QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks

Quantum neural networks (QNNs), an interdisciplinary field of quantum computing and machine learning, have attracted tremendous research interests due to the specific quantum advantages. Despite lots of efforts developed in computer vision domain, one has not fully explored QNNs for the real-world graph property classification and evaluated them in the quantum device. To bridge the gap, we propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections and relieve the error rate of quantum gates, and use skip connection to augment the quantum outputs with original node features to improve robustness. The experimental results show that our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets. The comprehensive evaluations in both simulator and real quantum machines demonstrate the applicability of QuanGCN to the future graph analysis problem.

RSC: Accelerating Graph Neural Networks Training via Randomized Sparse Computations

The training of graph neural networks (GNNs) is extremely time consuming because sparse graph-based operations are hard to be accelerated by hardware. Prior art explores trading off the computational precision to reduce the time complexity via sampling-based approximation. Based on the idea, previous works successfully accelerate the dense matrix based operations (e.g., convolution and linear) with negligible accuracy drop. However, unlike dense matrices, sparse matrices are stored in the irregular data format such that each row/column may have different number of non-zero entries. Thus, compared to the dense counterpart, approximating sparse operations has two unique challenges (1) we cannot directly control the efficiency of approximated sparse operation since the computation is only executed on non-zero entries; (2) sub-sampling sparse matrices is much more inefficient due to the irregular data format. To address the issues, our key idea is to control the accuracy-efficiency trade off by optimizing computation resource allocation layer-wisely and epoch-wisely. Specifically, for the first challenge, we customize the computation resource to different sparse operations, while limit the total used resource below a certain budget. For the second challenge, we cache previous sampled sparse matrices to reduce the epoch-wise sampling overhead. Finally, we propose a switching mechanisms to improve the generalization of GNNs trained with approximated operations. To this end, we propose Randomized Sparse Computation, which for the first time demonstrate the potential of training GNNs with approximated operations. In practice, rsc can achieve up to $11.6\times$ speedup for a single sparse operation and a $1.6\times$ end-to-end wall-clock time speedup with negligible accuracy drop.

Lehmer Transform and its Theoretical Properties

We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical moments. Theoretical properties of the proposed transform are presented. This transform could be very useful to provide an alternative method in analyzing non-stationary signals such as brain wave EEG.