A Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving
Ian D'Ambrosio (Nth Research Collective)
Aug 2026
Machine Learning
Abstract
Huang, Lou, and Xiao introduced Dynamic Mixture-of-Experts Serving and gave an O(sqrt(log k))-competitive randomized algorithm for its integral primal problem, where k is the number of replica GPUs beyond the mandatory copy of each expert. Their matching lower barrier applies to an auxiliary dual and leaves the primal order open. We prove that the randomized primal competitive ratio is in fact Theta(1) for arbitrary numbers of experts. The upper bound reduces reciprocal-max service costs to chasing positive bodies with covering row sparsity two. A finite tangent envelope approximates each reciprocal epigraph within a constant factor, summable positive resets convert accumulated service into movement, and a nonexpansive balanced projection removes the positive-body algorithm's resource augmentation. Combining the resulting fractional path with Lazy Threshold Rounding gives
E[ALG] <= 10 C_PB OPT + (5 C_PB + 2) k + 16,
where C_PB is the absolute constant from Chasing Positive Bodies at resource augmentation one and covering sparsity two. The full reduction, rounding composition, and quantified main theorem are machine-checked in Lean 4 relative to exact formal interfaces for the two cited source theorems. Deterministic rational controls and a fresh independent replay accompany the formal proof.
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EquiPocket is proposed, an E(3)-equivariant Graph Neural Network for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms.
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It is shown that the maximum hypergraph density of any multiclass hypothesis class is upper-bounded by its DS dimension, which proves a longstanding conjecture of Daniely and Shalev-Shwartz (2014) and determines the optimal dependence of the sample complexity on the DS dimension for multiclass as well as list learning.
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct conclusion. Mathematically, a measurement operator is Hermitian with eigenvalues in [0,1]. By noticing that this constraint on each eigenvalue is the same as that imposed on fermions by the Pauli exclusion principle, we interpret every eigenmode of a measurement operator as an independent effective fermionic mode. Under this perspective, various objective functions in quantum hypothesis testing can be viewed as the total expected energy associated with these fermionic occupation numbers. By instead fixing a temperature and minimizing the total expected fermionic free energy, we find that optimal measurements for these modified objective functions are Fermi-Dirac thermal measurements, wherein their eigenvalues are specified by Fermi-Dirac distributions. In the low-temperature limit, their performance closely approximates that of optimal measurements for quantum hypothesis testing, and we show that their parameters can be learned by classical or hybrid quantum-classical optimization algorithms. This leads to a new quantum machine-learning model, termed Fermi-Dirac machines, consisting of parameterized Fermi-Dirac thermal measurements-an alternative to quantum Boltzmann machines based on thermal states. Beyond hypothesis testing, we show how general semidefinite optimization problems can be solved using this approach, leading to a novel paradigm for semidefinite optimization on quantum computers, in which the goal is to implement thermal measurements rather than prepare thermal states. Finally, we propose quantum algorithms for implementing Fermi-Dirac thermal measurements, and we also propose second-order hybrid quantum-classical optimization algorithms.
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Rafael Muñoz-Terol, Jesús Peral, Sandra Amador et al.· Heliyon· 4 citations· ⚡1
SimulRAG, a simulator-based RAG framework with a generalized retrieval interface that translates between text and simulator parameters/outputs, is proposed, which improves informativeness and factuality over the strongest adapted RAG baselines, while UE+SBA enhances claim-level efficiency and quality.
Haozhou Xu, D. Wu, M. Chinazzi et al.· arXiv.org· 3 citations
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