A Geometric Attention Transformer with the E8 Root System: Sovereign-Lila-E8 (Lie Lattice Attention Language Model)

We introduce Sovereign-Lila-E8 (Lie Lattice Attention Language Model), a Trans-former architecture that incorporates the root system of the exceptional Lie algebraE8 into the attention mechanism. By softly quantizing hidden states into the 240roots of E8 and adding geometric biases to attention scores, the model achieves densesemantic packing and improved long-context coherence. Trained on the TinyStoriesdataset with only 40 million parameters, our model generates coherent stories up to 512tokens—the full training length—and extrapolates gracefully to 1500 tokens withoutfalling into repetitive loops. In contrast, a comparable baseline (Microsoft’s 33M/60Mmodel) exhibits hard loops after 300–500 tokens. We provide mathematical details,experimental results, and qualitative examples. Our model achieves a validation loss of0.46–0.6, significantly lower than standard Transformer baselines of comparable scale.