3 papers
math.PR2025
A theoretical basis for model collapse in recursive training
Vivek Shripad Borkar
It is known that recursive training from generative models can lead to the so called `collapse' of the simulated probability distribution. This note shows that one in fact gets two…
math.OC2025
A dynamic view of some anomalous phenomena in SGD
Vivek Shripad Borkar
It has been observed by Belkin et al.\ that over-parametrized neural networks exhibit a `double descent' phenomenon. That is, as the model complexity (as reflected in the number of…
math.PR2024
Stochastic Approximation with Two Time Scales: The General Case
Vivek S Borkar
Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.