# Learning Continuous Semantic Representations of Symbolic Expressions

arXiv: https://arxiv.org/abs/1611.01423 · HTML: https://mlsanity.com/paper/1611.01423/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2016.

## Built on by (most cited first, 25 of 25)

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- [Generating Symbolic Reasoning Problems with Transformer GANs](https://mlsanity.com/paper/2110.10054/) (2021)
- [Learning from Expert Factors: Trajectory-level Reward Shaping for Formulaic Alpha Mining](https://mlsanity.com/paper/2507.20263/) (2025)
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- [Semantic Representations of Mathematical Expressions in a Continuous Vector Space](https://mlsanity.com/paper/2211.08142/) (2022)
- [Learning from Noisy Crowd Labels with Logics](https://mlsanity.com/paper/2302.06337/) (2023)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [LAMNER: Code Comment Generation Using Character Language Model and Named Entity Recognition](https://mlsanity.com/paper/2204.09654/) (2022)
- [Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networks](https://mlsanity.com/paper/2212.05200/) (2022)
- [E-Gen: Leveraging E-Graphs to Improve Continuous Representations of Symbolic Expressions](https://mlsanity.com/paper/2501.14951/) (2025)
- [Symbolic Density Estimation for Discrete Distributions](https://mlsanity.com/paper/2605.21813/) (2026)
- [Epistemic Graph: A Plug-And-Play Module For Hybrid Representation Learning](https://mlsanity.com/paper/2305.18731/) (2023)
- [Toward Neurosymbolic Program Comprehension](https://mlsanity.com/paper/2502.01806/) (2025)
- [Prime Convolutional Model: Breaking the Ground for Theoretical Explainability](https://mlsanity.com/paper/2503.02773/) (2025)
- [SNIP++: Fine-Grained Symbolic-Numerical Alignment for Symbolic Regression](https://mlsanity.com/paper/2609.31965/) (2026)

## Abstract (arXiv)

Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of learning continuous semantic representations of algebraic and logical expressions. These networks are trained to represent semantic equivalence, even of expressions that are syntactically very different. The challenge is that semantic representations must be computed in a syntax-directed manner, because semantics is compositional, but at the same time, small changes in syntax can lead to very large changes in semantics, which can be difficult for continuous neural architectures. We perform an exhaustive evaluation on the task of checking equivalence on a highly diverse class of symbolic algebraic and boolean expression types, showing that our model significantly outperforms existing architectures.