Identifying Axiomatic Mathematical Transformation Steps using Tree-Structured Pointer Networks
Abstract: The classification of mathematical relations has become a new area of research in deep
learning. A major focus lies on determining mathematical equivalence, as this problem is
expensive to solve with rule-based systems due to the large search space. While previous
work has simply approached the task as a binary classification without providing further
insight into the underlying decision, we aim to iteratively find a sequence of necessary steps
to transform a mathematical expression into an arbitrary equivalent form. Each step in
this sequence is specified by an axiom together with its position of application. We denote
this task as Stepwise Equation Transformation Identification (SETI) task. To solve the
task efficiently, we further propose TreePointerNet, a novel architecture which exploits the
inherent tree structure of mathematical equations and consists of three key building blocks:
(i) a transformer model tailored to work on hierarchically tree-structured equations, making
use of (ii) a copy-pointer mechanism to extract the exact location of a transformation in the
tree and finally (iii) custom embeddings that map distinguishable occurrences of the same
token type to a common embedding. In addition, we introduce new datasets of equations for
the SETI task. We benchmark our model against various baselines and perform an ablation
study to quantify the influence of our custom embeddings and the copy-pointer component.
Furthermore, we test the robustness of our model on data of unseen complexity. Our results
clearly show that incorporating the hierarchical structure, embeddings and copy-pointer into
a single model is highly beneficial for solving the SETI task
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Hongsheng_Li3
Submission Number: 3607
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