Summary and Contributions: The authors suggest a statistical state-space model to infer latent variables that exist in addition to position information in hippocampal data. The authors examine a scenario where the neural activity fluctuates between several alternative representations while being in the same environment. They then decode the active representation at each moment in time – both for the original environments and for intermediate (morphed) environments. The analysis shows that neural representation in the same environment changes between different trials. Furthermore, the analysis suggests that representations might change within single trials.
Strengths: The results highlight the fact that multiple representations might exist for the same environment (in line with recent results by Sheintuch et al, Current Biology 2020). Incorporating multiple representations into a decoding model is, to the best of my knowledge, a novel contribution.
Weaknesses: It is not clear how allowing for multiple representations of the same environment contributes to decoding. While it is clear that the framework takes this into account, there is no analysis of the effect this has on decoding. One of the main claims – rapid fluctuations (within trial) of representations – is only weakly supported. The analysis seems very sensitive to the signal-to-noise ratio, but this is not sufficiently discussed.
Correctness: The claim of multiple representations is shown in Figure 2, but no statistics are provided about its prevalence. This phenomenon has been reported elsewhere (Sheintuch et al), so is probably correct. The claim of rapid fluctuations seems weakly supported. Figure 2 shows within-trial fluctuations, but these are based on single cells. This implies high sensitivity to SNR. When analyzing the full population, the rapid fluctuations seem to almost vanish (Figure 4B). This is also in line with the reports of Sheintuch et al, where transitions were only between trials.
Clarity: The paper is clearly written, and the methods are explained well. One point that requires more elaboration is the definition of I_j,k and K_j. For instance, in equation 1 is the same p_k used for different js? It would be useful to include a sketch of z_t and I_jk in figure 1.
Relation to Prior Work: The work of Sheintuch et al is highly relevant and not mentioned here. Also unmentioned are the papers mentioned in the introduction of this work that describe multiple representations of the same environment.
Additional Feedback: POST REBUTTAL UPDATE: The authors answered some of my concerns, but not all. Specifically, they showed that incorporating multiple representations improves decoding, and that representations fluctuate within single trials. Although I'm left unsure about the interplay between fluctuations - in a single trial of a morph, do representation oscillate between single versions of the base environments or between all combinations? I am still worried that most of the results are from single cell analyses, which are greatly affected by low SNR. And in the population analysis - there is no mention of the effect of SNR, although it seems to matter quite a lot. Overall - I raise my score from 5 to 6 -------------------------------------------------- 1. L170-171: Were other values of K tested for k-means? Were all cells place cells? 2. Figure 2: it would be helpful to flip the order of rows in panel C and include the 0,1 morph levels. This would make the similarity fraction point in a manner consistent with row ordering. 3. L218: “moment-to-moment fluctuations”. The figure shows S as a function of position, and not of time. It would be helpful to also view this as a function of time. 4. L263: “shifts to environment 1 by positions 180-450” . Is each trial a single sweep? The wording of the sentence suggests events that unfold as a function of time, and not of space. 5. Figure 4B: Is there a relation between the positions with ambiguity (around 300) and the SNR? It’s hard to see, but figure 2B seems to show less place fields there.
Summary and Contributions: The authors propose a new type of state-space modelling framework, specifically meant to address issues with variability if neural firing, and ambiguous environments, The performance of the decoder is tested on a data set from hippocampal place cells.
Strengths: - The background is well described, and the model is described in a good amount of detail - The contribution seems interesting and promising - The writing is good and the figures clear - This is certainly relevant to the NeurIPS community and seems novel
Weaknesses: - Lack of comparison with other algorithms (see below)
Correctness: - I am not an expert on this area, but I did not spot any errors
Clarity: - Clear and well written
Relation to Prior Work: - It would be useful to have comparison to other models, e.g. how this relates to other types of bayesian smoothing and filtering, hidden markov models etc. A direct comparison with the output of other models would have been even better- While the conditioning on X is stated to be implicit, it might still be preferable to have it part of the notation as a reminder, e.g. with subscript X
Additional Feedback: - While the conditioning on X is stated to be implicit, it might still be preferable to have it part of the notation as a reminder, e.g. with subscript X
Summary and Contributions: This submission presents a state-space-based modeling framework to study the hippocampal remapping. This method allows instantaneous estimation of the environment represented by the neural population. The authors applied the algorithm to analyze the calcium imaging data collected when the mouse was moving though ambiguous virtual environment under different morph levels. The authors found that the states represented in the neural population can rapidly fluctuate even within a single trial.
