# Unraveling the geometry of visual relational reasoning

arXiv: https://arxiv.org/abs/2502.17382 · HTML: https://mlsanity.com/paper/2502.17382/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 51 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [RAVEN: A Dataset for Relational and Analogical Visual rEasoNing](https://mlsanity.com/paper/1903.02741/) (2019)
- [Measuring abstract reasoning in neural networks](https://mlsanity.com/paper/1807.04225/) (2018)
- [Stratified Rule-Aware Network for Abstract Visual Reasoning](https://mlsanity.com/paper/2002.06838/) (2020)
- [A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices](https://mlsanity.com/paper/2203.04571/) (2022)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Learning Perceptual Inference by Contrasting](https://mlsanity.com/paper/1912.00086/) (2019)
- [Emergent Symbols through Binding in External Memory](https://mlsanity.com/paper/2012.14601/) (2020)
- [The Scattering Compositional Learner: Discovering Objects, Attributes, Relationships in Analogical Reasoning](https://mlsanity.com/paper/2007.04212/) (2020)
- [A Benchmark for Compositional Visual Reasoning](https://mlsanity.com/paper/2206.05379/) (2022)
- [Deep Learning Methods for Abstract Visual Reasoning: A Survey on Raven's Progressive Matrices](https://mlsanity.com/paper/2201.12382/) (2022)
- [Deep Learning Models of the Retinal Response to Natural Scenes](https://mlsanity.com/paper/1702.01825/) (2017)
- [How Far Are We from Intelligent Visual Deductive Reasoning?](https://mlsanity.com/paper/2403.04732/) (2024)
- [Improving Generalization for Abstract Reasoning Tasks Using Disentangled Feature Representations](https://mlsanity.com/paper/1811.04784/) (2018)
- [Learning Algebraic Representation for Systematic Generalization in Abstract Reasoning](https://mlsanity.com/paper/2111.12990/) (2021)
- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [Dynamic Inference with Neural Interpreters](https://mlsanity.com/paper/2110.06399/) (2021)
- [Neural Foundations of Mental Simulation: Future Prediction of Latent Representations on Dynamic Scenes](https://mlsanity.com/paper/2305.11772/) (2023)
- [Slot Abstractors: Toward Scalable Abstract Visual Reasoning](https://mlsanity.com/paper/2403.03458/) (2024)

## Built on by (most cited first, 3 of 3)

- [Geometry-aware similarity metrics for neural representations on Riemannian and statistical manifolds](https://mlsanity.com/paper/2603.28764/) (2026)
- [An Analysis of Residual-Stream Geometry Across Transformer Depth](https://mlsanity.com/paper/2607.18348/) (2026)
- [Intuition vectors](https://mlsanity.com/paper/2609.32619/) (2026)

## Abstract (arXiv)

Humans readily generalize abstract relations, such as recognizing "constant" in shape or color, whereas neural networks struggle, limiting their flexible reasoning. To investigate mechanisms underlying such generalization, we introduce SimplifiedRPM, a novel benchmark for systematically evaluating abstract relational reasoning, addressing limitations in prior datasets. In parallel, we conduct human experiments to quantify relational difficulty, enabling direct model-human comparisons. Testing four models, ResNet-50, Vision Transformer, Wild Relation Network, and Scattering Compositional Learner (SCL), we find that SCL generalizes best and most closely aligns with human behavior. Using a geometric approach, we identify key representation properties that accurately predict generalization and uncover a fundamental trade-off between signal and dimensionality: novel relations compress into training-induced subspaces. Layer-wise analysis reveals where relational structure emerges, highlights bottlenecks, and generates concrete hypotheses about abstract reasoning in the brain. Motivated by these insights, we propose SNRloss, a novel objective explicitly balancing representation geometry. Our results establish a geometric foundation for relational reasoning, paving the way for more human-like visual reasoning in AI and opening promising avenues for extending geometric analysis to broader cognitive tasks.