Comments (7)
For Hessians, is it just the same coloring but on the adjacency matrix?
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What methods are used in the bidirectional coloring?
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In case of direct recovery, star coloring would work for Hessians. If we plan on extending the stack to include substitution based evaluation, we will have to employ acylic coloring as well.
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We can use either greedy distance-2 coloring (similar to distance-1 coloring) or partial distance-2 coloring in cases where we do not mix both forward and backward AD modes.
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Star coloring must satisfy the two conditions: (1) every pair of adjacent vertices receives distinct colors (a distance-1 coloring), and (2) every path on four vertices uses at least three colors.
Acyclic coloring has the conditions: (1) the coloring corresponds to a distance-1 coloring, and (2) vertices in every cycle of the graph are assigned at least three distinct colors. The name acyclic comes from the fact that subgraph induced by vertices assigned any two colors is a collection of trees—and hence is acyclic.
reference: What Color is your Jacobian?
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Add some acyclic coloring to the list as well then since substitution seems to be the proper way to handle bidirectional and forward-over-reverse.
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The original paper does not talk about acyclic coloring and I can't find any good resources that discuss it either. Will add it to the to-do as soon as I get a reliable paper on it.
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Related Issues (20)
- Hessian decompression implementation HOT 3
- matrix_colors can overwrite input (remove stored zeros) HOT 2
- complex number support? HOT 3
- Examples in README.md rely on deprecated package HOT 1
- Different numerical behaviour after updating SparseDiffTools.jl from v1.16.1 to v1.16.3 HOT 11
- Define `SparseJacFunction` struct HOT 7
- Sparsity Detection not working in combination with OffsetArrays
- control on chunk_size in chunk_size HOT 8
- Report Weird Behavior HOT 8
- Repeated HVPs With Sub-Sampling HOT 3
- Threaded Jacobian calls HOT 4
- Hessian Vector Product Operator HOT 2
- `autoback_hesvec` fails with `SparseMatrixCSC` HOT 4
- In-place `*_jacvec!` assumes square jacobian HOT 5
- Readme uses deprecated package SparsityDetection HOT 1
- Support for structured sparsity in sparse hessian
- `BandedMatrix` sparsity computes only diagonal elements HOT 2
- Unable to compute sparse jacobian for reaction system (UndefVarError: m not defined) HOT 2
- tril
- Documentation offline HOT 2
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