How Should Geometry Guide Latent Reasoning? MeRa for Spatial Prediction

Post-encoder refinement revisits an encoded history before prediction, but additional depth alone does not specify which relations guide that retrieval. For spatial tasks, this raises a specific question: how should iterative refinement use the geometry of the input? We study this question through MeRa (Metric-space Reasoning), a modular post-encoder interface that combines distance-conditioned cross-attention, fixed encoder memory, and gated residual updates. The original experimental record reports higher NDCG@10 with MeRa in six backbone–dataset settings, with relative gains of 2.5–13.9% for GETNext and 5.8–27.7% for LSTM. On NYC GETNext, the reported gap between refinement without and with distance bias is 4.5%. We characterize finite-depth sensitivity and fixed-memory information access, clarifying what the architecture guarantees and what must be assessed empirically. Depth comparisons and a CLEVR-derived nearest-object task provide complementary observations. The results motivate geometry-conditioned refinement as a design choice; unresolved historical run alignment and evaluation provenance limit causal and cross-protocol performance claims. Code is available at https://anonymous.4open.science/r/MeRaa.