Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
Higham.Functions of Matrices: Theory and Computation
15 Pith papers cite this work. Polarity classification is still indexing.
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A forward-only Lanczos gradient approximation for Hermitian matrix function bilinear forms whose error scales with the same residual norm as the forward approximation and appears stable without reorthogonalization.
A square root form of the second-order covariance update is presented for the first time, improving numerical accuracy and efficiency in recursive estimation algorithms.
Develops finite-dimensional approximations to push-forwards on locally analytic functionals with explicit error bounds from Hankel moment matrices and proves convergence for data-driven recovery of analytic vector fields from flow map data.
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
Augmented Krylov subspaces jointly approximate quadratic forms and log-dets for faster MLE-based hyperparameter tuning in kernel-based linear system identification.
Develops mixed-precision iterative refinement for low-rank Lyapunov equations with rounding error analysis enabling reduced precision for moderately conditioned problems.
New dimension and model reduction techniques for linear Bayesian inverse problems with rank-deficient priors, with approximation guarantees and efficiency demonstrations for high-dimensional inference.
Decoupling local and synchronization transitions yields a linearly convergent MTTA algorithm that is accelerated to quadratic convergence and represented in tensor-train format, enabling computation on systems with up to billions of states.
Derives criteria for when state-dependent proto-area two-jets in approximate holographic codes are compatible with metric two-jets, including polyhedral realizations, X-ray transform tangent spaces, and quadratic obstructions to geometry.
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
Lie Group VAE framework diagnoses latent non-commutativity through algebraic and reconstruction diagnostics then calibrates a stability constraint to align decoder behavior, showing improved consistency on dSprites, 3DShapes, 3DCars and CelebA versus beta-VAE, CLG-VAE and CFASL baselines.
Rust sparse kernels match Eigen and PSBLAS performance for CSC formats but trail PETSc's blocked CSR optimizations.
citing papers explorer
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Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry
Quantum algorithm block-encodes Riccati solutions for m-particle m-hole RPA using Riesz projectors and QSVT, claiming linear system-size scaling under sparsity and polynomial cost in excitation rank m.
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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions
A forward-only Lanczos gradient approximation for Hermitian matrix function bilinear forms whose error scales with the same residual norm as the forward approximation and appears stable without reorthogonalization.
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Covariance Square Root Second-Order Mapping
A square root form of the second-order covariance update is presented for the first time, improving numerical accuracy and efficiency in recursive estimation algorithms.
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Finite-dimensional approximations of push-forwards on locally analytic functionals
Develops finite-dimensional approximations to push-forwards on locally analytic functionals with explicit error bounds from Hankel moment matrices and proves convergence for data-driven recovery of analytic vector fields from flow map data.
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Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
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Muon Does Not Converge on Convex Lipschitz Functions
Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
-
Kernel-based linear system identification using augmented Krylov subspaces
Augmented Krylov subspaces jointly approximate quadratic forms and log-dets for faster MLE-based hyperparameter tuning in kernel-based linear system identification.
-
Mixed-precision iterative refinement for low-rank Lyapunov equations
Develops mixed-precision iterative refinement for low-rank Lyapunov equations with rounding error analysis enabling reduced precision for moderately conditioned problems.
-
Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances
New dimension and model reduction techniques for linear Bayesian inverse problems with rank-deficient priors, with approximation guarantees and efficiency demonstrations for high-dimensional inference.
-
Tensor methods for the computation of MTTA in large systems of loosely interconnected components
Decoupling local and synchronization transitions yields a linearly convergent MTTA algorithm that is accelerated to quadratic convergence and represented in tensor-train format, enabling computation on systems with up to billions of states.
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Nonlinear Geometrizability of State-Dependent Proto-Area in Approximate Holographic Codes
Derives criteria for when state-dependent proto-area two-jets in approximate holographic codes are compatible with metric two-jets, including polyhedral realizations, X-ray transform tangent spaces, and quadratic obstructions to geometry.
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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
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Commutator-Induced Uncertainty in VAEs
Lie Group VAE framework diagnoses latent non-commutativity through algebraic and reconstruction diagnostics then calibrates a stability constraint to align decoder behavior, showing improved consistency on dSprites, 3DShapes, 3DCars and CelebA versus beta-VAE, CLG-VAE and CFASL baselines.
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Evaluating Rust for Sparse Matrix Kernels in Scientific Computing
Rust sparse kernels match Eigen and PSBLAS performance for CSC formats but trail PETSc's blocked CSR optimizations.
- Computing k-means in mixed precision