Physics of Language Models: Part 4.1, Architecture Design and the Magic of Canon Layers

Understanding architectural differences in language models is challenging, especially at academic-scale pretraining (e.g., 1.3B parameters, 100B tokens), where results are often dominated by noise and randomness. To overcome this, we introduce controlled synthetic pretraining tasks that isolate and evaluate core model capabilities. Within this framework, we discover Canon layers: lightweight architectural components--named after the musical term "canon"--that promote horizontal information flow across neighboring tokens. Canon layers compute weighted sums of nearby token representations and integrate seamlessly into Transformers, linear attention, state-space models, or any sequence architecture.