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The efficient coding hypothesis proposes that the response properties ofsensory systems are adapted to the statistics of their inputs such that theycapture maximal information about the environment, subject to biologicalconstraints. While elegant, information theoretic properties are notoriouslydifficult to measure in practical settings or to employ as objective functionsin optimization. This difficulty has necessitated that computational modelsdesigned to test the hypothesis employ several different information metricsranging from approximations and lower bounds to proxy measures likereconstruction error. Recent theoretical advances have characterized a noveland ecologically relevant efficiency metric, the manifold capacity, which isthe number of object categories that may be represented in a linearly separablefashion. However, calculating manifold capacity is a computationally intensiveiterative procedure that until now has precluded its use as an objective. Herewe outline the simplifying assumptions that allow manifold capacity to beoptimized directly, yielding Maximum Manifold Capacity Representations (MMCR).The resulting method is closely related to and inspired by advances in thefield of self supervised learning (SSL), and we demonstrate that MMCRs arecompetitive with state of the art results on standard SSL benchmarks. Empiricalanalyses reveal differences between MMCRs and representations learned by otherSSL frameworks, and suggest a mechanism by which manifold compression givesrise to class separability. Finally we evaluate a set of SSL methods on a suiteof neural predictivity benchmarks, and find MMCRs are higly competitive asmodels of the ventral stream.

Learning Efficient Coding of Natural Images with Maximum Manifold Capacity Representations