@article{Liu2026, 
author = {Jiazhen Liu and Gonglin Yuan and Jiahuan Tang},
title = {Stochastic three-term conjugate gradient: a tensor correction algorithmic framework for nonconvex optimization in machine learning},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {10},
pages = {7201-7221},
keywords = {machine learning, nonconvex optimization, spine large models, tensor, three-term conjugate gradient, sufficient descent},
url = {https://www.sciopen.com/article/10.3934/era.2026311},
doi = {10.3934/era.2026311},
abstract = {In large-scale, nonconvex optimization for machine learning, such as the training of spine large models, the balance between efficient high-order geometric features of nonconvex landscapes identification and computational stability remains challenging. This paper proposes a tensor stochastic three-term conjugate gradient (TSTCG) algorithm to address two issues under a stochastic CG framework, the insufficient curvature awareness of the stochastic gradient descent and the heavy reliance on line searches. By introducing an implicit correction mechanism based on third-order tensor information, the algorithm fuses function values and gradient differences to reconstruct evolution vectors, effectively enhancing search precision in ill-conditioned curvature regions. Simultaneously, leveraging a specially designed three-term denominator structure allows the algorithm to process sufficient descent property, line search reliance reduction, and efficient fixed step-size updates. Finally, the nonconvexity proofs and numerical experiments demonstrate that TSTCG outperforms other mainstream stochastic optimization algorithms in terms of convergence efficiency and stability.}
}