Do you know how a neural network trains itself to do some job? In this article, we will see the whole process of how a neural network learns. The main goal of a network is to reduce the loss incurring while predicting the outputs. To minimize this loss, we will apply some optimization technique called Gradient descent. In this technique, we update the value of parameters while backpropagating in the network, i.e., find the derivates of the error function with respect to the weights to decrease the loss function and use this Gradient to update the current weight.

In machine learning, backpropagation (backprop,[1] BP) is a widely used algorithm for training feedforward neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions generally. These classes of algorithms are all referred to generically as "backpropagation".[2] In fitting a neural network, backpropagation computes the gradient of the loss function with respect to the weights of the network for a single input–output example, and does so efficiently, unlike a naive direct computation of the gradient with respect to each weight individually. This efficiency makes it feasible to use gradient methods for training multilayer networks, updating weights to minimize loss; gradient descent, or variants such as stochastic gradient descent, are commonly used. The backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this is an example of dynamic programming.[3]

Neural networks have shown significant advancements in recent years. From facial recognition tools in smartphone Face ID, to self driving cars, the applications of neural networks have influenced every industry. This subset of machine learning is comprised of node layers, containing an input layer, one or more hidden layers, and an output layer. Each node is interconnected like human brain and has an associated weight and threshold. Suppose the output value of a node is higher than the specified threshold value, it implies that the node is activated and ready to relay data to the next layer of the neural network. There are various activation functions like Threshold function, Piecewise linear function or Sigmoid function.

A semi-supervised learning method for spiking neural networks is proposed. The proposed method consists of supervised learning by backpropagation and subsequent unsupervised learning by spike-timing-dependent plasticity (STDP), which is a biologically plausible learning rule. Numerical experiments show that the proposed method improves the accuracy without additional labeling when a small amount of labeled data is used. This feature has not been achieved by existing semi-supervised learning methods of discriminative models. It is possible to implement the proposed learning method for event-driven systems. Hence, it would be highly efficient in real-time problems if it were implemented on neuromorphic hardware. The results suggest that STDP plays an important role other than self-organization when applied after supervised learning, which differs from the previous method of using STDP as pre-training interpreted as self-organization.

Many concepts have been proposed for meta learning with neural networks (NNs), e.g., NNs that learn to control fast weights, hyper networks, learned learning rules, and meta recurrent neural networks (Meta RNNs). Our Variable Shared Meta Learning (VS-ML) unifies the above and demonstrates that simple weight-sharing and sparsity in an NN is sufficient to express powerful learning algorithms. A simple implementation of VS-ML called Variable Shared Meta RNN allows for implementing the backpropagation learning algorithm solely by running an RNN in forward-mode. It can even meta-learn new learning algorithms that improve upon backpropagation, generalizing to different datasets without explicit gradient calculation.

A complete understanding of neural network mathematics for backpropagation in more complex networks requires an understanding of more esoteric multivariable calculus notions, like the Jacobian. I'll post an article in the future on this once I have a better grasp of the concept itself. But, we can achieve quite a lot of intuition at a slightly more basic level. Turns out that we already did a bulk of the work -- computing backpropagation on a larger neural network just requires a few logical steps. Ignoring the biases, let's see if we can use similar logic to backpropagate through are more complex network, this time to two different weights.

Recent significant developments, such as GPT-3, have been driven by this conjecture. However, as models scale-up, training them efficiently with backpropagation becomes difficult. Because model, pipeline, and data parallelism distribute parameters and gradients over compute nodes, communication is challenging to orchestrate: this is a bottleneck to further scaling. In this work, we argue that alternative training methods can mitigate these issues, and can inform the design of extreme-scale training hardware. Indeed, using a synaptically asymmetric method with a parallelizable backward pass, such as Direct Feedback Alignement, communication needs are drastically reduced. We present a photonic accelerator for Direct Feedback Alignment, able to compute random projections with trillions of parameters. We demonstrate our system on benchmark tasks, using both fully-connected and graph convolutional networks. Our hardware is the first architecture-agnostic photonic co-processor for training neural networks. This is a significant step towards building scalable hardware, able to go beyond backpropagation, and opening new avenues for deep learning.

Gradient descent and backpropagation have enabled neural networks to achieve remarkable results in many real-world applications. Despite ongoing success, training a neural network with gradient descent can be a slow and strenuous affair. We present a simple yet faster training algorithm called Zeroth-Order Relaxed Backpropagation (ZORB). Instead of calculating gradients, ZORB uses the pseudoinverse of targets to backpropagate information. ZORB is designed to reduce the time required to train deep neural networks without penalizing performance. To illustrate the speed up, we trained a feed-forward neural network with 11 layers on MNIST and observed that ZORB converged 300 times faster than Adam while achieving a comparable error rate, without any hyperparameter tuning. We also broaden the scope of ZORB to convolutional neural networks, and apply it to subsamples of the CIFAR-10 dataset. Experiments on standard classification and regression benchmarks demonstrate ZORB's advantage over traditional backpropagation with Gradient Descent.

Traditional backpropagation of error, though a highly successful algorithm for learning in artificial neural network models, includes features which are biologically implausible for learning in real neural circuits. An alternative called target propagation proposes to solve this implausibility by using a top-down model of neural activity to convert an error at the output of a neural network into layer-wise and plausible 'targets' for every unit. These targets can then be used to produce weight updates for network training. However, thus far, target propagation has been heuristically proposed without demonstrable equivalence to backpropagation. Here, we derive an exact correspondence between backpropagation and a modified form of target propagation (GAIT-prop) where the target is a small perturbation of the forward pass. Specifically, backpropagation and GAIT-prop give identical updates when synaptic weight matrices are orthogonal. In a series of simple computer vision experiments, we show near-identical performance between backpropagation and GAIT-prop with a soft orthogonality-inducing regularizer.

I find it hard to get step by step and detailed explanations about Neural Networks in one place. Always some part of the explanation was missing in courses or in the videos. So I tried to gather all the information and explanations in one blog post (step by step). I would separate this blog in 8 sections as I find it most relevant. Artificial Neural Network is computing system inspired by biological neural network that constitute animal brain.