# How can representation dimension dominate structurally pruned LLMs?

arXiv: https://arxiv.org/abs/2503.04377 · HTML: https://mlsanity.com/paper/2503.04377/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [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)
- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [Scaling Laws for Sparsely-Connected Foundation Models](https://mlsanity.com/paper/2309.08520/) (2023)
- [Geometry is All You Need: A Unified Taxonomy of Matrix and Tensor Factorization for Compression of Generative Language Models](https://mlsanity.com/paper/2410.03040/) (2024)

## Abstract (arXiv)

Pruning assumes a subnetwork exists in the original deep neural network, which can achieve comparative model performance with less computation than the original. However, it is unclear how the model performance varies with the different subnetwork extractions. In this paper, we choose the representation dimension (or embedding dimension, model dimension, the dimension of the residual stream in the relevant literature) as the entry point to this issue. We investigate the linear transformations in the LLM transformer blocks and consider a specific structured pruning approach, SliceGPT, to extract the subnetworks of different representation dimensions. We mechanistically analyse the activation flow during the model forward passes, and find the representation dimension dominates the linear transformations, model predictions, and, finally, the model performance. Explicit analytical relations are given to calculate the pruned model performance (perplexity and accuracy) without actual evaluation, and are empirically validated with Llama-3-8B-Instruct and Phi-3-mini-4k-Instruct.