<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi Jon,<div class=""><br class=""></div><div class="">Some parts yes, others the opposite. In this case, unfortunately, most compact to lard:<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On May 27, 2022, at 4:02 AM, Jon Zingale <<a href="mailto:jonzingale@gmail.com" class="">jonzingale@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:#333333">Just to verify that I am reading you, the additive classifier *should*<br class="">do a horrible job exactly because N+1 << 2^N. </div></div></div></blockquote><div><br class=""></div><div>Yes.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:#333333">Selection is nullified by linearity, while modularity benefits from linearity. </div></div></div></blockquote><div><br class=""></div><div>Other way around. Selection is a weak algorithm, so its efficacy benefits from any kind of separability it can see. Modularizing into some units that tend to focus function into local loci concentrates information selection can amplify into the linear part of the regression. Thus we would expect to see selection for modularization in its own right, above and beyond selection for whatever particular function may be beneficial. In principle, any separability could be helpful, but there is the caveat that selection has to be able to recognize it. Because DNA is a linear polymer, and because crossover (in sexual organisms), or various forms of breakage and repair (much more generally) tend to disrupt things that are distant on the genome, the particular modularization that makes linearity a better approximation is also more likely to survive under heredity.</div><div><br class=""></div><div>The argument for modularization for its own sake is the theme of work by Marc Kirschner and John Gerhart, which they put under the name “facilitated variation”. There is a PNAS article by that title, and they have a large book Cells, Embryos, and Evolution, which is the more-technical development of the same ideas.</div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:#333333">As a consequence,<br class="">and through an evo-devo lens, biology optimizes about this paradox.<br class=""></div></div></div></blockquote><div><br class=""></div>Yes.</div><div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:#333333">Do I have this right about selection? In a recent conversation with Nick,<br class="">I got the impression that this paradox of heritability is the source of<br class="">one of his *bugs*.<br class=""></div></div></div></blockquote><div><br class=""></div><div>Let me send you another thing, which had been on my to-read list for far too long. But recently having been put in a hole where the internet don’t shine (with much bandwidth) — oh blessed castaway — I have finally actually read it. It is a constructively explicit application of linear representation with sets of increasing order. Here is the URL:</div><div><a href="https://eprints.whiterose.ac.uk/162674/" class="">https://eprints.whiterose.ac.uk/162674/</a></div><div>and in case it gives you trouble, we are looking for </div><div>“Generic Context-Aware Group Contributions” by Flamm et al.</div><div><br class=""></div><div>Here they are doing chemistry, and the objective function to be approximated might be something like a Gibbs free energy of formation, or a solubility, or things of that kind. The objects they study are molecules, represented as graphs. So they don’t need to take a non-parametric approach based on cumulants or equivalent, and can instead use the representation given by the graph. </div><div><br class=""></div><div>One can imagine, however, lots of ways of looking for representations of functional interplay of genetically determined components, and if one had advanced some such representation, the approach to using it would be similar in spirit to the one here. In a way it is all quite simple, but still I am relieved at the clarity and good mental organization these authors bring to the presentation.</div><div><br class=""></div><div>All best, </div><div><br class=""></div><div>Eric</div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><div><br class=""></div><br class=""><blockquote type="cite" class=""><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small;color:#333333"><br class="">"""<br class="">A much better decomposition, of course, is not to use structureless<br class="">sets like cumulants, but rather to find representations of algorithmic<br class="">architectures that can be put into a frame of statistical identification.<br class="">"""<br class=""><br class="">Are cumulants structureless? I keep thinking of them as being analogous<br class="">to moments and effectively differential information, but OTOH, maybe all<br class="">the *logs* stills this. Idk, I am a newbie here. The other idea your<br class="">comment calls to mind is the work being done to *learn algebraic<br class="">varieties*. Like varieties (the geometric objects they are) are the<br class="">consequence of an underlying algebra of operations (polynomial rings),<br class="">representations of programs (as denotation-level objects) can be learned<br class="">despite the inevitably wide variety of implementations.<br class=""><br class="">Thank you for the references and the consideration.<br class=""></div></div>
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