# Tending Towards Stability: Convergence Challenges in Small Language Models

arXiv: https://arxiv.org/abs/2410.11451 · HTML: https://mlsanity.com/paper/2410.11451/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Are Large Pre-Trained Language Models Leaking Your Personal Information?](https://mlsanity.com/paper/2205.12628/) (2022)
- [Breaking the Softmax Bottleneck: A High-Rank RNN Language Model](https://mlsanity.com/paper/1711.03953/) (2017)
- [Similarity Analysis of Contextual Word Representation Models](https://mlsanity.com/paper/2005.01172/) (2020)
- [Neural Networks Learn Statistics of Increasing Complexity](https://mlsanity.com/paper/2402.04362/) (2024)
- [Fine-Tuned Transformers Show Clusters of Similar Representations Across Layers](https://mlsanity.com/paper/2109.08406/) (2021)
- [Why do small language models underperform? Studying Language Model Saturation via the Softmax Bottleneck](https://mlsanity.com/paper/2404.07647/) (2024)
- [Understanding the Inner Workings of Language Models Through Representation Dissimilarity](https://mlsanity.com/paper/2310.14993/) (2023)
- [On Training Data Influence of GPT Models](https://mlsanity.com/paper/2404.07840/) (2024)

## Built on by (most cited first, 7 of 7)

- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [FLAME-MoE: A Transparent End-to-End Research Platform for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2505.20225/) (2025)
- [Spectral Insights into Data-Oblivious Critical Layers in Large Language Models](https://mlsanity.com/paper/2506.00382/) (2025)
- [Inference-Time Decomposition of Activations (ITDA): A Scalable Approach to Interpreting Large Language Models](https://mlsanity.com/paper/2505.17769/) (2025)
- [Disentangling Geometry, Performance, and Training in Language Models](https://mlsanity.com/paper/2602.20433/) (2026)
- [Revisiting Anisotropy in Language Transformers: The Geometry of Learning Dynamics](https://mlsanity.com/paper/2604.08764/) (2026)
- [Bounds of Chain-of-Thought Robustness: Reasoning Steps, Embed Norms, and Beyond](https://mlsanity.com/paper/2509.21284/) (2025)

## Abstract (arXiv)

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.