arXiv subjects

Boyuan Yao

Publications and source records attributed to Boyuan Yao.

3 recordsLinked to original sources

arXiv2026

Faster Stochastic Algorithms for Minimax Optimization under Polyak--Łojasiewicz Conditions

This paper considers stochastic first-order algorithms for minimax optimization under Polyak--Łojasiewicz (PL) conditions. We propose SPIDER-GDA for solving the finite-sum problem of the form $\min_x \max_y f(x,y)\triangleq \frac{1}{n} \sum_{i=1}^n f_i(x,y)$, where the objective function $f(x,y)$ is $μ_x$-PL in $x$ and $μ_y$-PL in $y$; and each $f_i(x,y)$ is $L$-smooth. We prove SPIDER-GDA could find an $ε$-optimal solution within ${\mathcal O}\left((n + \sqrt{n}\,κ_xκ_y^2)\log (1/ε)\right)$ stochastic first-order oracle (SFO) complexity, which is better than the state-of-the-art method whose SFO upper bound is ${\mathcal O}\big((n + n^{2/3}κ_xκ_y^2)\log (1/ε)\big)$, where $κ_x\triangleq L/μ_x$ and $κ_y\triangleq L/μ_y$. For the ill-conditioned case, we provide an accelerated algorithm to reduce the computational cost further. It achieves $\tilde{\mathcal O}\big((n+\sqrt{n}\,κ_xκ_y)\log (κ_y/ε) \log(1/ε)\big)$ SFO upper bound when $κ_y \gtrsim \sqrt{n}$. Our ideas can also be applied to a more general setting where the objective function only satisfies the PL condition for one variable. Numerical experiments validate the superiority of proposed methods.

math.OC↗

arXiv2026

Derivative-Informed Fourier Neural Operator: Universal Approximation and Applications to PDE-Constrained Optimization

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error jointly on output and Fréchet derivative samples of a high-fidelity operator (e.g., a parametric PDE solution operator). As a result, a DIFNO can closely emulate not only the high-fidelity operator's response but also its sensitivities. To motivate the use of DIFNOs instead of conventional FNOs as surrogate models, we show that accurate surrogate-driven PDE-constrained optimization requires accurate surrogate Fréchet derivatives. Then, we establish (i) simultaneous universal approximation of continuously differentiable operators and their Fréchet derivatives by FNOs on compact sets, and (ii) universal approximation of continuously differentiable operators by FNOs in weighted Sobolev spaces with input measures that have unbounded supports. Our theoretical results certify the capability of FNOs for accurate derivative-informed operator learning and for the solution of PDE-constrained optimization problems. Furthermore, we develop efficient training schemes that leverage dimensionality reduction and multi-resolution techniques to significantly reduce memory and computational costs in Fréchet derivative learning. Numerical examples on nonlinear diffusion--reaction, Helmholtz, and Navier--Stokes equations demonstrate that DIFNOs are superior in sample complexity for operator learning and solving infinite-dimensional PDE-constrained inverse problems, achieving high accuracy at low training sample sizes.

cs.LG↗

arXiv2023

Colossal-Auto: Unified Automation of Parallelization and Activation Checkpoint for Large-scale Models

In recent years, large-scale models have demonstrated state-of-the-art performance across various domains. However, training such models requires various techniques to address the problem of limited computing power and memory on devices such as GPUs. Some commonly used techniques include pipeline parallelism, tensor parallelism, and activation checkpointing. While existing works have focused on finding efficient distributed execution plans (Zheng et al. 2022) and activation checkpoint scheduling (Herrmann et al. 2019, Beaumont et al. 2021}, there has been no method proposed to optimize these two plans jointly. Moreover, ahead-of-time compilation relies heavily on accurate memory and computing overhead estimation, which is often time-consuming and misleading. Existing training systems and machine learning pipelines either physically execute each operand or estimate memory usage with a scaled input tensor. To address these challenges, we introduce a system that can jointly optimize distributed execution and gradient checkpointing plans. Additionally, we provide an easy-to-use symbolic profiler that generates memory and computing statistics for any PyTorch model with a minimal time cost. Our approach allows users to parallelize their model training on the given hardware with minimum code change based. The source code is publicly available at Colossal-AI GitHub or https://github.com/hpcaitech/ColossalAI

cs.LG↗