A developer has trained a 30M-parameter Tauformer, a topological transformer that replaces standard dot-product attention with a Laplacian-derived scalar called a taumode. The model, inspired by GPT-2, uses 6 layers and 384 embedding dimensions, processing sequences of 1024 tokens. Initial results show the model converged quickly, with validation loss dropping to 1.91 after 4,500 steps.

This approach aims to inject domain structure directly into the attention mechanism by using a Graph Laplacian from an embedding space. By scoring keys with a scalar rather than full vectors, Tauformer can reduce memory usage, as its KV-cache only needs values plus a compact scalar stream. The early training phase demonstrated effective learning at this scale.

The run kept the taumode fixed, but later volatility suggests future experiments will focus on adaptive taumode strategies. The next tests plan to scale to 100M parameters. Researchers are also investigating the correlation between cross-entropy loss and taumode convergence, which may reveal how the model's learned representations become smoother during training.