First: what is equivariance? Well, it’s a fancy way of saying that if you rotate an image by some angle, the output of your model should also be rotated by the same angle (or at least close to it). This might seem like common sense, but as we all know in AI land, things are never quite that simple.

So why is equivariance important? Well, for starters, it allows us to generalize better to new data points. If our model can handle rotations and other transformations without losing accuracy, then we’re less likely to overfit on the training set and more likely to perform well on unseen data.

But here’s where things get interesting: CNNs are not inherently equivariant! In fact, they’re actually invariant meaning that if you rotate an image by some angle, the output of your model will be the same as if you hadn’t rotated it at all.

Now, don’t panic just yet there is a way to make CNNs equivariant! It involves adding some fancy math called group theory and convolutional operations that are specifically designed for this purpose. But before we dive into the details of how it works, let’s take a step back and ask ourselves: why do we even care about equivariance in the first place?

Well, as AI researchers, our ultimate goal is to create models that can accurately predict outcomes based on input data. And if those predictions are going to be useful in real-world applications (like self-driving cars or medical diagnosis), then they need to be able to handle a wide variety of inputs not just the ones we see during training time.

So by making our models equivariant, we’re essentially future-proofing them against any potential changes in input data. And that’s pretty ***** cool if you ask me! But enough talk for now Let’s get started with some code and see how it all works in practice.

In the next installment of this series (which will be coming soon to a blog near you), we’ll explore some popular techniques for making CNNs equivariant, as well as their benefits and drawbacks. Later !