Paper ID: | 1908 |
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Title: | A forward model at Purkinje cell synapses facilitates cerebellar anticipatory control |

The authors design an architecture for modeling cerebellar behavior. The model is shown to be an adaptive LTI filter.

The paper is complete, interesting and properly explained. Throughout the text there are some typos. I am not able to perform an actual review of this paper, it is too far away from my field. Therefore I give marks based on a general impression.

1-Less confident (might not have understood significant parts)

A cerebellar theory is outlined by which a feedforward tracking controller can be trained to anticipate a reflexive feedback controller to explain smooth pursuit movements. The theory applies to linear, time invariant plants and extends previous work by proposing an optimality theory for the dynamics of the synaptic eligibility trace.

This is a solid theory paper that extends classical work from Marr, Albus, Lisbeger, Fujita, Porrill, and Kawato on adaptive filter models of cerebellum and combination with feedforward and feedback control theory. The theory is restricted to the linear case and could only work there. However, the conceptual idea of feedforward anticipation of a reflex controller is interesting enough to me that I was pleased with the paper. I would like the paper to include a discussion of nonlinear MIMO plants, in which case the rule would need to be generalized to be backpropagation-through-time through the system dynamics or real-time recurrent learning, right? It's worth a mention as this makes the theory more problematic (multidimensional eligibility traces, for example), and I would like to understand your thinking on the issue. Also, how would the forward model be learned? Some discussion is needed because I think it's a problem rarely discussed in presentations of this family of models.

2-Confident (read it all; understood it all reasonably well)

The authors extend the classic cerebellar model of Marr-Albus (1969). By doing so they also provide a framework to obtain an optimal eligibility trace. Their contribution is important in understanding the cerebellar function, but also may find practical applications in control-system problems. I would like to make a few comments regarding the exposition of their solution and its context with respect to previous works.

1) As a person from outside the control theory field, I found it difficult to follow some of the derivations and arguments in the manuscript. In particular, the authors might explain in more detail the meaning of matrices A, B, C and D on page 4 (perhaps also by referring back to them in Figure 2). They should also present the form of these matrices used in the simulations in section 3.4. Similarly, the quantities k_p and k_i on page 6 are not defined. They might be trivial for control theorist, but not for readers outside the field. 2) From what I understood, the eligibility trace (h_j on page 5) is computed from the known system transition matrix and cerebellar basis. However, in realistic biological setup this matrix will not be a priori known. How will the eligibility trace be estimated in the cerebellum? Is this matrix hard-coded in the cerebellar architecture? If so, how is it adapted to new tasks? If it is learnt, what would the learning rule be? 3) The framework proposed by the authors has some similarities with predictive coding proposed for vision (Rao and Ballard, Nat Neurosci, 1999). Could the authors expose the similarities and differences? One key difference seems to be that in the authors' approach the error signal e[n] is not used to compute the predicted output o[n], but only to adjust the weights. How would the authors motivate this choice? 4) If the goal of the study is to find a realistic model of cerebellum, the authors should discuss their results in context of experimental findings about cerebellum architecture and function. For example, human study performed by Blakmore et al. (NeuroReport, 2001) suggest that the cerebellum encodes the error signal. Is this finding consistent with what the authors propose? If not, could their model be used to explain the data? Minor comments: line 4: extend -> extent line 164: with relation -> with respect to line 165: get derive -> derive line 170: different -> difference line 177: e[k,n] -> did the authors mean e[k - n]? line 181: "has been computing convolving" - not clear what is meant, please correct line 202: subtracted to the current weight -> subtracted from the current weight line 220: meaning of symbols k_p and k_i is not clear line 226: why these values? what does "spaced by" mean? Is this spacing between tuning curves of different fibers? line 248: are crucial for not only that but also to account -> are not only crucial for [the delays?] but also they account line 304: what predictions precisely do the authors mean?

2-Confident (read it all; understood it all reasonably well)

The authors apply a feed-forward adaptive filter model of the cerebellum in eyeblink classical conditioning to prediction in smooth pursuit. They conclude that an eligibility trace in the learning rule is key to successful control.

Pros: - Interesting and novel application of eyeblink conditioning model to smooth pursuit. This gives a basis for a combined model with the potential to shed light on common cerebellar mechanisms underlying both tasks. I see this as the main contribution of the paper (which the title does not do justice). - Some good conceptual advances in understanding the learning and control in these types of models; for example, counter-factual vs factual is new to me, and an elucidating way of framing the problem. Cons: - Multiple typos: in references (e.g. first line should say (Bastian, 2006 and Lepora et al 2002 does not match [11]), equation formatting (e.g. dangling fullstops, the 'recompalir5' in one eqution, and lack of equation numbering, Fig ??); the text is generally well written however. Gives the impression of hurried writing for the deadline. Obviously, this is something that can be corrected given time. - While I like the paper and think I can see and appreciate its novelty, I am not sure that it does a good job in expressing its novelty and interest to a wider audience (who have not worked on modelling the cerebellum). The point about eligibility traces is abstract and is close to similar points made in cited papers. As I say above, I think the main novel contribution is a unified model of smooth pursuit and eyeblink conditioning, but this is not well articulated in the title, abstract and introduction. - This may be due to non-careful reading on my part, but I am unclear how the CS/US structure of classical conditioning maps on to the task in smooth pursuit. Does the CS indicate that the target is about to start moving, so the motor command for the smooth pursuit can be anticipated?

2-Confident (read it all; understood it all reasonably well)