General-purpose mobile robots need to complete tasks without exact human instructions. Large language models (LLMs) is a promising direction for realizing commonsense world knowledge and reasoning-based planning. Vision-language models (VLMs) transform environment percepts into vision-language semantics interpretable by LLMs. However, completing complex tasks often requires reasoning about information beyond what is currently perceived. We propose latent compositional semantic embeddings z* as a principled learning-based knowledge representation for queryable spatio-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 probabilistic bound for estimating separability of related and unrelated semantics. We prove that z* is discoverable by iterative optimization by gradient descent from visual appearance and singular descriptions. We experimentally verify our findings on four embedding spaces incl. CLIP and SBERT. Our results show that z* can represent up to 10 semantics encoded by SBERT, and up to 100 semantics for ideal uniformly distributed high-dimensional embeddings. We demonstrate that a simple dense VLM trained on the COCO-Stuff dataset can learn z* for 181 overlapping semantics by 42.23 mIoU, while improving conventional non-overlapping open-vocabulary segmentation performance by +3.48 mIoU compared with a popular SOTA model.

We present a novel connectionist model for acquiring the semantics of a simple language through the behavioral experiences of a real robot. We focus on the "compositionality" of semantics, a fundamental character- istic of human language, which is the ability to understand the meaning of a sentence as a combination of the meanings of words. We also pay much attention to the "embodiment" of a robot, which means that the robot should acquire semantics which matches its body, or sensory-motor system. The essential claim is that an embodied compositional semantic representation can be self-organized from generalized correspondences between sentences and behavioral patterns. This claim is examined and confirmed through simple experiments in which a robot generates corre- sponding behaviors from unlearned sentences by analogy with the corre- spondences between learned sentences and behaviors.