Multiscale optimization in neural nets

Pyramid Convolutional RNN for MRI Image Reconstruction

Fast and accurate MRI image reconstruction from undersampled data is crucial in clinical practice. Deep learning based reconstruction methods have shown promising advances in recent years. However, recovering fine details from undersampled data is still challenging. In this paper, we introduce a novel deep learning based method, Pyramid Convolutional RNN (PC-RNN), to reconstruct images from multiple scales. Based on the formulation of MRI reconstruction as an inverse problem, we design the PC-RNN model with three convolutional RNN (ConvRNN) modules to iteratively learn the features in multiple scales. Each ConvRNN module reconstructs images at different scales and the reconstructed images are combined by a final CNN module in a pyramid fashion. The multi-scale ConvRNN modules learn a coarse-to-fine image reconstruction. Unlike other common reconstruction methods for parallel imaging, PC-RNN does not employ coil sensitive maps for multi-coil data and directly model the multiple coils as multi-channel inputs. The coil compression technique is applied to standardize data with various coil numbers, leading to more efficient training. We evaluate our model on the fastMRI knee and brain datasets and the results show that the proposed model outperforms other methods and can recover more details. The proposed method is one of the winner solutions in the 2019 fastMRI competition.

A Telescopic Binary Learning Machine for Training Neural Networks

This paper proposes a new algorithm based on multiscale stochastic local search with binary representation for training neural networks [binary learning machine (BLM)]. We study the effects of neighborhood evaluation strategies, the effect of the number of bits per weight and that of the maximum weight range used for mapping binary strings to real values. Following this preliminary investigation, we propose a telescopic multiscale version of local search, where the number of bits is increased in an adaptive manner, leading to a faster search and to local minima of better quality. An analysis related to adapting the number of bits in a dynamic way is presented. The control on the number of bits, which happens in a natural manner in the proposed method, is effective to increase the generalization performance. The learning dynamics are discussed and validated on a highly nonlinear artificial problem and on real-world tasks in many application domains; BLM is finally applied to a problem requiring either feedforward or recurrent architectures for feedback control.

Noise injection into inputs in sparsely connected Hopfield and winner-take-all neural networks

In this paper, we show that noise injection into inputs in unsupervised learning neural networks does not improve their performance as it does in supervised learning neural networks. Specifically, we show that training noise degrades the classification ability of a sparsely connected version of the Hopfield neural network, whereas the performance of a sparsely connected winner-take-all neural network does not depend on the injected training noise.