Title: Circuit Complexity Bounds for Visual Autoregressive Model
Primary area: generative models
Keywords: generative models, complexity

Abstract: Understanding the expressive ability of a specific model is essential for grasping its capacity limitations. A recent breakthrough in image generation is the introduction of Visual Autoregressive ($\mathsf{VAR}$) Models, which employ a scalable coarse-to-fine "next-scale prediction" framework. 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 $d$ and $\mathrm{poly}(d)$ 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.