Understanding Momentum in Deep Learning

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It helps them move faster towards the right direction and avoid getting stuck in local minima (which can be frustrating).

Here’s how it works: let’s say you have a weight that needs to update its value based on some input data. Normally, this would involve calculating the gradient of your loss function with respect to that weight, multiplying it by a learning rate, and then updating the weight accordingly. But with Momentum, things get a little more interesting!

First, you calculate the same gradient as before (let’s call it g). Then, instead of just using this gradient to update your weight (which would be like taking one small step at a time), you multiply it by some momentum factor (let’s say m) and add that product to your previous velocity (v from the last iteration). This gives us an updated velocity:

v = m * v + g

Now, instead of updating our weight directly based on this gradient, we update it using our new velocity:

w = w learning_rate * v

So basically, Momentum helps us take bigger steps towards the right direction by combining our current gradient with some momentum from previous iterations. This can be especially helpful when training deep neural networks because they have a lot of weights that need to update simultaneously and it’s easy for them to get stuck in local minima (which is where Momentum comes in handy).

Here’s an example code snippet using TensorFlow:

# Define our model, loss function, optimizer, etc.
model = ... # Define the model
loss_fn = ... # Define the loss function
optimizer = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9) # Set learning rate and momentum factor for the optimizer

# Train the model using Momentum optimization
for epoch in range(num_epochs): # Loop through the specified number of epochs
    for batch_index, (x, y) in enumerate(train_dataset): # Loop through the training dataset
        with tf.GradientTape() as tape: # Use GradientTape to track the operations for automatic differentiation
            predictions = model(x) # Make predictions using the model
            loss = loss_fn(y, predictions) # Calculate the loss between the predictions and the actual labels
        
        # Calculate the gradient of our loss function with respect to each weight
        gradients = tape.gradient(loss, model.trainable_variables) # Use the tape to calculate the gradients of the loss with respect to the trainable variables
        
        # Update our weights using Momentum optimization (with a learning rate of 0.1 and momentum factor of 0.9)
        optimizer.apply_gradients(zip(gradients, model.trainable_variables)) # Use the optimizer to update the weights based on the calculated gradients

And that’s it! With this simple modification to your training process using Momentum optimization, you can help your weights move faster towards the right direction and avoid getting stuck in local minima.

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