Programming by Backprop: Learning Behaviour from Symbolic Descriptions

Large language models (LLMs) are typically trained to acquire behaviours from demonstrations or experience, yet much of their training data consists of symbolic descriptions: instructions, rules, and strategies that specify procedures without examples. We investigate whether LLMs can learn to execute such behaviours directly from their abstract description, a process we term Programming by Backprop (PBB). We study this phenomenon in two domains: first, using source code as a canonical form of procedural description by comparing models finetuned on algorithms versus execution examples; and second, extending beyond code to abstract grammar rules, testing whether models learn to generate compliant text. Our findings show that PBB can be elicited through targeted finetuning, demonstrating that LLMs can acquire new behaviours from symbolic descriptions, albeit not yet with full reliability. Once elicited, PBB enables models to internalise reusable procedural abstractions - generalising across inputs, executing procedures implicitly in a forward pass, and benefiting further from chain-of-thought reasoning. These results position PBB as a distinct pathway through which LLMs acquire behavioural skills from symbolic descriptions, with implications for both more efficient capability acquisition and aligning models through formal specifications rather than demonstrations alone.