arXiv subjects

Achille Fokoue

Publications and source records attributed to Achille Fokoue.

28 records · Page 2Linked to original sources

arXiv2020

A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving

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 automated 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).

cs.AI↗

arXiv2020

Improving Graph Neural Network Representations of Logical Formulae with Subgraph Pooling

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting structure-aware neural methods to work with the underlying graph representations of logical expressions. While more effective than character and token-level approaches, graph-based methods have often made representational trade-offs that limited their ability to capture key structural properties of their inputs. In this work we propose a novel approach for embedding logical formulae that is designed to overcome the representational limitations of prior approaches. Our architecture works for logics of different expressivity; e.g., first-order and higher-order logic. We evaluate our approach on two standard datasets and show that the proposed architecture achieves state-of-the-art performance on both premise selection and proof step classification.

cs.AI↗

arXiv2020

An Experimental Study of Formula Embeddings for Automated Theorem Proving in First-Order Logic

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.

cs.AI↗

arXiv2020

Path-Based Contextualization of Knowledge Graphs for Textual Entailment

In this paper, we introduce the problem of knowledge graph contextualization -- that is, given a specific NLP task, the problem of extracting meaningful and relevant sub-graphs from a given knowledge graph. The task in the case of this paper is the textual entailment problem, and the context is a relevant sub-graph for an instance of the textual entailment problem -- where given two sentences p and h, the entailment relationship between them has to be predicted automatically. We base our methodology on finding paths in a cost-customized external knowledge graph, and building the most relevant sub-graph that connects p and h. We show that our path selection mechanism to generate sub-graphs not only reduces noise, but also retrieves meaningful information from large knowledge graphs. Our evaluation shows that using information on entities as well as the relationships between them improves on the performance of purely text-based systems.

cs.AI↗

arXiv2019

Infusing Knowledge into the Textual Entailment Task Using Graph Convolutional Networks

Textual entailment is a fundamental task in natural language processing. Most approaches for solving the problem use only the textual content present in training data. A few approaches have shown that information from external knowledge sources like knowledge graphs (KGs) can add value, in addition to the textual content, by providing background knowledge that may be critical for a task. However, the proposed models do not fully exploit the information in the usually large and noisy KGs, and it is not clear how it can be effectively encoded to be useful for entailment. We present an approach that complements text-based entailment models with information from KGs by (1) using Personalized PageR- ank to generate contextual subgraphs with reduced noise and (2) encoding these subgraphs using graph convolutional networks to capture KG structure. Our technique extends the capability of text models exploiting structural and semantic information found in KGs. We evaluate our approach on multiple textual entailment datasets and show that the use of external knowledge helps improve prediction accuracy. This is particularly evident in the challenging BreakingNLI dataset, where we see an absolute improvement of 5-20% over multiple text-based entailment models.

cs.CL↗

arXiv2019

Answering Science Exam Questions Using Query Rewriting with Background Knowledge

Open-domain question answering (QA) is an important problem in AI and NLP that is emerging as a bellwether for progress on the generalizability of AI methods and techniques. Much of the progress in open-domain QA systems has been realized through advances in information retrieval methods and corpus construction. In this paper, we focus on the recently introduced ARC Challenge dataset, which contains 2,590 multiple choice questions authored for grade-school science exams. These questions are selected to be the most challenging for current QA systems, and current state of the art performance is only slightly better than random chance. We present a system that rewrites a given question into queries that are used to retrieve supporting text from a large corpus of science-related text. Our rewriter is able to incorporate background knowledge from ConceptNet and -- in tandem with a generic textual entailment system trained on SciTail that identifies support in the retrieved results -- outperforms several strong baselines on the end-to-end QA task despite only being trained to identify essential terms in the original source question. We use a generalizable decision methodology over the retrieved evidence and answer candidates to select the best answer. By combining query rewriting, background knowledge, and textual entailment our system is able to outperform several strong baselines on the ARC dataset.

