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Hou-biao Li

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Published work

12 published item(s)

preprint2026arXiv

Multi-level Self-supervised Pretraining on Compositional Hierarchical Graph for Molecular Property Prediction

Self-supervised pretraining on molecular graphs has emerged as a promising approach for molecular property prediction, yet most existing methods operate at a single structural granularity and treat bond information as auxiliary edge attributes rather than as an independent semantic layer. In this work, we propose MolCHG, a multi-level self-supervised pretraining framework built upon a novel Compositional Hierarchical Graph that organizes molecular structure into four types of nodes across three semantic levels. By introducing a bond graph that operates in parallel with the atom graph, our architecture elevates bond-level information to independently evolving node representations, enabling fragment nodes to aggregate atom-level and bond-level semantics on an equal footing. We design three level-specific pretraining objectives: an atom-bond cross-view contrastive task that aligns the atom-view and bond-view representations within each fragment, a fragment-level functional group prediction task to inject domain-relevant chemical knowledge, and graph-level structure prediction tasks to encode global molecular topology. Experiments on nine MoleculeNet benchmarks demonstrate that MolCHG achieves the best performance on seven datasets across both classification and regression tasks, remaining competitive with the strongest baselines on the rest. Ablation studies further confirm that the multi-level supervision signals are complementary and that each component contributes to the overall performance.

preprint2022arXiv

Greedy double subspaces coordinate descent method via orthogonalization

The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively projects the estimate onto a solution space formed by two greedily selected hyperplanes via Gram-Schmidt orthogonalization. Our methods may be regarded as a simple block version of coordinate descent method which involves two active columns. The convergence analysis of this method is provided and numerical simulations also confirm the effectiveness for matrices with highly coherent columns.

preprint2022arXiv

Neural Theorem Provers Delineating Search Area Using RNN

Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graphs link prediction has been limited due to their computational inefficiency. A new RNNNTP method is proposed in this paper, using a generalized EM-based approach to continuously improve the computational efficiency of Neural Theorem Provers(NTPs). The RNNNTP is divided into relation generator and predictor. The relation generator is trained effectively and interpretably, so that the whole model can be carried out according to the development of the training, and the computational efficiency is also greatly improved. In all four data-sets, this method shows competitive performance on the link prediction task relative to traditional methods as well as one of the current strong competitive methods.

preprint2022arXiv

RNNCTPs: A Neural Symbolic Reasoning Method Using Dynamic Knowledge Partitioning Technology

Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graph link prediction is limited due to their low computational efficiency. In this paper, we propose a new neural symbolic reasoning method: RNNCTPs, which improves computational efficiency by re-filtering the knowledge selection of Conditional Theorem Provers (CTPs), and is less sensitive to the embedding size parameter. RNNCTPs are divided into relation selectors and predictors. The relation selectors are trained efficiently and interpretably, so that the whole model can dynamically generate knowledge for the inference of the predictor. In all four datasets, the method shows competitive performance against traditional methods on the link prediction task, and can have higher applicability to the selection of datasets relative to CTPs.

preprint2020arXiv

Two CSCS-based iteration methods for solving absolute value equations

Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration method and the nonlinear CSCS-like iteration method for AVEs involving the Toeplitz matrix. Then, we analyze the convergence of the Picard-CSCS iteration method for solving AVEs. By using the theory about nonsmooth analysis, we particularly prove the convergence of the nonlinear CSCS-like iterationsolver for AVEs. The advantage of these methods is that they do not require the storage of coefficient matrices at all, and the sub-system of linear equations can be solved efficiently via the fast Fourier transforms (FFTs). Therefore, computational cost and storage can be saved in practical implementations. Numerical examples including numerical solutions of nonlinear fractional diffusion equations are reported to show the effectiveness of the proposed methods in comparison with some existing methods.

preprint2015arXiv

Numerical Gradient Schemes for Heat Equations Based on the Collocation Polynomial and Hermite Interpolation

As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is unconditionally stable and convergent with the order $O(τ^2+h^4)$ under the maximum norm. In this article, a new numerical gradient scheme based on the collocation polynomial and Hermite interpolation is presented. Moreover, the convergence order of this kind of method is also $O(τ^2+h^4)$ under the discrete maximum norm when the space step size is just twice the one of H-OCD method, which accelerates the computational process and makes the result much smoother to some extent. In addition, some corresponding analyses are made and the Richardson extrapolation technique is also considered in time direction. The results of numerical experiments are also consistent with these theoretical analysis.

