A key requirement is that the concepts be interpretable. Existing CBMs tackle this desideratum using a variety of heuristics based on unclear notions of interpretability, and fail to acquire concepts with the intended semantics.
All the material can be found in any text in nonlinear systems such as [28]. That is, the system can remain arbitrarily close to the equilibrium point if it starts sufficiently close.
While our presentation focuses on this finite-sum structure, most of our convergence results can easily be adapted to the general stochastic setting (see App. D).