# PRISM: A Category-Theoretic Framework for Measuring and Refining Multimodal Analogies

arXiv: https://arxiv.org/abs/2610.01383 · HTML: https://mlsanity.com/paper/2610.01383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 58 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Visual Programming: Compositional visual reasoning without training](https://mlsanity.com/paper/2211.11559/) (2022)
- [HealthBench: Evaluating Large Language Models Towards Improved Human Health](https://mlsanity.com/paper/2505.08775/) (2025)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [DALL-Eval: Probing the Reasoning Skills and Social Biases of Text-to-Image Generation Models](https://mlsanity.com/paper/2202.04053/) (2022)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [Automatic Understanding of Image and Video Advertisements](https://mlsanity.com/paper/1707.03067/) (2017)
- [MemeCap: A Dataset for Captioning and Interpreting Memes](https://mlsanity.com/paper/2305.13703/) (2023)
- [I Spy a Metaphor: Large Language Models and Diffusion Models Co-Create Visual Metaphors](https://mlsanity.com/paper/2305.14724/) (2023)
- [Evaluating the Robustness of Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2411.14215/) (2024)
- [MetaCLUE: Towards Comprehensive Visual Metaphors Research](https://mlsanity.com/paper/2212.09898/) (2022)
- [KiVA: Kid-inspired Visual Analogies for Testing Large Multimodal Models](https://mlsanity.com/paper/2407.17773/) (2024)
- [Multimodal Analogical Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2210.00312/) (2022)
- [VISALOGY: Answering Visual Analogy Questions](https://mlsanity.com/paper/1510.08973/) (2015)
- [LLMs as Models for Analogical Reasoning](https://mlsanity.com/paper/2406.13803/) (2024)
- [AnaloBench: Benchmarking the Identification of Abstract and Long-context Analogies](https://mlsanity.com/paper/2402.12370/) (2024)
- [Generating Correct Answers for Progressive Matrices Intelligence Tests](https://mlsanity.com/paper/2011.00496/) (2020)
- [Analogical Reasoning Inside Large Language Models: Concept Vectors and the Limits of Abstraction](https://mlsanity.com/paper/2503.03666/) (2025)
- [Beneath Surface Similarity: Large Language Models Make Reasonable Scientific Analogies after Structure Abduction](https://mlsanity.com/paper/2305.12660/) (2023)
- [Relevant or Random: Can LLMs Truly Perform Analogical Reasoning?](https://mlsanity.com/paper/2404.12728/) (2024)
- [DeepGAR: Deep Graph Learning for Analogical Reasoning](https://mlsanity.com/paper/2211.10821/) (2022)
- [VOILA: Evaluation of MLLMs For Perceptual Understanding and Analogical Reasoning](https://mlsanity.com/paper/2503.00043/) (2025)

## Abstract (arXiv)

Analogical reasoning involves identifying and preserving relational structures across domains. However, existing approaches to AI-driven multimodal analogy generation lack an interpretable measure of whether this structure is understood and maintained in the generated output. We address this gap with Pullback Refinement via Interpretable Structural Mapping (PRISM), a modality-agnostic framework for measuring and improving relational alignment in multimodal analogies, evaluated on visual metaphor generation. PRISM represents analogies as explicit relational mappings grounded in category theory and uses VLMs to instantiate these structures across modalities. Its first component, the pullback score, quantifies relational alignment from the resulting graph representation. On the AnaloBench benchmark, selecting the correct analogy purely by pullback score achieves 82.5% accuracy, demonstrating that the score captures meaningful relational information. PRISM's second component is an iterative refinement loop that uses the pullback score as an in-context feedback signal to iteratively revise the generated image towards greater relational depth. VLM-as-a-judge and human evaluations show that PRISM consistently improves metaphor consistency and analogy appropriateness over zero- shot generation, with human participants preferring the refined output in 57.65% of pairwise comparisons. However, a qualitative analysis reveals that refinement can favour visually crowded compositions rather than genuinely deeper relational correspondences.