stage4-condensation-dynamics

Some notion of morphism between random-variable models beyond Eisenstat's single-source index maps, whether relational, support-sensitive or built from sigma-algebra homomorphisms, carries the same concept with a correspondence theorem.

A representation of one agent interpreting another as a belief-haver, in which the two agents' givens are related by a map rather than assumed identical, carries a correspondence between their concepts.

A time-indexed version of condensation states how concepts persist and deform as a theory changes and what survives an ontological shift.

A notion of one structure implementing another represents objects that move between variables without letting arbitrary computation make every structure implement every other.

Petersen's theory of abstraction, Wentworth's natural abstraction and natural latents, and Eisenstat's condensation are related precisely: Petersen's theory to Wentworth's, natural latents to condensation, and Petersen's theory to condensation, each relation stated as a reduction or a complementarity.

Each of condensation's three scores is interpreted as an expected cost under a stated convention: the simple and conditioned scores as explanation lengths, and the reconstruction score as a measure of over-parameterization given the givens.

An algorithmic version of condensation, with description length in place of entropy, carries a correspondence theorem, directly or once variable-cost symbols remove its trouble with single events.

Two latent-variable models that both perfectly condense one random-variable model stand in correspondence: each latent of either model is almost everywhere a function of the other model's latents above the same given variables.

Eisenstat's correspondence theorem for condensation can be improved until it reflects concepts shared between reasoning agents and kept across changes of theory well.

In Eisenstat's category of random-variable models an equivalence is an isomorphism almost everywhere, and Proposition 4.7 characterizes it through almost-everywhere functional dependence of the contributing models.

The given variables two latent-variable models share do part of the work that makes their correspondence meaningful, in a form that generalizes to models whose givens are related by a morphism rather than identical.

Conditioning models over different ontologies, linked by a common-information structure of sigma-algebra homomorphisms, admit calibrated refinement across ontologies through bridges, with an anticipation structure that allows a variable future ontology.

The superconditioning account of calibration across ontologies can be improved until it reflects ontological shifts in real reasoners well.

The li-deference framework models only the AI's outwardly expressed beliefs, forced by training into the humans' language, so it does not model ontology mismatch between humans and AIs or ontology-shift problems.

Abstraction theory, as Petersen and Wentworth develop it, supplies tools that the implementation-relations line, natural latents and condensation each lack, which a one-page account can name.

A condensation-like theory with a correspondence theorem exists when the fixed retrieval policy is dropped, a set of questions is treated as one product question, and the score trades storage cost against retrieval cost.

A variation of condensation in which notebooks may contain instructions for retrieving other notebooks has a correspondence theorem.

Condensing a neural network's internal activations as given variables yields more interpretable features, and models built to resemble condensation are more interpretable, within the limits that condensation is less tight than information theory and is not a model of cognition.

Condensation's single-source morphisms suffice to carry the same concept between agents.