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We present evidence that language models (LMs) of code can learn to representthe formal semantics of programs, despite being trained only to performnext-token prediction. Specifically, we train a Transformer model on asynthetic corpus of programs written in a domain-specific language fornavigating 2D grid world environments. Each program in the corpus is precededby a (partial) specification in the form of several input-output grid worldstates. Despite providing no further inductive biases, we find that a probingclassifier is able to extract increasingly accurate representations of theunobserved, intermediate grid world states from the LM hidden states over thecourse of training, suggesting the LM acquires an emergent ability to interpretprograms in the formal sense. We also develop a novel interventional baselinethat enables us to disambiguate what is represented by the LM as opposed tolearned by the probe. We anticipate that this technique may be generallyapplicable to a broad range of semantic probing experiments. In summary, thispaper does not propose any new techniques for training LMs of code, butdevelops an experimental framework for and provides insights into theacquisition and representation of formal semantics in statistical models ofcode. Our code is available athttps://github.com/charlesjin/emergent-semantics.

Emergent Representations of Program Semantics in Language Models Trained on Programs