A Markovian View of Iterative-Feedback Loops in Image Generative Models: Neural Resonance and Model Collapse

TL;DR

This paper models iterative feedback in image generative models as a Markov process, revealing neural resonance as a key factor in model collapse, and offers diagnostics and insights to understand and mitigate this degeneration.

Contribution

It introduces a Markovian framework to analyze feedback-induced collapse in generative models and identifies neural resonance as a core phenomenon causing degeneration.

Findings

Neural resonance leads to low-dimensional invariant structures in latent space.

Feedback process ergodicity and contraction are necessary for resonance.

Eight-pattern taxonomy characterizes collapse behaviors.

Abstract

AI training datasets will inevitably contain AI-generated examples, leading to ``feedback'' in which the output of one model impacts the training of another. It is known that such iterative feedback can lead to model collapse, yet the mechanisms underlying this degeneration remain poorly understood. Here we show that a broad class of feedback processes converges to a low-dimensional invariant structure in latent space, a phenomenon we call neural resonance. By modeling iterative feedback as a Markov Chain, we show that two conditions are needed for this resonance to occur: ergodicity of the feedback process and directional contraction of the latent representation. By studying diffusion models on MNIST and ImageNet, as well as CycleGAN and an audio feedback experiment, we map how local and global manifold geometry evolve, and we introduce an eight-pattern taxonomy of collapse behaviors. Neural resonance provides a unified explanation for long-term degenerate behavior in generative models and provides practical diagnostics for identifying, characterizing, and eventually mitigating collapse.