ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Abstract

We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradient-boosting guidance, we manually create abstracted features by considering arity-based encodings of formulas. For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses. The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework.To provide competitive real-time performance of the GNNs, we have developed a new context-based approach to evaluation of generated clauses in E. Clauses are evaluated jointly in larger batches and with respect to a large number of already selected clauses (context) by the GNN that estimates their collectively most useful subset in several rounds of message passing. This means that approximative inference rounds done by the GNN are efficiently interleaved with precise symbolic inference rounds done inside E. The methods are evaluated on the MPTP large-theory benchmark and shown to achieve comparable realtime performance to state-of-the-art symbol-based methods. The methods also show high complementarity, solving a large number of hard Mizar problems.

Improving ENIGMA-style Clause Selection while Learning From History

“…The idea to improve clause selection by learning from previous prover experience goes, to the best of our knowledge, back to Schulz [8,30] and has more recently been successfully employed by the ENIGMA system and others [7,[15][16][17]22].…”

“…In the beginning, the authors of ENIGMA experimented with various forms of hand-crafted numerical clause features [16,17]. An attractive alternative explored in later work [7,15,22] is the use of artificial neural networks, which can be understood as extracting the most relevant features automatically.…”

“…Otherwise the learned advice cannot meaningfully cary over to previously unsolved problems. While the assumption of aligned signature has been employed by the early systems [16,22], the most recent version of ENIGMA [15,24] can work in a "signature agnostic" mode.…”

“…We denote it M −R to stress that clauses with high L are treated as small from the perspective of the selection and therefore preferred. This scheme has been used by Loos et al [22] and in the latest ENGIMA [15,37].…”

Neural Precedence Recommender

“…In [26], [15] and [27], the authors propose similar GNN architectures to solve tasks on FOL problems. They use the GNNs to solve classification tasks such as premise selection.…”