[SOLVED] Are weights shared across all inputs and outputs?

Are weights shared across all inputs and outputs?

I've just started reading Deep Learning with JavaScript.

Here's the code example from the chapter Predicting the duration of a download.

const trainData = {
  sizeMB:  [0.080, 9.000, 0.001, 0.100, 8.000, 5.000, 0.100, 6.000, 0.050, 0.500,
            0.002, 2.000, 0.005, 10.00, 0.010, 7.000, 6.000, 5.000, 1.000, 1.000],
  timeSec: [0.135, 0.739, 0.067, 0.126, 0.646, 0.435, 0.069, 0.497, 0.068, 0.116,
            0.070, 0.289, 0.076, 0.744, 0.083, 0.560, 0.480, 0.399, 0.153, 0.149]
};
const testData = {
  sizeMB:  [5.000, 0.200, 0.001, 9.000, 0.002, 0.020, 0.008, 4.000, 0.001, 1.000,
            0.005, 0.080, 0.800, 0.200, 0.050, 7.000, 0.005, 0.002, 8.000, 0.008],
  timeSec: [0.425, 0.098, 0.052, 0.686, 0.066, 0.078, 0.070, 0.375, 0.058, 0.136,
            0.052, 0.063, 0.183, 0.087, 0.066, 0.558, 0.066, 0.068, 0.610, 0.057]
};
const trainTensors = {
 sizeMB: tf.tensor2d(trainData.sizeMB, [20, 1]),
 timeSec: tf.tensor2d(trainData.timeSec, [20, 1])
};
const testTensors = {
  sizeMB: tf.tensor2d(testData.sizeMB, [20, 1]),
  timeSec: tf.tensor2d(testData.timeSec, [20, 1])
};
const model = tf.sequential([tf.layers.dense({inputShape: [1], units: 1})]);
model.compile({optimizer: 'sgd', loss: 'meanAbsoluteError'});

model.fit(trainTensors.sizeMB, trainTensors.timeSec, { epochs: 10 })
  .then(() => {})

Before I move on from this chapter I'd like to understand a couple of things.

At the heart of the layer is a linear function y = kernel * x + bias. This function maps inputs and outputs. Variables kernel and bias are adjusted in the process of training. My question is: Does each pair (input/output) have its own instance of a linear function with its own state? In other words, is there only one pair (kernel/bias) or 20 pairs?

Solution

There is only one pair (kernel, bias) by layer which makes the training parameters in the case of a dense layer. They are also called the weights of the layers. These weights are initialized when the model is created and updated during the training.

If there is to be a state for each input/output, the model could not be used for predicting data it has not seen.

model.getWeights() will return the array of the model weights. model.layers[indexOfLayer].getWeights() will return the array of weights of a specific layer