JuliaDiff / JuliaDiff/ChainRules.jl

Make sensitivities for structured matrix arguments structured

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design
Dominant language
Julia
Stars
475
Forks
98
PR merge metrics
No merged PRs in 30d

Description

Quoting Will in #29:

FWIW, the other thing to think about is what is actually happening computationally under the hood. Ultimately the Diagonal matrix type doesn't use any off-diagonal elements when used in e.g. a matrix-matrix multiply - the Diagonal type simply doesn't allow you to have non-zero off-diagonal elements, so it's a slightly odd question to ask what happens if you perturb the off-diagonals by an infinitesimal amount (i.e. compute the gradient w.r.t. them).

It's this slightly weird situation in which thinking about a Diagonal matrix as a regular dense matrix that happens to contain zeros on its off-diagonals isn't really faithful to the semantics of the type (not sure if I've really phrased that correctly, but hopefully the gist is clear)

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Research direction

Start by reading the discussion quoted from issue #29 and examining how Julia's Diagonal type behaves in matrix-matrix multiplication. Determine the intended sensitivity semantics for structured matrix arguments, especially off-diagonal elements, and define completion as an agreed design that faithfully reflects those semantics.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
devtools
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
25/100

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