Different Language Models Learn Similar Number Representations (arxiv.org)

Recent research has revealed that various language models, including Transformers and LSTMs, exhibit a fascinating phenomenon known as convergent evolution in how they learn to represent numbers. The study finds that these models utilize periodic features, particularly with dominant periods at $T=2, 5, 10$, to classify numbers in a way that intertwines linguistic and numerical understanding. Notably, while many models develop features characterized by spikes in the Fourier domain, only a subset achieves geometrically separable features necessary for accurate classification of numbers modulo $T$. This discovery is significant for the AI/ML community as it uncovers the complexities behind feature learning across different architectures and training methods. The researchers emphasize that factors like data type, model architecture, and training approaches are crucial for helping language models learn these essential number representations. By elucidating the dual pathways through which models can acquire geometrically separable features—via co-occurrence signals or multi-token addition tasks—the study enhances our understanding of how language models can be improved for better reasoning and numerical capabilities in applications such as natural language processing and cognitive computing.