Zach Furman

Gradient descent navigates a continuous parameter space using only local information.

If both processes are somehow arriving at similar destinations, compositional solutions to learning problems, then something interesting is happening in how neural network loss landscapes are structured, something we do not yet understand.

We will return to this issue at the end of the post.

So the hypothesis raises as many questions as it answers.

But it offers something valuable.

A frame.

If deep learning is doing a form of program synthesis, that gives us a way to connect disparate observations about generalization, about convergence of representations, about why scaling works, into a coherent picture.

Whether this picture can make sense of more than just these particular examples is what we'll explore next.

There's a details box here with the title clarifying the hypothesis.

The box contents are omitted from this narration.

Subheading.

Why this isn't enough.

The preceding case studies provide a strong existence proof.

Deep neural networks are capable of learning and implementing non-trivial, compositional algorithms.

The evidence that Inception V1 solves image classification by composing circuits, or that a transformer solves modular addition by discovering a Fourier-based algorithm, is quite hard to argue with.

And, of course, there are more examples than these which we have not discussed.

Still, the question remains.

Is this the exception or the rule?

It would be completely consistent with the evidence presented so far for this type of behavior to just be a strange-edge case.

Unfortunately, mechanistic interpretability is not yet enough to settle the question.