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Introduction to JAX and Deep Learning

Convolutions

Explore the concept of convolutions as a mathematical operation that modifies one function by another. Learn the difference between continuous and discrete convolutions and their applications in machine learning. Understand how to implement one-dimensional convolutions using JAX's numpy and scipy libraries for vectors, gaining practical skills in signal processing and deep learning contexts.

We'll cover the following...

For two functions, f and g, convolution (represented by *) is a mathematical operation expressing how the shape of f is modified by g.

(f∗g)(t):=∫−∞∞f(τ)g(t−τ)dτ(f * g)(t) := \int_{-\infty}^\infty f(\tau) g(t - \tau) \, d\tau

Example

As an example, we have ...

f(x) and g(x) represent the sine and cosine waves respectively