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• Existing exact methods for parameterizing doubly stochastic matrices scale factorially with the number of streams (d).limitation 90%
• Kronecker-factorized approaches for parameterizing doubly stochastic matrices are efficient but expressivity-limited.limitation 90%
• The go-mHC method provides an exact parameterization of doubly stochastic matrices that scales as O(d³).method 90%
• go-mHC exposes a single hyperparameter s that continuously interpolates between a computationally efficient boundary and the fully expressive Birkhoff polytope.technical 90%
• On synthetic stream-mixing tasks, go-mHC achieves the minimum theoretical loss while converging up to 10× faster than alternatives.result 85%
• Spectral analysis indicates that go-mHC fills the Birkhoff polytope far more completely than Kronecker-factorized baselines.result 85%
• The method composes naturally with Kronecker-factorized methods, substantially recovering expressivity at similar FLOP costs.technical 85%
• The approach was validated in a 30M parameter GPT-style language model.result 90%

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