Mathematics Colloquia and Seminars

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Learning from experience is critical for wiring the adult brain since the genome cannot hold enough information to store the entire blueprint. Attneave and Barlow pioneered the idea that learning is guided by efficient coding, or the removal of redundant structure in signals from the periphery. Complementary theories proposed that learning is driven by the goal of forming sparse patterns of activity for any given representation. Models in which learning is designed to optimize the efficiency and sparsity of neural representations have succeeded in reproducing the structure of actual receptive fields in early sensory pathways. However, for all their strengths, the models that combine efficient coding and sparseness have not been able to explain learning in all parts of the brain. In particular, they offer no explanation how different cortical areas communicate. The sparse, distributed and high-dimensional representations predicted by those models seem difficult to transmit through the pathways that link cortical regions; this is because the fibers that connect two regions are far fewer in number than the populations of neurons in each region (Schuez et al. Cerebral Cortex, 2006). Here, we propose that the need to establish communication through axonal projections is a yet unrecognized principle that drives representational learning in the brain. Our idea is inspired by compressive sampling, a method for signal processing that uses random subsampling and sparse regression to compress and reconstruct sparse high-dimensional signals. By combining compressive sampling with the unsupervised learning of sparse codes, we found a principle for learning that is able to establish and maintain lossless communication through bottlenecks like cortico-cortical tracts. In the new scheme, we first assume that signals sent through a given fiber tract subsample the pattern of activity in the presynaptic region. Then, neurons in the postsynaptic region use the subsampled signals to learn response properties that permit recovery of the full information represented in the presynaptic region. The proposed principle not only solves the hard problem of communication between higher brain regions but also generalizes to peripheral brain regions, where it achieves results comparable to those obtained by efficient sensory coding (Isely et al. NIPS 2010).