Multimodal Spatial Reasoning

Evaluation of multimodal reasoning models is typically reduced to a single accuracy score, implicitly treating reasoning as a unitary capability. We introduce MathLens, a benchmark of textbook-style geometry problems that exposes this assumption by operationally decomposing performance into perception, reasoning, and multimodal-specific components. Each problem is derived from a symbolic specification and accompanied by visual diagrams, text-only variants, multimodal questions, and targeted perceptual probes, enabling controlled measurement of each component. Using this decomposition, we show that common training strategies are associated with systematically different capability profiles that are invisible under aggregate accuracy. Across the models we study, reinforcement learning primarily improves perceptual grounding and robustness to diagram variation, while our analysis suggests that textual SFT yields gains through reflective reasoning. In contrast, as perception and reasoning improve, a growing fraction of remaining errors fall outside these components and are categorized as multimodal-specific. These results suggest that apparent progress in multimodal reasoning reflects shifting balances among subskills rather than uniform advancement, motivating evaluation beyond scalar accuracy.

A common belief in multimodal research is that the perceptual weaknesses of vision--language models can be compensated by stronger language reasoning (e.g., chain-of-thought, in-context learning, or external tools). We challenge this assumption. We argue that for a broad class of visual tasks hard to specify in language, failures stem from a structural fatality where the temporal decision of when to reason strictly dictates the spatial constraint of where reasoning takes place. When visual reasoning is deferred to language generation, current architectures do not merely delay computation; they displace it from the continuous visual representation to a discrete textual space. Consequently, the sequential Perception-then-Reasoning'' paradigm degenerates perception into a passive, one-off feature encoding process, rendering it functionally equivalent to Reasoning-in-Text-Space'', where task-critical spatial signals are collapsed before reasoning begins. We substantiate this claim with the Turing Eye Test (TET): tasks that must be resolved in visual space and are hard to verbalize; results show text-only reasoning cannot remedy these perceptual failures. Our findings suggest rethinking the architectural divide: shifting from reasoning about perception to reasoning within perception. This facilitates actively reasoning-driven perception that operates directly on pixel-level visual representations, rather than within a collapsed textual space.