# Enhancing Neural Mathematical Reasoning by Abductive Combination with Symbolic Library

arXiv: https://arxiv.org/abs/2203.14487 · HTML: https://mlsanity.com/paper/2203.14487/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving](https://mlsanity.com/paper/1910.06611/) (2019)
- [Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems](https://mlsanity.com/paper/1609.07197/) (2016)

## Built on by (most cited first, 4 of 4)

- [A Symbolic Framework for Evaluating Mathematical Reasoning and Generalisation with Transformers](https://mlsanity.com/paper/2305.12563/) (2023)
- [Logical Tasks for Measuring Extrapolation and Rule Comprehension](https://mlsanity.com/paper/2211.07727/) (2022)
- [Exploring the Limits of Fine-grained LLM-based Physics Inference via Premise Removal Interventions](https://mlsanity.com/paper/2404.18384/) (2024)
- [TANGO: Treating Tokens as Operators](https://mlsanity.com/paper/2608.22117/) (2026)

## Abstract (arXiv)

Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This paper demonstrates that some abilities can be achieved through abductive combination with discrete systems that have been programmed with human knowledge. On a mathematical reasoning dataset, we adopt the recently proposed abductive learning framework, and propose the ABL-Sym algorithm that combines the Transformer neural models with a symbolic mathematics library. ABL-Sym shows 9.73% accuracy improvement on the interpolation tasks and 47.22% accuracy improvement on the extrapolation tasks, over the state-of-the-art approaches. Online demonstration: http://math.polixir.ai