<p>English Language Teaching (ELT) has been long struggling with modeling contextual semantics, idiomatic expressions and pragmatic phenomena of nuance that are not well modeled by means of rules or other superficial computational techniques. Although the recent progress in deep learning is promising, most of the architectures have challenges of being unstable in optimization and the ability to represent non-linear semantic interactions. The purpose of this gap is to provide a new framework which will combine Deep Maxout Networks with an Improved Crisscross Optimization (ICO) algorithm. Maxouts can offer high-fidelity discrimination between compositional and idiomatic language through piecewise-linear competition based on features, and stable and efficient convergence based on ICO, a slightly gradient refinement algorithm which integrates population-based exploration with gradient refinement. The model was trained on the two-billion-word Oxford English Corpus, which is the most comprehensive resource of authentic use of English, and is therefore the state of the art in idiom classification (F1 92.7%) and the best among competitors in estimating semantic similarity and predicting errors in learners. Findings prove that the concept of architecture-optimization co-design based on real-world linguistic data may lead to the development of robust, pedagogically significant instruments of the next-generation adaptive language learning system at the point of convergence between artificial intelligence and applied linguistics.</p>