Just to verify that I am reading you, the additive classifier *should* do a horrible job exactly because N+1 << 2^N. Selection is nullified by linearity, while modularity benefits from linearity. As a consequence, and through an evo-devo lens, biology optimizes about this paradox. Do I have this right about selection? In a recent conversation with Nick, I got the impression that this paradox of heritability is the source of one of his *bugs*.
""" A much better decomposition, of course, is not to use structureless sets like cumulants, but rather to find representations of algorithmic architectures that can be put into a frame of statistical identification. """ Are cumulants structureless? I keep thinking of them as being analogous to moments and effectively differential information, but OTOH, maybe all the *logs* stills this. Idk, I am a newbie here. The other idea your comment calls to mind is the work being done to *learn algebraic varieties*. Like varieties (the geometric objects they are) are the consequence of an underlying algebra of operations (polynomial rings), representations of programs (as denotation-level objects) can be learned despite the inevitably wide variety of implementations. Thank you for the references and the consideration.
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