This paper that is built on top of Bhaskara etal. Moreover, the described analysis is related to the recovery of assemblies of neurons. Overall, the paper gave a detailed analysis of the tensor decomposition using l 1and a general case although a better differentiation with respect to [3] is needed. Moreover, the proposed application of recovering assemblies of neurons is misleading. For instance, the application aim is not clear enough because the abstract mentioned recovering assemblies of neurons but on the main text and problem formulation aims to talks about assembly association and the structure intersection of cell assembly intersection, and also how the problem is posed since there is ambiguous definitions, e.g. Moreover, what would it happen if there is no association among neurons but there is still an overlap as have been shown in different papers [1,2]?

We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons. Assemblies are large sets of neurons representing specific memories or concepts.