Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively in the context of Lawvere metric spaces. We construct a meaningful notion of magnitude for flow graphs based on the observation that topological entropy provides a suitable map into the max-plus semiring, and we outline its utility. Subsequently, we identify a separate point of contact between magnitude and topological entropy in digraphs that yields an analogue of volume entropy for geodesic flows. Finally, we sketch the utility of this construction for feature engineering in downstream applications with generic digraphs. 1 The only exception of which we are aware is [6], which details a nontrivial example of magnitude for a certain Vectcategory; see also Example 6.4.5 of [23].
We report benchmarks for a recently developed algorithm on the bbob and bbob-largescale benchmarking testbeds in COCO. This algorithm is designed for expensive high-dimensional multimodal objectives (such as arise in hyperparameter optimization or via simulations), and this regime introduces challenges for benchmarking. In particular, while the COCO experimental procedure yields evidence that this algorithm improves on the state of the art, the COCO framework also exhibits shortcomings for the very low evaluation budgets involved here. Consequently, we also report the results of ad hoc experiments that demonstrate a more obvious if less rigorous advantage for the algorithm over its nearest competition.
CCS CONCEPTS• Computing methodologies → Continuous space search.
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