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SUMMARY:Graduate Student Colloquium: Daniel Quigley
DESCRIPTION:A Primer on the Mathematics of Artificial Neural Networks\nDaniel Quigley\nPhD Student\nUniversity of Wisconsin-Milwaukee \nArtificial neural networks (ANNs\, or\, simply\, neural networks) are ubiquitous\, not least of all in the context of modern machine learning. This presentation is a primer on the mathematics that underlie the mechanics of relatively simple feedforward ANNs. A sketch of the proof for the universal approximation theorem is given\, which states that a (fully connected) ANN with at least one hidden layer (of a sufficient number of neurons)\, together with a non-linear activation function\, can approximate any continuous function on a compact set to arbitrary accuracy. This presentation contributes to the movement for providing mathematical explanations and descriptions of ANNs\, favoring a functional analytical and well-founded framework at the expense of algorithmic aspects of deep learning otherwise concerned with identifying the most suitable deep ANNs for specific applications.
URL:https://uwm.edu/math/event/graduate-student-colloquium-daniel-quigley/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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SUMMARY:Colloquium: Dr. Jay Pantone
DESCRIPTION:Experimental Methods in Combinatorics\nDr. Jay Pantone\nAssistant Professor of Mathematics\nMarquette University \nWhat number comes next in the sequence\n1\, 2\, 4\, 8\, 16\, 32\, … ? \nHow about\n1\, 2\, 3\, 5\, 8\, 13\, … ? \nOr maybe\n1\, 3\, 14\, 84\, 592\, 4659\, … ? \nMany questions in combinatorics have the form “How many objects are there that have size n and that satisfy certain properties?” For example\, there are n! permutations (rearrangements) of n distinct objects\, there are 2^n binary strings of length n\, and the number of sequences of n coin flips that never have two tails in a row is the nth Fibonacci number. The “counting sequence” of a set of objects is the sequence a_0\, a_1\, a_2\, …\, where a_n is the number of objects of size n. \nAs a result of theoretical advances and more powerful computers\, it is becoming common to be able to compute a large number of initial terms of the counting sequence of a set of objects that you’d like to study. From these initial terms\, can you guess future terms? Can you guess a formula for the nth term in the sequence? Can you guess the asymptotic behavior as n tends to infinity? \nRigorously\, you can prove basically nothing from just some known initial terms. But\, perhaps surprisingly\, there are several empirical techniques that can use these initial terms to shed some light on the nature of a sequence. \nAs we talk about two such techniques — automated conjecturing of generating functions\, and the method of differential approximation — we’ll exhibit their usefulness through a variety of combinatorial topics\, including chord diagrams\, permutation classes\, and inversion sequences.
URL:https://uwm.edu/math/event/colloquium-dr-jay-pantone/
LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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