Q-Jamba: Quaternion-Native Hybrid State-Space Language Models with 3.4× Parameter Compression

We introduce Q-Jamba, a family of quaternion-native language model architectures that achieve 3.4× parameter compression through Hamilton weight sharing while matching or exceeding standard transformer quality. All linear projections are replaced with QuaternionLinear layers that construct full m×n weight matrices from mn/4 learned parameters via the Hamilton block structure. We extend this principle to selective state spaces, proposing Q-Mamba — to our knowledge, the first SSM with Hamilton recurrence — and Q-Jamba, a hybrid that interleaves Q-Mamba blocks with quaternion attention. On a 9-task reasoning benchmark (n=5 seeds each), Q-Linear (547K params) significantly outperforms a parameter-matched standard transformer (559K params) with Cohen's d≈5.0. Q-Jamba 4:2 (813K params) achieves the lowest validation loss of all arms (0.421±0.004 vs. 0.506±0.016, p