Mitigating Model Collapse through Dreaming Learning
Abstract
Training generative models on synthetic data causes loss of diversity and a decrease in performance, a phenomenon known as model collapse. We study this degeneration spectrally in a controlled Markov setting. The eigenvalue spectrum of the learned transition operator offers a direct view of the process, since the subdominant eigenvalues set how fast the chain mixes and therefore how much of the state space it continues to explore. We find that sampling at temperature Ts < 1 acts on the operator like repeated sharpening, pushing it toward a deterministic system: the subdominant eigenvalues approach the unit circle and the spectral gap narrows. When Ts < 1, even data accumulation does not appear to arrest this drift. We then analyze Dreaming Learning, a regulariser that, in parallel with regular training, adds a loss term on the model's own samples drawn at a raised temperature Td > 1. Because high-temperature samples flatten the predicted distribution, training on them keeps the entries of the learned operator from becoming vanishingly small, which in turn keeps the eigenvalues bounded away from the unit circle. Measurements of the spectra over 5000 generations are consistent with this picture, and the mitigation effect persists in more complex settings such as LSTM language models and a 124M-parameter GPT-2.
Related
- Iterative Calibration and Learning: Mitigating Teacher Bias in LLM Distillation without Target-Domain Reward Feedback
- Mitigating workplace bullying through authentic leadership: Evidence from hospital nurses in Jordan
- MAEM: Mitigating Recency Bias via a Replay-Free, Capacity-Controlled Dynamic Mixture of Experts for Class-Incremental Graph Learning
- Coven-Meyerowitz T2 necessity through coprime stripe collapse
- On AI and Progress in Mathematics: Dreaming a Mathematical Universal Machine
BibTeX
@misc{benati2026mitigating,
title = {{Mitigating Model Collapse through Dreaming Learning}},
author = {Matteo Benati and Alessandro Londei and Denise Lanzieri and Raffaello Mastromarino and Vittorio Loreto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30009},
eprint = {2610.30009},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30009},
}
RIS
TY - UNPB
TI - Mitigating Model Collapse through Dreaming Learning
AU - Matteo Benati
AU - Alessandro Londei
AU - Denise Lanzieri
AU - Raffaello Mastromarino
AU - Vittorio Loreto
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30009
UR - https://arxiv.org/abs/2610.30009
AB - Training generative models on synthetic data causes loss of diversity and a decrease in performance, a phenomenon known as model collapse. We study this degeneration spectrally in a controlled Markov setting. The eigenvalue spectrum of the learned transition operator offers a direct view of the process, since the subdominant eigenvalues set how fast the chain mixes and therefore how much of the state space it continues to explore. We find that sampling at temperature T_s < 1 acts on the operator like repeated sharpening, pushing it toward a deterministic system: the subdominant eigenvalues approach the unit circle and the spectral gap narrows. When T_s < 1, even data accumulation does not appear to arrest this drift. We then analyze Dreaming Learning, a regulariser that, in parallel with regular training, adds a loss term on the model's own samples drawn at a raised temperature T_d > 1. Because high-temperature samples flatten the predicted distribution, training on them keeps the entries of the learned operator from becoming vanishingly small, which in turn keeps the eigenvalues bounded away from the unit circle. Measurements of the spectra over 5000 generations are consistent with this picture, and the mitigation effect persists in more complex settings such as LSTM language models and a 124M-parameter GPT-2.
ER -