Multimodal Large Language Models (MLLMs) perform well on tasks such as visual question answering, but it remains unclear whether their reasoning relies more on memorized world knowledge or on the visual information present in the input image. To investigate this, we introduce Visual CounterFact, a new dataset of visually-realistic counterfactuals that put world knowledge priors (e.g, red strawberry) into direct conflict with visual input (e.g, blue strawberry). Using Visual CounterFact, we show that model predictions initially reflect memorized priors, but shift toward visual evidence in mid-to-late layers. This dynamic reveals a competition between the two modalities, with visual input ultimately overriding priors during evaluation. To control this behavior, we propose Pixels Versus Priors (PvP) steering vectors, a mechanism for controlling model outputs toward either world knowledge or visual input through activation-level interventions. On average, PvP successfully shifts 99.3% of color and 80.8% of size predictions from priors to counterfactuals. Together, these findings offer new tools for interpreting and controlling factual behavior in multimodal models.

Despite strong performance on vision-language tasks, Multimodal Large Language Models (MLLMs) struggle with mathematical problem-solving, with both open-source and state-of-the-art models falling short of human performance on visual-math benchmarks. To systematically examine visual-mathematical reasoning in MLLMs, we (1) evaluate their understanding of geometric primitives, (2) test multi-step reasoning, and (3) explore a potential solution to improve visual reasoning capabilities. Our findings reveal fundamental shortcomings in shape recognition, with top models achieving under 50% accuracy in identifying regular polygons. We analyze these failures through the lens of dual-process theory and show that MLLMs rely on System 1 (intuitive, memorized associations) rather than System 2 (deliberate reasoning). Consequently, MLLMs fail to count the sides of both familiar and novel shapes, suggesting they have neither learned the concept of “sides” nor effectively process visual inputs. Finally, we propose Visually Cued Chain-of-Thought (VC-CoT) prompting, which enhances multi-step mathematical reasoning by explicitly referencing visual annotations in diagrams, boosting GPT-4o’s accuracy on an irregular polygon side-counting task from 7% to 93%. Our findings suggest that System 2 reasoning in MLLMs remains an open problem, and visually-guided prompting is essential for successfully engaging visual reasoning.