Structural Analogy as Quotient-Space Alignment in Predictive Systems

Analogy plays a central role in cognition and, more generally, in how systems represent and relate structured information. Large language models exhibit striking analogical behavior, but existing debates frame this either as emergent reasoning or as surface-level pattern completion. We argue this comparison is misguided. Rather than asking whether artificial analogy resembles human analogy, we ask which equivalence classes a predictive system stabilizes and whether those align across systems. We formalize this perspective using a structural framework grounded in equivalence relations and quotient constructions. Any finite-capacity predictive system must partition its input space into equivalence classes that preserve predictive behavior. We show that predictive training drives representations toward partitions consistent with predictive equivalence, yielding a quotient structure that captures invariant relationships. This reframes analogy as alignment between quotient structures across systems, providing a substrate-neutral account of analogical correspondence grounded in predictive structure rather than surface similarity or internal mechanism.