Enhanced Gradient Descent Algorithms for Quaternion-Valued Neural Networks

Author(s):  
Călin-Adrian Popa
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhipeng Liu ◽  
Rui Feng ◽  
Xiuhan Li ◽  
Wei Wang ◽  
Xiaoling Wu

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.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ximing Li ◽  
Luna Rizik ◽  
Valeriia Kravchik ◽  
Maria Khoury ◽  
Netanel Korin ◽  
...  

AbstractComplex biological systems in nature comprise cells that act collectively to solve sophisticated tasks. Synthetic biological systems, in contrast, are designed for specific tasks, following computational principles including logic gates and analog design. Yet such approaches cannot be easily adapted for multiple tasks in biological contexts. Alternatively, artificial neural networks, comprised of flexible interactions for computation, support adaptive designs and are adopted for diverse applications. Here, motivated by the structural similarity between artificial neural networks and cellular networks, we implement neural-like computing in bacteria consortia for recognizing patterns. Specifically, receiver bacteria collectively interact with sender bacteria for decision-making through quorum sensing. Input patterns formed by chemical inducers activate senders to produce signaling molecules at varying levels. These levels, which act as weights, are programmed by tuning the sender promoter strength Furthermore, a gradient descent based algorithm that enables weights optimization was developed. Weights were experimentally examined for recognizing 3 × 3-bit pattern.


2021 ◽  
Vol 7 (3) ◽  
pp. 41
Author(s):  
Emre Baspinar ◽  
Luca Calatroni ◽  
Valentina Franceschi ◽  
Dario Prandi

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.


Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3240
Author(s):  
Tehreem Syed ◽  
Vijay Kakani ◽  
Xuenan Cui ◽  
Hakil Kim

In recent times, the usage of modern neuromorphic hardware for brain-inspired SNNs has grown exponentially. In the context of sparse input data, they are undertaking low power consumption for event-based neuromorphic hardware, specifically in the deeper layers. However, using deep ANNs for training spiking models is still considered as a tedious task. Until recently, various ANN to SNN conversion methods in the literature have been proposed to train deep SNN models. Nevertheless, these methods require hundreds to thousands of time-steps for training and still cannot attain good SNN performance. This work proposes a customized model (VGG, ResNet) architecture to train deep convolutional spiking neural networks. In this current study, the training is carried out using deep convolutional spiking neural networks with surrogate gradient descent backpropagation in a customized layer architecture similar to deep artificial neural networks. Moreover, this work also proposes fewer time-steps for training SNNs with surrogate gradient descent. During the training with surrogate gradient descent backpropagation, overfitting problems have been encountered. To overcome these problems, this work refines the SNN based dropout technique with surrogate gradient descent. The proposed customized SNN models achieve good classification results on both private and public datasets. In this work, several experiments have been carried out on an embedded platform (NVIDIA JETSON TX2 board), where the deployment of customized SNN models has been extensively conducted. Performance validations have been carried out in terms of processing time and inference accuracy between PC and embedded platforms, showing that the proposed customized models and training techniques are feasible for achieving a better performance on various datasets such as CIFAR-10, MNIST, SVHN, and private KITTI and Korean License plate dataset.


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