This repository contains scripts for training different variations of the SpinalNet and its counterparts.

Deep neural networks (DNNs) have achieved the state of the art performance in numerous fields. However, DNNs need high computation times, and people always expect better performance in a lower computation. Therefore, we study the human somatosensory system and design a neural network (SpinalNet) to achieve higher accuracy with fewer computations. Hidden layers in traditional NNs receive inputs in the previous layer, apply activation function, and then transfer the outcomes to the next layer. In the proposed SpinalNet, each layer is split into three splits: 1) input split, 2) intermediate split, and 3) output split. Input split of each layer receives a part of the inputs. The intermediate split of each layer receives outputs of the intermediate split of the previous layer and outputs of the input split of the current layer. The number of incoming weights becomes significantly lower than traditional DNNs. The SpinalNet can also be used as the fully connected or classification layer of DNN and supports both traditional learning and transfer learning. We observe significant error reductions with lower computational costs in most of the DNNs. Traditional learning on the VGG-5 network with SpinalNet classification layers provided the state-of-the-art (SOTA) performance on QMNIST, Kuzushiji-MNIST, EMNIST (Letters, Digits, and Balanced) datasets. Traditional learning with ImageNet pre-trained initial weights and SpinalNet classification layers provided the SOTA performance on STL-10, Fruits 360, Bird225, and Caltech-101 datasets. The scripts of the proposed SpinalNet are available at the following link: https://github.com/dipuk0506/SpinalNet

torch, torchvision, numpy, random, matplotlib, time, os, copy, math.

Scripts are independent. The user can download an individual script and run. Except for scripts of the 'Transfer Learning' folder, scripts are downloading data from PyTorch during the execution.

KMNIST, QMNINT, EMNIST (Digits, Letters, Balanced), STL-10, Bird-225, Caltech-101,Fruits-360

The SpinalNet tries to mimic the human somatosensory system to receive large data efficiently and to achieve better performance. (a) Half part of the human somatosensory system, presenting how our spinal cord receives sensory signals from our body. (b) Structure of the proposed SpinalNet. The proposed NN consists of the input row, the intermediate row, and the output row. The intermediate row contains multiple hidden layers. Each hidden layer receives a portion of the input. All layers except the first layer also receive outputs of the previous layer. The output layer adds the weighted outputs of all hidden neurons of the intermediate row. The user can also construct and train a SpinalNet for any arbitrary number of inputs, intermediate neurons, and outputs.

• Single hidden layer NN of large width is a universal approximator.

• If we can prove that, SpinalNet of a large depth can be equivalent to the single hidden layer NN of large width, the universal approximation is proved.

Following figure presents the visual proof of the universal approximation theorem for the proposed SpinalNet. A simplified version of SpinalNet in (a) can act as a NN of a single hidden layer, drawn in (b). Similarly, a 4 layer SpinalNet in (d)can be equal to a NN of one hidden layer (HL), containing four neurons, shown in (c).

Any traditional hidden layer can be converted to a spinal hidden layer. The traditional hidden layer in (a) is converted to a spinal hidden layer in (b). A spinal hidden layer has the structure of the proposed SpinalNet.

Detailed classification results are available in the paper. Link to the paper: https://arxiv.org/abs/2007.03347

[1] https://www.kaggle.com/dipuk0506/spinalnet-tl-pytorch-bird225-99-5

[2] https://www.kaggle.com/dipuk0506/spinalnet-cifar10-97-5-accuracy

[3] https://www.kaggle.com/dipuk0506/spinalnet-fruit360-99-99-accuracy