Kaixin Gao

Naicheng Guo, Xiaolei Liu, Shaoshuai Li et al.

Sequential recommendation (SR) learns users' preferences by capturing the sequential patterns from users' behaviors evolution. As discussed in many works, user-item interactions of SR generally present the intrinsic power-law distribution, which can be ascended to hierarchy-like structures. Previous methods usually handle such hierarchical information by making user-item sectionalization empirically under Euclidean space, which may cause distortion of user-item representation in real online scenarios. In this paper, we propose a Poincaré-based heterogeneous graph neural network named PHGR to model the sequential pattern information as well as hierarchical information contained in the data of SR scenarios simultaneously. Specifically, for the purpose of explicitly capturing the hierarchical information, we first construct a weighted user-item heterogeneous graph by aliening all the user-item interactions to improve the perception domain of each user from a global view. Then the output of the global representation would be used to complement the local directed item-item homogeneous graph convolution. By defining a novel hyperbolic inner product operator, the global and local graph representation learning are directly conducted in Poincaré ball instead of commonly used projection operation between Poincaré ball and Euclidean space, which could alleviate the cumulative error issue of general bidirectional translation process. Moreover, for the purpose of explicitly capturing the sequential dependency information, we design two types of temporal attention operations under Poincaré ball space. Empirical evaluations on datasets from the public and financial industry show that PHGR outperforms several comparison methods.

Wei Yuan, Kai-Xin Gao

Many adaptive optimization methods have been proposed and used in deep learning, in which Adam is regarded as the default algorithm and widely used in many deep learning frameworks. Recently, many variants of Adam, such as Adabound, RAdam and Adabelief, have been proposed and show better performance than Adam. However, these variants mainly focus on changing the stepsize by making differences on the gradient or the square of it. Motivated by the fact that suitable damping is important for the success of powerful second-order optimizers, we discuss the impact of the constant $ε$ for Adam in this paper. Surprisingly, we can obtain better performance than Adam simply changing the position of $ε$. Based on this finding, we propose a new variant of Adam called EAdam, which doesn't need extra hyper-parameters or computational costs. We also discuss the relationships and differences between our method and Adam. Finally, we conduct extensive experiments on various popular tasks and models. Experimental results show that our method can bring significant improvement compared with Adam. Our code is available at https://github.com/yuanwei2019/EAdam-optimizer.

Naicheng Guo, Xiaolei Liu, Shaoshuai Li et al.

Session-based recommendation (SBR) learns users' preferences by capturing the short-term and sequential patterns from the evolution of user behaviors. Among the studies in the SBR field, graph-based approaches are a relatively powerful kind of way, which generally extract item information by message aggregation under Euclidean space. However, such methods can't effectively extract the hierarchical information contained among consecutive items in a session, which is critical to represent users' preferences. In this paper, we present a hyperbolic contrastive graph recommender (HCGR), a principled session-based recommendation framework involving Lorentz hyperbolic space to adequately capture the coherence and hierarchical representations of the items. Within this framework, we design a novel adaptive hyperbolic attention computation to aggregate the graph message of each user's preference in a session-based behavior sequence. In addition, contrastive learning is leveraged to optimize the item representation by considering the geodesic distance between positive and negative samples in hyperbolic space. Extensive experiments on four real-world datasets demonstrate that HCGR consistently outperforms state-of-the-art baselines by 0.43$\%$-28.84$\%$ in terms of $HitRate$, $NDCG$ and $MRR$.

Kai-Xin Gao, Xiao-Lei Liu, Zheng-Hai Huang et al.

Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018), proposes an interpretation of viewing natural gradient update as a diagonal method, and corrects the inaccurate re-scaling factor in the Kronecker-factored eigenbasis. Gao et al. (2020) considers a new approximation to the natural gradient, which approximates the Fisher information matrix (FIM) to a constant multiplied by the Kronecker product of two matrices and keeps the trace equal before and after the approximation. In this work, we combine the ideas of these two methods and propose Trace-restricted Eigenvalue-corrected Kronecker Factorization (TEKFAC). The proposed method not only corrects the inexact re-scaling factor under the Kronecker-factored eigenbasis, but also considers the new approximation method and the effective damping technique proposed in Gao et al. (2020). We also discuss the differences and relationships among the Kronecker-factored approximations. Empirically, our method outperforms SGD with momentum, Adam, EKFAC and TKFAC on several DNNs.

Kai-Xin Gao, Xiao-Lei Liu, Zheng-Hai Huang et al.

Second-order optimization methods have the ability to accelerate convergence by modifying the gradient through the curvature matrix. There have been many attempts to use second-order optimization methods for training deep neural networks. Inspired by diagonal approximations and factored approximations such as Kronecker-Factored Approximate Curvature (KFAC), we propose a new approximation to the Fisher information matrix (FIM) called Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) in this work, which can hold the certain trace relationship between the exact and the approximate FIM. In TKFAC, we decompose each block of the approximate FIM as a Kronecker product of two smaller matrices and scaled by a coefficient related to trace. We theoretically analyze TKFAC's approximation error and give an upper bound of it. We also propose a new damping technique for TKFAC on convolutional neural networks to maintain the superiority of second-order optimization methods during training. Experiments show that our method has better performance compared with several state-of-the-art algorithms on some deep network architectures.