Who Is Left of Whom? Tracing Spatial Evidence and Role Binding in Relative-Position Reasoning

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High instance-level accuracy can mask inconsistencies in spatial reasoning when objects exchange positions or their roles are reversed in the query. The internal representations supporting relative-position reasoning remain poorly understood. We investigate two complementary components of this process: tracking object locations in the input and representing their query roles. Across three VLMs with visual or textual inputs and their language-model backbones, activation patching reveals a staged progression from early-layer source representations through intermediate-layer query-object representations to late-layer answer states. Targeted interventions further establish causal links along this progression: manipulating source-side representations shifts location information at query-object mentions and ultimately alters relation predictions. Beyond object-location information, we also identify a stable query-side direction associated with the roles of the two objects in the comparison. Steering along directions estimated on synthetic scenes generalizes to natural-image benchmarks, improving accuracy and both forms of paired consistency in most settings without retraining. Our findings reveal complementary components of relational reasoning across visual and textual settings and show how targeted interventions can improve the consistency of models' behavior.