Strengths: I enjoyed reading the paper. The probabilistic framework to study remapping is quite appealing. Previously most remapping analyses are done by taking the averaged firing rate maps at the time scale of minutes (except for a few studies). The analysis of the hippocampal calcium imaging dataset is quite detailed. The results presented in Fig 2,3,4 are scientifically interesting. In particular, I found Fig 4B,C to be informative.
Weaknesses: * While I appreciate the probabilistic approach in the paper, the algorithm seems to be a quite straight-forward extension of previous state-space models (HMMs). So I feel the algorithm by itself does not carry too much novelty. * The results from this algorithm is not compared to alternative methods. Would simple methods, such as PCA, also yield similar results shown in Fig 4B,C,D? It would be helpful to justify the necessity of using such more complicated method to analyze these data. The applicability of the proposed method seems to be quite restrictive. The paper would be stronger if the authors could demonstrate or propose some other potentially applications. Overall, I feel that the scientific results presented upon further substantiation (based on larger sample size) could result in a solid scientific paper in a scientific journal. It’s unclear to me how appealing the current manuscript would be for the NeurIPS audience partly due to the incremental technical contributions. Another technical issue: the Gamma model in Eq (6) is likely a poor model for the deconvolve calcium response. It would be useful to show how well the model can fit the data. ***************modified after rebuttal I thank the authors for the feedback. After seeing everything, I remain slight negative about this manuscript. But I also feel this is a borderline paper- perhaps the arguments could be made either way. I am still slightly negative, because I think i) the algorithmic contribution is too incremental; ii) I am not convinced the benefit/gain of modeling the transition probability, and whether one could already obtains most of the results at the population level by running simple procedure such as PCA etc. The authors' rebuttal did not fully address these issues.
Correctness: The claims and method appears to be sound.
Clarity: The paper is well written and relatively easy to follow.
Relation to Prior Work: yes, the relation to the previous work is well described.
Additional Feedback: More detailed comments: * Line 204-206. Is trial 5 and 96 from the same recording session? * It is a bit odd that Fig 1 does not contain X_i. It would be useful to add that in. * I notice that ref  is now published as a paper at Cell. It would be good to update the reference. * The title seems to be too vague. It might be beneficial to replace it with a more specific title.
Summary and Contributions: This paper explores the significance of trial to trial variability in neural responses, and also moment to moment variability within a single trial, particularly in uncertain environments. The paper proposes a state-space modeling framework to address both issues, and then interprets neurophysiological data in terms of the framework.
Strengths: The neurophysiological phenomenon being addressed seems very important, and computationalists need to be more aware of the variability in neural responses. The theoretical framework presented proposes on interpretation of data that seem otherwise noisy. The theory itself seems sensible.
Weaknesses: Although the model is a nice instantiation of a qualitative theory, I'm uncertain what value the model adds beyond the qualitative theory. The primary validation of the model is the fact that its interpretations seem to be consistent with the level of uncertainty in the environment (the morph level). I'm left with lots of questions: What implications does this model have for cognition more broadly? Can the model predict phenomena it wasn't explicitly designed to explain? If brains are constantly inferring a latent representation that characterizes the environment, where does this representation live in the brain? I can't tell whether the model is a mechanism designed to explain data or whether it is supposed to give insight into computation in the brain. I'd hope a NeurIPS paper would do the latter and would be more enthusiastic about the paper if it was able to step back from the nitty gritty of the data and give a bigger picture view of why a non-neuroscientist should care about the phenomena and the model. An alternative hypothesis I wonder about is whether the brain has intrinsic stochasticity, as the model seems to indicate, or whether there are factors driving switches that are presently unaccounted for. For example, could the trial-to-trial variation be driven by recency effects (experience on the last few trials) in a systematic manner? Would such sequential dependencies be evidence against the current model?
Correctness: The work seems well carried out, although I did not look at the appendix to evaluate the details of the modeling.
Clarity: The paper is very well written. I realize that there are only 8 pages, but details of the experiment are sketchy, which made it challenging to understand exactly what the data represent. It would have helped to explain the experiment and present the data early in the paper to help motivate the model and make its purpose more concrete.
Relation to Prior Work: The framing of the work in terms of existing literature is outstanding. Very clear.