3 papers
math.OC2026
A Counterexample to Fourier Alignment in Single-Neuron Modular Addition
Gautam Neelakantan Memana
We give a negative solution to MAIS-O60. We first construct an example in which an initially active ReLU neuron becomes completely inactive in finite time and thereafter remains fr…
math.AP2026
Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs
Gautam Neelakantan Memana
We establish a comparison principle for viscosity subsolutions and supersolutions of a broad class of second-order quasilinear, maximally subelliptic PDEs on general manifolds. In…
math.AP2024
A regularity theorem for fully nonlinear maximally subelliptic PDE
Gautam Neelakantan Memana
We prove a sharp interior regularity theorem for fully nonlinear maximally subelliptic PDE in non-isotropic Sobolev spaces adapted to maximally subelliptic operators. This result c…