arXiv 2026Preprint
PRISM: A Category-Theoretic Framework for Measuring and Refining Multimodal Analogies
Measuring relational structure to guide the refinement of visual metaphors.
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.
@article{zeisler2026prism,
author = {Zeisler, Mirella and Shirekar, Ojas and Licǎ, Mircea and
Raman, Chirag},
title = {PRISM: {A} {Category-Theoretic} {Framework} for {Measuring}
and {Refining} {Multimodal} {Analogies}},
journal = {arXiv preprint arXiv:2610.01383},
date = {2026},
url = {https://arxiv.org/abs/2610.01383},
abstract = {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.}
}













