  Recent success of pre-trained language models (LMs) has spurred widespread
interest in the language capabilities that they possess. However, efforts to
understand whether LM representations are useful for symbolic reasoning tasks
have been limited and scattered. In this work, we propose eight reasoning
tasks, which conceptually require operations such as comparison, conjunction,
and composition. A fundamental challenge is to understand whether the
performance of a LM on a task should be attributed to the pre-trained
representations or to the process of fine-tuning on the task data. To address
this, we propose an evaluation protocol that includes both zero-shot evaluation
(no fine-tuning), as well as comparing the learning curve of a fine-tuned LM to
the learning curve of multiple controls, which paints a rich picture of the LM
capabilities. Our main findings are that: (a) different LMs exhibit
qualitatively different reasoning abilities, e.g., RoBERTa succeeds in
reasoning tasks where BERT fails completely; (b) LMs do not reason in an
abstract manner and are context-dependent, e.g., while RoBERTa can compare
ages, it can do so only when the ages are in the typical range of human ages;
(c) On half of our reasoning tasks all models fail completely. Our findings and
infrastructure can help future work on designing new datasets, models and
objective functions for pre-training.
