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As someone who works in merging differential equations and machine learning, I have found this kind of work essential for what I do. Pervasive AD that allows me

mlevental 8y ago
how do you use AD for diffeqs? do you really have systems of diffeqs large enough that you need AD for evaluating a solution at a particular point? or do you need backbrop for something that i can't imagine?
- ChrisRackauckas 8y ago
  For parameter estimation. In parameter estimation, you have to evaluate the derivative of a cost function based on an ODE solution, which is usually something like the L2 norm between your numerical solution points and your data. The gradient of this cost function requires calculating the gradient of the solution with respect to the parameters, which can be done quite well via AD. We are finding that AD methods work better than the traditional sensitivity analysis methods in many cases.
  - mlevental 8y ago
    >parameter estimation you mean given some data that's modeled by an ODE you want to fit the ODE to the data (and therefore discover parameters of the ODE that would have produced that data) ?
    - ChrisRackauckas 8y ago
      Yes exactly.
EE84M3i 8y ago
As someone who works in merging differential equations and machine learning, I have found this kind of work essential for what I do. Pervasive AD that allows merging neural networks and diffeq solvers is allowing us to explore all of kinds of new models and new problems. Sure it doesn't impact vanilla machine learning all that much (though Zygote.jl does allow for a lot of optimizations that wouldn't be possible with tracing-based AD), but it definitely opens up a new wave of AI possibilities. I thought I was having some kind of stroke or terrible deja-vu (didn't I read this comment earlier this morning?) until I realized you copy and pasted your comment from 20 hours ago on https://news.ycombinator.com/item?id=18594103 https://news.ycombinator.com/item?id=18594103
- ChrisRackauckas 8y ago
  Yeah, the other thread caught on so I copy/pasted this post to the thread people were using. But now this thread caught on too... something weird happened but :shrug:.
dnautics 8y ago
there are a few things about Flux that bugs me. It automatically assumes that I want to optimize matrix multiplications by parallelizing those against cores, which has Amdahl scaling, instead of parallelizing across samples in the batch, which has Gustafson scaling. It would probably help if batches and minibatches (or something like that) were datatypes, which they are not. Doing something like this would probably also help with distributing computation, down the line. I'm also not entirely sure what is going on under the hood with Tracker types, and the documentation is not that great, which became a problem when I was trying to chase down errors in something really custom I was doing. I much prefer Knet's way of autodifferentiating, which is more intuitive to me, but Knet's layering doesn't feel as nice as Flux's. I really wish GPU computation in Julia had a different semantic - by making it a 'virtual computational node', accessible using Distributed module with the same semantics as a totally separate node. That would really make async distributed batch processing a thing, the system could profile all the nodes in use and if we really want to get fancy be able to use something like JUMP to make best use of the processing power available to it.
- taliesinb 8y ago
  Can you elaborate on what you mean by "parallelizing those against cores" vs "parallelizing across samples in a batch"?
  - dnautics 8y ago
    so for example, if you want to do M = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1] v1 = [1,2,3,4] (column vector) v2 = [4,5,6,7] (column vector) you can either do (M * v1, M * v2) on two cores as r1a = [1 0 0 0 0 1 0 0] * v1 (core 1) r1b = [0 0 1 0 0 0 0 1] * v1 (core 2) r2a = [1 0 0 0 0 1 0 0] * v2 (core 1) r2b = [0 0 1 0 0 0 0 1] * v2 (core 2) then r1 = flatten([r1a, r1b]) r2 = flatten([r2a, r2b]) OR, you could just have the whole model in each core: r1 = M * v1 (core 1) r2 = M * v2 (core 2)
    - taliesinb 8y ago

mlevental 8y ago

how do you use AD for diffeqs? do you really have systems of diffeqs large enough that you need AD for evaluating a solution at a particular point? or do you need backbrop for something that i can't imagine?

ChrisRackauckas 8y ago
For parameter estimation. In parameter estimation, you have to evaluate the derivative of a cost function based on an ODE solution, which is usually something like the L2 norm between your numerical solution points and your data. The gradient of this cost function requires calculating the gradient of the solution with respect to the parameters, which can be done quite well via AD. We are finding that AD methods work better than the traditional sensitivity analysis methods in many cases.
- mlevental 8y ago
  >parameter estimation you mean given some data that's modeled by an ODE you want to fit the ODE to the data (and therefore discover parameters of the ODE that would have produced that data) ?
  - ChrisRackauckas 8y ago
    Yes exactly.

EE84M3i 8y ago

As someone who works in merging differential equations and machine learning, I have found this kind of work essential for what I do. Pervasive AD that allows merging neural networks and diffeq solvers is allowing us to explore all of kinds of new models and new problems. Sure it doesn't impact vanilla machine learning all that much (though Zygote.jl does allow for a lot of optimizations that wouldn't be possible with tracing-based AD), but it definitely opens up a new wave of AI possibilities. I thought I was having some kind of stroke or terrible deja-vu (didn't I read this comment earlier this morning?) until I realized you copy and pasted your comment from 20 hours ago on https://news.ycombinator.com/item?id=18594103 https://news.ycombinator.com/item?id=18594103

ChrisRackauckas 8y ago
Yeah, the other thread caught on so I copy/pasted this post to the thread people were using. But now this thread caught on too... something weird happened but :shrug:.

dnautics 8y ago

there are a few things about Flux that bugs me. It automatically assumes that I want to optimize matrix multiplications by parallelizing those against cores, which has Amdahl scaling, instead of parallelizing across samples in the batch, which has Gustafson scaling. It would probably help if batches and minibatches (or something like that) were datatypes, which they are not. Doing something like this would probably also help with distributing computation, down the line. I'm also not entirely sure what is going on under the hood with Tracker types, and the documentation is not that great, which became a problem when I was trying to chase down errors in something really custom I was doing. I much prefer Knet's way of autodifferentiating, which is more intuitive to me, but Knet's layering doesn't feel as nice as Flux's. I really wish GPU computation in Julia had a different semantic - by making it a 'virtual computational node', accessible using Distributed module with the same semantics as a totally separate node. That would really make async distributed batch processing a thing, the system could profile all the nodes in use and if we really want to get fancy be able to use something like JUMP to make best use of the processing power available to it.

taliesinb 8y ago
Can you elaborate on what you mean by "parallelizing those against cores" vs "parallelizing across samples in a batch"?
- dnautics 8y ago
  so for example, if you want to do M = [1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1] v1 = [1,2,3,4] (column vector) v2 = [4,5,6,7] (column vector) you can either do (M * v1, M * v2) on two cores as r1a = [1 0 0 0 0 1 0 0] * v1 (core 1) r1b = [0 0 1 0 0 0 0 1] * v1 (core 2) r2a = [1 0 0 0 0 1 0 0] * v2 (core 1) r2b = [0 0 1 0 0 0 0 1] * v2 (core 2) then r1 = flatten([r1a, r1b]) r2 = flatten([r2a, r2b]) OR, you could just have the whole model in each core: r1 = M * v1 (core 1) r2 = M * v2 (core 2)
  - taliesinb 8y ago