Circuit Complexity Bounds for Visual Autoregressive Model

TL;DR

This paper establishes circuit complexity bounds for the Visual AutoRegressive (VAR) model, revealing its limitations in expressive power despite high performance in image generation tasks.

Contribution

It provides the first rigorous circuit complexity bounds for VAR models, linking them to uniform TC^0 threshold circuits and highlighting their expressive limitations.

Findings

VAR model is equivalent to a uniform TC^0 threshold circuit with certain parameters

First rigorous complexity bounds for VAR models

Highlights inherent limitations in VAR's expressive power

Abstract

Understanding the expressive ability of a specific model is essential for grasping its capacity limitations. Recently, several studies have established circuit complexity bounds for Transformer architecture. Besides, the Visual AutoRegressive (VAR) model has risen to be a prominent method in the field of image generation, outperforming previous techniques, such as Diffusion Transformers, in generating high-quality images. We investigate the circuit complexity of the VAR model and establish a bound in this study. Our primary result demonstrates that the VAR model is equivalent to a simulation by a uniform $\mathsf{TC}^0$ threshold circuit with hidden dimension $d \leq O(n)$ and $\mathrm{poly}(n)$ precision. This is the first study to rigorously highlight the limitations in the expressive power of VAR models despite their impressive performance. We believe our findings will offer valuable insights into the inherent constraints of these models and guide the development of more efficient and expressive architectures in the future.