Automatic classification of sound commands is becoming increasingly important, especially for embedded and mobile devices. Many of these devices contain both microphones and cameras. The manufacturers that develop and produce them would like to use the same methodology for sound and image classification tasks. It's possible to achieve by representing sound commands as images, and then use convolutional neural networks when classifying images as well as sounds. In this research, we tried several approaches to the problem of sound classification that we applied in TensorFlow Speech Recognition Challenge organized by Google Brain team on the Kaggle platform. Here we show different representations of sounds (Wave frames, Spectrograms, Mel-Spectrograms, MFCCs) and apply several 1D and 2D convolutional neural networks to get the best performance. As a novelty of our work, we developed and trained from scratch two 1d network architectures that are topologically similar to 2d VGG and ResNet network types. These networks show similar performance with 2d networks when sound signal is represented by using melgrams. Our experiments reveal that we found appropriate sound representation and corresponding convolutional neural networks. As a result, we achieved good classification accuracy (91.8%) that allowed us to finish the challenge on 8-th place among 1315 teams.

We consider the multimode generalization of the normally ordered factorization formula of squeezings. This formula allows us to establish relationships between various representations of squeezed states, to calculate partial traces, mean values, and variations. The main results are expressed in terms of the matrix representation of canonical transformations, which is a convenient and numerically stable mathematical tool. Explicit representations are given for the inner product and the composition of generalized multimode squeezings. Explicitly solvable evolution problems are considered.

In this paper, we consider quantum multidimensional problems solvable by using the second quantization method. A multidimensional generalization of the Bogolyubov factorization formula, which is an important particular case of the Campbell-Baker-Hausdorff formula, is established. The inner product of multidimensional squeezed states is calculated explicitly; this relationship justifies a general construction of orthonormal systems generated by linear combinations of squeezed states. A correctly defined path integral representation is derived for solutions of the Cauchy problem for the Schrödinger equation describing the dynamics of a charged particle in the superposition of orthogonal constant (E,H)-fields and a periodic electric field. We show that the evolution of squeezed states runs over compact one-dimensional matrix-valued orbits of squeezed components of the solution, and the evolution of coherent shifts is a random Markov jump process which depends on the periodic component of the potential.