# Folded Context Condensation in Path Integral Formalism for Infinite Context Transformers

arXiv: https://arxiv.org/abs/2405.04620 · HTML: https://mlsanity.com/paper/2405.04620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 7 May 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Efficient Attention: Attention with Linear Complexities](https://mlsanity.com/paper/1812.01243/) (2018)
- [Leave No Context Behind: Efficient Infinite Context Transformers with Infini-attention](https://mlsanity.com/paper/2404.07143/) (2024)
- [Analogy between Boltzmann machines and Feynman path integrals](https://mlsanity.com/paper/2301.06217/) (2023)

## Abstract (arXiv)

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.