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    <abstract>Multimodal large language models (MLLMs) still struggle with spatial reasoning, particularly on tasks requiring consistent geometric understanding across multiple image regions. While recent works incorporate depth supervision into MLLMs, it remains unclear what forms of geometric learning are most beneficial for spatial reasoning transfer. In this work, we propose Multi-point Geometric Consistency Alignment (MGCA), a geometry-guided post-training framework that uses depth annotations as verifiable geometric feedback without requiring depth input at inference time. MGCA samples multiple image regions and optimizes the model through a unified geometric reward that jointly captures metric grounding and relative geometric consistency. Specifically, the reward combines a metric depth objective with a margin-aware ranking objective and is optimized via Group Relative Policy Optimization (GRPO). Experiments on multiple spatial reasoning benchmarks show that MGCA consistently improves spatial understanding and outperforms comparable open-weight MLLMs of similar scale. More importantly, our analysis reveals that optimizing relative ordering alone can achieve high ranking accuracy while failing to learn transferable geometric representations due to the lack of metric grounding. In contrast, jointly optimizing metric depth and relational consistency leads to substantially stronger spatial reasoning performance. These findings suggest that effective spatial alignment in MLLMs requires metrically grounded relational learning, rather than relation-only supervision.</abstract>
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%0 Conference Proceedings
%T Depth as Verifiable Geometric Feedback: Enhancing Spatial Reasoning in Multimodal Large Language Models
%A Zhang, Yepeng
%A Xu, Ruohang
%A Yue, Zihao
%A Xu, Boshen
%A Jin, Qin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F zhang-etal-2026-depth
%X Multimodal large language models (MLLMs) still struggle with spatial reasoning, particularly on tasks requiring consistent geometric understanding across multiple image regions. While recent works incorporate depth supervision into MLLMs, it remains unclear what forms of geometric learning are most beneficial for spatial reasoning transfer. In this work, we propose Multi-point Geometric Consistency Alignment (MGCA), a geometry-guided post-training framework that uses depth annotations as verifiable geometric feedback without requiring depth input at inference time. MGCA samples multiple image regions and optimizes the model through a unified geometric reward that jointly captures metric grounding and relative geometric consistency. Specifically, the reward combines a metric depth objective with a margin-aware ranking objective and is optimized via Group Relative Policy Optimization (GRPO). Experiments on multiple spatial reasoning benchmarks show that MGCA consistently improves spatial understanding and outperforms comparable open-weight MLLMs of similar scale. More importantly, our analysis reveals that optimizing relative ordering alone can achieve high ranking accuracy while failing to learn transferable geometric representations due to the lack of metric grounding. In contrast, jointly optimizing metric depth and relational consistency leads to substantially stronger spatial reasoning performance. These findings suggest that effective spatial alignment in MLLMs requires metrically grounded relational learning, rather than relation-only supervision.
%R 10.18653/2026.findings-emnlp.2206
%U https://aclanthology.org/2026.findings-emnlp.2206/
%U https://doi.org/10.18653/2026.findings-emnlp.2206
%P 47258-47274

Markdown (Informal)

[Depth as Verifiable Geometric Feedback: Enhancing Spatial Reasoning in Multimodal Large Language Models](https://aclanthology.org/2026.findings-emnlp.2206/) (Zhang et al., Findings 2026)

• Depth as Verifiable Geometric Feedback: Enhancing Spatial Reasoning in Multimodal Large Language Models (Zhang et al., Findings 2026)

ACL

• Yepeng Zhang, Ruohang Xu, Zihao Yue, Boshen Xu, and Qin Jin. 2026. Depth as Verifiable Geometric Feedback: Enhancing Spatial Reasoning in Multimodal Large Language Models. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 47258–47274, Budapest, Hungary. Association for Computational Linguistics.