# Compositionality Emerges in a Narrow Depth-Connectivity Regime: Architecture Constraints and Solution Manifolds

arXiv: https://arxiv.org/abs/2606.19941 · HTML: https://mlsanity.com/paper/2606.19941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 57 of its 70 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 30 of 57)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [When and why vision-language models behave like bags-of-words, and what to do about it?](https://mlsanity.com/paper/2210.01936/) (2022)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [Ablating Concepts in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.13516/) (2023)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [T2I-CompBench++: An Enhanced and Comprehensive Benchmark for Compositional Text-to-image Generation](https://mlsanity.com/paper/2307.06350/) (2023)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [DepGraph: Towards Any Structural Pruning](https://mlsanity.com/paper/2301.12900/) (2023)
- [Structured Pruning Learns Compact and Accurate Models](https://mlsanity.com/paper/2204.00408/) (2022)
- [Soft Threshold Weight Reparameterization for Learnable Sparsity](https://mlsanity.com/paper/2002.03231/) (2020)
- [Does CLIP Bind Concepts? Probing Compositionality in Large Image Models](https://mlsanity.com/paper/2212.10537/) (2022)

## Abstract (arXiv)

Compositionality is believed to be the foundation for generalization, enabling models to reuse meaningful primitives in novel combinations. Yet, models trained with standard gradient-based optimization rarely, and often only weakly, exhibit compositional internal structure, and it remains unclear how or why such compositionality forms. In this work, we show that compositionality emerges in a narrow connectivity-depth sweet spot. Along the connectivity axis, compositionality only appears in some specifically sparse networks, heavily depends on which connections remain rather than on weights' sparsity alone. Along the depth axis, compositionality emerges within a narrow, target-dependent regime, peaking at specific depths, while both shallower and deeper networks fail. When either the depth or connectivity condition is violated, gradient descent silently converges to fractured solutions rather than compositional ones. To discover and exploit this emergence, we introduce (i) similarity-based pruning (SP) to recover compositional connectivity and (ii) a heuristic depth predictor to estimate where compositionality is most likely to appear. Finally, we support these empirical findings with a theoretical framework based on compositional sparsity, volume-ratio arguments, and feature-interference bounds, explaining why compositional solutions are reachable only in a narrow depth-connectivity regime.