In this work, we present a generalized formulation of the Transformer algorithm by reinterpreting its core mechanisms within the framework of Path Integral formalism. In this perspective, the attention mechanism is recast as a process that integrates all possible transition paths leading to future token states, with temporal evolution governed by the Feed-Forward Network. By systematically mapping each component of the Transformer to its counterpart in the Path Integral formulation, we obtain a more compact and efficient representation, in which the contextual information of a sequence is condensed into memory-like segments. These segments are recurrently processed across Transformer layers, enabling more effective long-term information retention. We validate the effectiveness of this approach through the Passkey retrieval task and a summarization task, demonstrating that the proposed method preserves historical information while exhibiting memory usage that scales linearly with sequence length. This contrasts with the non-linear memory growth typically observed in standard attention mechanisms. We expect that this quantum-inspired generalization of the Transformer architecture will open new avenues for enhancing both the efficiency and expressiveness of future Transformer models.
View on arXiv@article{paeng2025_2405.04620,
title={ Folded Context Condensation in Path Integral Formalism for Infinite Context Transformers },
author={ Won-Gi Paeng and Daesuk Kwon and Kyungwon Jeong and Honggyo Suh },
journal={arXiv preprint arXiv:2405.04620},
year={ 2025 }
}