Du Jiang

Bohang Zhang, Du Jiang, Di He et al.

Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is rather limited, and a principled understanding of how to design expressive $\ell_\infty$ Lipschitz networks is still lacking. In this paper, we bridge the gap by studying certified $\ell_\infty$ robustness from a novel perspective of representing Boolean functions. We derive two fundamental impossibility results that hold for any standard Lipschitz network: one for robust classification on finite datasets, and the other for Lipschitz function approximation. These results identify that networks built upon norm-bounded affine layers and Lipschitz activations intrinsically lose expressive power even in the two-dimensional case, and shed light on how recently proposed Lipschitz networks (e.g., GroupSort and $\ell_\infty$-distance nets) bypass these impossibilities by leveraging order statistic functions. Finally, based on these insights, we develop a unified Lipschitz network that generalizes prior works, and design a practical version that can be efficiently trained (making certified robust training free). Extensive experiments show that our approach is scalable, efficient, and consistently yields better certified robustness across multiple datasets and perturbation radii than prior Lipschitz networks. Our code is available at https://github.com/zbh2047/SortNet.

Ruichen Li, Haotian Ye, Du Jiang et al.

Neural network-based variational Monte Carlo (NN-VMC) has emerged as a promising cutting-edge technique of ab initio quantum chemistry. However, the high computational cost of existing approaches hinders their applications in realistic chemistry problems. Here, we report the development of a new NN-VMC method that achieves a remarkable speed-up by more than one order of magnitude, thereby greatly extending the applicability of NN-VMC to larger systems. Our key design is a novel computational framework named Forward Laplacian, which computes the Laplacian associated with neural networks, the bottleneck of NN-VMC, through an efficient forward propagation process. We then demonstrate that Forward Laplacian is not only versatile but also facilitates more developments of acceleration methods across various aspects, including optimization for sparse derivative matrix and efficient neural network design. Empirically, our approach enables NN-VMC to investigate a broader range of atoms, molecules and chemical reactions for the first time, providing valuable references to other ab initio methods. The results demonstrate a great potential in applying deep learning methods to solve general quantum mechanical problems.

Ruichen Li, Yuzhi Liu, Du Jiang et al.

Spin plays a fundamental role in understanding electronic structure, yet many real-space wavefunction methods fail to adequately consider it. We introduce the Spin-Adapted Antisymmetrization Method (SAAM), a general procedure that enforces exact total spin symmetry for antisymmetric many-electron wavefunctions in real space. In the context of neural network-based quantum Monte Carlo (NNQMC), SAAM leverages the expressiveness of deep neural networks to capture electron correlation while enforcing exact spin adaptation via group representation theory. This framework provides a principled route to embed physical priors into otherwise black-box neural network wavefunctions, yielding a compact representation of correlated system with neural network orbitals. Compared with existing treatments of spin in NNQMC, SAAM is more accurate and efficient, achieving exact spin purity without any additional tunable hyperparameters. To demonstrate its effectiveness, we apply SAAM to study the spin ladder of iron-sulfur clusters, a long-standing challenge for many-body methods due to their dense spectrum of nearly degenerate spin states. Our results reveal accurate resolution of low-lying spin states and spin gaps in [Fe$_2$S$_2$] and [Fe$_4$S$_4$] clusters, offering new insights into their electronic structures. In sum, these findings establish SAAM as a robust, hyperparameter-free standard for spin-adapted NNQMC, particularly for strongly correlated systems.

Bohang Zhang, Du Jiang, Di He et al.

Recently, Zhang et al. (2021) developed a new neural network architecture based on $\ell_\infty$-distance functions, which naturally possesses certified $\ell_\infty$ robustness by its construction. Despite the novel design and theoretical foundation, so far the model only achieved comparable performance to conventional networks. In this paper, we make the following two contributions: $\mathrm{(i)}$ We demonstrate that $\ell_\infty$-distance nets enjoy a fundamental advantage in certified robustness over conventional networks (under typical certification approaches); $\mathrm{(ii)}$ With an improved training process we are able to significantly boost the certified accuracy of $\ell_\infty$-distance nets. Our training approach largely alleviates the optimization problem that arose in the previous training scheme, in particular, the unexpected large Lipschitz constant due to the use of a crucial trick called $\ell_p$-relaxation. The core of our training approach is a novel objective function that combines scaled cross-entropy loss and clipped hinge loss with a decaying mixing coefficient. Experiments show that using the proposed training strategy, the certified accuracy of $\ell_\infty$-distance net can be dramatically improved from 33.30% to 40.06% on CIFAR-10 ($ε=8/255$), meanwhile outperforming other approaches in this area by a large margin. Our results clearly demonstrate the effectiveness and potential of $\ell_\infty$-distance net for certified robustness. Codes are available at https://github.com/zbh2047/L_inf-dist-net-v2.