arXiv:1809.06582v2 [cs.CV] 12 Dec 2018 XXX (2019) 1001–1098 1001 Symbolic Tensor Neural Networks for Digital Media – from Tensor Processing via BNF Graph Rules to CREAMS Applications * Wladyslaw Skarbek Institute of Radioelectronics and Multimedia Technology Faculty of Electronics and Information Technology Warsaw University of Technology Nowowiejska 15/19, 00-665 Warszawa, Poland Abstract. This tutorial material on Convolutional Neural Networks (CNN) and its applications in digital media research is based on the concept of Symbolic Tensor Neural Networks. The set of STNN expressions is specified in Backus-Naur Form (BNF) which is annotated by constraints typical for labeled acyclic directed graphs (DAG). The BNF induction begins from a collection of neural unit symbols with extra (up to five) decoration fields (including tensor depth and shar- ing fields). The inductive rules provide not only the general graph structure but also the specific shortcuts for residual blocks of units. A syntactic mechanism for network fragments modulariza- tion is introduced via user defined units and their instances. Moreover, the dual BNF rules are specified in order to generate the Dual Symbolic Tensor Neural Network (DSTNN). The joined interpretation of STNN and DSTNN provides the correct flow of gradient tensors, back propa- gated at the training stage. The proposed symbolic representation of CNNs is illustrated for six generic digital media applications (CREAMS): Compression, Recognition, Embedding, Anno- tation, 3D Modeling for human-computer interfacing, and data Security based on digital media objects. In order to make the CNN description and its gradient flow complete, for all presented applications, the symbolic representations of mathematically defined loss/gain functions and gra- dient flow equations for all used core units, are given. The tutorial is to convince the reader that STNN is not only a convenient symbolic notation for public presentations of CNN based solu- tions for CREAMS problems but also that it is a design blueprint with a potential for automatic generation of application source code. Keywords: convolutional neural network, tensor neural network, deep learning, deep digital media application Address for correspondence: w.skarbek@ire.pw.edu.pl ∗ This is a tutorial submitted to the ”Special Issue on Deep Neural Networks for Digital Media Algorithms” of Fundamenta Informaticae.