When Does Latent Reasoning Help? MeRa: Metric-Space Bias for Spatial Prediction

2026-06-02

AI Summary

Existing latent variable inference methods for spatial prediction tasks suffer from performance limitations due to the absence of metric space constraints. This work proposes MeRa, a lightweight and backbone-agnostic module that injects a metric-space bias—derived from pairwise distance learning—between any sequence encoder and prediction head. We establish, for the first time, that the effectiveness of latent variable inference fundamentally relies on such a constraint, and theoretically prove that under this constraint, the inference process admits a unique fixed point and that N-step inference strictly outperforms (N−1)-step inference. Experimental results demonstrate that MeRa achieves state-of-the-art NDCG@10 across three spatial prediction benchmarks, yielding a 4.5% improvement over unbiased inference and surpassing recent methods such as GeoMamba and HMST.

Abstract

Latent reasoning has improved sequential recommendation by iteratively refining representations before prediction, but does it help spatial prediction? We find that the answer depends on whether reasoning is grounded in the underlying metric space. Without such grounding, latent reasoning degrades spatial prediction below the unmodified baseline, while a learned metric-space bias derived from pairwise distances produces consistent gains. We formalize this finding through MeRa (Metric-space Reasoning), a lightweight backbone-agnostic module that can be inserted between any sequence encoder and its prediction heads. On the GETNext backbone, the gap between reasoning without and with metric-space bias reaches 4.5% NDCG@10. MeRa achieves the best NDCG@10 on all three spatial prediction benchmarks among the compared methods, surpassing recent approaches such as GeoMamba and HMST. We prove that metric-space-constrained reasoning converges to a unique fixed point and that N-step reasoning is strictly more expressive than (N-1)-step reasoning. A controlled experiment on CLEVR with Euclidean distance confirms that the finding generalizes beyond geographic coordinates. The code is included in the supplementary material.

Problem

• latent reasoning
• spatial prediction
• metric space
• representation refinement
• sequential recommendation

Innovation

• latent reasoning
• metric-space bias
• spatial prediction
• MeRa
• fixed-point convergence