Hessian
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Related Articles from SNS
Revisiting Zeroth-Order Hessian Approximation: A Single-Step Policy Optimization Lens
Announce Type: new Abstract: Accurate Zeroth-Order (ZO) Hessian estimation is a cornerstone of derivative-free methods, essential for tasks such as bilevel optimization, Bayesian inference, and uncertainty quantification. However, obtaining a complete suite of low-variance estimators for the Hessian and its inverse in high-dimensional settings remains a significant challenge. To address this, we propose a unified framework that reinterprets ZO Hessian approximation through the lens of...
Hessian-recovery-based C0 finite element methods for non-divergence form elliptic equations
arXiv:2606.03276v1 Announce Type: new Abstract: A Hessian-recovery-based C0 finite element framework is proposed for second-order elliptic equations in non-divergence form. The construction is based on a direct approximation of the strong non-divergence operator: the Hessian D2u is replaced by a recovered Hessian Hhuh, so that A : D2u is approximated by A : Hhuh. The resulting discretizations include a nodal formulation and a Galerkin-type formulation for general Lagrange finite element...
High-fidelity neutral atom gates leveraging low-rank Hessian optimization
arXiv:2606.05060v1 Announce Type: cross Abstract: Quantum optimal control can produce fast and robust multi-qubit gates, but experimentally calibrating the resulting high-dimensional waveforms remains challenging because direct searches over large parameter spaces converge slowly. Building on the low-rank structure of quantum-control landscapes, we develop and benchmark a Hessian-based calibration method for optimal-control gates. The method identifies the few waveform directions that affect...
Augmented Roothaan-Hall Hessian Applied to Spin-Restricted Open-Shell Density-Functional Theory
arXiv:2606.03709v1 Announce Type: new Abstract: We generalize the augmented Roothaan-Hall (ARH) Hessian formalism to the self-consistent field (SCF) optimization of spin-restricted open-shell (RO) wavefunctions, encompassing high-spin, low-spin, and two-determinant electronic states. A detailed ARH formulation is presented. We demonstrate that ARH is a highly efficient optimization algorithm for rapidly identifying accurate SCF minima, primarily owing to its systematic construction of an...
RPA as a Hessian Closure: Effective Functionals and Source-Variable Duality Across DFT, LR-TDDFT, 1RDMFT, and MBPT
Announce Type: new Abstract: We present a variational formulation of the random phase approximation (RPA) that places density functional theory (DFT), linear-response time-dependent density functional theory (LR-TDDFT), one-body reduced density matrix functional theory (1RDMFT), and Green's function many-body perturbation theory (MBPT) into a common source-variable hierarchy. The central claim is that RPA is not best defined by any one problem-specific formula, diagrammatic resummation, or...
Neural Legendre-Fenchel transform with Hessian Preconditioning
Announce Type: new Abstract: The Legendre-Fenchel (LF) transform is a fundamental tool in convex analysis and machine learning that maps lower semi-continuous functions to their convex conjugates. In practice, when closed-form formula are not available for expressing convex conjugates of given functions, one must approximate them using various techniques. One recent such versatile numerical method is the deep Legendre transform method which relies on neural networks although it remains...
On the Superlinear Relationship between SGD Noise Covariance and Loss Landscape Curvature
Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) introduces anisotropic noise that is correlated with the local curvature of the loss landscape, thereby biasing optimization toward flat minima. Prior work often assumes an equivalence between the Fisher Information Matrix and the Hessian for negative log-likelihood losses, leading to the claim that the SGD noise covariance $\mathbf{C}$ is proportional to the Hessian $\mathbf{H}$. We show that this assumption holds only under...
Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations
arXiv:2509.00406v3 Announce Type: replace Abstract: We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs,...
Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning
Announce Type: replace Abstract: We investigate why deep neural networks suffer from loss of plasticity in continual learning, and thus fail to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. Analyzing a linearized ReLU network, we derive explicit $\epsilon$-rank conditions for successful training and prove...
PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials
Announce Type: replace-cross Abstract: Many materials properties depend on higher-order derivatives of the potential energy surface, yet machine learned interatomic potentials (MLIPs) trained with a standard loss on energy, force, and stress errors can exhibit error in curvature, degrading the prediction of vibrational properties. We introduce phonon fine-tuning (PFT), which directly supervises second-order force constants of materials by matching MLIP energy Hessians to DFT-computed force...