Wow, I wish you'd written the article. Thank you. I can only imagine what you'd be able to explain if you had as much space as the author...
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?
Differential programming is not tied to functional programming. The Python library PyTorch enables differential programming since you can use almost arbitrary python code and differentiate it, including if-then control flow, allowing you to use gradient descent to optimize the parameters of your model.
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.
Comments
Wow, I wish you'd written the article. Thank you. I can only imagine what you'd be able to explain if you had as much space as the author...
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?
Differential programming is not tied to functional programming. The Python library PyTorch enables differential programming since you can use almost arbitrary python code and differentiate it, including if-then control flow, allowing you to use gradient descent to optimize the parameters of your model.
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.
Thank you, this added a lot more clarity.