On Computational Limits and Provably Efficient Criteria of Visual Autoregressive Models: A Fine-Grained Complexity Analysis
Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song
2025-01-10
Summary
This paper talks about finding ways to make a new type of AI for creating images, called Visual Autoregressive (VAR) Models, work faster and more efficiently.
What's the problem?
The current best VAR model is very slow, taking a time that grows really fast as the image size increases (specifically, it grows with the fourth power of the image size). This makes it impractical for larger images or real-time applications.
What's the solution?
The researchers did a detailed math analysis to figure out when VAR models can be made to run faster. They found a specific point where the math used in VAR becomes too complex to speed up beyond a certain level. They also came up with some clever math tricks to make VAR run faster in certain situations.
Why it matters?
This research matters because it helps us understand the limits of how fast we can make these AI image generators work. By knowing these limits and finding ways to work around them, we can create AI that makes high-quality images more quickly. This could lead to better and faster tools for things like creating video game graphics, special effects in movies, or even helping artists and designers in their work.
Abstract
Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.