Ziyan Luo

Shenglong Zhou, Ouya Wang, Ziyan Luo et al.

The recent advancement of foundation models (FMs) has brought about a paradigm shift, revolutionizing various sectors worldwide. The popular optimizers used to train these models are stochastic gradient descent-based algorithms, which face inherent limitations, such as slow convergence and stringent assumptions for convergence. In particular, data heterogeneity arising from distributed settings poses significant challenges to their theoretical and numerical performance. This paper develops an algorithm, PISA (Preconditioned Inexact Stochastic Alternating Direction Method of Multipliers). Grounded in rigorous theoretical guarantees, the algorithm converges under the sole assumption of Lipschitz continuity of the gradient on a bounded region, thereby removing the need for other conditions commonly imposed by stochastic methods. This capability enables the proposed algorithm to tackle the challenge of data heterogeneity effectively. Moreover, the algorithmic architecture enables scalable parallel computing and supports various preconditions, such as second-order information, second moment, and orthogonalized momentum by Newton-Schulz iterations. Incorporating the latter two preconditions in PISA yields two computationally efficient variants: SISA and NSISA. Comprehensive experimental evaluations for training or fine-tuning diverse deep models, including vision models, large language models, reinforcement learning models, generative adversarial networks, and recurrent neural networks, demonstrate superior numerical performance of SISA and NSISA compared to various state-of-the-art optimizers.

Ziyan Luo, Xujie Si

Solving Constrained Horn Clauses (CHCs) is a fundamental challenge behind a wide range of verification and analysis tasks. Data-driven approaches show great promise in improving CHC solving without the painstaking manual effort of creating and tuning various heuristics. However, a large performance gap exists between data-driven CHC solvers and symbolic reasoning-based solvers. In this work, we develop a simple but effective framework, "Chronosymbolic Learning", which unifies symbolic information and numerical data points to solve a CHC system efficiently. We also present a simple instance of Chronosymbolic Learning with a data-driven learner and a BMC-styled reasoner. Despite its relative simplicity, experimental results show the efficacy and robustness of our tool. It outperforms state-of-the-art CHC solvers on a dataset consisting of 288 benchmarks, including many instances with non-linear integer arithmetics.

Yunfang Fu, Qiuqi Ruan, Ziyan Luo et al.

In this paper, a novel approach via embedded tensor manifold regularization for 2D+3D facial expression recognition (FERETMR) is proposed. Firstly, 3D tensors are constructed from 2D face images and 3D face shape models to keep the structural information and correlations. To maintain the local structure (geometric information) of 3D tensor samples in the low-dimensional tensors space during the dimensionality reduction, the $\ell_0$-norm of the core tensors and a tensor manifold regularization scheme embedded on core tensors are adopted via a low-rank truncated Tucker decomposition on the generated tensors. As a result, the obtained factor matrices will be used for facial expression classification prediction. To make the resulting tensor optimization more tractable, $\ell_1$-norm surrogate is employed to relax $\ell_0$-norm and hence the resulting tensor optimization problem has a nonsmooth objective function due to the $\ell_1$-norm and orthogonal constraints from the orthogonal Tucker decomposition. To efficiently tackle this tensor optimization problem, we establish the first-order optimality condition in terms of stationary points, and then design a block coordinate descent (BCD) algorithm with convergence analysis and the computational complexity. Numerical results on BU-3DFE database and Bosphorus databases demonstrate the effectiveness of our proposed approach.