On Computational Limits and Provably Efficient Criteria of Visual Autoregressive Models: A Fine-Grained Complexity Analysis

• URL: http://arxiv.org/abs/2501.04377v2
• Date: Sun, 02 Feb 2025 23:48:36 GMT
• Title: On Computational Limits and Provably Efficient Criteria of Visual Autoregressive Models: A Fine-Grained Complexity Analysis
• Authors: Yekun Ke, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song,
• Abstract summary: We analyze the computational limits and efficiency criteria of Visual Autoregressive ($mathsf/$) Models. We prove that assuming the Strong Exponential Time Hypothesis ($mathsfSETH$) from fine-grained complexity theory, a sub-quartic time algorithm for $mathsf/$ models is impossible. Our technique will shed light on advancing scalable and efficient image generation in $mathsf/$ frameworks.
• Score: 22.641550077885686
• License:
• Abstract: Recently, Visual Autoregressive ($\mathsf{VAR}$) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine ``next-scale prediction'' paradigm. Suppose that $n$ represents the height and width of the last VQ code map generated by $\mathsf{VAR}$ models, the state-of-the-art algorithm in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes $O(n^{4+o(1)})$ time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of $\mathsf{VAR}$ Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which $\mathsf{VAR}$ computations can achieve sub-quadratic time complexity. We have proved that assuming the Strong Exponential Time Hypothesis ($\mathsf{SETH}$) from fine-grained complexity theory, a sub-quartic time algorithm for $\mathsf{VAR}$ 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 $\mathsf{VAR}$ model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in $\mathsf{VAR}$ frameworks.

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