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This paper proposes CPES, a curvature-informed potential energy surface graph neural network for protein-ligand binding affinity prediction. It integrates physics-informed curvature representations to model conformational flexibility and achieves improved predictive performance on benchmark datasets.
This paper investigates why the Muon optimizer outperforms Adam in large language model training, showing from a curvature perspective that Muon incurs a smaller curvature penalty due to lower normalized directional sharpness, with advantages amplified by data imbalance.
The article explains that attention entropy collapse in deep transformer layers is a geometric consequence of training, not a bug, and proposes a three-line temperature schedule to prevent it.
After 8 years, the author rewrote the open-source pytorch-hessian-eigenthings library, providing efficient eigendecomposition of Hessian and other curvature matrices for PyTorch models using iterative methods like Lanczos.