# Looking Inside LLMs: Small-World Connectivity as a Signature of Reasoning Performance

arXiv: https://arxiv.org/abs/2610.12304 · HTML: https://mlsanity.com/paper/2610.12304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Determining Layer-wise Sparsity for Large Language Models Through a Theoretical Perspective](https://mlsanity.com/paper/2502.14770/) (2025)
- [Eigenspectrum Analysis of Neural Networks without Aspect Ratio Bias](https://mlsanity.com/paper/2506.06280/) (2025)
- [Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2312.05840/) (2023)
- [Truly Assessing Fluid Intelligence of Large Language Models through Dynamic Reasoning Evaluation](https://mlsanity.com/paper/2506.02648/) (2025)

## Abstract (arXiv)

Understanding large language model (LLM) reasoning requires looking beyond behavioral performance to examine how reasoning ability is reflected in internal organization. Inspired by neuroscience findings linking higher intelligence to stronger small-world organization in functional brain networks, we investigate small-world connectivity as a structural signature of LLM reasoning. We construct functional graphs from attention-head activation similarities and find that a higher small-world index (SWI), capturing local clustering and short global paths, consistently correlates with better fluid reasoning performance across models and training checkpoints. Since local clustering is central to small-world organization, we further examine how heads important for model performance connect within and across communities. We find that these heads tend to have a larger share of connection weight within their own communities (high core scores) and a more concentrated weight distribution across communities (low bridge scores). These observations motivate the hypothesis that high core and low bridge scores serve as structural indicators of head importance for reasoning capability. We validate this hypothesis through pruning, introducing Small-World Allocation (SWA), a hierarchical sparsity allocation method guided by these scores. Across six LLMs, SWA better preserves small-world organization and model performance than competing allocation strategies, reducing WikiText perplexity by up to 20%. Together, these findings identify small-world functional connectivity as a measurable signature of LLM reasoning performance, offering a structural perspective that complements behavioral evaluation.