Gradient-Sensitive Optimization for Convolutional Neural Networks

Convolutional neural networks (CNNs) are effective models for image classification and recognition. Gradient descent optimization (GD) is the basic algorithm for CNN model optimization. Since GD appeared, a series of improved algorithms have been derived. Among these algorithms, adaptive moment estimation (Adam) has been widely recognized. However, local changes are ignored in Adam to some extent. In this paper, we introduce an adaptive learning rate factor based on current and recent gradients. According to this factor, we can dynamically adjust the learning rate of each independent parameter to adaptively adjust the global convergence process. We use the factor to adjust the learning rate for each parameter. The convergence of the proposed algorithm is proven by using the regret bound approach of the online learning framework. In the experimental section, comparisons are conducted between the proposed algorithm and other existing algorithms, such as AdaGrad, RMSprop, Adam, diffGrad, and AdaHMG, on test functions and the MNIST dataset. The results show that Adam and RMSprop combined with our algorithm can not only find the global minimum faster in the experiment using the test function but also have a better convergence curve and higher test set accuracy in experiments using datasets. Our algorithm is a supplement to the existing gradient descent algorithms, which can be combined with many other existing gradient descent algorithms to improve the efficiency of iteration, speed up the convergence of the cost function, and improve the final recognition rate.

A Cortical-Inspired Sub-Riemannian Model for Poggendorff-Type Visual Illusions

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches, embedding the sub-Riemannian heat kernel into the neuronal interaction term, in agreement with the intrinsically anisotropic functional architecture of V1 based on both local and lateral connections. For the numerical realisation of both models, we consider standard gradient descent algorithms combined with Fourier-based approaches for the efficient computation of the sub-Laplacian evolution. Our numerical results show that the use of the sub-Riemannian kernel allows us to reproduce numerically visual misperceptions and inpainting-type biases in a stronger way in comparison with the previous approaches.