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This paper investigates how hallucination rates in Large Language Models(LLMs) may be controlled via a symbolic data generation framework, exploring afundamental relationship between the rate of certain mathematical errors andtypes of input intervention. Specifically, we systematically generate data fora derivation generation task using a symbolic engine, applying targetedinterventions to prompts to perturb features of mathematical derivations suchas the surface forms of symbols, equational tree structures, and mathematicalcontext. We then evaluate the effect of prompt interventions across a range ofLLMs including fine-tuned T5 models, GPT, and LLaMa-based models. Ourexperiments suggest that T5-Large can outperform the few-shot performance ofGPT-4 on various evaluation sets generated via the framework. However, anextensive evaluation based on human analysis, template-based error detection,and text generation metrics reveals model weaknesses beyond what thereference-based metrics singularly describe. We use these results to tiecharacteristic distributional footprints of interventions to the humanevaluation of LLM derivation quality, potentially leading to significantcontrol over fine-grained mathematical capabilities of language models withrespect to specific types of errors.

Controlling Equational Reasoning in Large Language Models with Prompt Interventions