Population adaptation in efficient balanced networks

Thank you for submitting your article "Population adaptation in efficient balanced networks" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Timothy Behrens as the Senior Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

This is a little jewel of a paper. It shows how adaptation in neurons and excitation-inhibition balance in the network can be viewed as arising from an optimisation principle. The simple cost function to be minimised is the sum of a term representing the error in signal transmission and one representing the metabolic cost of neuronal firing. The authors describe simple examples, working up to a model for orientation tuning, where they show how it naturally explains the main features of some classic observed perceptual adaptation effects. They show how understanding the phenomenon requires considering the whole local network, not just single neurons. Clearly and elegantly written, the paper was a pleasure to read, and it lays a good foundation for both further theoretical elaboration and experimental investigations.

Note that some of these are suggestions, designed to improve the paper; the authors should use their best judgment as to whether or not to include them.

1) After Equation 2, δ_j should be δ_ij. (It doesn't make sense to have δ_j depend on i.)

2) We would suggest taking some of the inline equations and making them displayed. In particular, the equations for ŝ, r_i, f_i, g_i and Ω_ij. As a reader, we find it much easier to find relevant variables if we don't have to crawl through lines of text.

3) The same applies to the inline equations in Materials and methods (e.g., o_i).

4) I would also suggest putting just a little more detail of the derivation in the main text. I know these equations have been derived in a number of places, but for those who haven't memorized the derivations, even the Materials and methods will be tough to follow (especially since you switch to the multi-stimulus case). Why not just say, in the main text,

Neuron i spikes when

(s(t) – ŝ(t) – w_i)² + mu sum_j (f_j + δ_ij)² <

(s(t) – ŝ(t))^2 + mu sum_j f_j².

Define

V_i = g_i (sum_j w_j (s_j – ŝ_j) – mu f_i),

with a spike emitted when V_i > 1/2, at which point it is reset to -1/2. That, and a small amount of algebra, gives you Equation 2.

5) Along the same lines, we would strongly suggest that the authors expand the description in the network model section a bit. I think many readers would find the path from Equation 3 to Equation 5 a bit magical. I know the details are there in the 2013 Boerlin et al. paper, but, because of the importance of the present paper, I think filling them in here would complete the story presented here and make its message more accessible.

6) Materials and methods has a fair number of typos (we think): it's a mix of the one stimulus case (as in the main text) and the multi-stimulus case. Please check very carefully. The things we noticed:

- above Equation 3: W_ij should be w_ij.

- Equation 3: r_i should be f_i.

- one of the w's should be a transpose.

7) It would help to use Greek letters to label stimulus.

Reviewer #1:

While neuronal adaptation is useful for a number of reasons, it would seem to make it hard for downstream neurons to decode responses, since they would have to know the state of adaptation. The authors provide an elegant solution: they write down a cost function that explicitly takes metabolic cost into account, then apply a technique that Sophie Deneve pioneered about a decade ago to derive the optimal network. Through magic that to this day I don't fully understand, everything works, and downstream neurons don't have to know anything about the state of adaptation to decode near optimally. On top of that, an explanation of the famous tilt illusion falls naturally out of their formalism -- something that is hard to explain by Bayesian methods.

Reviewer #2:

This is a little jewel of a paper. It shows how adaptation in neurons and excitation-inhibition balance in the network can be viewed as arising from an optimisation principle. The simple cost function to be minimised is the sum of a term representing the error in signal transmission and one representing the metabolic cost of neuronal firing. The authors describe simple examples, working up to a model for orientation tuning, where they show how it naturally explains the main features of some classic observed perceptual adaptation effects. They show how understanding the phenomenon requires considering the whole local network, not just single neurons. Clearly and elegantly written, the paper was a pleasure to read, and it lays a good foundation for both further theoretical elaboration and experimental investigations.

I would only ask the authors to expand the description in the network model section a bit. I think many readers would find the path from Equation 3 to Equation 5 a bit magical. I know the details are there in the 2013 Boerlin et al. paper, but, because of the importance of the present paper, I think filling them in here would complete the story presented here and make its message more accessible.