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Disclaimer: I have no idea how machine learning algorithms work. I work with problems so huge they do not fit on a single device. Multiple devices each own a

Disclaimer: I have no idea how machine learning algorithms work. I work with problems so huge they do not fit on a single device. Multiple devices each own a small piece of the global problem. They solve a local problem and they must communicate over a network in order to solve the global problem. This is almost universally true. You would know more than I in this field, and I expect it really is better to swap a partition than it is to use a network. There are certain methods in HPC applications that are almost universally avoided because of how terribly they scale to a large distributed memory system. Matrix multiplies are one of them. Outside of a handful of ab initio computational chemistry algorithms (which are incredibly important), basically the only reason someone does a large dense matrix-multiply on a supercomputer is usually because they're running a benchmark and they're not solving a real science problem. Folks more knowledgeable than me here feel free to jump in.

mathisfun123 3y ago
You guys are talking past each other but really talking about the same thing - arithmetic intensity. You're talking about FEA or some other grid solver/discretized PDE/DFT type thing where the matmuls are small because the mesh is highly refined and you've assumed the potentials/fields/effects are hyper-local. But that's not accident or dumb luck - the problems in scientific HPC are modeled using these kinds potentials post-hoc ie so that they can be distributed across so many cores. What I'm saying is it's not like a global solver (ie taking into account all to all interactions) wouldn't be more accurate right? It's just an insane proposition because surprise surprise that would require an enormous matmul during the update, which you can't do efficiently, even on a GPU, for the same reason the ML folks can't: the arithmetic intensity isn't high enough and so you can incur i/o costs (memory or network, same thing at this scale).
BobbyJo 3y ago
> There are certain methods in HPC applications that are almost universally avoided because of how terribly they scale to a large distributed memory system. Matrix multiplies are one of them. Neural networks, which are the basis for nearly all modern AI, are implemented as a mixture of sparse and dense matrix multiplies, depending on the neural architecture.

mathisfun123 3y ago

You guys are talking past each other but really talking about the same thing - arithmetic intensity. You're talking about FEA or some other grid solver/discretized PDE/DFT type thing where the matmuls are small because the mesh is highly refined and you've assumed the potentials/fields/effects are hyper-local. But that's not accident or dumb luck - the problems in scientific HPC are modeled using these kinds potentials post-hoc ie so that they can be distributed across so many cores. What I'm saying is it's not like a global solver (ie taking into account all to all interactions) wouldn't be more accurate right? It's just an insane proposition because surprise surprise that would require an enormous matmul during the update, which you can't do efficiently, even on a GPU, for the same reason the ML folks can't: the arithmetic intensity isn't high enough and so you can incur i/o costs (memory or network, same thing at this scale).

BobbyJo 3y ago

> There are certain methods in HPC applications that are almost universally avoided because of how terribly they scale to a large distributed memory system. Matrix multiplies are one of them. Neural networks, which are the basis for nearly all modern AI, are implemented as a mixture of sparse and dense matrix multiplies, depending on the neural architecture.