Neural codes are inevitably shaped by various kinds of biological constraints, e.g.

The authors derive optimal monotonic tuning functions under metabolic constraints by reformulating the problem as a constraint optimization problem, which apparently can be solved in closed form. Overall, the paper is of very high quality, but it is too dense and covers too much material for a 8 page NIPS paper. Before I make some more specific comments, I would urge the authors to focus on the single neuron/pair of neuron cases for this paper and leave the population analysis for a later publication or a extended journal version. The population part is only sketched in the paper and I am not quite sure if I understand the results and implications (also, there is no figure for this part, which doesn't help understanding it better). Specific comments: Equations 3 and 4: I am not sure I understand how equation 4 is a special case of equation 3. Figures 1-3: I find those figures very hard to parse.

Neural codes are inevitably shaped by various kinds of biological constraints, e.g.

Neural codes are inevitably shaped by various kinds of biological constraints, \emph{e.g.} noise and metabolic cost. Here we formulate a coding framework which explicitly deals with noise and the metabolic costs associated with the neural representation of information, and analytically derive the optimal neural code for monotonic response functions and arbitrary stimulus distributions. For a single neuron, the theory predicts a family of optimal response functions depending on the metabolic budget and noise characteristics. Interestingly, the well-known histogram equalization solution can be viewed as a special case when metabolic resources are unlimited. For a pair of neurons, our theory suggests that under more severe metabolic constraints, ON-OFF coding is an increasingly more efficient coding scheme compared to ON-ON or OFF-OFF. The advantage could be as large as one-fold, substantially larger than the previous estimation. Some of these predictions could be generalized to the case of large neural populations. In particular, these analytical results may provide a theoretical basis for the predominant segregation into ON- and OFF-cells in early visual processing areas. Overall, we provide a unified framework for optimal neural codes with monotonic tuning curves in the brain, and makes predictions that can be directly tested with physiology experiments.