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.
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KLR Hopfield networks store up to 16-20 times their neuron count before dynamical instability from crosstalk noise causes collapse, with sharp attractor boundaries observed via morphing and SNR analysis.
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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.
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Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks
KLR Hopfield networks store up to 16-20 times their neuron count before dynamical instability from crosstalk noise causes collapse, with sharp attractor boundaries observed via morphing and SNR analysis.