arXiv:2608. 14220v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "a is to b as c is to d", usually denoted a : b :: c : d.
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arXiv:2608. 11724v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "A is to B as C is to D".
Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiomatic framework by characterizing valid analogies through a set of postulates.
arXiv:2603. 19066v2 Announce Type: replace-cross Abstract: Four-term word analogies (A:B::C:D) are classically modeled geometrically as parallelograms: adding the vector B-A+C produces D.
Analogical proportions link four items a, b, c, d by a relation stating that ``a is to b as c is to d", a, b, c, d being the formal representation of real world entities, ranging from simple numerical values to more complex structures such as profiles. Accordingly, $a, b, c, d$ could be atomic values like Boolean, nominal or numerical values, more generally vectors of such values, or even families of items represented by logical formulas.
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
arXiv:2607. 20502v1 Announce Type: new Abstract: To allow for principled comparison between two probabilistic graphical models defined over non-identical variable sets, they have to be lifted to a common measurable space.