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The adaptation of neural codes to the statistics of their environment is wellcaptured by efficient coding approaches. Here we solve an inverse problem:characterizing the objective and constraint functions that efficient codesappear to be optimal for, on the basis of how they adapt to different stimulusdistributions. We formulate a general efficient coding problem, with flexibleobjective and constraint functions and minimal parametric assumptions. Solvingspecial cases of this model, we provide solutions to broad classes of Fisherinformation-based efficient coding problems, generalizing a wide range ofprevious results. We show that different objective function types imposequalitatively different adaptation behaviors, while constraints enforcecharacteristic deviations from classic efficient coding signatures. Despiteinteraction between these effects, clear signatures emerge for bothunconstrained optimization problems and information-maximizing objectivefunctions. Asking for a fixed-point of the neural code adaptation, we find anobjective-independent characterization of constraints on the neural code. Weuse this result to propose an experimental paradigm that can characterize boththe objective and constraint functions that an observed code appears to beoptimized for.

Adaptation Properties Allow Identification of Optimized Neural Codes