# Solving ARC visual analogies with neural embeddings and vector arithmetic: A generalized method

arXiv: https://arxiv.org/abs/2311.08083 · HTML: https://mlsanity.com/paper/2311.08083/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain](https://mlsanity.com/paper/2305.07141/) (2023)
- [Emergent Symbols through Binding in External Memory](https://mlsanity.com/paper/2012.14601/) (2020)
- [Fast and flexible: Human program induction in abstract reasoning tasks](https://mlsanity.com/paper/2103.05823/) (2021)
- [A Review of Emerging Research Directions in Abstract Visual Reasoning](https://mlsanity.com/paper/2202.10284/) (2022)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [Evaluating Understanding on Conceptual Abstraction Benchmarks](https://mlsanity.com/paper/2206.14187/) (2022)

## Built on by (most cited first, 8 of 8)

- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [Combining Induction and Transduction for Abstract Reasoning](https://mlsanity.com/paper/2411.02272/) (2024)
- [ARC-GEN: A Mimetic Procedural Benchmark Generator for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.00162/) (2025)
- [ARCLE: The Abstraction and Reasoning Corpus Learning Environment for Reinforcement Learning](https://mlsanity.com/paper/2407.20806/) (2024)
- [Don't throw the baby out with the bathwater: How and why deep learning for ARC](https://mlsanity.com/paper/2506.14276/) (2025)
- [Implicit Rule Induction with Test-Time Task Embeddings in ARC-like Tasks](https://mlsanity.com/paper/2609.21181/) (2026)
- [Vector Symbolic Algebras for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.08747/) (2025)
- [Addressing and Visualizing Misalignments in Human Task-Solving Trajectories](https://mlsanity.com/paper/2409.14191/) (2024)

## Abstract (arXiv)

Analogical reasoning derives information from known relations and generalizes this information to similar yet unfamiliar situations. One of the first generalized ways in which deep learning models were able to solve verbal analogies was through vector arithmetic of word embeddings, essentially relating words that were mapped to a vector space (e.g., king - man + woman = __?). In comparison, most attempts to solve visual analogies are still predominantly task-specific and less generalizable. This project focuses on visual analogical reasoning and applies the initial generalized mechanism used to solve verbal analogies to the visual realm. Taking the Abstraction and Reasoning Corpus (ARC) as an example to investigate visual analogy solving, we use a variational autoencoder (VAE) to transform ARC items into low-dimensional latent vectors, analogous to the word embeddings used in the verbal approaches. Through simple vector arithmetic, underlying rules of ARC items are discovered and used to solve them. Results indicate that the approach works well on simple items with fewer dimensions (i.e., few colors used, uniform shapes), similar input-to-output examples, and high reconstruction accuracy on the VAE. Predictions on more complex items showed stronger deviations from expected outputs, although, predictions still often approximated parts of the item's rule set. Error patterns indicated that the model works as intended. On the official ARC paradigm, the model achieved a score of 2% (cf. current world record is 21%) and on ConceptARC it scored 8.8%. Although the methodology proposed involves basic dimensionality reduction techniques and standard vector arithmetic, this approach demonstrates promising outcomes on ARC and can easily be generalized to other abstract visual reasoning tasks.