Perceptron

Overview

A Perceptron is a simple function that takes a vector input {% \vec{v} %}, multiplies it by a matrix of weights and then applies the sign (1 for positive input, 0 for negative) function to its single output. in order to be able to optimize the perceptron using tensor-flow's optimizers, we need a differentiable function as the activation function. In this case, we use the sigmoid function and create the percetron as

Code

The following code creates a perceptron using the sequential model of tensor-flow.

await $src('https://cdn.jsdelivr.net/npm/@tensorflow/tfjs@2.0.0/dist/tf.min.js');

let  model = tf.sequential();
model.add(tf.layers.dense({units: 1, activation: 'sigmoid', inputShape: [2]}));
				

Try it!

The perceptron created here is initiallized with random weights, so even though it hasnt been trained on data yet, it can still be applied to a set of inputs.

As specified above, this perceptron has 2 inputs, so to apply it, you need to create a tensor with two inputs. The following code applies the perceptron to a single input.

let input = tf.tensor([[1, 2]]);
let output = model.predict(input);
				

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The perceptron can also be applied to a batch of inputs. The following code will run the perceptron on each array in the tensor.

let input2 = tf.tensor([[1, 2],[2,4]]);
let output2 = model.predict(input2);
				

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Fitting

Fitting the perceptron as constructed, then just follows the basic procedure of Fitting Sequential Models.

let X = [[1,1],[1,2],[3,1]];
let y= [[1],[1],[0]];

let xs = tf.tensor(X);
let ys = tf.tensor(y);

model.compile({
    loss:tf.losses.meanSquaredError,
    optimizer:tf.train.adam(0.1)
});

await model.fit(xs,ys,{
    batchSize:2,
    shuffle:true,
    epochs:100
});
				

Try it!

MultiClass Classification

Multi Class classification can be modeled by using mutiple perceptrons run in parallel. (see multi class classification)

const model = tf.sequential({
  layers:[
    tf.layers.dense({inputShape:[20],units:9,activation:'softmax'})
  ]
});
				

Ass an example, please see Digit Recognition Example.