Newest papers

Mitigating Model Collapse through Dreaming Learning

Matteo Benati, Alessandro Londei, Denise Lanzieri, Raffaello Mastromarino, Vittorio Loreto · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30009 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

训练生成模型对合成数据造成多样性损失和性能下降,这种现象被称为模型崩溃。我们在控制的马尔科夫环境中以光谱方式研究这种退化。学习过渡操作员的eigenvalue频谱提供了一个直接的过程视图,因为下主导的eigenvalues设置了链混合的速度,因此它继续探索的状态空间的数量。我们发现,在温度$T_s < 1$时的样本作用于操作员,就像重复的加密一样,推动它走向一个决定性的系统:下主导的eigenvalues接近单位圈,光谱差缩小了。当$T_s < 1$时,即使数据积累也不会阻止这种流动。然后我们分析Dreaming Learning,一个调节器,并在定期训练的同时,在

Machine translation (Meta M2M100); the English original follows.

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 $T_s < 1$ 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.

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Topics: Eigenvalues and eigenvectors, Operator (biology), Bounded function, Set (abstract data type), Markov chain, Spectrum (functional analysis)

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