On Computational Limits and Provably Efficient Criteria of Visual
  Autoregressive Models: A Fine-Grained Complexity Analysis
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.
6780a7fdaf887f31d643cb55
Yekun Ke
admin_assigned
2025-01-10T08:26:56.992Z
6600cb94e95908a2a60f3abd
/avatars/82cdb1ef4ab4caacfa8d9f4c4f538222.svg
keyekun
user
keyekun
6780a7fdaf887f31d643cb56
Xiaoyu Li
6780a7fdaf887f31d643cb57
Yingyu Liang
6780a7fdaf887f31d643cb58
Zhizhou Sha
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2025-01-10T08:26:20.704Z
6335604ea01bd734f72316b0
/avatars/4c6611dabd492106ffb2e82fd680d983.svg
Zhizhou Sha
user
JamesSand
6780a7fdaf887f31d643cb59
Zhenmei Shi
admin_assigned
2025-01-10T08:26:12.739Z
64b769d7fa7eabaae5fb7f2f
https://cdn-avatars.huggingface.co/v1/production/uploads/64b769d7fa7eabaae5fb7f2f/AbxVphanApZDfj3cOI1tb.jpeg
Zhenmei Shi
user
Zhenmei
6780a7fdaf887f31d643cb5a
Zhao Song
On Computational Limits and Provably Efficient Criteria of Visual
  Autoregressive Models: A Fine-Grained Complexity Analysis
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.
Analysis of Visual Autoregressive (VAR) models identifies conditions for sub-quadratic time complexity and presents efficient constructions using low-rank approximations, advancing scalable image generation.
Visual Autoregressive VAR next-scale prediction quadratic time Strong Exponential Time Hypothesis SETH fine-grained complexity low-rank approximations