Effective Math-Aware Ad-Hoc Retrieval based on Structure Search and Semantic Similarities

Abstract

Despite the prevalence of digital scientific and educational contents on the Internet, only a few search engines are capable to retrieve them efficiently and effectively. The main challenge in freely searching scientific literature arises from the presence of structured math formulas and their heterogeneous and contextually important surrounding words. This thesis introduces an effective math-aware, ad-hoc retrieval model that incorporates structure search and semantic similarities. Transformer-based neural retrievers have been adopted to capture additional semantics using domain-adapted supervised retrieval.

To enable structure search, I suggest an unsupervised retrieval model that can filter potential mathematical formulas based on structure similarity. This similarity is determined by measuring the largest common substructure(s) in a formula tree representation, known as the Operator Tree (OPT). The structure matching is approximated by employing maximum matching of path-based structure features. The proposed structure similarity measurement can be tailored based on the desired effectiveness and efficiency trade-offs. It may consider various node types, such as operators and operands, and accommodate different numbers of common subtrees with varying weights. In addition to structure similarity, this unsupervised model also captures symbol substitutions through a greedy matching algorithm applied to the matched substructure(s).

To achieve efficient structure search, I introduce a dynamic pruning algorithm to the problem of structure retrieval. The proposed retrieval algorithm efficiently identifies the maximum common subtree among formula candidates and safely eliminates potential structure matches that exceed a dynamic threshold. To accomplish this, three rank-safe pruning strategies are suggested and compared against exhaustive search baselines. Additionally, more aggressive thresholding policies are proposed to balance effectiveness with further speed improvements. A novel hierarchical inverted index has been implemented. This index is designed to be compatible with traditional information retrieval (IR) infrastructure and optimization techniques.

To capture other semantic similarities, I have incorporated neural retrievers into a hybrid setting with structure search. This approach has achieved the state-of-the-art effectiveness in recent math information retrieval tasks. In comparison to strict and unsupervised matching, I have found that supervised neural retrievers are able to capture additional semantic similarities in a highly complementary manner. In order to learn effective representations in heterogeneous math contents, I have proposed a novel pretraining architecture that can improve the contextual awareness between math and its surrounding texts. This pretraining scheme generates effective downstream single-vector representations, eliminating the efficiency bottleneck from using multi-vector dense representations.

In the end, the thesis examines future directions, specifically the integration of recent advancements in language modeling. This includes incorporating ongoing exciting developments of large language models for improved math information retrieval. A preliminary evaluation has been conducted to assess the impact of these advancements.