Currently, large language models (LLMs) have significant limitations in spatial reasoning, particularly in the absence of visual input. To address this issue, we introduce SODA (Spatial OODA), which draws inspiration from the OODA cognitive loop (Observe, Orient, Decide, Act), originally designed to enhance human decision-making in dynamic environments. Specifically, we embed the OODA loop into multiple control tasks, generating the SPOD-143k dataset, and successfully integrate it into LLMs through a two-phase and spatia-aware training strategy (SFT and GRPO). Furthermore, to fill the gap in evaluating spatial reasoning in purely text-based LLMs, we introduce the SPOD-Bench benchmark, including multiple tasks divided into three levels of difficulty. Experimental results show that SODA significantly enhances the spatial reasoning capabilities of LLMs across testing scenarios including SPOD-Bench, SPACE and applications, providing a replicable and effective paradigm for improving the spatial cognition of LLMs.

Humans naturally possess the spatial reasoning ability to form and manipulate images and structures of objects in space. There is an increasing effort to endow Vision-Language Models (VLMs) with similar spatial reasoning capabilities. However, it remains unclear whether these models truly understand and manipulate spatial objects or not. To address this question, we propose a new evaluation framework aimed at assessing the performance of VLMs in spatial deformation reasoning tasks. Specifically, we construct a benchmark for spatial deformation reasoning from 2D to 3D. We explore whether the model can effectively perform spatial deformation reasoning from two directions: forward reasoning (given the operations, find the final state) and reverse reasoning (given the final state, determine the operations). We adopt a ladder competition format, using the number of deformation steps as the level classification criterion, with the goal of exploring the boundaries of the model’s deformation reasoning capabilities. Interestingly, the benchmarking results reveal that almost no model demonstrates plausible spatial deformation reasoning abilities. Furthermore, even after applying targeted training and mainstream reasoning enhancement methods, the models are still unable to perform well on 3D spatial deformation reasoning.