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• W41200557 abstract "We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation regime where jamming is isostatic and critical. We characterise the critical jamming phase through exponents describing the distributions law of forces and gaps. Surprisingly we find that these exponents coincide with the corresponding ones recently computed in high dimensional hard spheres. In addition, modifying the perceptron to a random linear programming problem, we show that isostaticity is not a sufficient condition for singular force and gap distributions. For that, fragmentation of the space of solutions (replica symmetry breaking) appears to be a crucial ingredient. We hypothesise universality for a large class of non-convex constrained satisfaction problems with continuous variables." @default.
• W41200557 created "2016-06-24" @default.
• W41200557 creator A5052777339 @default.
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• W41200557 date "2016-02-23" @default.
• W41200557 modified "2023-09-25" @default.
• W41200557 title "The simplest model of jamming" @default.
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• W41200557 doi "https://doi.org/10.1088/1751-8113/49/14/145001" @default.
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