The aim of this paper is to outline a new approach in the digital realization of Boolean Neural Networks. Each cell in the gate array performs the binary addition/subtraction function. Space iteration of such digital circuit enables the calculation of all output functions of neurons in the network. The topology of the network influences the connections between neurons and therefore the connections in PGA.

- I.e. instead of averaging the loss over the entire dataset, we average over a minibatch.
- Constraining the size of the weights means that the weights cannot

grow arbitrarily large to fit the training data, and in this way

reduces overfitting. - The optical architecture used in this work is based on an SOI (silicon-on-insulator) platform which consists of several metalines; each metaline consists of a series of meta-atoms21.
- When this

happen, the neuron is unlikely to come back to life since the gradient

of the ReLU function is 0 when its input is negative.

Then we will build (effectively) the same graph in Keras, to see just

how simple solving a machine learning problem can be. Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn

and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy

and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.

Optical Neural Networks (ONNs) uses photons instead of electrons for computation, which enables surmounting the inherent limitations of electronics and improves the energy efficiency, processing speed and computational throughput. In ONNs, the neuron functionality and interconnectivity can be implemented with optical and photonic devices and the nature of light propagation. Here an on-chip diffractive optical neural network (DONN) is utilized to perform optical logic operations. In this configuration, the encoded light at the input layer is decoded through the hidden layers (1D-metasurfaces). The 1D-metasurfaces, named as metalines, are trained to scatter the encoded light into one of two small specified areas at the output layer, one of which represents logic state “1” and the other stands for “0”.

So after personal readings, I finally understood how to go about it, which is the reason for this medium post.

## Videos on Neural Networks

Software Engineer with huge interest in Machine learning and Computer Vision. While taking the Udacity Pytorch Course by Facebook, I found it difficult understanding how the Perceptron xor neural network works with Logic gates (AND, OR, NOT, and so on). I decided to check online resources, but as of the time of writing this, there was really no explanation on how to go about it.

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For the XOR gate, the truth table on the left side of the image below depicts that if there are two complement inputs, only then the output will be 1. The points when plotted in the x-y plane on the right gives us the information that they are not linearly separable like in the case of OR and AND gates(at least in two dimensions). Before starting with part 2 of implementing logic gates using Neural networks, you would want to go through part1 first. This took me one entire day to write and this is already exhilirating. This is just a small glimpse of what neural networks are capable of. I believe future projects will grow by leaps and bounds as I dive in deeper to refine my techniques in using my own tools.

This function performs only one pass through the neural network updating all the weights and calculating cumulative error at the output node. We replicate the dataset using numpy arrays, which helps us with fast matrix computations, with the same structure as that discussed in earlier sections. We represent bits with zeros and ones, but they do not give a very accuracte prediction and learning rates, therefore we decide to change them to floating points.This increases the neural network’s learning ability by a factor of 10. A connection between two neurones is established by passing neurone A ( from neurone) and neurone B ( to neurone) to the constructor. By adjusting the weights the neural network can archieve “learning”. Thereafter, by using near-to-far field transformation22,23, or scalar-wave approximation24,25, or spatial domain electromagnetic propagation26, the fields can be propagated between metasurface layers.

## Keras and Tensorflow

This is due to the NOT gate which I didn’t want to get bogged down in because it wouldn’t be fun to see this gate again. If you are familiar with logical gates you might notice that an inner part of this expression this is an XNOR gate. Now we could imagine coding up a logical network for this data by hand. We’d use our business rules to define who we think is and isn’t at risk from the flu. We might come up with something like the following, where a prediction of 1 indicates the patient is a risk and a prediction 0 means they are not at risk.

The tables here

show how we can set up the inputs \( x_1 \) and \( x_2 \) in order to yield a

specific target \( y_i \). We could program this logical network if we had a huge amount of domain expertise, or if we did a very large amount of descriptive analytics of medical records. However, trying to avoid hard coding this network, which would use huge resources of expert domain knowledge, developer time, and could introduce lots of biases, is why we as modelers build models in the first place. Now, the overall output has to be greater than 0 so that the output is 1 and the definition of the AND gate is satisfied.

Scikit-learn implements a few improvements from our neural network,

such as early stopping, a varying learning rate, different

optimization methods, etc. We now perform a grid search to https://forexhero.info/ find the optimal hyperparameters for the network. Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around \( 98\% \) (\( 2\% \) error rate).

High-quality binary classifiers are essential for a wide range of applications, including natural language processing, computer vision, fraud detection, and medical diagnosis, among many others. Like all statistical methods, supervised learning using neural

networks has important limitations. This is especially important when

one seeks to apply these methods, especially to physics problems. Often, the same or

better performance on a task can be achieved by using a few

hand-engineered features (or even a collection of random

features). In this guide we will analyze the same data as we did in our NumPy and

scikit-learn tutorial, gathered from the MNIST database of images. We

will give an introduction to the lower level Python Application

Program Interfaces (APIs), and see how we use them to build our graph.

