AttentionX: Exploiting Consensus Discrepancy In Attention from A Distributed Optimization Perspective

TL;DR

AttentionX introduces a novel way to enhance transformer attention by integrating consensus discrepancy inspired by distributed optimization, leading to improved performance on vision and language models.

Contribution

It extends standard Attention by incorporating consensus discrepancy inspired by PDMM, a distributed optimization method, to improve transformer performance.

Findings

Promising results on ViT and nanoGPT benchmarks.

Enhanced attention mechanism improves model convergence.

Demonstrates the effectiveness of distributed optimization concepts in transformers.

Abstract

In this paper, we extend the standard Attention in transformer by exploiting the consensus discrepancy from a distributed optimization perspective, referred to as AttentionX. It is noted that the primal-dual method of multipliers (PDMM) \cite{Zhang16PDMM} is designed to iteratively solve a broad class of distributed optimization problems over a pear-to-pear (P2P) network, where neighbouring nodes gradually reach consensus as specified by predefined linear edge-constraints in the optimization process. In particular, at each iteration of PDMM, each node in a network first performs information-gathering from neighbours and then performs local information-fusion. From a high-level point of view, the $KQ$-softmax-based weighted summation of $V$-representations in Attention corresponds information-gathering from neighbours while the feature-processing via the feed-forward network (FFN) in transformer corresponds to local information fusion. PDMM exploits the Lagrangian multipliers to capture the historical consensus discrepancy in the form of residual errors of the linear edge-constraints, which plays a crucial role for the algorithm to converge. Inspired by PDMM, we propose AttentionX to incorporate the consensus discrepancy in the output update-expression of the standard Attention. The consensus discrepancy in AttentionX refers to the difference between the weighted summation of $V$-representations and scaled $V$-representions themselves. Experiments on ViT and nanoGPT show promising performance.