Event-based backpropagation can compute exact gradients for spiking neural networks

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.

FCN-Based 3D Reconstruction with Multi-Source Photometric Stereo

As a classical method widely used in 3D reconstruction tasks, the multi-source Photometric Stereo can obtain more accurate 3D reconstruction results compared with the basic Photometric Stereo, but its complex calibration and solution process reduces the efficiency of this algorithm. In this paper, we propose a multi-source Photometric Stereo 3D reconstruction method based on the fully convolutional network (FCN). We first represent the 3D shape of the object as a depth value corresponding to each pixel as the optimized object. After training in an end-to-end manner, our network can efficiently obtain 3D information on the object surface. In addition, we added two regularization constraints to the general loss function, which can effectively help the network to optimize. Under the same light source configuration, our method can obtain a higher accuracy than the classic multi-source Photometric Stereo. At the same time, our new loss function can help the deep learning method to get a more realistic 3D reconstruction result. We have also used our own real dataset to experimentally verify our method. The experimental results show that our method has a good effect on solving the main problems faced by the classical method.

Selection Consistency of Lasso-Based Procedures for Misspecified High-Dimensional Binary Model and Random Regressors

We consider selection of random predictors for a high-dimensional regression problem with a binary response for a general loss function. An important special case is when the binary model is semi-parametric and the response function is misspecified under a parametric model fit. When the true response coincides with a postulated parametric response for a certain value of parameter, we obtain a common framework for parametric inference. Both cases of correct specification and misspecification are covered in this contribution. Variable selection for such a scenario aims at recovering the support of the minimizer of the associated risk with large probability. We propose a two-step selection Screening-Selection (SS) procedure which consists of screening and ordering predictors by Lasso method and then selecting the subset of predictors which minimizes the Generalized Information Criterion for the corresponding nested family of models. We prove consistency of the proposed selection method under conditions that allow for a much larger number of predictors than the number of observations. For the semi-parametric case when distribution of random predictors satisfies linear regressions condition, the true and the estimated parameters are collinear and their common support can be consistently identified. This partly explains robustness of selection procedures to the response function misspecification.

Gene-Based Multiclass Cancer Diagnosis with Class-Selective Rejections

Supervised learning of microarray data is receiving much attention in recent years. Multiclass cancer diagnosis, based on selected gene profiles, are used as adjunct of clinical diagnosis. However, supervised diagnosis may hinder patient care, add expense or confound a result. To avoid this misleading, a multiclass cancer diagnosis with class-selective rejection is proposed. It rejects some patients from one, some, or all classes in order to ensure a higher reliability while reducing time and expense costs. Moreover, this classifier takes into account asymmetric penalties dependant on each class and on each wrong or partially correct decision. It is based onν-1-SVM coupled with its regularization path and minimizes a general loss function defined in the class-selective rejection scheme. The state of art multiclass algorithms can be considered as a particular case of the proposed algorithm where the number of decisions is given by the classes and the loss function is defined by the Bayesian risk. Two experiments are carried out in the Bayesian and the class selective rejection frameworks. Five genes selected datasets are used to assess the performance of the proposed method. Results are discussed and accuracies are compared with those computed by the Naive Bayes, Nearest Neighbor, Linear Perceptron, Multilayer Perceptron, and Support Vector Machines classifiers.