A proto-area family defines a bulk geometry only when it sews through a single boundary-length map, with a gauge-invariant two-jet criterion and BKM–Jacobi matching as necessary and sufficient conditions.
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18 Pith papers cite this work, alongside 2,108 external citations. Polarity classification is still indexing.
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Local surrogate models for harmonic vibrational entropy in multilattices achieve linear scaling with sublattice-resolved locality proofs and controlled truncation error on finite-range models.
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.
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.
RDGC is the least affine-invariant length of an admissible metric path to a Hessian-relative condition target, with global Green and bordered Jacobi–KKT response laws on Hadamard path space.
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.
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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.
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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When does a state-dependent proto-area define a bulk geometry?
A proto-area family defines a bulk geometry only when it sews through a single boundary-length map, with a gauge-invariant two-jet criterion and BKM–Jacobi matching as necessary and sufficient conditions.
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Local Surrogates for Harmonic Vibrational Entropy in Multilattices
Local surrogate models for harmonic vibrational entropy in multilattices achieve linear scaling with sublattice-resolved locality proofs and controlled truncation error on finite-range models.
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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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Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response
RDGC is the least affine-invariant length of an admissible metric path to a Hessian-relative condition target, with global Green and bordered Jacobi–KKT response laws on Hadamard path space.
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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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Nystr\"om Approximation on Manifolds
Introduces Riemannian Nyström approximation via subspace projections and Haar-Grassmann sketching for tangent operators, plus a randomized Newton method, tested on SPD and Grassmann manifolds.
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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.
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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.
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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.
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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.
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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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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.
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