Academic Writing -Equation representation for a neural network

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Hi there. I'm a PhD student in computer engineering and my thesis is on data mining. My expertise includes deep learning and recommender systems, both in theoretical analysis and implementation. I have strong experience in deriving updating equations of auto-encoders. For auto encoder denoising, I have seen some papers in the literature. In my understanding, the neural network here consists of three layers, the input neutrons in layer L1, the auto-encoder hidden units in layer L2, and the classifier output in layer L3. The second task is a variation which injecting noise on L1 and L2. This is not a deep neural network, and I can provide my full derivation for this case with more details. If you think my experience fits this project, please do not hesitate contacting me and I will provide my plan to complete this project. Thank you.