cs.AI↗

arXiv2019

High-Fidelity Vector Space Models of Structured Data

Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued vector of a fixed, pre-specified size. In this work, we introduce a novel approach that compiles structured data into a satisfiability problem which has in its set of solutions at least (and often only) the input data. The satisfiability problem is constructed from constraints which are generated automatically a priori from a given signature, thus trivially allowing for a bag-of-words-esque vector representation of the input to be constructed. The method is demonstrated in two areas, automated reasoning and natural language processing, where it is shown to produce vector representations of natural-language sentences and first-order logic clauses that can be precisely translated back to their original, structured input forms.

cs.AI↗

arXiv2018

Improving Natural Language Inference Using External Knowledge in the Science Questions Domain

Natural Language Inference (NLI) is fundamental to many Natural Language Processing (NLP) applications including semantic search and question answering. The NLI problem has gained significant attention thanks to the release of large scale, challenging datasets. Present approaches to the problem largely focus on learning-based methods that use only textual information in order to classify whether a given premise entails, contradicts, or is neutral with respect to a given hypothesis. Surprisingly, the use of methods based on structured knowledge -- a central topic in artificial intelligence -- has not received much attention vis-a-vis the NLI problem. While there are many open knowledge bases that contain various types of reasoning information, their use for NLI has not been well explored. To address this, we present a combination of techniques that harness knowledge graphs to improve performance on the NLI problem in the science questions domain. We present the results of applying our techniques on text, graph, and text-to-graph based models, and discuss implications for the use of external knowledge in solving the NLI problem. Our model achieves the new state-of-the-art performance on the NLI problem over the SciTail science questions dataset.

cs.AI↗

arXiv2017

An effective algorithm for hyperparameter optimization of neural networks

A major challenge in designing neural network (NN) systems is to determine the best structure and parameters for the network given the data for the machine learning problem at hand. Examples of parameters are the number of layers and nodes, the learning rates, and the dropout rates. Typically, these parameters are chosen based on heuristic rules and manually fine-tuned, which may be very time-consuming, because evaluating the performance of a single parametrization of the NN may require several hours. This paper addresses the problem of choosing appropriate parameters for the NN by formulating it as a box-constrained mathematical optimization problem, and applying a derivative-free optimization tool that automatically and effectively searches the parameter space. The optimization tool employs a radial basis function model of the objective function (the prediction accuracy of the NN) to accelerate the discovery of configurations yielding high accuracy. Candidate configurations explored by the algorithm are trained to a small number of epochs, and only the most promising candidates receive full training. The performance of the proposed methodology is assessed on benchmark sets and in the context of predicting drug-drug interactions, showing promising results. The optimization tool used in this paper is open-source.

cs.AI↗

arXiv2014

A Principled Approach to Bridging the Gap between Graph Data and their Schemas

Although RDF graphs have schema information associated with them, in practice it is very common to find cases in which data do not fully conform to their schema. A prominent example of this is DBpedia, which is RDF data extracted from Wikipedia, a publicly editable source of information. In such situations, it becomes interesting to study the structural properties of the actual data, because the schema gives an incomplete description of the organization of a dataset. In this paper we have approached the study of the structuredness of an RDF graph in a principled way: we propose a framework for specifying structuredness functions, which gauge the degree to which an RDF graph conforms to a schema. In particular, we first define a formal language for specifying structuredness functions with expressions we call rules. This language allows a user or a database administrator to state a rule to which an RDF graph may fully or partially conform. Then we consider the issue of discovering a refinement of a sort (type) by partitioning the dataset into subsets whose structuredness is over a specified threshold. In particular, we prove that the natural decision problem associated to this refinement problem is NP-complete, and we provide a natural translation of this problem into Integer Linear Programming (ILP). Finally, we test this ILP solution with two real world datasets, DBpedia Persons and WordNet Nouns, and 4 different and intuitive rules, which gauge the structuredness in different ways. The rules give meaningful refinements of the datasets, showing that our language can be a powerful tool for understanding the structure of RDF data.

cs.DB↗