Numerical data plays a crucial role in various real-world domains like finance, economics, and science. Thus, understanding and reasoning with numbers are essential in these fields. Recent benchmarks have assessed the numerical reasoning abilities of language models, revealing their limitations in limited and specific numerical aspects. In this paper, we propose a complete hierarchical taxonomy for numerical reasoning skills, encompassing over ten reasoning types across four levels: representation, number sense, manipulation, and complex reasoning. We conduct a comprehensive evaluation of state-of-the-art models on all reasoning types. To identify challenging reasoning types for different model types, we develop a diverse and extensive set of numerical probes and measure performance shifts. By employing a semi-automated approach, we focus on the tabular Natural Language Inference (TNLI) task as a case study. While no single model excels in all reasoning types, FlanT5 (few-/zero-shot) and GPT3.5 (few-shot) demonstrate strong overall numerical reasoning skills compared to other models in our probes.

Recent methods based on pre-trained language models have exhibited superior performance over tabular tasks (e.g., tabular NLI), despite showing inherent problems such as not using the right evidence and inconsistent predictions across inputs while reasoning over the tabular data (Gupta et al., 2021). In this work, we utilize Pattern-Exploiting Training (PET) (i.e., strategic MLM) on pre-trained language models to strengthen these tabular reasoning models’ pre-existing knowledge and reasoning abilities. Our upgraded model exhibits a superior understanding of knowledge facts and tabular reasoning compared to current baselines. Additionally, we demonstrate that such models are more effective for underlying downstream tasks of tabular inference on INFOTABS. Furthermore, we show our model’s robustness against adversarial sets generated through various character and word level perturbations.