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Related Articles from SNS
Finite-Temperature de Bruijn Identities: Fisher Information as the Spectral Gap of Blahut--Arimoto Dynamics
arXiv:2606.03813v1 Announce Type: new Abstract: We uncover a finite-temperature extension of de Bruijn's identity -- the classical relation $\frac{d}{dt}h(X+\sqrt{t}Z)=\frac{1}{2}J(X)$ connecting differential entropy and Fisher information. Our framework is the spectral theory of Blahut--Arimoto (BA) dynamics, recently developed by Wang~\cite{Wang2026} for the analysis of rate-distortion optimization. The central observation is elementary yet profound: for Gaussian sources, the spectral gap...
Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms
arXiv:2606.04767v1 Announce Type: new Abstract: The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability. We propose a principled, attack-agnostic robustness metric based on the spectral norm of the Fisher Information Matrix (FIM), which quantifies the worst-case sensitivity of the model's output distribution to input perturbations. Theoretically, we establish that the FIM equals...
Fundamental Limits of Non-Hermitian Sensing from Quantum Fisher Information
arXiv:2603.10614v2 Announce Type: replace-cross Abstract: Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate.
Multiparameter Maximum Information States for Coherent Diffraction Measurements
arXiv:2606.01445v2 Announce Type: replace Abstract: In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the...
Multiparameter Maximum Information States for Coherent Diffraction Measurements
arXiv:2606.01445v1 Announce Type: new Abstract: In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the...
Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions. We analyze this structural conflict using the Fisher Information Matrix to quantify the effective degrees of freedom ($d_{eff}$) in a physics-constrained model. Unlike the classical $d_{eff}$ which measures how many parameter directions are informed by data against a...
Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions. We analyze this structural conflict using the Fisher Information Matrix to quantify the effective degrees of freedom ($d_{eff}$) in a physics-constrained model. Unlike the classical $d_{eff}$ which measures how many parameter directions are informed by data against a...
Non-existence of Information-Geometric Fermat Structures: Violation of Dual Lattice Consistency in Statistical Manifolds with $L^n$ Structure
Announce Type: replace Abstract: This paper reformulates Fermat's Last Theorem as an embedding problem of information-geometric structures. We reinterpret the Fermat equation as an $n$-th moment constraint, constructing a statistical manifold $\mathcal{M}_n$ of generalized normal distributions via the Maximum Entropy Principle. By Chentsov's Theorem, the natural metric is the Fisher information metric ($L^2$); however, the global structure is governed by the $L^n$ moment constraint.
Inversion-Free Natural Gradient Descent on Riemannian Manifolds
arXiv:2604.02969v2 Announce Type: replace-cross Abstract: The natural gradient method is a central tool for statistical optimisation, but its broader application is hindered by the assumption of a Euclidean parameter space, the repeated estimation of the Fisher information matrix (FIM), and the computational cost of its subsequent inversion. This paper proposes an intrinsic, inversion-free natural gradient method for statistical models whose parameters lie on general Riemannian manifolds....
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...