Self-attention in transformers corresponds exactly to Power Voronoi diagrams under tropical geometry, yielding tight bounds of Theta(N to the power of d_model times L) linear regions.
Tropnnc: Structured neural network compression using tropical geometry.arXiv preprint arXiv:2409.03945
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MoE Top-k routing equals the k-th elementary symmetric tropical polynomial, making sparsity combinatorial depth that scales capacity by binom(N,k) and gives MoE combinatorial resilience on manifolds.
citing papers explorer
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Expressivity of Transformers: A Tropical Geometry Perspective
Self-attention in transformers corresponds exactly to Power Voronoi diagrams under tropical geometry, yielding tight bounds of Theta(N to the power of d_model times L) linear regions.
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Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry
MoE Top-k routing equals the k-th elementary symmetric tropical polynomial, making sparsity combinatorial depth that scales capacity by binom(N,k) and gives MoE combinatorial resilience on manifolds.