Reviewer #1 (Public Review):
This work seeks to understand how behaviour-related information is represented in the neural activity of the primate motor cortex. To this end, a statistical model of neural activity is presented that enables a non-linear separation of behaviour-related from unrelated activity. As a generative model, it enables the separate analysis of these two activity modes, here primarily done by assessing the decoding performance of hand movements the monkeys perform in the experiments. Several lines of analysis are presented to show that while the neurons with significant tuning to movements strongly contribute to the behaviourally-relevant activity subspace, less or un-tuned neurons also carry decodable information. It is further shown that the discovered subspaces enable linear decoding, leading the authors to conclude that motor cortex read-out can be linear.
Strengths:
In my opinion, using an expressive generative model to analyse neural state spaces is an interesting approach to understanding neural population coding. While potentially sacrificing interpretability, this approach allows capturing both redundancies and synergies in the code as done in this paper. The model presented here is a natural non-linear extension of a previous linear model (PSID) and
Weaknesses:
First, the model in the paper is almost identical to an existing VAE model (TNDM) that makes use of weak supervision with behaviour in the same way [1]. This paper should at least be referenced. If the authors wish they could compare their model to TNDM, which combines a state space model with smoothing similar to LFADS. Given that TNDM achieves very good behaviour reconstructions, it may be on par with this model without the need for a Kalman filter (and hence may achieve better separation of behaviour-related and unrelated dynamics).
Second, in my opinion, the claims regarding identifiability are overstated - this matters as the results depend on this to some extent. Recent work shows that VAEs generally suffer from identifiability problems due to the Gaussian latent space [2]. This paper also hints that weak supervision may help to resolve such issues, so this model as well as TNDM and CEBRA may indeed benefit from this. In addition however, it appears that the relative weight of the KL Divergence in the VAE objective is chosen very small compared to the likelihood (0.1%), so the influence of the prior is weak and the model may essentially learn the average neural trajectories while underestimating the noise in the latent variables. This, in turn, could mean that the model will not autoencode neural activity as well as it should, note that an average R2 in this case will still be high (I could not see how this is actually computed). At the same time, the behaviour R2 will be large simply because the different movement trajectories are very distinct. Since the paper makes claims about the roles of different neurons, it would be important to understand how well their single trial activities are reconstructed, which can perhaps best be investigated by comparing the Poisson likelihood (LFADS is a good baseline model). Taken together, while it certainly makes sense that well-tuned neurons contribute more to behaviour decoding, I worry that the very interesting claim that neurons with weak tuning contain behavioural signals is not well supported.
Third, and relating to this issue, I could not entirely follow the reasoning in the section arguing that behavioural information can be inferred from neurons with weak selectivity, but that it is not linearly decodable. It is right to test if weak supervision signals bleed into the irrelevant subspace, but I could not follow the explanations. Why, for instance, is the ANN decoder on raw data (I assume this is a decoder trained fully supervised) not equal in performance to the revenant distilled signals? Should a well-trained non-linear decoder not simply yield a performance ceiling? Next, if I understand correctly, distilled signals were obtained from the full model. How does a model perform trained only on the weakly tuned neurons? Is it possible that the subspaces obtained with the model are just not optimally aligned for decoding? This could be a result of limited identifiability or model specifics that bias reconstruction to averages (a well-known problem of VAEs). I, therefore, think this analysis should be complemented with tests that do not depend on the model.
Finally, a more technical issue to note is related to the choice to learn a non-parametric prior instead of using a conventional Gaussian prior. How is this implemented? Is just a single sample taken during a forward pass? I worry this may be insufficient as this would not sample the prior well, and some other strategy such as importance sampling may be required (unless the prior is not relevant as it weakly contributed to the ELBO, in which case this choice seems not very relevant). Generally, it would be useful to see visualisations of the latent variables to see how information about behaviour is represented by the model.
Summary:
This paper presents a very interesting analysis, but I have several concerns as to well the analysis supports the main conclusions. I think the work could benefit from an additional complementary analysis that seeks to confirm with another method if weakly tuned neurons indeed show an encoding that differs qualitatively from the strongly tuned ones.
[1] Hurwitz, Cole, et al. "Targeted neural dynamical modeling." Advances in Neural Information Processing Systems 34 (2021): 29379-29392.<br /> [2] Hyvarinen, Aapo, Ilyes Khemakhem, and Hiroshi Morioka. "Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning." arXiv preprint arXiv:2303.16535 (2023).