3 papers
cs.LG2026
Why Deep Jacobian Spectra Separate: Depth-Induced Scaling and Singular-Vector Alignment
Nathanaël Haas, François Gatine, Augustin M Cosse +1
Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically availa…
cs.IT2025
Infinite families of graphs and stable completion of arbitrary matrices, Part I
Augustin Cosse
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the c…
cs.IT2024
Sparse recovery from quadratic equations, part II: hardness and incoherence
Augustin Cosse
We study the square root bottleneck in the recovery of sparse vectors from quadratic equations. It is acknowledged that a sparse vector , $\| \mathbf…