Model Collapse as Cultural Evolution

Background

The phenomenon of model collapse in large language models (LLMs) has been recognized but remains inadequately explained linguistically. This study aims to understand the structural degradation process and its order within these models by leveraging iterated learning theory from cultural evolution, which focuses on how information is transmitted across generations.

Key Points

• Non-Monotonic Trajectory of Compositionality: The study demonstrates that compositional structures in LLMs initially improve but then deteriorate under unfiltered self-training. This non-monotonic behavior is a critical finding.

• Predictive Power and Confirmatory Evidence: Five falsifiable predictions were derived from iterated learning theory, with three being uniquely discriminative for the theory. The study tests these theories by self-training LLaMA-2-7B and Mistral-7B across 10 generations in English, German, and Turkish.

• Compression-Communication Tradeoff: Compositionality's non-monotonic behavior supports the hypothesis that there is a trade-off between compression (model size) and communication (performance). This insight provides a deeper understanding of how LLMs self-train.

Significance

The findings have several significant implications:

• Linguistic Insight into Model Collapse: By grounding model collapse in linguistic theory, this study offers a new framework for understanding the degradation process.

• Principles for Self-Training Pipelines: The research identifies task-grounded filtering as essential to maintaining compositional integrity during self-training. This insight can guide the design of more effective LLM training pipelines.

• Empirical Validation and Statistical Confidence: Large effect sizes (Hedges' $g > 1.6$) and Bayesian evidence ($\mathrm{BF}_{10} > 100$) provide strong support for the iterated learning theory, offering robust empirical validation.

• Alignment with Human Behavioral Data: The study shows that LLM regularization gradients closely match human behavioral data (with an $R^2 = 0.94$), reinforcing the theoretical framework's alignment with observed human language behavior.

These results reframe model collapse as a cultural transmission phenomenon, highlighting the importance of structured training processes in maintaining linguistic and compositional integrity within large language models.