Qiao-Chu He

Jiaping Wang, Simiao Zhang, Qiao-Chu He et al.

The machine learning and data science community has made significant while dispersive progress in accelerating transformer-based large language models (LLMs), and one promising approach is to replace the original causal attention in a generative pre-trained transformer (GPT) with \emph{exponentially decaying causal linear attention}. In this paper, we present LeetDecoding, which is the first Python package that provides a large set of computation routines for this fundamental operator. The launch of LeetDecoding was motivated by the current lack of (1) clear understanding of the complexity regarding this operator, (2) a comprehensive collection of existing computation methods (usually spread in seemingly unrelated fields), and (3) CUDA implementations for fast inference on GPU. LeetDecoding's design is easy to integrate with existing linear-attention LLMs, and allows for researchers to benchmark and evaluate new computation methods for exponentially decaying causal linear attention. The usage of LeetDecoding does not require any knowledge of GPU programming and the underlying complexity analysis, intentionally making LeetDecoding accessible to LLM practitioners. The source code of LeetDecoding is provided at \href{https://github.com/Computational-Machine-Intelligence/LeetDecoding}{this GitHub repository}, and users can simply install LeetDecoding by the command \texttt{pip install leet-decoding}.

Peng Zhao, Yun Yang, Qiao-Chu He

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that under suitable restricted isometry conditions, overparameterization leads to implicit regularization: if we directly apply gradient descent to the residual sum of squares with sufficiently small initial values, then under some proper early stopping rule, the iterates converge to a nearly sparse rate-optimal solution that improves over explicitly regularized approaches. In particular, the resulting estimator does not suffer from extra bias due to explicit penalties, and can achieve the parametric root-n rate when the signal-to-noise ratio is sufficiently high. We also perform simulations to compare our methods with high dimensional linear regression with explicit regularization. Our results illustrate the advantages of using implicit regularization via gradient descent after overparameterization in sparse vector estimation.