Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations

States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within input features. In this paper, we present a quantum-inspired multilinear model, named Residual Tensor Train (ResTT), to capture the multiple multilinear correlations of features, from low to high orders, within a single model. ResTT is able to build a robust decision boundary in a high-dimensional space for solving fitting and classification tasks. In particular, we prove that the fully-connected layer and the Volterra series can be taken as special cases of ResTT. Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the existing TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network and benchmark deep learning models on MNIST and Fashion-MNIST datasets. Moreover, ResTT achieves better performance than other statistical methods on two practical examples with limited data which are known to have complex feature interactions.Comment: 12 pages, 6 figure

CFI2P: Coarse-to-Fine Cross-Modal Correspondence Learning for Image-to-Point Cloud Registration

In the context of image-to-point cloud registration, acquiring point-to-pixel correspondences presents a challenging task since the similarity between individual points and pixels is ambiguous due to the visual differences in data modalities. Nevertheless, the same object present in the two data formats can be readily identified from the local perspective of point sets and pixel patches. Motivated by this intuition, we propose a coarse-to-fine framework that emphasizes the establishment of correspondences between local point sets and pixel patches, followed by the refinement of results at both the point and pixel levels. On a coarse scale, we mimic the classic Visual Transformer to translate both image and point cloud into two sequences of local representations, namely point and pixel proxies, and employ attention to capture global and cross-modal contexts. To supervise the coarse matching, we propose a novel projected point proportion loss, which guides to match point sets with pixel patches where more points can be projected into. On a finer scale, point-to-pixel correspondences are then refined from a smaller search space (i.e., the coarsely matched sets and patches) via well-designed sampling, attentional learning and fine matching, where sampling masks are embedded in the last two steps to mitigate the negative effect of sampling. With the high-quality correspondences, the registration problem is then resolved by EPnP algorithm within RANSAC. Experimental results on large-scale outdoor benchmarks demonstrate our superiority over existing methods

Low-Frequency Oscillation Suppression in Series Resonant Dual-Active-Bridge Converters under Fault Tolerant Operation

When an open-switch fault occurs in the inverter-side of the series resonant dual-active-bridge (SRDAB) converter, the rectified DC voltage will drop by a half. One solution to maintain the continuous power supply of the converter is to regulate the duty-cycle of the rectifier output voltage. Nevertheless, it may excite the resonance between the resonant inductors and the DC capacitors and lead to severe low-frequency oscillations, which appears as the envelope of the high-frequency current. This phenomenon may trigger the over-current protection and make the SRDAB fail to ride through the fault. In this paper, a low-frequency equivalent model is proposed for the SRDAB, enabling frequency-domain analysis of the conventional single-loop voltage control. It is revealed that the oscillation depends on the duty-cycle and control parameters, and it is not possible to suppress such oscillations by the conventional control method. Thus, a dual-loop fault tolerant control method consists of an outer voltage control-loop, an inner current envelope control-loop. Also a non-linear correction unit is proposed to suppress the oscillation. Experimental tests on a 1-kW SRDAB are performed. The test results have validated the effectiveness of the proposal in terms of oscillation suppression