Novel local learning rule for neural adaptation fits Hopfield memory networks efficiently and optimally
© Hillar et al; licensee BioMed Central Ltd. 2013
Published: 8 July 2013
We present an algorithm to store binary memories in a Little-Hopfield neural network using minimum probability flow, a recent technique to fit parameters in energy-based probabilistic models. For memories without noise, our algorithm provably achieves optimal pattern storage and outperforms classical methods both in speed and memory recovery. Moreover, when trained on noisy or corrupted versions of a fixed set of binary patterns, our algorithm finds networks which correctly store the originals. We also demonstrate this finding visually with the unsupervised storage and clean-up of large binary fingerprint images from significantly corrupted samples.
In 1982, motivated by neural modeling work of  and the Ising spin glass model from statistical physics , Hopfield introduced a method for the storage and retrieval of binary patterns in an auto-associative neural-network . However, existing techniques for training Little-Hopfield networks suffer either from limited pattern capacity or excessive training time, and they exhibit poor performance when trained on unlabeled, corrupted memories.
Our main theoretical contributions here are the introduction of a tractable and neurally-plausible algorithm MPF for the optimal storage of patterns in a Little-Hopfield network, a proof that the capacity of such a network is at least one pattern per neuron, and a novel local learning rule for training neural networks. Our approach is inspired by minimum probability flow , which fits probabilistic models without computations with a partition function.
- Hopfield JJ: Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A. 1982, 79: 2554-2558. 10.1073/pnas.79.8.2554.PubMed CentralView ArticlePubMedGoogle Scholar
- Ising E: Beitrag zur Theorie des Ferromagnetismus. Zeitschrift fur Physik. 1925, 31:Google Scholar
- Little WA: The existence of persistent states in the brain. Math Biosciences. 1974, 19:Google Scholar
- Sohl-Dickstein J, Battaglino P, DeWeese MR: Minimum probability flow learning. PRL. 2011Google Scholar
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