“We propose the Error Depth Hypothesis: stronger models make fewer but deeper errors that resist self-correction.”

“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”

“The paper finds a partial extension of Poincaré duality theorem to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking.”

“The strongest results arise when priors are combined with content embeddings (AUC~0.815), while content-only models remain above chance but substantially weaker (AUC~0.626).”

“The number of captured loops exhibits a pronounced peak at $ξ_{\textrm{peak}}≈ 12.5$, arising from the competition between rocket-driven ejection at small $ξ$ and the declining intrinsic loop abundance at large $ξ$.”

“Price counterfactuals are nonparametrically identified by recentered instruments -- which combine exogenous shocks to prices with endogenous product characteristics -- under a weaker index restriction and a new condition we term faithfulness.”

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“The code is a messy but works for my needs.”

“Models trained on different datasets have highly similar representations of small molecules, and machine learning interatomic potentials converge in representation space as they improve in performance, suggesting that foundation models learn a common underlying representation of physical reality.”

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“We present a new research direction for superalignment, together with promising initial results: can we leverage the generalization properties of deep learning to control strong models with weak supervisors?”