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Existing convergence analyses of Muon either assume exact orthogonalization or analyze classical Newton--Schulz polynomials, and guarantee only stationarity, so it is unresolved what Muon's five tuned Newton--Schulz steps preserve and whether that suffices to reach a prescribed neural-network training loss. We establis...
The Hypergraph Adaptive waveLet Operator (HALO), which lifts the domain to a hypergraph and learns in its spectral wavelet domain, achieves best or near-best accuracy among frequency-, transformer-, DeepONet-, state-space-, and graph-based baselines and sustains stable multi-step rollouts.
MAGE is introduced, an agentic framework that organizes PDE discovery as a confidence governed hypothesis validation loop inspired by the scientific cycle of observation, hypothesis, and falsification, and supports further study of structured agentic reasoning for library-free governing-law discovery.
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