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General-purpose mobile robots need to complete tasks without exact humaninstructions. Large language models (LLMs) is a promising direction forrealizing commonsense world knowledge and reasoning-based planning.Vision-language models (VLMs) transform environment percepts intovision-language semantics interpretable by LLMs. However, completing complextasks often requires reasoning about information beyond what is currentlyperceived. We propose latent compositional semantic embeddings z* as aprincipled learning-based knowledge representation for queryablespatio-semantic memories. We mathematically prove that z* can always be found,and the optimal z* is the centroid for any set Z. We derive a probabilisticbound for estimating separability of related and unrelated semantics. We provethat z* is discoverable by iterative optimization by gradient descent fromvisual appearance and singular descriptions. We experimentally verify ourfindings on four embedding spaces incl. CLIP and SBERT. Our results show thatz* can represent up to 10 semantics encoded by SBERT, and up to 100 semanticsfor ideal uniformly distributed high-dimensional embeddings. We demonstratethat a simple dense VLM trained on the COCO-Stuff dataset can learn z* for 181overlapping semantics by 42.23 mIoU, while improving conventionalnon-overlapping open-vocabulary segmentation performance by +3.48 mIoU comparedwith a popular SOTA model.

Compositional Semantics for Open Vocabulary Spatio-semantic Representations