# An Algebraic Approach to Learning and Grounding

arXiv: https://arxiv.org/abs/2204.02813 · HTML: https://mlsanity.com/paper/2204.02813/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 6 Apr 2022.

## Builds on (most cited first, 17 of 17)

- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Multimodal Compact Bilinear Pooling for Visual Question Answering and Visual Grounding](https://mlsanity.com/paper/1606.01847/) (2016)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Learning by Abstraction: The Neural State Machine](https://mlsanity.com/paper/1907.03950/) (2019)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [Gated-Attention Architectures for Task-Oriented Language Grounding](https://mlsanity.com/paper/1706.07230/) (2017)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [Learning Surrogate Losses](https://mlsanity.com/paper/1905.10108/) (2019)
- [On Correctness of Automatic Differentiation for Non-Differentiable Functions](https://mlsanity.com/paper/2006.06903/) (2020)
- [Visual Explanation by High-Level Abduction: On Answer-Set Programming Driven Reasoning about Moving Objects](https://mlsanity.com/paper/1712.00840/) (2017)

## Abstract (arXiv)

We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial algebra alg and a finite set of examples (varphi1, O1), (varphi2, O2), ldots, each consisting of an algebraic term varphii and a set of objects~Oi. The objective is to simultaneously fill in the missing algebraic operations in alg and ground the variables of every varphii in Oi, so that the combined value of the terms is optimised. We demonstrate the applicability of this framework through case studies in grammatical inference, picture-language learning, and the grounding of logic scene descriptions.