# Solving Inverse Problems in Stochastic Self-Organizing Systems through Invariant Representations

arXiv: https://arxiv.org/abs/2506.11796 · HTML: https://mlsanity.com/paper/2506.11796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Zero-Shot Learning by Convex Combination of Semantic Embeddings](https://mlsanity.com/paper/1312.5650/) (2013)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [Modern Evolution Strategies for Creativity: Fitting Concrete Images and Abstract Concepts](https://mlsanity.com/paper/2109.08857/) (2021)
- [Automating the Search for Artificial Life with Foundation Models](https://mlsanity.com/paper/2412.17799/) (2024)
- [Nomic Embed Vision: Expanding the Latent Space](https://mlsanity.com/paper/2406.18587/) (2024)
- [Fr'echet Wavelet Distance: A Domain-Agnostic Metric for Image Generation](https://mlsanity.com/paper/2312.15289/) (2023)
- [Deep Learning Representation using Autoencoder for 3D Shape Retrieval](https://mlsanity.com/paper/1409.7164/) (2014)
- [Optimization Methods for Inverse Problems](https://mlsanity.com/paper/1712.00154/) (2017)

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

- [Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components](https://mlsanity.com/paper/2606.11258/) (2026)

## Abstract (arXiv)

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge in modeling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations. This task becomes particularly difficult when observations have a strong stochastic component, yielding diverse yet equivalent patterns. Traditional inverse methods fail in this setting, as pixel-wise metrics cannot capture feature similarities between variable outcomes. In this work, we introduce a novel inverse modeling method specifically designed to handle stochasticity in the observable space, leveraging the capacity of visual embeddings to produce robust representations that capture perceptual invariances. By mapping the pattern representations onto an invariant embedding space, we can effectively recover unknown causal parameters without the need for handcrafted objective functions or heuristics. We evaluate the method on three self-organizing systems: a physical, a biological, and a social one; namely, a reaction-diffusion system, a model of embryonic development, and an agent-based model of social segregation. We show that the method reliably recovers parameters despite stochasticity in the pattern outcomes. We further apply the method to real biological patterns, highlighting its potential as a tool for both theorists and experimentalists to investigate the dynamics underlying complex stochastic pattern formation.