Tending Towards Stability: Convergence Challenges in Small Language Models

TL;DR

This paper investigates why small language models underperform during late training stages, analyzing how their convergence dynamics differ from larger models and linking these issues to the effective rank of their parameters.

Contribution

The study provides a detailed analysis of training dynamics in small versus large models, highlighting the impact of parameter effective rank on convergence stability.

Findings

Larger models stabilize early in training, within 20%.

Small models show slower, less stable convergence.

Lower effective rank correlates with convergence issues.

Abstract

Increasing the number of parameters in language models is a common strategy to enhance their performance. However, smaller language models remain valuable due to their lower operational costs. Despite their advantages, smaller models frequently underperform compared to their larger counterparts, even when provided with equivalent data and computational resources. Specifically, their performance tends to degrade in the late pretraining phase. This is anecdotally attributed to their reduced representational capacity. Yet, the exact causes of this performance degradation remain unclear. We use the Pythia model suite to analyse the training dynamics that underlie this phenomenon. Across different model sizes, we investigate the convergence of the Attention and MLP activations to their final state and examine how the effective rank of their parameters influences this process. We find that nearly all layers in larger models stabilise early in training - within the first 20% - whereas layers in smaller models exhibit slower and less stable convergence, especially when their parameters have lower effective rank. By linking the convergence of layers' activations to their parameters' effective rank, our analyses can guide future work to address inefficiencies in the learning dynamics of small models.