## Transformers and Tropical Algebra: A New Perspective A recent study has demonstrated that the self-attention mechanism of Transformers, a fundamental pillar in natural language processing, can be interpreted through tropical algebra, specifically in the high-confidence regime. This discovery offers a new geometric perspective on the inner workings of these models. The research highlights how softmax attention, a key component of Transformers, transforms into a tropical matrix product. This implies that the Transformer's forward pass executes a dynamic programming algorithm, specifically a variant of the Bellman-Ford algorithm for finding the shortest path, on a latent graph determined by the similarities between tokens. ## Implications for Chain-of-Thought Reasoning This geometric interpretation suggests that chain-of-thought reasoning, a technique that enhances the reasoning abilities of language models, inherently emerges from the execution of a shortest-path (or longest-path) algorithm within the model's computation. In other words, the Transformer, in its processing, searches for the optimal path through the information, simulating a structured thought process. Transformers have revolutionized the field of artificial intelligence, finding application in various fields, from machine translation to text generation. Thoroughly understanding the internal mechanisms of these models is crucial for developing even more efficient and powerful architectures.