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I have a computational graph (DAG) consisting of element-wise operations (potentially with broadcasting) and reshape/reduce operations (reshaping/sum/max). I'm trying to understand how vertical kernel fusion is performed and whether it's something that can be done without developing/using external tools like a linear algebra compiler or some custom IR format (like HLO IR for JAX).

The first thing that came to my mind was that I could simply have symbols corresponding to element-wise operations (like * for multiplication and sin( for sine) and once the computational graph is assembled, literally concatenate these symbols corresponding to element-wise operations into one big operation (custom schema to keep track of data pointer names, but still I imagine that's possible). And since I'm only using element-wise operations, the data access is very predictable and linear, so it's perhaps possible to automatically generate performant-ish kernels for both CPU and potentially other processing units.

Is this possible? Am I on the right track here? Or is another approach typically used? If so, where can I read more about it.

thanks :)

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