Unravelling the Logic: Investigating the Generalisation of Transformers in Numerical Satisfiability Problems

Transformer models have achieved remarkable performance in many formal reasoning tasks. Nonetheless, the extent of their comprehension pertaining to logical semantics and rules of inference remains somewhat uncertain. Evaluating such understanding necessitates a rigorous examination of these models' generalisation capacity to out-of-distribution data. In this study, we probe the generalisation prowess of Transformer models with respect to the hitherto unexplored domain of numerical satisfiability problems. Our investigation reveals that Transformers exhibit minimal scale and noise invariance, alongside limited vocabulary and number invariance. However, even when Transformer models experience a notable decline in performance on out-of-distribution test sets, they often still surpass the random baseline by a considerable margin.