Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Momentum Accelerates Evolutionary Dynamics   We combine momentum from machine learning with evolutionary dynamics, where
momentum can be viewed as a simple mechanism of intergenerational memory. Using
information divergences as Lyapunov functions, we show that momentum
accelerates the convergence of evolutionary dynamics including the replicator
equation and Euclidean gradient descent on populations. When evolutionarily
stable states are present, these methods prove convergence for small learning
rates or small momentum, and yield an analytic determination of the relative
decrease in time to converge that agrees well with computations. The main
results apply even when the evolutionary dynamic is not a gradient flow. We
also show that momentum can alter the convergence properties of these dynamics,
for example by breaking the cycling associated to the rock-paper-scissors
landscape, leading to either convergence to the ordinarily non-absorbing
equilibrium, or divergence, depending on the value and mechanism of momentum.

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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph