VSS: Formalising Natural Language in a VSA Semantic Space

Formalising natural language means turning a sentence into the answers to a declared list of questions, answers that can be checked, compared and acted upon. We introduce the VSA Semantic Space (VSS), a construction within vector-symbolic architectures dedicated to this task, and the VSS Reader, which learns it from examples. A world, a domain of events, declares its questions in a short list, the legend. The reader multiplies each word's fixed random vector by a learned address, built from keys for word categories and pairs of categories, and sums the results into one state; a single objective, the cosine with the state that the legend's answers define, trains the keys. Because word vectors never enter the learned parameters and nesting reuses the same keys, the reader reads names and objects held out from training as well as seen ones (1.000, where a transformer given the same word vectors reaches 0.215, and 0.253 when also given the categories), and reads reports nested one level deeper than in training, with negation, modality, conditionals, quantifier scope and prohibitions. On WikiSQL, reading the question alone, it learns the query structure with less data than baselines given the same input. Each answer carries a margin, each question an occupancy signal and each sentence a residual, so the reader abstains where it is unsure and keeps what it could not place. A model takes megabytes, trains in minutes and reads on a CPU, with no language model at reading time. In two-systems terms, large language models act as a fluent first system; the VSS points to a checkable second one that can learn from the first during training and run without it, and to a new way of approaching the formalisation of language and the questions of alignment, trust, explainability and bias that depend on it. Code, experiment logs and full results: https://github.com/ml-circuits-research/vsa-semantic-space (the paper reports commit e531283).