# Structured Relational Representations

arXiv: https://arxiv.org/abs/2505.12143 · HTML: https://mlsanity.com/paper/2505.12143/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Can Neural Networks Understand Logical Entailment?](https://mlsanity.com/paper/1802.08535/) (2018)
- [Systematic Visual Reasoning through Object-Centric Relational Abstraction](https://mlsanity.com/paper/2306.02500/) (2023)
- [Interacting Monoidal Structures with Applications in Computing](https://mlsanity.com/paper/2411.03821/) (2024)

## Abstract (arXiv)

Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring further inquiry, about the appropriate level of abstraction at which such invariants should be defined and which aspects of a system they should characterize. Interpretation of the environment relies on abstract knowledge structures to make sense of the current state, which leads to interactions, essential drivers of learning and knowledge acquisition. Interpretation operates at the level of higher-order relational knowledge; hence, we propose that invariant structures must be where knowledge resides, specifically as partitions defined by the closure of relational paths within an abstract knowledge space. These partitions serve as the core invariant representations, forming the structural substrate where knowledge is stored and learning occurs. On the other hand, inter-partition connectors enable the deployment of these knowledge partitions encoding task-relevant transitions. Thus, invariant partitions provide the foundational primitives of structured representation. We formalize the computational foundations for structured relational representations of the invariant partitions based on closed semiring, a relational algebraic structure.