## XOR

From previous scenarios, we had found the values of W0, W1, W2 to be -3,2,2 respectively. Placing these values in the Z equation yields an output -3+2+2 which is 1 and greater than 0. This will, therefore, be classified as 1 after passing through the sigmoid function. AND gate operation is a simple multiplication operation between the inputs. Now that we are done with the necessary basic logic gates, we can combine them to give an XNOR gate. The high-level API currently supports most of recent deep learning models, such as Convolutions, LSTM, BiRNN, BatchNorm, PReLU, Residual networks, Generative networks…

The Perceptron output is 0.888, which indicates the probability of output y being a 1. Cell nucleus or Soma processes the information received from dendrites. Synapse is the connection between an axon and other neuron dendrites. Where \( \eta \) is known as the learning rate, which controls how big a step we take towards the minimum. This update can be repeated for any number of iterations, or until we are satisfied with the result.

Some create 2 classes of neurones and name them InputNeurone and WorkingNeurone but with this approach the neurones are directly charaterized by its activation function. First let me explain You what a neurone in the context of machine learning is. Developed the design principle and performed FDTD simulations for meta-atoms.

For example, instead of a traditional recurrent neural network architecture, with several sequential nodes, the gated recurrent unit uses several cells consecutively, each containing three models (example cell pictured below). A gated neural network uses processes known called update gate and reset gate. This allows the neural network to carry information forward across multiple units by storing values in memory. When a critical point is reached, the stored values are used to update the current state. This issue is evident when comparing designs 1 and 2, designs 3 and 4, designs 6 and 7, as well as designs 13 and 14, which only differ in the number of slots in a meta-atom (and therefore the number of meta-atoms in each metaline).

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Furthermore, in

a MLP with only linear activation functions, each layer simply

performs a linear transformation of its inputs. Here, the output \( y \) of the neuron is the value of its activation function, which have as input

a weighted sum of signals \( x_i, \dots ,x_n \) received by \( n \) other neurons. In this tutorial I am going to use a neural network to emulate the behaviour of a network of logical gates. We’ll be looking at exactly what each neuron in the network is doing and how this fits into the whole.

This algorithm enables neurons to learn and processes elements in the training set one at a time. In other words, this operation lets the model

learn the optimal scale and mean of the inputs for each layer. In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and

standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current

mini-batch, from this the name batch normalization.

Then final_delta and hidden_delta help us update the weight matrices, which enables us to learn. If we are negligent of the vast underlying complexity of human mind, it becomes easy for us to say that we can replicate human mind in machine code but that would be a far fetched fantasy. It can be very motivating to think of such fantasies and form goals that seem unachievable.

A neural network link that contains computations to track features and uses Artificial Intelligence in the input data is known as Perceptron. This neural links to the artificial neurons using simple logic gates with binary outputs. An artificial neuron invokes the mathematical function and has node, input, weights, and output equivalent to the cell nucleus, dendrites, synapse, and axon, respectively, compared to a biological neuron. The optical architecture used in this work is based on an SOI (silicon-on-insulator) platform which consists of several metalines; each metaline consists of a series of meta-atoms21.

The main advantage of our design over other works1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,35,36,37 is that a single structure with the same structural and geometrical parameters can be used for all logic operations. In this section I am going to assume that you are at least somewhat comfortable with the ideas of neural networks. I’ll be throwing around the words bias, weight and activation function and I shan’t be taking the time to explain what I mean beyond this simple diagram. In this tutorial I want to show you how you can train a neural networks to perform the function of a network of logical gates.

- Artificial neural networks are computational systems that can learn to

perform tasks by considering examples, generally without being

programmed with any task-specific rules. - I have ideas to extend this demonstration further by producing a Jupyter notebook to implement something along these lines in Keras.
- Developed the design principle and performed FDTD simulations for meta-atoms.
- However, it is now common to use the terms Single Layer Perceptron (SLP) (1 hidden layer) and

Multilayer Perceptron (MLP) (2 or more hidden layers) to refer to feed-forward neural networks with any activation function. - Watching with a curious eye as to how do they walk, talk, or do, child’s mind starts to adapt its actions to mimic those of the others.

On the other hand, they have difficulty to be integrated with silicon-based optical devices. It is noteworthy to mention that it is possible to train the diffractive optical neural network to perform any other logic operations like NAND, NOR, XOR and XNOR or even all the seven basic logic operations at the same time. Depending on the number and complexity of the tasks that the neural network is trained for, the number of neurons, the number of diffractive layers, and the distance between layers may subject to change. Furthermore, it is possible to design the multifunctional logic gate such that it can perform other functions as well which ease the integration of the gates with other devices.