Abstract-An efficient algorithm for recurrent neural network training is presented. The approach increases the training speed for tasks where a length of the input sequence may vary significantly. The proposed approach is based on the optimal batch bucketing by input sequence length and data parallelization on multiple graphical processing units. The baseline training performance without sequence bucketing is compared with the proposed solution for a different number of buckets. An example is given for the online handwriting recognition task using an LSTM recurrent neural network. The evaluation is performed in terms of the wall clock time, number of epochs, and validation loss value.

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Handwritten mathematical expressions are an essential part of many domains, including education, engineering, and science. The pervasive availability of computationally powerful touch-screen devices, similar to the recent emergence of deep neural networks as high-quality sequence recognition models, result in the widespread adoption of online recognition of handwritten mathematical expressions. Also, a deeper study and improvement of such technologies is necessary to address the current challenges posed by the extensive usage of distance learning, and remote work due to the world pandemic. This paper delineates the stateof-the-art recognition methods along with the user's experience in pen-centric applications for operating with handwritten mathematical expressions. Recognition methods have been categorized into classes, with a description of their merits and limitations. Particular attention is paid to end-to-end approaches based on encoder-decoder architecture and multi-modal input. Evaluation protocols and open benchmark datasets are considered as well as the comparison of the recognition performance, based on open competition results. The use of handwritten math recognition is illustrated by examples of applications for various fields and platforms. A distinctive part of the survey is that we also considered how UI design relies on the use of different recognition approaches, which is aimed at helping potential researchers improve the performance of the introduced approaches toward the best responses in practical applications. Finally, this paper presents the prospective survey of future research directions in handwritten mathematical expression recognition and their applications.

Text-based interaction using mobile devices is now ubiquitous, its main outlets being social networks, messengers, email conversations, virtual assistants, accessibility applications, etc. Its status implies the need to facilitate text input by the user and to devise ways to provide verbal feedback. In this paper, we discuss a method of unique text generation for mobile devices and its evaluation methodology as a solution for both stated challenges. We consider the opportunities given by the use of context (location, weather, scheduled events, etc.), the limitations in terms of computational resources and data usage, and the inherent subjectivity of creative task assessment given the number variety of possibly acceptable outputs. The comparison with other text generation approaches shows that the use of coherence metrics helps to achieve higher quality in terms of human perception. The Spearman correlation between the values of the proposed coherence metric and the human assessment of text readability is 0.86, which indicates the high quality of the metrics and the effectiveness of the method as a whole.

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