# Increasing Skill Level Recruits Deeper Attention Layers in a Frozen Chess Transformer

arXiv: https://arxiv.org/abs/2609.23917 · HTML: https://mlsanity.com/paper/2609.23917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Acquisition of Chess Knowledge in AlphaZero](https://mlsanity.com/paper/2111.09259/) (2021)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Emergent World Models and Latent Variable Estimation in Chess-Playing Language Models](https://mlsanity.com/paper/2403.15498/) (2024)
- [Evidence of Learned Look-Ahead in a Chess-Playing Neural Network](https://mlsanity.com/paper/2406.00877/) (2024)
- [Maia-2: A Unified Model for Human-AI Alignment in Chess](https://mlsanity.com/paper/2409.20553/) (2024)
- [Chessformer: A Unified Architecture for Chess Modeling](https://mlsanity.com/paper/2605.19091/) (2026)
- [What Affects the Effective Depth of Large Language Models?](https://mlsanity.com/paper/2512.14064/) (2025)

## Abstract (arXiv)

Chess involves complex reasoning in a deterministic environment, which makes it a useful setting for studying the mechanisms of computation inside transformers. The Maia-3 chess transformer takes Elo, a measure of competitive chess skill, as an input to the pre-trained network, so we can vary the skill the network is conditioned on with no change to its weights. Here we investigate how turning this skill dial affects self-attention. Ablating every attention head at every Elo from 700 to 2500, we find 1) increasing skill pushes the causal center of mass of the computation deeper, monotonically, for every chess piece and move type we measured; 2) the depth migration is much greater for specific tactics, especially knight forks, than for other move types; 3) the migration consists of deeper heads getting recruited for more specialized computations while one shared shallow head keeps a roughly constant contribution. These results may shed light on how conditioning inputs redistribute computation in larger transformers.