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Self-planting: digging holes in rough landscapes | | Dhruv Sharma
; Jean-Philippe Bouchaud
; Marco Tarzia
; Francesco Zamponi
; | | Date: |
4 Jun 2019 | | Abstract: | Motivated by a potential application in economics, we investigate a simple
dynamical scheme to produce planted solutions in optimization problems with
continuous variables. We consider the perceptron model as a prototypical model.
Starting from random input patterns and perceptron weights, we find a locally
optimal assignment of weights by gradient descent; we then remove misclassified
patterns (if any), and replace them by new, randomly extracted patterns. This
"remove and replace" procedure is iterated until perfect classification is
achieved. We call this procedure "self-planting" because the "planted" state is
not pre-assigned but results from a co-evolution of weights and patterns. We
find an algorithmic phase transition separating a region in which self-planting
is efficiently achieved from a region in which it takes exponential time in the
system size. We conjecture that this transition might exist in a broad class of
similar problems. | | Source: | arXiv, 1906.1490 | | Services: | Forum | Review | PDF | Favorites | |
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