arXiv subjects

Yufa Zhou

Publications and source records attributed to Yufa Zhou.

21 records · Page 2Linked to original sources

arXiv2024

Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time

The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce the quadratic time complexity of computing the gradients in multi-layer transformer models? This paper proves that a novel fast approximation method can calculate the gradients in almost linear time $n^{1+o(1)}$ where $n$ is the input sequence length, while it maintains a polynomially small approximation error $1 / \mathrm{poly}(n)$ across the entire model. Our theory holds for general loss functions and when the multi-layer transformer model contains many practical sub-modules, such as residual connection, casual mask, and multi-head attention. By improving the efficiency of gradient computation, we hope that this work will facilitate more effective training and deployment of long-context language models based on our theoretical results.

cs.LG↗

arXiv2024

Differentially Private Attention Computation

Large language models (LLMs), especially those based on the Transformer architecture, have had a profound impact on various aspects of daily life, such as natural language processing, content generation, research methodologies, and more. Nevertheless, a crucial concern regarding the inference results of large language models is the issue of security and privacy. Given that large language models can generate results that may leak sensitive confidential or copyright information in many scenarios, it is crucial to compute the attention matrix with provable privacy guarantees, as attention is all you need. In this work, we propose a novel and efficient algorithm for approximating the attention matrix while providing differential privacy (DP) guarantees. To achieve this, we build on recent advancements in fast attention computation and differentially private matrix publishing.

cs.LG↗

arXiv2024

Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective

Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking. In this paper, we bridge this gap by providing a detailed examination of these smoothness properties for the case where the target data distribution is a mixture of Gaussians, which serves as a universal approximator for smooth densities such as image data. We prove that if the target distribution is a $k$-mixture of Gaussians, the density of the entire diffusion process will also be a $k$-mixture of Gaussians. We then derive tight upper bounds on the Lipschitz constant and second momentum that are independent of the number of mixture components $k$. Finally, we apply our analysis to various diffusion solvers, both SDE and ODE based, to establish concrete error guarantees in terms of the total variation distance and KL divergence between the target and learned distributions. Our results provide deeper theoretical insights into the dynamics of the diffusion process under common data distributions.

cs.LG↗