Zigzag Persistence of Large Language Models Representations
Abstract
We analyze internal representations of large language models with zigzag persistent homology, treating depth as a discrete time axis for point clouds of last-token embeddings. At each layer we build a k-nearest-neighbors clique complex, connect adjacent layers via intersections, and summarize the resulting diagrams with effective persistence images. From these we derive two descriptors: Births’ Relative Frequency (at what rate new p-dimensional features appear) and Inter-Layer Persistence (how long they survive across depth). On the SST movie reviews dataset and three open-source models (Llama-3.1, OSS-20B, Phi-4), we consistently observe three evolving phases: early rapid changes, a middle regime of stable organization, and a final reorganization before output. Using the stability signal (inter-layer persistence) to guide where to remove contiguous blocks of layers, we find that pruning within high-persistence regions maintains 5-shot MMLU performance (with the same trend visible even for the more pruning-sensitive OSS-20B). This suggests that zigzag-based summaries capture meaningful, system-level dynamics and can inform lightweight pruning.
Authors
Yuri Gardinazzi, Karthik Viswanathan, Giada Panerai, Alessio Ansuini, Alberto Cazzaniga, Matteo Biagetti
Journal
Proceedings of Machine Learning Research (PMLR) 2025
Publication Date
01/06/2026