  A particular direction of recent advance about stochastic deep-learning
algorithms has been about uncovering a rather mysterious heavy-tailed nature of
the stationary distribution of these algorithms, even when the data
distribution is not so. Moreover, the heavy-tail index is known to show
interesting dependence on the input dimension of the net, the mini-batch size
and the step size of the algorithm. In this short note, we undertake an
experimental study of this index for S.G.D. while training a $\relu$ gate (in
the realizable and in the binary classification setup) and for a variant of
S.G.D. that was proven in Karmakar and Mukherjee (2022) for ReLU realizable
data. From our experiments we conjecture that these two algorithms have similar
heavy-tail behaviour on any data where the latter can be proven to converge.
Secondly, we demonstrate that the heavy-tail index of the late time iterates in
this model scenario has strikingly different properties than either what has
been proven for linear hypothesis classes or what has been previously
demonstrated for large nets.
