Abstract
We introduce an information maximizing neural network that employs only local learning rules, simple activation functions, and feedback in its functioning. The network consists of an input layer, an output layer that can be overcomplete, and a set of auxiliary layers comprising feed-forward, lateral, and feedback connecwtions. The auxiliary layers implement a novel ”neural multigrid,” and each computes a Fourier mode of a key infomax learning vector. Initially, a partial multigrid computes only low frequency modes of this learning vector, resulting in a spatially correlated topographic map. As higher frequency modes of the learning vector are gradually added, an infomax solution emerges, maximizing the entropy of the output without disrupting the map’s topographic order. When feed-forward and feedback connections to the neural multigrid are passed through a nonlinear activation function, infomax emerges in a phase-independent topographic map. Information rates estimated by Principal Components Analysis (PCA) are comparable to those of standard infomax, indicating the neural multigrid successfully imposes a topographic order on the optimal infomax-derived bases.
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Kozloski, J., Cecchi, G., Peck, C., Rao, A.R. (2007). Topographic Infomax in a Neural Multigrid. In: Liu, D., Fei, S., Hou, Z., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72393-6_60
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DOI: https://doi.org/10.1007/978-3-540-72393-6_60
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