTP: An Expander-Graph Guided Structured Post-training Pruning Method for Large Language Models](https://mlsanity.com/paper/2508.09471/) (2025)
- [SHUFFLESPARSE: Learned Shuffles for Structured Sparse Networks](https://mlsanity.com/paper/2510.14812/) (2025)
- [TensorCommitments: A Lightweight Verifiable Inference for Language Models](https://mlsanity.com/paper/2602.12630/) (2026)
- [A Replicate-and-Quantize Strategy for Plug-and-Play Load Balancing of Sparse Mixture-of-Experts LLMs](https://mlsanity.com/paper/2602.19938/) (2026)
- [Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization](https://mlsanity.com/paper/2603.00910/) (2026)
- [Structural Sensitivity in Compressed Transformers: Relative Error Propagation and Layer Removal](https://mlsanity.com/paper/2603.20991/) (2026)

## Abstract (arXiv)

Recent work on pruning large language models (LLMs) has shown that one can eliminate a large number of parameters without compromising performance, making pruning a promising strategy to reduce LLM model size. Existing LLM pruning strategies typically assign uniform pruning ratios across layers, limiting overall pruning ability; and recent work on layerwise pruning of LLMs is often based on heuristics that can easily lead to suboptimal performance. In this paper, we leverage Heavy-Tailed Self-Regularization (HT-SR) Theory, in particular the shape of empirical spectral densities (ESDs) of weight matrices, to design improved layerwise pruning ratios for LLMs. Our analysis reveals a wide variability in how well-trained, and thus relatedly how prunable, different layers of an LLM are. Based on this, we propose AlphaPruning, which uses shape metrics to allocate layerwise sparsity ratios in a more theoretically principled manner. AlphaPruning can be used in conjunction with multiple existing LLM pruning methods. Our empirical results show that AlphaPruning prunes LLaMA-7B to 80% sparsity while maintaining reasonable perplexity, marking a first in the literature on LLMs. We have open-sourced our code at https://github.com/haiquanlu/AlphaPruning.