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Generative Transformer-based models have achieved remarkable proficiency onsolving diverse problems. However, their generalization ability is not fullyunderstood and not always satisfying. Researchers take basic mathematical taskslike n-digit addition or multiplication as important perspectives forinvestigating their generalization behaviors. Curiously, it is observed thatwhen training on n-digit operations (e.g., additions) in which both inputoperands are n-digit in length, models generalize successfully on unseenn-digit inputs (in-distribution (ID) generalization), but fail miserably andmysteriously on longer, unseen cases (out-of-distribution (OOD)generalization). Studies try to bridge this gap with workarounds such asmodifying position embedding, fine-tuning, and priming with more extensive orinstructive data. However, without addressing the essential mechanism, there ishardly any guarantee regarding the robustness of these solutions. We bring thisunexplained performance drop into attention and ask whether it is purely fromrandom errors. Here we turn to the mechanistic line of research which hasnotable successes in model interpretability. We discover that the strong IDgeneralization stems from structured representations, while behind theunsatisfying OOD performance, the models still exhibit clear learned algebraicstructures. Specifically, these models map unseen OOD inputs to outputs withequivalence relations in the ID domain. These highlight the potential of themodels to carry useful information for improved generalization.

It Ain't That Bad: Understanding the Mysterious Performance Drop in OOD Generalization for Generative Transformer Models