Is ConFIG 'non-conflicting' or not in the table of torchJD documentation?

[huzeou]

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!

[PierreQuinton]

Hey, as far as I remember, ConFIG is originally only defined on full rank matrices that are well conditioned. As Aggregators are mapping from any matrix to their aggregation, we had to use the pseudo-inverse definition, that works on those matrices too, 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 ConFIG can conflict on some inputs, it is not non-conflicting.

[huzeou]

Thank you! This is quite helpful