Tending Towards Stability: Convergence Challenges in Small Language Models (2410.11451v1)

Abstract: Increasing the number of parameters in LLMs is a common strategy to enhance their performance. However, smaller LLMs 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.

• The paper reveals that small language models experience prolonged, unstable convergence compared to larger models, highlighting critical differences in training dynamics.
• It employs the Pythia model suite and introduces proportional effective rank (PER) to analyze activation and gradient behaviors across model sizes.
• The findings suggest that optimizing effective rank could enhance training efficiency, offering actionable strategies for improving small model performance.

Convergence Challenges in Small LLMs

The paper, "Tending Towards Stability: Convergence Challenges in Small LLMs," addresses the persistent issue of performance degradation in smaller LMs. While larger models have demonstrated notable success in various tasks by scaling parameters, smaller models remain integral due to reduced operational costs and environmental impacts. However, smaller models face convergence issues that this paper seeks to elucidate.

Key Findings

The authors leverage the Pythia model suite to examine training dynamics across models of differing sizes. Their analysis indicates distinct disparities between the convergence behaviours of smaller and larger models:

1. Faster Convergence in Larger Models: Larger models achieve convergence in both Attention and MLP activations significantly earlier than their smaller counterparts. Within the initial 20% of training, nearly all layers of the larger models approximate their final state, whereas smaller models exhibit protracted and unstable convergence.
2. Influence of Effective Rank: The paper introduces the concept of proportional effective rank (PER) to assess convergence in relation to parameter dimensionality. Larger models often display a higher effective rank, suggesting that higher-dimensional parameter spaces facilitate quicker and more stable convergence of activations.
3. Gradients and Parameters: The rank and stability of parameters and gradients further sway convergence dynamics. Larger models benefit from gradients that span a higher proportion of dimensions, indicating a more effective learning signal distribution across layers.

Implications

The research puts forth a correlation between effective rank and convergence patterns, proposing significant theoretical and practical implications. For small model efficiency, understanding and improving learning dynamics through effective rank adjustments could alleviate training inefficiencies. Additionally, PER-driven insights offer avenues for optimizing training techniques, particularly in resource-constrained environments.

Speculation and Future Work

Future research could explore causal interventions aimed at increasing effective rank to enhance small model convergence. This may involve architectural adjustments or novel training regimes. Expanding analysis to diverse datasets and languages would further validate the applicability of these findings.

While this paper is rooted in examination rather than intervention, its contributions lay a foundational understanding of convergence discrepancies and emphasize the critical need for targeted improvements in small LMs. The exploration of effective rank concepts and dynamics is a promising step toward more efficient and accessible language modeling technologies.