Our speech recognition system uses the seq2seq model. When processing, recognizing and classifying an audio signal, Smart Neural Integral Euqation uses 3 main components: a linguistic, acoustic and lexical model for each of the languages we work with (English, Russian, Ukrainian). SmartIE is based on the idea of using the tangent space of a (sub-) Riemannian manifold to classify incoming sound. To extract feautures from sound, SmartIE covariance matrices as descriptors. Transforming the space of matrices using a metric with affine invariance, we obtain a Riemannian manifold. Thanks to this approach, the neural network reaches the WER (word error rate) indicator up to 5%

Instead of using conventional RNN neural networks for the problem of language generation, which offer a discrete approach to modeling, our technology - Smart Neural Integral Euqation, is based on continuous normalizing streams for speech synthesis. The continuous normalizing flow is given by two dynamics: hidden nodes and their probability density, using the formula for the instantaneous change of variables. Unlike discrete normalizing streams, CNF does not impose any restrictions on its architecture and allows you to use a rather flexible function to transform a stream. With the help of SmartIE, the mean opinion score of more than 4.5 and the conditional logarithmic likelihood of more than 4 are achieved.

The generation of questions and tasks for users is guided by the SmartIE model. SmartIE is constantly learning in real time, thereby ensuring personalization of test tasks. By implementing complex language models using continuous invariant spaces, SmartIE forms dependencies between lexical concepts. Using our technologies, the word error rate is minimized up to 10%

On the basis of SmartIE, a neural network module of a bot-tutor has been developed, which is responsible for the task of improving the quality of user training, which is formulated as an optimization problem on a sub-Riemannian space with introduced constraints. The management of the personalization of the pedagogical process is built using the PhR-scale - a unique development from DeepNoesa: phenomenological reduction of the scale, which allows you to stimulate the neurophysiological processes underlying scientific creative activity.

Visualization of training material is carried out on the basis of a neuromathematical model of human visual perception (visual cortex 1, 2, 3 and other levels) using Gaussian filters, Laplepass operators, as well as Lie groups for the implementation at the architectural level of a neural network, the invariance properties characteristic of human visual perception. Thanks to SmartIE, mind-maps can be created personalized using neurogeometric algorithms, taking into account the neurophysiological characteristics of the student.