Convolutional residual neural networks (ConvResNets), though overparametersized, can achieve remarkable prediction performance in practice, which cannot be well explained by conventional wisdom. To bridge this gap, we study the performance of ConvResNeXts trained with weight decay, which cover ConvResNets as a special case, from the perspective of nonparametric classification. Our analysis allows for infinitely many building blocks in ConvResNeXts, and shows that weight decay implicitly enforces sparsity on these blocks. Specifically, we consider a smooth target function supported on a low-dimensional manifold, then prove that ConvResNeXts can adapt to the function smoothness and low-dimensional structures and efficiently learn the function without suffering from the curse of dimensionality. Our findings partially justify the advantage of overparameterized ConvResNeXts over conventional machine learning models.

Energy storage cells have been widely used in many applications. Depending on the application, energy storage cells are connected in series to match the voltage requirement. Each the energy storage cell has individual differences such as internal impedance and self-discharging, which cause cell voltage imbalance. This paper proposes a switched capacitor voltage equalizer. The proposed equalizer combines a double-tiered switched capacitor voltage equalizer with a modularized switched capacitor voltage equalizer. The time to make the cell voltages equal of the proposed equalizer is less affected by the voltage difference than either that of the double-tired switched capacitor voltage equalizer or that of the modularized switched capacitor voltage equalizer. The simulation and the circuit experiments are presented.