Geometry as Evidence, Not Exclusion: Support-Aware Correction for Spatial Reasoning
Abstract
Spatial executors may assess only some candidate answers, yet multiplying their scores with a full-question prediction excludes every unassessed candidate at any positive exponent. This conflates preference within the assessed set with probability allocation across its boundary. At exponent one, 88–92% of new errors across three natural-language 3D grounding settings occur when the initially correct parent winner is excluded. Geometry-Specific Correction (GSC) is a training-free rule expressing geometry as bounded evidence relative to a same-support relation-null reference. It preserves parent support and exactly recovers the parent under null evidence. A controlled comparison isolates allocation: a smoothed product and unclipped GSC have identical conditional predictions on each side of the boundary, yet the reference allocation improves natural-language 3D accuracy by 1.88–2.22 points. With one correction strength selected on SR3D and transferred unchanged, GSC improves all 11 parent–benchmark settings across five benchmarks, with positive paired intervals and gains up to 7.37 points in 3D grounding and 6.48 in RGB reasoning. Bounded-product controls attain comparable 3D accuracy, while GSC additionally specifies exact relation-null behavior. On ViewSpatial, omitting specified frame operations removes 60–80% of the gain and swapping entity roles reverses it. Support allocation is therefore a consequential design choice for partial spatial evidence.
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