DeepOBS includes a stochastic quadratic problem with an eigenspectrum similar to what has been reported for neural networks.
Other stochastic quadratic problems (of different dimensionality or with a different Hessian structure) can be created easily using the net_quadratic_deep
class.
deepobs.pytorch.testproblems.testproblems_modules
net_quadratic_deep
quadratic/quadratic_deep