# Learning by Analogy: A Causal Framework for Composition Generalization

arXiv: https://arxiv.org/abs/2512.10669 · HTML: https://mlsanity.com/paper/2512.10669/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 73 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 30 of 52)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [ELLA: Equip Diffusion Models with LLM for Enhanced Semantic Alignment](https://mlsanity.com/paper/2403.05135/) (2024)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Training-Free Structured Diffusion Guidance for Compositional Text-to-Image Synthesis](https://mlsanity.com/paper/2212.05032/) (2022)
- [LayoutGPT: Compositional Visual Planning and Generation with Large Language Models](https://mlsanity.com/paper/2305.15393/) (2023)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [Training-Free Layout Control with Cross-Attention Guidance](https://mlsanity.com/paper/2304.03373/) (2023)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [BoxDiff: Text-to-Image Synthesis with Training-Free Box-Constrained Diffusion](https://mlsanity.com/paper/2307.10816/) (2023)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [LLM-grounded Diffusion: Enhancing Prompt Understanding of Text-to-Image Diffusion Models with Large Language Models](https://mlsanity.com/paper/2305.13655/) (2023)
- [Mastering Text-to-Image Diffusion: Recaptioning, Planning, and Generating with Multimodal LLMs](https://mlsanity.com/paper/2401.11708/) (2024)
- [Linguistic Binding in Diffusion Models: Enhancing Attribute Correspondence through Attention Map Alignment](https://mlsanity.com/paper/2306.08877/) (2023)
- [SANA 1.5: Efficient Scaling of Training-Time and Inference-Time Compute in Linear Diffusion Transformer](https://mlsanity.com/paper/2501.18427/) (2025)
- [Dense Text-to-Image Generation with Attention Modulation](https://mlsanity.com/paper/2308.12964/) (2023)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)

## Built on by (most cited first, 1 of 1)

- [Do Transformers Have the Ability for Periodicity Generalization?](https://mlsanity.com/paper/2601.22690/) (2026)

## Abstract (arXiv)

Compositional generalization -- the ability to understand and generate novel combinations of learned concepts -- enables models to extend their capabilities beyond limited experiences. While effective, the data structures and principles that enable this crucial capability remain poorly understood. We propose that compositional generalization fundamentally requires decomposing high-level concepts into basic, low-level concepts that can be recombined across similar contexts, similar to how humans draw analogies between concepts. For example, someone who has never seen a peacock eating rice can envision this scene by relating it to their previous observations of a chicken eating rice. In this work, we formalize these intuitive processes using principles of causal modularity and minimal changes. We introduce a hierarchical data-generating process that naturally encodes different levels of concepts and their interaction mechanisms. Theoretically, we demonstrate that this approach enables compositional generalization supporting complex relations between composed concepts, advancing beyond prior work that assumes simpler interactions like additive effects. Critically, we also prove that this latent hierarchical structure is provably recoverable (identifiable) from observable data like text-image pairs, a necessary step for learning such a generative process. To validate our theory, we apply insights from our theoretical framework and achieve significant improvements on benchmark datasets.