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.

There is a recent focus on designing architectures that have an Integer Linear Programming (ILP) layer following a neural model (referred to asNeural ILP in this paper).

However, ifτ is too high, most of the unlabeled data points would not be used for consistency regularization. Based on these insights, we setτ as 0.95 in our experiments. We describe further details of the experimental setup. To train the ReMixMatch, we gradually increased the coefficient of the loss associated with the unlabeled data points, following [4]. We found that without this gradual increase, the validation loss of the ReMixMatch did not converge.