preprint2014arXiv

From Sylvester's determinant identity to Cramer's rule

The object of this paper is to introduce a new and fascinating method of solving large linear equations, based on Cramer's rule or Gaussian elimination but employing Sylvester's determinant identity in its computation process. In addition, a scheme suitable for parallel computing is presented for this kind of generalized Chiò's determinant condensation processes, which makes this new method have a property of natural parallelism. Finally, some numerical experiments also confirm our theoretical analysis.

preprint2014arXiv

Recycling BiCG for families of shifted linear systems

Many problems in science and engineering fields require the solution of shifted linear systems. To solve such systems efficiently, the recycling BiCG (RBiCG) algorithm in [SIAM J. SCI. COMPUT, 34 (2012) 1925-1949] is extended in this paper. However, the shift-invariant property could no longer hold over the augmented Krylov subspace due to adding the recycling spaces. To remedy this situation, a strategy to enforce the collinearity condition on the shifted system is adopted and then a short term recurrence for the solution update of the shifted system is derived when the seed system is solving. The new method not only improves the convergence but also has a potential to simultaneously compute approximate solutions for shifted linear systems using only as many matrix-vector multiplications as the solution of a single system requires. In addition, some numerical experiments also confirm the efficiency of our method.

preprint2014arXiv

Some new bounds for the Hadamard product and the Fan product of matrices

If $A$ and $B$ are nonnegative matrices, a sharp upper bound on the spectral radius $ρ(A\circ B)$ for the Hadamard product of two nonnegative matrices is given, and the minimum eigenvalue $τ(A\star B)$ of the Fan product of two $M$-matrices $A$ and $B$ is discussed. In addition, we also give a sharp lower bound on $τ(A\circ B^{-1})$ for the Hadamard product of $A$ and $B^{-1}$. Several examples, illustrating that the given bound is stronger than the existing bounds, are also given.

preprint2013arXiv

A SQMRCGstab Algorithm for Families of Shifted Linear Systems

This study is mainly focused on iterative solutions to shifted linear systems arising from a Quantum Chromodynamics (QCD) problem. To solve such system efficiently, we explore a kind of shifted QMRCGstab (SQMRCGstab) methods, which is derived by extending the quasi-minimum residual to the shifted BiCGstab. The shifted QMRCGstab method takes advantage of the shifted structure, so that the number of matrix-vector products and the number of inner products are the same as a single linear system. Moreover, the SQMRCGstab achieves a smoothing of the residual compared to the shifted BiCGstab, and is more competitive than the MS-QMRIDR(s) and the shifted BiCGstab on the QCD problem. Numerical examples show also the efficiency of the method when one applies it to the real problems.

preprint2013arXiv

A Symmetric Rank-one Quasi Newton Method for Non-negative Matrix Factorization

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix approximation is proposed. This method mainly bases on the active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. Our method improves the recent results of those methods in [Pattern Recognition, 45(2012)3557-3565; SIAM J. Sci. Comput., 33(6)(2011)3261-3281; Neural Computation, 19(10)(2007)2756-2779, etc.]. Moreover, the object function decreases faster than many other NMF methods. In addition, some numerical experiments are presented in the synthetic data, imaging processing and text clustering. By comparing with the other six nonnegative matrix approximation methods, our experiments confirm to our analysis.

preprint2013arXiv

Strang-type preconditioners for solving fractional diffusion equations by boundary value methods

The finite difference scheme with the shifted Grünwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with initial values. Recently, boundary value method (BVM) was developed as a popular algorithm for solving large systems of ODEs. This method requires the solutions of one or more nonsymmetric, large and sparse linear systems. In this paper, the GMRES method with the block circulant preconditioner is proposed for solving these linear systems. One of the main results is that if an $A_{ν_1,ν_2}$-stable boundary value method is used for an m-by-m system of ODEs, then the preconditioner is invertible and the preconditioned matrix can be decomposed as I+L, where I is the identity matrix and the rank of L is at most $2m(ν_1+ν_2)$. It means that when the GMRES method is applied to solve the preconditioned linear systems, the method will converge in at most $2m(ν_1+ν_2)+1$ iterations.Finally, extensive numerical experiments are reported to illustrate the effectiveness of our methods for solving the fractional diffusion equations.