patrick-kidger / patrick-kidger/diffrax
Paper - Correcting auto-differentiation in neural-ODE training
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Description
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Does the use of auto-differentiation yield reasonable updates to deep neural networks that represent neural ODEs? Through mathematical analysis and numerical evidence, we find that when the neural network employs high-order forms to approximate the underlying ODE flows (such as the Linear Multistep Method (LMM)), brute-force computation using auto-differentiation often produces non-converging artificial oscillations. In the case of Leapfrog, we propose a straightforward post-processing technique that effectively eliminates these oscillations, rectifies the gradient computation and thus respects the updates of the underlying flow.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
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Research direction
Start by reading the linked paper and then inspect Diffrax's autodifferentiable numerical ODE solver entry points; the issue names no files or tests. Establish whether the paper's proposed correction fits the project, and define completion with an agreed implementation scope and numerical evidence.
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Assessment
- Tech stack
- python
- Domain
- machine-learning
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 15/100