Web-based interactive module with multiple representations for learning geometry theorem proving

Yang, Hsi-Hsun; Yin, Sheng-Kai; Wong, Wing-Kwong

doi:10.1109/compsym.2010.5685525

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…Current research delves into exploring mathematical theorem datasets (e.g., INT [190], Feit-Thompson [64], and IsarStep [92]) to develop novel machine learning-based theoremproving strategies. For instance, the format of IsarStep is shown in 14.…”

Section: Theorem Provingmentioning

confidence: 99%

“…For instance, the format of IsarStep is shown in 14. Huang et al [64] introduced the Feit-Thompson dataset, encompassing 1,602 lemmas, expanding into 83,478 proof states for Yilun Zhao 1 Yunxiang Li 2 Chenying Li 3 Rui Zhang 4 1 Yale University 2 The Chinese University of Hong Kong 3 Northeastern University 4 Penn State University ilun.zhao@yale.edu 1155124348@link.cuhk.edu.hk li.chenyin@northeastern.edu rmz5227@psu.edu Abstract reasoning over hybrid data containxtual and tabular content (e.g., finans) has recently attracted much atten-NLP community. However, existing nswering (QA) benchmarks over hynly include a single flat table in each and thus lack examples of multirical reasoning across multiple hitables.…”

Section: Theorem Provingmentioning

confidence: 99%

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Geography of Technology Transfer in China

Liu

2023

East China Normal University Scientific Reports

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Graphs can model complex relationships between objects, enabling a myriad of Web applications such as online page/article classification and social recommendation. While graph neural networks (GNNs) have emerged as a powerful tool for graph representation learning, in an end-to-end supervised setting, their performance heavily relies on a large amount of task-specific supervision. To reduce labeling requirement, the "pre-train, fine-tune" and "pre-train, prompt" paradigms have become increasingly common. In particular, prompting is a popular alternative to fine-tuning in natural language processing, which is designed to narrow the gap between pre-training and downstream objectives in a task-specific manner. However, existing study of prompting on graphs is still limited, lacking a universal treatment to appeal to different downstream tasks. In this paper, we propose GraphPrompt, a novel pre-training and prompting framework on graphs. GraphPrompt not only unifies pre-training and downstream tasks into a common task template, but also employs a learnable prompt to assist a downstream task in locating the most relevant knowledge from the pre-trained model in a task-specific manner. Finally, we conduct extensive experiments on five public datasets to evaluate and analyze GraphPrompt. CCS CONCEPTS• Computing methodologies → Learning latent representations; • Information systems → Data mining.

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Section: Theorem Provingmentioning

confidence: 99%

Section: Theorem Provingmentioning

confidence: 99%

Geography of Technology Transfer in China

Liu

2023

East China Normal University Scientific Reports

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“…But given any set of initial axioms, many problems will inevitably be out of reach of search. 15 Abstraction learning provides a means to progress much beyond the limit of search methods.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, deep neural networks trained via RL emerged as a tool to learn policies (distributions over actions to take given a state) and value functions (an estimate of rewards that can be obtained from a given state) from raw representations, such as strings or pixels. Both policies and value functions can be used to guide search algorithms, making deep RL suitable for learning to search in large-scale problems such as finding proofs [14][15][16]. Given the availability of proofs generated by human mathematicians in large formalization projects, researchers have explored the use of human-written proofs as supervised training data to guide proof search [14,16,17].…”

Section: Related Workmentioning

confidence: 99%

Peano: learning formal mathematical reasoning

Poesia

Goodman

2023

Phil. Trans. R. Soc. A.

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General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might that inform automated mathematical reasoning? We posit that central to both puzzles is the structure of procedural abstractions underlying mathematics. We explore this idea in a case study on five sections of beginning algebra on the Khan Academy platform. To define a computational foundation, we introduce Peano, a theorem-proving environment where the set of valid actions at any point is finite. We use Peano to formalize introductory algebra problems and axioms, obtaining well-defined search problems. We observe existing reinforcement learning methods for symbolic reasoning to be insufficient to solve harder problems. Adding the ability to induce reusable abstractions (‘tactics’) from its own solutions allows an agent to make steady progress, solving all problems. Furthermore, these abstractions induce an order to the problems, seen at random during training. The recovered order has significant agreement with the expert-designed Khan Academy curriculum, and second-generation agents trained on the recovered curriculum learn significantly faster. These results illustrate the synergistic role of abstractions and curricula in the cultural transmission of mathematics. This article is part of a discussion meeting issue ‘Cognitive artificial intelligence’.

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“…It is the sub-model π(g|s ′ ) mapping from the encoded state s ′ ∈ R D to a subset of goals g ⊆ s ′ . A majority of approaches apply Breadth First Search (Bansal et al 2019a;Huang et al 2019) or Best First Search for goal selection. TACTICZERO (Wu et al 2021a) showed an improvement by considering the likelihood of proving distinct sets of goals (fringes) equivalent to the original goal.…”

Section: Learning Approachmentioning

confidence: 99%

BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Proving

Lamont,

Norrish,

Dezfouli

et al. 2024

AAAI

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Artificial Intelligence for Theorem Proving (AITP) has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread across several ITP systems. This presents a significant challenge to the comparison of methods, which are often complex and difficult to replicate. Addressing this, we present BAIT, a framework for the fair and streamlined comparison of learning approaches in ITP. We demonstrate BAIT’s capabilities with an in-depth comparison, across several ITP benchmarks, of state-of-the-art architectures applied to the problem of formula embedding. We find that Structure Aware Transformers perform particularly well, improving on techniques associated with the original problem sets. BAIT also allows us to assess the end-to-end proving performance of systems built on interactive environments. This unified perspective reveals a novel end-to-end system that improves on prior work. We also provide a qualitative analysis, illustrating that improved performance is associated with more semantically-aware embeddings. By streamlining the implementation and comparison of Machine Learning algorithms in the ITP context, we anticipate BAIT will be a springboard for future research.

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Web-based interactive module with multiple representations for learning geometry theorem proving

Cited by 3 publications

References 12 publications

Geography of Technology Transfer in China

Geography of Technology Transfer in China

Peano: learning formal mathematical reasoning

BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Proving

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