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Numerical reasoning over natural language has been a long-standing goal forthe research community. However, cutting-edge language models have provendifficult to reliably generalize to a broad range of numbers, although theyhave shown proficiency in reasoning over common and simple numbers. In thispaper, we propose a novel method to elicit and exploit the numerical reasoningknowledge hidden in pre-trained language models using simple anchor numbers.Concretely, we first leverage simple numbers as anchors to probe the implicitlyinferred arithmetic expressions from language models, and then explicitly applythe expressions on complex numbers to get corresponding answers. To inverselyelicit arithmetic expressions, we transform and formulate the task as ananalytically solvable linear system. Experimental results on several numericalreasoning benchmarks demonstrate that our approach significantly improvesnumerical reasoning capabilities of existing LMs. More importantly, ourapproach is training-free and simply works in the inference phase, making ithighly portable and achieving consistent performance benefits across a varietyof language models (GPT-3, T5, BART, etc) in all zero-shot, few-shot, andfine-tuning scenarios.

Reflection of Thought: Inversely Eliciting Numerical Reasoning in Language Models via Solving Linear Systems