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Poster Session B: Wednesday, August 13, 1:00 – 4:00 pm, de Brug & E‑Hall

A mathematical theory of relational generalization in the face of exceptions

Luke Cheng¹, Samuel Lippl¹; ¹Columbia University

Presenter: Luke Cheng

Relational reasoning is a cornerstone of higher-order cognition in humans and animals, enabling zero-shot generalization to novel situations using rules like transitivity. In the real world, agents need to flexibly decide when to apply these rules and when to learn exceptions from them. It has remained unclear how standard learning systems can accomplish this. To investigate this topic, we introduce a new task paradigm: transitive inference with exceptions. This requires subjects to infer an ordered relation and generalize using the transitive rule but also requires them to memorize a certain violation to this rule. We use a standard statistical learning system to understand the minimal inductive biases necessary to perform this task. Intriguingly, these models can generalize where possible and memorize exceptions where necessary. However, successful generalization depends on their representational geometry: an overly conjunctive representation yields a systematic pattern of errors in generalization. Ultimately, we introduce a novel task paradigm for understanding relational reasoning in the real world, explain how a standard learning system can generalize on this task, and make systematic predictions for human behavior.

Topic Area: Predictive Processing & Cognitive Control

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