Surya Ganguli presented exciting new results improving from his last NIPS workshop and last COSYNE workshop talks. Our experimental limitations put us to analyze severely subsampled data, and we often find correlations and low-dimensional dynamics. Surya asks “How would dynamical portraits change if we record from more neurons?” This time he had detailed results for single-trial experiments. Using matrix perturbation, random matrix, and non-commutative probability theory, they show a sharp phase transition in recoverability of the manifold. Their model was linear Gaussian, namely $R = U X + Z$, where X is a low-rank neural trajectories over time, U is a sparse subsampling matrix, and Z is additive Gaussian noise. The bound for recovery had a form of $\mathrm{SNR} \sqrt{MP} \geq K$, where K is the dimension of the latent dynamics, P is the temporal duration (samples), M is the number of subsampled neurons, and SNR denotes the signal-to-noise ratio of a single neuron.