Circuit Complexity Bounds for Visual Autoregressive Model
Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhenmei Shi, Zhao Song
TL;DR
The paper analyzes the circuit complexity of Visual AutoRegressive (VAR) models, showing that VARs admit a uniform $\mathsf{TC}^0$ circuit representation with poly$(n)$ size and $O(1)$ depth when the precision is $\mathrm{poly}(n)$. By decomposing VAR into three phases—Phase 1: VAR Transformer, Phase 2: Feature Map Reconstruction, and Phase 3: VQ-VAE Decoder—the authors construct TC$^0$ simulations for upsampling, attention, MLP/LN, convolutions, and decoder components. The main result establishes that VAR cannot exceed the expressive power of $\mathsf{TC}^0$ under these resource bounds, highlighting inherent limitations despite strong empirical performance. These insights offer a rigorous baseline for understanding efficiency and guiding the design of future, more expressive visual-generation architectures.
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.