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Transformers can execute algorithms on data given in their input. We ask whether they can do the same for causal discovery. We study a standard continuous method that repeatedly updates a candidate causal graph while enforcing acyclicity. We explicitly construct a fixed-weight transformer whose forward pass exactly rep...
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...
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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