You are able to build simple neural networks (feedforward/autoencoders)
You are familiar with multivariate Taylor series, the gradient and the Hessian (see background if not)
You understand (at a high level) stochastic gradient descent, and its accelerations to replicate some second order behavior using past values of gradients
You can train networks using stochastic gradient descent/variants
You understand autoencoder architectures (linear activations) in relation to the singular value decomposition
You can train autoencoders to project training datasets to low dimensional (potentially non-linear) manifolds