Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs).

However,existingapproachesusually require alargesetofhuman annotated explanations fortraining while collecting a large set of explanations is not only time consuming but also expensive.

The left part is about some existing approaches, e.g., IRNet [

Modelers use automatic differentiation (AD) of computation graphs to implement complex deep learning models without defining gradient computations.

Remark 3Toreachkxt x k2 kx0 x k2 weneedt log ( / )log ( q) iter thattheinputd (see B for adiscussion). AIDE: Fastand Communication Efficient Distributed Optimization.arXivpreprint,

In theorem proving, the task of selecting useful premises from alarge library to unlock the proof of a given conjecture is crucially important. This presents a challenge foralltheorem provers,especially theonesbasedonlanguage models, due to their relative inability to reason over huge volumes of premises in text form.