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ButterflyMoE: Compression-Scalable Ternary Experts via Structured Butterfly Orbits

In current Mixture of Experts (MoE) architectures, linear memory scaling is present, the memory grows as the number of experts increases. $N$ independent expert weight matrices require $\mathcal{O}(N \cdot d^2)$ memory which exceeds the memory budget of edge devices. Current compression methods like quantization, pruning, and low-rank factorization reduce constant factors, but the scaling bottleneck is still unresolved. We introduce ButterflyMoE, a method which treats experts not as independent matrices but as geometric reorientations of a shared quantized substrate. Diversity amongst the experts arises from viewing different angles of the shared capacity and not from redundant storage. Learned rotations are applied to a shared ternary prototype. With this, each expert yields $\mathcal{O}(d^2 + N \cdot d \log d)$ memory-reducing per-expert cost from $\mathcal{O}(d^2)$ to $\mathcal{O}(d \log d)$. The key insight is that training these rotations with quantization reduces activation outliers and stabilizes extreme low-bit training where other static methods collapse. Across language modeling benchmarks, ButterflyMoE achieves 80$\times$ memory reduction at 8 experts with a highly favorable memory-accuracy tradeoff.At this 80x compression ButterflyMoE outperforms an equal memory dense baseline, showing that orbital parameterization extracts fundamentally more utility per byte. When scaled up to 256 experts, ButterflyMoE asymptotically compresses the memory by 150 $\times$. ButterflyMoE reduces the constant factor of linear scaling with compression ratio growing with the expert count.

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