Figure 6.

The many meanings of optimal. (a) The visual system computes intermediate representations, c, of the input x: x ↦ c ↦ ŷ. Although only one is shown, there could be several layers of representations. Encoding is moving from x to c, while decoding is moving from c to a useful quantity ŷ, which is latent in x and c. (b) Some theories restrict optimization to the encoding or decoding step, constraining or ignoring the other step. Other theories impose fewer constraints and/or use a loss function ℒ that depends on both input and output representations. Many different optimization theories can be derived by choosing different objective functions and constraints.