相关论文: The Mean-Field Dynamics of Transformers

The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform…

We model the evolution of tokens within a deep stack of Transformer layers as a continuous-time flow on the unit sphere, governed by a mean-field interacting particle system, building on the framework introduced in (Geshkovski et al.,…

Transformers perform inference by iteratively transforming token representations across layers. This layerwise computation has been studied empirically, and recent mean-field theories of Transformer dynamics explain how attention can drive…

The evolution of tokens through deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to the synchronization phenomenon in Kuramoto models. In this…

Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of…

Transformers are extremely successful machine learning models whose mathematical properties remain poorly understood. Here, we rigorously characterize the behavior of transformers with hardmax self-attention and normalization sublayers as…

The forward pass of a Transformer can be seen as an interacting particle system on the unit sphere: time plays the role of layers, particles that of token embeddings, and the unit sphere idealizes layer normalization. In some weight…

Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens. This representation is then exploited by the attention function, which learns dependencies between tokens and…

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at…

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Transformer self-attention can be interpreted as a gradient flow on the unit sphere, in which tokens evolve under softmax interaction potentials and tend to form clusters. While prior work has established clustering behavior for single-head…

Transformers have emerged as a powerful neural network architecture capable of tackling a wide range of learning tasks. In this work, we provide a theoretical analysis of their ability to automatically extract structure from data in an…

We study the effect of normalization schemes on token representations in deep transformers. Modeling their evolution as interacting particles on the sphere, we show that normalization acts as a form of speed regulation. This perspective…

Transformer-based models have achieved remarkable success across a wide range of domains, yet our understanding of their training dynamics remains limited. In this work, we identify a recurrent focus-dilution cycle in attention learning and…

In this paper, we study the evolution of tokens through the depth of encoder-only transformer models at inference time by modeling them as a system of particles interacting in a mean-field way and studying the corresponding dynamics. More…

Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that…

This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…

We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the…

Viewing Transformers as interacting particle systems, we describe the geometry of learned representations when the weights are not time dependent. We show that particles, representing tokens, tend to cluster toward particular limiting…

This research endeavors to offer insights into unlocking the further potential of transformer-based architectures. One of the primary motivations is to offer a geometric interpretation for the attention mechanism in transformers. In our…