Emergent neural dynamics and geometry for generalization in a transitive inference task

Abstract

The ability to make inferences using abstract rules and relations has long been understood to be a hallmark of human intelligence, as evidenced in logic, mathematics, and language. Intriguingly, modern work in animal cognition has established that this ability is evolutionarily widespread, indicating an ancient and possibly foundational role in natural intelligence. Despite this importance, it remains an open question how inference using abstract rules is implemented in the brain - possibly due to a lack of competing hypotheses at the level of collective neural activity and of behavior. Here we report the generation and analysis of a collection of neural networks (NNs) that perform transitive inference (TI), a classical cognitive task that requires inference of a single abstract relation between novel combinations of inputs (if A > B and B > C, then A > C). We found that NNs generated using standard training methods (i) generalize fully (i.e. to all novel combinations of inputs), (ii) generalize when inference requires working memory (WM), a capacity thought to be essential for inference in living subjects, (iii) express multiple emergent behaviors long documented in humans and animals, in addition to novel behaviors not previously studied, and (iv) adopt different solutions that yield alternative predictions for both behavior and collective neural activity. Further, a subset of NNs expressed a "subtractive" solution that was characterized in neural activity space by a simple dynamical pattern (an oscillation) and geometric arrangement (ordered collinearity). Together, these findings show how collective neural activity can accomplish generalization according to an abstract rule, and provide a series of testable hypotheses not previously established in the study of TI. More broadly, these findings suggest new ways to understand how neural systems realize abstract rules and relations.

A mathematical theory of relational generalization in transitive inference

“…With respect to similarity-based relational learning models, our account could be seen as an endpoint to a series of investigations of TI behavior: expanding upon previous studies [30,53,54], we show comprehensively that the principle of norm minimization enables any model with partly conjunctive representations to generalize transitively and further gives rise to naturalistic behavior on TI. Importantly, norm minimization is implicated not only in gradient flow and ridge regression (the examples we consider), but also a much broader range of learning models [129], including reinforcement learning [130].…”

“…7b,e, green line). Our account may therefore be able to explain why previous studies [53,54] found empirically that feedforward ... neural networks generalize transitively. Surprisingly, we found that networks trained in the rich regime performed worse at TI.…”

“…They also leave unclear how the brain, which is not constrained in this way [52], could implement TI. Intriguingly, several studies have found that generic neural networks can generalize transitively, suggesting that statistical learning principles can sometimes give rise to a suitable relational inductive bias [30,[53][54][55]. However, TI in neural networks has largely been studied through simulations, rather than analytically [cf.…”

An active neural mechanism for relational learning and fast knowledge reassembly

“…To investigate potential brain mechanisms of transitive inference, it is also possible to train artificial neural networks on a given ordered list, and observe their behavior [De Lillo et al, 2001, Kay et al, 2023, Nelli et al, 2023]. Trained networks often exhibit transitive inference over the learned lists, and their neural dynamics and representational geometry can be analyzed directly.…”