Salih Atici

Hongyi Pan, Emadeldeen Hamdan, Xin Zhu et al.

In this paper, we propose a set of transform-based neural network layers as an alternative to the $3\times3$ Conv2D layers in Convolutional Neural Networks (CNNs). The proposed layers can be implemented based on orthogonal transforms such as the Discrete Cosine Transform (DCT), Hadamard transform (HT), and biorthogonal Block Wavelet Transform (BWT). Furthermore, by taking advantage of the convolution theorems, convolutional filtering operations are performed in the transform domain using element-wise multiplications. Trainable soft-thresholding layers, that remove noise in the transform domain, bring nonlinearity to the transform domain layers. Compared to the Conv2D layer, which is spatial-agnostic and channel-specific, the proposed layers are location-specific and channel-specific. Moreover, these proposed layers reduce the number of parameters and multiplications significantly while improving the accuracy results of regular ResNets on the ImageNet-1K classification task. Furthermore, they can be inserted with a batch normalization layer before the global average pooling layer in the conventional ResNets as an additional layer to improve classification accuracy.

Hongyi Pan, Xin Zhu, Salih Atici et al.

In this paper, we propose a novel Discrete Cosine Transform (DCT)-based neural network layer which we call DCT-perceptron to replace the $3\times3$ Conv2D layers in the Residual neural Network (ResNet). Convolutional filtering operations are performed in the DCT domain using element-wise multiplications by taking advantage of the Fourier and DCT Convolution theorems. A trainable soft-thresholding layer is used as the nonlinearity in the DCT perceptron. Compared to ResNet's Conv2D layer which is spatial-agnostic and channel-specific, the proposed layer is location-specific and channel-specific. The DCT-perceptron layer reduces the number of parameters and multiplications significantly while maintaining comparable accuracy results of regular ResNets in CIFAR-10 and ImageNet-1K. Moreover, the DCT-perceptron layer can be inserted with a batch normalization layer before the global average pooling layer in the conventional ResNets as an additional layer to improve classification accuracy.

Hongyi Pan, Salih Atici, Ahmet Enis Cetin

In this paper, we introduce a convolutional network which we call MultiPodNet consisting of a combination of two or more convolutional networks which process the input image in parallel to achieve the same goal. Output feature maps of parallel convolutional networks are fused at the fully connected layer of the network. We experimentally observed that three parallel pod networks (TripodNet) produce the best results in commonly used object recognition datasets. Baseline pod networks can be of any type. In this paper, we use ResNets as baseline networks and their inputs are augmented image patches. The number of parameters of the TripodNet is about three times that of a single ResNet. We train the TripodNet using the standard backpropagation type algorithms. In each individual ResNet, parameters are initialized with different random numbers during training. The TripodNet achieved state-of-the-art performance on CIFAR-10 and ImageNet datasets. For example, it improved the accuracy of a single ResNet from 91.66% to 92.47% under the same training process on the CIFAR-10 dataset.

Salih Atici, Hongyi Pan, Ahmet Enis Cetin

In this paper, we propose a novel optimization algorithm for training machine learning models called Input Normalized Stochastic Gradient Descent (INSGD), inspired by the Normalized Least Mean Squares (NLMS) algorithm used in adaptive filtering. When training complex models on large datasets, the choice of optimizer parameters, particularly the learning rate, is crucial to avoid divergence. Our algorithm updates the network weights using stochastic gradient descent with $\ell_1$ and $\ell_2$-based normalizations applied to the learning rate, similar to NLMS. However, unlike existing normalization methods, we exclude the error term from the normalization process and instead normalize the update term using the input vector to the neuron. Our experiments demonstrate that our optimization algorithm achieves higher accuracy levels compared to different initialization settings. We evaluate the efficiency of our training algorithm on benchmark datasets using ResNet-18, WResNet-20, ResNet-50, and a toy neural network. Our INSGD algorithm improves the accuracy of ResNet-18 on CIFAR-10 from 92.42\% to 92.71\%, WResNet-20 on CIFAR-100 from 76.20\% to 77.39\%, and ResNet-50 on ImageNet-1K from 75.52\% to 75.67\%.

Hongyi Pan, Xin Zhu, Salih Atici et al.

In this paper, we propose a novel Hadamard Transform (HT)-based neural network layer for hybrid quantum-classical computing. It implements the regular convolutional layers in the Hadamard transform domain. The idea is based on the HT convolution theorem which states that the dyadic convolution between two vectors is equivalent to the element-wise multiplication of their HT representation. Computing the HT is simply the application of a Hadamard gate to each qubit individually, so the HT computations of our proposed layer can be implemented on a quantum computer. Compared to the regular Conv2D layer, the proposed HT-perceptron layer is computationally more efficient. Compared to a CNN with the same number of trainable parameters and 99.26\% test accuracy, our HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using 11.5\% fewer parameters with 12.6\% fewer MACs.