A Novel Learnable Gradient Descent Type Algorithm for Non-convex Non-smooth Inverse Problems

Learnable Descent Algorithm for Nonsmooth Nonconvex Image Reconstruction

We propose a general learning based framework for solving nonsmooth and nonconvex image reconstruction problems. We model the regularization function as the composition of the $l_{2,1}$ norm and a smooth but nonconvex feature mapping parametrized as a deep convolutional neural network. We develop a provably convergent descent-type algorithm to solve the nonsmooth nonconvex minimization problem by leveraging the Nesterov's smoothing technique and the idea of residual learning, and learn the network parameters such that the outputs of the algorithm match the references in training data. Our meth…

面向具备可保证鲁棒性的张量PCA的可学习缩放梯度下降方法

Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA

针对现有鲁棒张量PCA方法依赖高计算成本张量核范数的问题，提出基于t-SVD框架的RTPCA-SGD方法，证明其线性收敛保证，并提出可学习自监督深度展开模型优化参数，实现性能与效率的双重提升。

CvxNet: Learnable Convex Decomposition

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or impl…

Learning Sparse Low-Precision Neural Networks With Learnable Regularization

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed with high-precision weights while quantized low-precision weights and activations are used in the forward pass to calculate the loss function for training. Thus, the gradient descent becomes suboptimal, and accuracy loss follows. In order to reduce the mismatch in the forward and backward passes, we utilize mean squared quantization error (MSQE) regularizat…

Convergent Block Coordinate Descent for Training Tikhonov Regularized Deep Neural Networks

By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm consisting of a sequence of numerically well-behaved convex optimizations. Using ideas from proximal point methods in convex analysis, we prove that this BCD algorithm will converge globally to a stationary point with R-linear convergence rate of order one. In experiments with the MNIST database, DNNs trained with this BCD algorithm consistently yielded bett…