ترغب بنشر مسار تعليمي؟ اضغط هنا

GamePad: A Learning Environment for Theorem Proving

74   0   0.0 ( 0 )
 نشر من قبل Daniel Huang
 تاريخ النشر 2018
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct machine-checkable proofs in a step-by-step manner. Hence, they provide an opportunity to explore theorem proving with human supervision. We use GamePad to synthesize proofs for a simple algebraic rewrite problem and train baseline models for a formalization of the Feit-Thompson theorem. We address position evaluation (i.e., predict the number of proof steps left) and tactic prediction (i.e., predict the next proof step) tasks, which arise naturally in tactic-based theorem proving.

قيم البحث

اقرأ أيضاً

Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automa ted theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action policy. We show through systematic analysis that these mechanisms allow TRAIL to significantly outperform previous reinforcement-learning-based theorem provers on two benchmark datasets for first-order logic automated theorem proving (proving around 15% more theorems).
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple strings to more involved graph-based embeddings -- little is known about how these different encodings compare. In this paper, we study and experimentally compare pattern-based embeddings that are applied in current systems with popular graph-based encodings, most of which have not been considered in the theorem proving context before. Our experiments show that the advantages of simpler encoding schemes in terms of runtime are outdone by more complex graph-based embeddings, which yield more efficient search strategies and simpler proofs. To support this, we present a detailed analysis across several dimensions of theorem prover performance beyond just proof completion rate, thus providing empirical evidence to help guide future research on neural-guided theorem proving towards the most promising directions.
Learning models that gracefully handle distribution shifts is central to research on domain generalization, robust optimization, and fairness. A promising formulation is domain-invariant learning, which identifies the key issue of learning which feat ures are domain-specific versus domain-invariant. An important assumption in this area is that the training examples are partitioned into domains or environments. Our focus is on the more common setting where such partitions are not provided. We propose EIIL, a general framework for domain-invariant learning that incorporates Environment Inference to directly infer partitions that are maximally informative for downstream Invariant Learning. We show that EIIL outperforms invariant learning methods on the CMNIST benchmark without using environment labels, and significantly outperforms ERM on worst-group performance in the Waterbirds and CivilComments datasets. Finally, we establish connections between EIIL and algorithmic fairness, which enables EIIL to improve accuracy and calibration in a fair prediction problem.
While current benchmark reinforcement learning (RL) tasks have been useful to drive progress in the field, they are in many ways poor substitutes for learning with real-world data. By testing increasingly complex RL algorithms on low-complexity simul ation environments, we often end up with brittle RL policies that generalize poorly beyond the very specific domain. To combat this, we propose three new families of benchmark RL domains that contain some of the complexity of the natural world, while still supporting fast and extensive data acquisition. The proposed domains also permit a characterization of generalization through fair train/test separation, and easy comparison and replication of results. Through this work, we challenge the RL research community to develop more robust algorithms that meet high standards of evaluation.
We convert the DeepMind Mathematics Dataset into a reinforcement learning environment by interpreting it as a program synthesis problem. Each action taken in the environment adds an operator or an input into a discrete compute graph. Graphs which com pute correct answers yield positive reward, enabling the optimization of a policy to construct compute graphs conditioned on problem statements. Baseline models are trained using Double DQN on various subsets of problem types, demonstrating the capability to learn to correctly construct graphs despite the challenges of combinatorial explosion and noisy rewards.

الأسئلة المقترحة

التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا