the primary challenge in these search problems is that it is typically impossible to know a priori whether the local maxima you've found is the global maxima, or if there's a better one out there, & if one invested a bit more into exploration, a better solution would be found

the issue is that, depending on the optimization landscape, it might take more energy to arrive at a better maxima than would make the improvement worthwhile; this is why one must take the specifics of their objective function and properties of their landscape into account

early on in the exploration phase, it is typically advantageous to optimize for optionality, investing energy into creating more possible search avenues, keeping many options open while one searches for higher maxima; this strategy is generally called breadth-first search

at some point tho, its necessary to "commit" & switch to exploitation mode, whatever that entails for your objective; could be anything from picking a partner, accepting a job offer, or even deciding which bagel place to go to. might always be a better one out there, but so what?

in exploitation mode, you're no longer searching but actively "using" your result; interestingly enough, this itself often presents new optimization problems! sure, you've chosen a bagel place, but which combination of toppings is best? time to explore the bagel topping space!

with many real-world optimization problems, there are many levels of decisions which need to be made, especially in domains with hidden dimensions, ie, factors which are local rather than global; different bagel places might have different topping options!

this is what is meant by a fractally-biphasic lifecycle; the optimization algorithm is self-similar, in that exploitation phases themselves contain smaller instances of the explore/exploit problem! depending on the nature of the optimization landscape, these can be deeply nested

thats cool and all, but what's the relationship to slime molds?

these organisms are rather primitive, being multinucleated acellular protists, often compared to fungi but much closer to amoebas. of primary interest here is the behavior of the plasmodium stage, how it seeks food

the slime mold expands and contracts its membrane, causing its cytoplasm to flow into certain regions, expanding it outwards in those directions; if it detects food it grows around it, consuming it and expanding, but if not, it contracts away from that region, leaving markers

through the 100 second period of these pulsations, the slime mold is effectively exploring its surroundings, executing a sort of physical breadth-first search. once it finds food, it builds "channels", tube-like structures enabling easier transport, and then it repeats.

here's the fun part: out of this very simple behavior emerges a form of intelligence; the slime mold is able to solve shortest-path problems! over many iterations, we see slime molds construct efficient and resilient networks of tubes between food clusters, on par w/ human algos!

these organisms present a model for study of biological computation, highly amenable to various situations; presented here is a slime mold routing around mountains in topographical models of the US and Germany. note the similarity to the aforementioned optimization landscapes

slime molds have been shown to be able to solve mazes; theyre fascinating to watch in action. you can quite literally see the explore/explore logic laid out in space! see how this one explores the maze, and then builds a pathway to bring back the discovered nutrients?

these organisms have been of great interest to researchers, in our quest to understand the various primitives of intelligence, as well as possibilities for building biological computers; some believe these slime molds to be viable candidates, having constructed basic logic gates!

there've been many attempts to model & simulate the logic of these organisms, w/ v promising results; long been fascinated by them, & greatly enjoy reading papers like these. the natural world is full of more wonders than we know

https://arxiv.org/abs/1106.0423

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RT @pee_zombie
slime molds are efficient biological 2-space minimum flow cost solvers and thats fuckin dope #slimemoldtwitter https://twitter.com/embryosophy/status/1340367…
https://twitter.com/pee_zombie/status/1342197082598334464

@pee_zombie nice thread! I'm interested in intuitions about hight-dimensional differentiable spaces: I've heard both that they contain a lot of local maxima, and that the contain no local maxima (the intuition there being that there's just too many dimensions for there being none to escape through (S)GD)