# High-Fidelity Vector Space Models of Structured Data

## TL;DR

This paper presents a novel method for converting structured data into fixed-size real-valued vectors by formulating it as a satisfiability problem, enabling precise representation and reconstruction in machine learning tasks.

## Contribution

Introduces a new approach that compiles structured data into satisfiability problems, facilitating accurate vector representations and reversible encoding for machine learning applications.

## Key findings

- Effective vector representations for structured data in NLP and reasoning
- Ability to reconstruct original data from vector form
- Demonstrated applicability in natural language and logic domains

## Abstract

Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued vector of a fixed, pre-specified size. In this work, we introduce a novel approach that compiles structured data into a satisfiability problem which has in its set of solutions at least (and often only) the input data. The satisfiability problem is constructed from constraints which are generated automatically a priori from a given signature, thus trivially allowing for a bag-of-words-esque vector representation of the input to be constructed. The method is demonstrated in two areas, automated reasoning and natural language processing, where it is shown to produce vector representations of natural-language sentences and first-order logic clauses that can be precisely translated back to their original, structured input forms.