The basic idea is to have an expressive programming language where all constructs are differentiable. Since the composition of diffeomorphisms is a diffeomorphism, large programs (like ray-tracers) will be differentiable as a result.
No. It has nothing to do with diffeomorphisms (which are necessarily between spaces of the same dimension), but with piecewise differentiable functions.
It sounds like you're just describing an evolution of functional programming; where each area of computation in the program is contextually generalizable, because its set of inputs and outputs is smooth and differentiable.
One followup question: are you sure the maps need to be (or are generally intended to be) isomorphic? That strikes me as very limiting. I follow your point about compositions of diffeomorphisms being diffeomorphisms themselves, but do you need that invertibility to make this paradigm work?
Traditionally deep learning just meant a sequence of functions applied compositionally (hence the "deep") where each function (termed a layer) is a matrix multiply followed by some well-behaved non-linear function ("activation function"). These were differentiable by design and optimized using gradient descent.
But now the models we want to build are more complex structurally than this merely sequential composition of functions. We want to be able to use control flow, accept multiple inputs, return multiple outputs, etc but we still want the model to be differentiable so we can use an iterative optimization procedure like gradient descent. So this extension from what deep learning traditionally meant (a fairly restrictive class of sequential function compositions) to complex, branching models are now termed differentiable programs.
No “coding” required.
https://github.com/thunguyenphuoc/RenderNet https://papers.nips.cc/paper/8014-rendernet-a-deep-convoluti...
That's just bs. If you just read the ray-tracer article it clearly states that f(scene parameters) -> image is not differentiable -- simply put because of sharp edges of objects being rendered. Also the word `diffeomorphism` makes no sense at all in this context.