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Steve Huntsman (Nov 03 2022 at 18:39):I'll be talking at the JMM session on topology, algebra, and geometry in data science on 5 Jan. Among other things, I'll be briefly advertising/ranting about magnitude homology and prospective applications for it.
The underlying position paper is here. (FWIW, arXiv seemed to really get wrapped around the axle about the "advertisement" and/or "rant" language: HAL is much more permissive with that and using PDFs instead of killing yourself with LaTeX wrangling).
I won't be talking about more concrete applications of magnitude to various problems in optimization, but some of these are here , here, and here.
I will be missing the ACT days and most of the rest too, but also won't be representing my employer when I am around, so if anyone wants to give me a piece of their mind (in exchange for a piece of mine) they are most welcome.
Steve Huntsman (Nov 23 2022 at 12:49):Just on the arXiv in time for Thanksgiving: Quality-diversity in dissimilarity spaces.
The theory of magnitude provides a mathematical framework for quantifying and maximizing diversity. We apply this framework to formulate quality-diversity algorithms in generic dissimilarity spaces. In particular, we instantiate and demonstrate a very general version of Go-Explore with promising performance.
I think this will probably be the last paper I write on applying (Lawvere metric) magnitude to optimization for a while. But there are many other (probably pretty good) applications I have in mind to statistical and ML-type problems, as well as what I think is a family of instantiations of magnitude involving arrow categories generated by data on a transitively closed directed acyclic graph. Over Vect these would be morally close to quantum circuits (though the actual results for unitaries appear trivially uninteresting) or more interestingly and usefully, to the sorts of "computational graphs" encountered in automatic differentiation.
Simonas Tutlys (Nov 23 2022 at 14:10):Very interesting concrete connection between QD algos and RL,exciting!
Steve Huntsman (Dec 06 2022 at 18:02):My paper Diversity Enhancement via Magnitude has been accepted to Evolutionary Multi-Criterion Optimization 2023
Steve Huntsman (May 22 2023 at 14:32):Steve Huntsman said:
Just on the arXiv in time for Thanksgiving: Quality-diversity in dissimilarity spaces.
The theory of magnitude provides a mathematical framework for quantifying and maximizing diversity. We apply this framework to formulate quality-diversity algorithms in generic dissimilarity spaces. In particular, we instantiate and demonstrate a very general version of Go-Explore with promising performance.
The nominee for best paper from the General Evolutionary Computation and Hybrids track at GECCO 2023. The paper includes code and examples, including scripts in the LaTeX source for reproducing results (Gitlab is annoying).
Steve Huntsman (May 22 2023 at 14:36):I'll also be talking in my personal capacity on 10 July at the Applications of Magnitude and Magnitude Homology to Network Analysis minisymposium at the SIAM Conference on Applied Algebraic Geometry at TU Eindhoven.
Steve Huntsman (May 22 2023 at 14:37):And giving a non-proceedings talk on enhancing diversity in multiobjective optimization at GECCO as well.