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Discrete perceptrons

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arxiv 1306.4375 v1 pith:OUINTOYP submitted 2013-06-17 math.PR math-phmath.MPstat.ML

Mihailo Stojnic This is my paper · ORCID
classification math.PRmath-phmath.MPstat.ML
keywords perceptronscitediscretewillgar88manymechanicspredictions
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Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to characterize perceptrons relied on a statistical mechanics approach. Many of such predictions obtained in \cite{Gar88} (and in a follow-up \cite{GarDer88}) were later on established rigorously as mathematical facts (see, e.g. \cite{SchTir02,SchTir03,TalBook,StojnicGardGen13,StojnicGardSphNeg13,StojnicGardSphErr13}). These typically related to spherical perceptrons. A lot of work has been done related to various other types of perceptrons. Among the most challenging ones are what we will refer to as the discrete perceptrons. An introductory statistical mechanics treatment of such perceptrons was given in \cite{GutSte90}. Relying on results of \cite{Gar88}, \cite{GutSte90} characterized many of the features of several types of discrete perceptrons. We in this paper, consider a similar subclass of discrete perceptrons and provide a mathematically rigorous set of results related to their performance. As it will turn out, many of the statistical mechanics predictions obtained for discrete predictions will in fact appear as mathematically provable bounds. This will in a way emulate a similar type of behavior we observed in \cite{StojnicGardGen13,StojnicGardSphNeg13,StojnicGardSphErr13} when studying spherical perceptrons.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Controlled Loosening-up (CLuP) -- achieving exact MIMO ML in polynomial time

    cs.IT 2019-09 reject novelty 6.0 of 10

    CLuP, an iterative convex optimization algorithm, is claimed to achieve MIMO ML detection performance in polynomial time, but the claim rests on heuristic random duality arguments and an empirical iteration count.

  2. Complexity analysis of the Controlled Loosening-up (CLuP) algorithm

    cs.IT 2019-09 conditional novelty 5.0 of 10

    Using Random Duality Theory, the paper argues that the CLuP algorithm reaches near-optimal MIMO ML detection in a small, dimension-independent number of quadratic-programming iterations.

  3. Starting CLuP with polytope relaxation

    cs.IT 2019-09 conditional novelty 4.0 of 10

    CLuP-plt, a CLuP detector variant that starts from a box-constrained least-squares solution, reaches near-ML error rates within three to five iterations in the tested MIMO settings.

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