Extracting Finite State Machines from Transformers

• URL: http://arxiv.org/abs/2410.06045v1
• Date: Tue, 8 Oct 2024 13:43:50 GMT
• Title: Extracting Finite State Machines from Transformers
• Authors: Rik Adriaensen, Jaron Maene,
• Abstract summary: We investigate the trainability of transformers trained on regular languages from a mechanistic interpretability perspective. We empirically find tighter lower bounds on the trainability of transformers, when a finite number of symbols determine the state. Our mechanistic insight allows us to characterise the regular languages a one-layer transformer can learn with good length generalisation.
• Score: 0.3069335774032178
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fueled by the popularity of the transformer architecture in deep learning, several works have investigated what formal languages a transformer can learn. Nonetheless, existing results remain hard to compare and a fine-grained understanding of the trainability of transformers on regular languages is still lacking. We investigate transformers trained on regular languages from a mechanistic interpretability perspective. Using an extension of the $L^*$ algorithm, we extract Moore machines from transformers. We empirically find tighter lower bounds on the trainability of transformers, when a finite number of symbols determine the state. Additionally, our mechanistic insight allows us to characterise the regular languages a one-layer transformer can learn with good length generalisation. However, we also identify failure cases where the determining symbols get misrecognised due to saturation of the attention mechanism.

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