weakness of the manuscript. Should the manuscript be rejected for this reason (which is not unlikely), I would like to encourage the authors to get the maths correct and resubmit to a leading computational neuroscience journal (e.g., PLoS CompBiol or PNAS). ORIGINALITY: 8 ============== The investigated question is around already for several years. The paper is original in that someone finally worked out the details of the maths of both representations. This is a very important contribution which requires a fine understanding of both theories. A big "Thanks" to the authors for this! Yet, I think that two relevant papers are missing: - Savin, C., Deneve, S. Spatio-temporal representations of uncertainty in spiking neural networks, Advances in Neural Information Processing Systems 27, 2014. This paper relaxes the assumption of a one-to-one correspondence between neurons and latent variables for sampling. - Bill J, Buesing L, Habenschuss S, Nessler B, Maass W, et al. (2015) Distributed Bayesian Computation and Self-Organized Learning in Sheets of Spiking Neurons with Local Lateral Inhibition. PLOS ONE In the discussion section, a similar relation between sampling and PPCs is outlined, for the case of a generative mixture model instead of the linear Gaussian model considered here. SIGNIFICANCE: 10 ================ Sampling vs PPC representations is a hotly debated topic for years, staging the main track talks of the most important computational neuroscience conferences. Reconciling the two views is highly relevant for anyone who studies neural representations of uncertainty. CONCLUSION ========== This is one of the papers, I feel thankful that it has finally been written (and researched, of course). Unfortunately, the paper suffers from an unjustifiable amount of typos and errors in the maths. If accepted to NIPS, I would suggest a talk rather than a poster. Overall, I tend to recommend acceptance, but I could perfectly understand if the quality of presentation does not merit acceptance at NIPS. Due to the very mixed impression, I assigned a separate score to each of the four reviewing criteria. The geometric mean leads to the suggested overall score 6/10. SPECIFIC COMMENTS ================= - L163ff: Strictly speaking the statement is correct: A complete basis A permits to perfectly model the noise in I \sim N(T(s), noise). But I think this is not what the authors mean in the following: The example addresses how well Ax approximates the template T(s) without a noise sample. If so, the discussion should be corrected. Errors in the derivation / equations ------------------------------------ Since I walked through the derivation anyway, I also include some suggestions. - Eq (1): The base measure is missing: ... + f(s); alternatively write p(s|r) \propto exp(...) to match eq (6) of the main result. - L66: Missing def. of PF_i; required e.g. in line 137 - L90: p(s|x) not r - L90 and general: The entire identification of r <--> multiple samples x^[1:t] is missing, but crucial for the paper. - Eq after L92: This should be eq (3). These are the "forward physics" from stimulus generation to spikes in the retina. The name p_exp(I|s) is used later in L109ff, so it should be assigned here. - Eq (3): Copy of the previous eq with wrong subscript. Could be deleted, right? - Eq after L106: Missing def of \bar x = 1/t \sum x^i (important: the mean is not weighted by p(x^i) ) - Eq after L107: p_exp(x|s) is not defined and also not needed: delete equation w/o replacement - L108 and L109: The equality assumption is undefined and not needed. Both lines can be deleted. The next eq is valid immediately (and would deserve a number). - L117 and eq 6: At some point r (from eq 1) and x^[1:t] must be identified with another. Here could be a good point. Section 4 could then refer to this in the discussion of binary x^i and longer spike counts r. Minor Points ------------ - Figure 1 is not referred to in the text. - L92: clarify "periphery" (e.g. retinal ganglion cells). This is an essential step, bringing the "pixel image" into the brain, and would deserve an extra sentence. - L113: The Gaussian converges to a dirac-delta. Then the integration leads to the desired statement. Typos ----- - Figure 1, binary samples, y_ticks: x_n (not N) - Caption Fig 1: e.g.,~ - L48: in _a_ pro... - L66: PF_n (not 2) - L71: ~and~ - L77: x^(i) not t [general suggestion: use different running indices for time and neurons; currently both are i] - Almost all the identity matrices render as "[]" (at least in my pdf viewer). Only in the eq after L92, it is displayed correctly. - Footnote 1: section_,_ valid for infinitely _many_ samples_,_ ... - L106: Dr - Caption Fig 2: asymptotic - L121: section 3 (?, not 4) - L126: neuron~s~ - Figure 3C: ylabels don't match notation in 3B (x and x'), but are illustrations of these points - L165: ~for~ - L200: invariant - L220: _is_ - L229: _easy_ or _simple_ - L230: correspond _to_ - L232: ~a~ - L242: ~the~
- L66: PF_n (not 2) - L71: ~and~ - L77: x^(i) not t [general suggestion: use different running indices for time and neurons; currently both are i] - Almost all the identity matrices render as "[]" (at least in my pdf viewer). Only in the eq after L92, it is displayed correctly.