Controlled Reformulation Testing for Logical Consistency in Large Language Models

Large language models (LLMs) frequently contradict themselves when the surface form of a logically equivalent question changes. We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. We evaluate several frontier LLMs and observe an accuracy-consistency gap where GPT-5.4-mini achieves $98.9\%$ base accuracy but only $60.3\%$ family-level consistency, while reasoning-optimized o4-mini achieves $96.9\%$ consistency. From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\%$ for GPT-5.4-mini) and double negation ($84.6\%$), while surface-level rephrasing remains robust ($94-100\%$). Increasing reasoning effort improves GPT-5.4-mini to $85.4\%$ consistency, but leaves GPT-5.4 unchanged overall because gains on nested negation are offset by failures on quantifier families. These results show that accuracy alone is not enough for evaluating logical reasoning in LLMs.

Interpreting Affine Recurrence Learning in GPT-style Transformers

Understanding the internal mechanisms of GPT-style transformers, particularly their capacity to perform in-context learning (ICL), is critical for advancing AI alignment and interpretability. In-context learning allows transformers to generalize during inference without modifying their weights, yet the precise operations driving this capability remain largely opaque. This paper presents an investigation into the mechanistic interpretability of these transformers, focusing specifically on their ability to learn and predict affine recurrences as an ICL task. To address this, we trained a custom three-layer transformer to predict affine recurrences and analyzed the model's internal operations using both empirical and theoretical approaches. Our findings reveal that the model forms an initial estimate of the target sequence using a copying mechanism in the zeroth layer, which is subsequently refined through negative similarity heads in the second layer. These insights contribute to a deeper understanding of transformer behaviors in recursive tasks and offer potential avenues for improving AI alignment through mechanistic interpretability. Finally, we discuss the implications of our results for future work, including extensions to higher-dimensional recurrences and the exploration of polynomial sequences.