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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 6: AAAI-21 Technical Tracks 6

Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units

February 1, 2023

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Authors

Ankur Mali

The Pennsylvania State University, PA, USA


Alexander G. Ororbia

Rochester Institute of Techonology, NY, USA


Daniel Kifer

The Pennsylvania State University, PA, USA


C. Lee Giles

The Pennsylvania State University, PA, USA


DOI:

10.1609/aaai.v35i6.16634


Abstract:

Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1)mathematical equation verification,which requires determining whether trigonometric and linear algebraic statements are valid identities or not, and (2)equation completion, which entails filling in a blank within an expression to make it true. Solving these tasks with deep learning requires that the neural model learn how to manipulate and compose various algebraic symbols, carrying this ability over to previously unseen expressions. Artificial neural net-works, including recurrent networks and transformers, struggle to generalize on these kinds of difficult compositional problems, often exhibiting poor extrapolation performance.In contrast, recursive neural networks (recursive-NNs) are,theoretically, capable of achieving better extrapolation due to their tree-like design but are very difficult to optimize as the depth of their underlying tree structure increases. To over-come this, we extend recursive-NNs to utilize multiplicative,higher-order synaptic connections and, furthermore, to learn to dynamically control and manipulate an external memory.We argue that this key modification gives the neural system the ability to capture powerful transition functions for each possible input. We demonstrate the effectiveness of our pro-posed higher-order, memory-augmented recursive-NN models on two challenging mathematical equation tasks, showing improved extrapolation, stable performance, and faster convergence. We show that our models achieve 1.53% average improvement over current state-of-the-art methods in equation verification and achieve 2.22% top-1 average accuracy and 2.96% top-5 average accuracy for equation completion.

Topics: AAAI

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HOW TO CITE:

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units Proceedings of the AAAI Conference on Artificial Intelligence (2021) 5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units AAAI 2021, 5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles (2021). Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units. Proceedings of the AAAI Conference on Artificial Intelligence, 5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. 2021. Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units. "Proceedings of the AAAI Conference on Artificial Intelligence". 5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. (2021) "Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units", Proceedings of the AAAI Conference on Artificial Intelligence, p.5006-5015

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles, "Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units", AAAI, p.5006-5015, 2021.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. "Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. "Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 5006-5015.

Ankur Mali||Alexander G. Ororbia||Daniel Kifer||C. Lee Giles. Recognizing and Verifying Mathematical Equations using Multiplicative Differential Neural Units. AAAI[Internet]. 2021[cited 2023]; 5006-5015.


ISSN: 2374-3468


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