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Is ConFIG 'non-conflicting' or not in the table of torchJD documentation? #345
Description
Hi there,
In the table https://torchjd.org/stable/docs/aggregation/, ConFIG is labelled as not 'non-conflicting' which seems to oppose the original paper's claim.
I wonder if it is because you are implying the case where the matrix is not full-rank and the pseudo-inverse only gives a 'least-squares' solution instead of exact solution?
Thanks!
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PierreQuinton commentedon May 16, 2025
Hey, as far as I remember,
ConFIGis originally only defined on full rank matrices that are well conditioned. AsAggregators are mapping from any matrix to their aggregation, we had to extend the definition to those matrices too (with the pseudo-inverse), and we did so with the original author (See #223). Because of this, the aggregator might conflict on some matrices.Note that such matrices correspond to Jacobians of those points whose image are close to the Pareto front and so they are relevant to multi-objective optimization as the goal is to reach the Pareto front.
You can find a counter example to the non-conflicting property here #223 (comment). Note that this corresponds to a Pareto stationary situation.
As
ConFIGcan conflict on some inputs, it is not non-conflicting.