This paper proposes a novel algorithm which learns a formal regular grammar from real-world continuous data, such as videos or other streaming data. Learning latent terminals, non-terminals, and productions rules directly from streaming data allows the construction of a generative model capturing sequential structures with multiple possibilities. Our model is fully differentiable, and provides easily interpretable results which are important in order to understand the learned structures. It outperforms the state-of-the-art on several challenging datasets and is more accurate for forecasting future activities in videos. We plan to open-source the code.
A grammar can be regarded as a device that enumerates the sentences of a language. We study a sequence of restrictions that limit grammars first to Turing machines, then to two types of system from which a phrase structure description of the generated language can be drawn, and finally to finite state IV[arkov sources (finite automata). These restrictions are shown to be increasingly heavy in the sense that the languages that can be generated by grammars meeting a given restriction constitute a proper subset of those that can be generated by grammars meeting the preceding restriction. Various formulations of phrase structure description are considered, and the source of their excess generative power over finite state sources is investigated in greater detail. SECTION 1 We investigate several conceptions of linguistic structure to determine whether or not they can provide simple and "revealing" grammars that generate all of the sentences of English and only these. We find that no finite-state Markov process that produces symbols with transition from state to state can serve as an English grammar. Furthermore, the particular subclass of such processes that produce n -order statistical approximations to English do not come closer, with increasing n , to matching the output of an English grammar. We formalize-the notions of "phrase structure" and show that this gives us a method for describing language which is essentially more powerful, though still representable as a rather elementary type of finite-state process. Nevertheless, it is successful only when limited to a small subset of simple sentences. We study the formal properties of a set of grammatical transformations that carry sentences with phrase structure into new sentences with derived phrase structure, showing that transformational grammars are processes of the same elementary type as phrase-structure grammars; that the grammar of English is materially simplified if phrase structure description is limited to a kernel of simple sentences from which all other sentences are constructed by repeated transformations; and that this view of linguistic structure gives a certain insight into the use and understanding of language.