Expander SAEs apply left-d-regular expander masks to TopK SAEs, learning only dn decoder parameters instead of mn and tracing a storage-fidelity frontier that reaches 293x compression with 84% retained performance on Qwen2.5-3B.
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The normalized orbit of a bounded normal operator can be a frame, providing a counterexample to Conjecture 3.
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SLayerGen generates crystals invariant to any space or layer group via autoregressive lattice and Wyckoff sampling plus equivariant diffusion, achieving gains over bulk models on diperiodic materials after correcting a prior loss inconsistency for hexagonal groups.
Every proper minor-closed graph class admits an optimal (1+o(1)) log n bit adjacency labeling scheme.
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Superconductivity in high-pressure MnB4 is induced by altermagnetic spin fluctuations, yielding extended-s pairing symmetry.
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O(n log n) algorithm and matching Omega(n log n) lower bound for partitioning a simple polygon's boundary into the minimum number of contiguous visible segments.
Introduces a method to design structure-specific relational inductive biases for a base transformer architecture, enabling end-to-end transcription of documents with intrinsic structures, demonstrated on sheet music, shape drawings, and mechanical engineering drawings.
The paper introduces a probabilistic sign rule for quotients of positive series and integral transforms that reduces monotonicity, log-supermodularity, and log-convexity to kernel sign criteria via moment identities, and applies it to derive new inequalities for hypergeometric, Stieltjes, and Prabha
SPoILeR uses multimodal pre-training to enable accurate novel view synthesis of infrared, polarimetric, and multispectral data from RGB-supervised fine-tuning on new scenes.
NEvo performs evolutionary search guided by a dynamic voxel-level encoding model to synthesize videos that maximize predicted activity in target brain ROIs, recovering known selectivities and revealing temporal dynamics differences.
Every n-vertex H-minor-free graph admits a 3-coloring with monochromatic components of size O_H(n^{4/9}).
The Spin-MInt algorithm is proven symplectic for general K electronic states via explicit verification of the condition MJM^T = J on the coadjoint orbit of the su(K) Lie-Poisson algebra.
The authors synthesize a typology of fourteen OSS sub-genres from a review of 3,925 papers and present a research agenda on cross-sub-genre generalization.
Structural identifiability analysis shows point sources restore identifiability for inferring spatial stochastic dynamics parameters from static snapshots, unlike distributed sources, with limits depending on modeling choices.
Maximal quantum leakage upper-bounds quantum inference accuracy; optimal encodings are pure states, with tight frames and equiangular tight frames optimal when system dimension is small.
In multistage SI(k)R models, the relationship between prevalence peak and weighted stage functional maxima varies with scaling of progression rates, converging under Erlang scaling to a delay model that justifies the factor-two approximation with error bounds and corrections.
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Parameterization-driven arbitrary Lagrangian-Eulerian method for large-deformation isogeometric fluid-structure interaction
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Projection-Based Reconstruction for Achieving High-Order Accuracy from Low-Order DGSEM Simulations
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Entropy correction artificial viscosity for high order DG methods using multiple artificial viscosities
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A spectral-subspace-augmented POD-Galerkin method for parametrized PDEs with limited snapshot data
SS-POD augments standard POD-Galerkin with a spectral-subspace partition and local POD to achieve lower out-of-sample error than either plain POD or pure spectral-Galerkin when only a handful of snapshots are available.
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Complementary families of approximating polynomials with applications to finite element methods applied to differential equations of arbitrary even spatial order
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Adjoint-based Perfusion Estimation from Dynamic Contrast-Enhanced Ultrasound: Advection-Diffusion and Two-Compartment Models
Adjoint equations with Tikhonov regularization enable gradient-based reconstruction of perfusion parameters from DCE-US data in advection-diffusion and two-compartment models, validated on synthetic and in vivo data.
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Kernel-based linear system identification using augmented Krylov subspaces
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Invariant domain preserving limiting of time explicit and time implicit discretizations for systems of conservation laws
A generalized flux-corrected transport limiter for systems of conservation laws enforces invariant domain preservation by expressing the high-order solution as a convex combination of low-order invariant-domain-preserving states, applicable to both explicit and implicit time discretizations.
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On the Practical Impact of Local Linear Instabilities in Entropy-Stable Schemes
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Adaptive anisotropic composite quadratures for residual minimisation in neural PDE approximations
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
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A Shifted Cohesive-Zone Method for Non-Interface-Fitted Meshes with Applications to Crystal Plasticity
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Neural parametric representations for thin-shell shape optimisation
A neural network with periodic activations parameterizes thin-shell mid-surfaces so that network weights can be optimized to minimize structural compliance subject to a volume limit.
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A high order stabilization-free virtual element method for general second-order elliptic eigenvalue problem
A novel high-order stabilization-free virtual element method is developed for general second-order elliptic eigenvalue problems, with optimal a priori error estimates for eigenspaces and eigenvalues, validated on various polygonal meshes.
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Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
A mixed formulation for Cosserat rod dynamics is cast as an infinite-dimensional nonlinear port-Hamiltonian system and discretized with structure-preserving finite elements to yield energy-momentum consistent time integration.
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A pressure-projection formulation in a least-squares meshfree method for the incompressible Navier-Stokes equations using a staggered-variable arrangement
A least-squares meshfree method for incompressible flows introduces a local primal-dual grid to achieve consistent staggered discretization and local divergence-free velocities.
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Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schr\"odinger equations
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Mixed-precision iterative refinement for low-rank Lyapunov equations
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A lattice Boltzmann method for Biot's consolidation model of linear poroelasticity
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Evolving finite elements for advection diffusion with an evolving interface
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Efficient Krylov solvers for inverse source problem in 2D space-time fractional diffusion equation
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Locally conservative redistribution limiting and applications to the approximation of conservation equations, Part II
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Multiscale Fourier Neural Operator for Inverse Wave Scattering in Highly Oscillatory Media
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An indefinite LOBPCG type of algorithm for detecting a definite Hermitian matrix pair
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A-priori error estimation for space-time Galerkin POD for linear evolution problems
An a-priori error estimate for space-time Galerkin POD is derived for linear parabolic evolution problems, bounding the FOM-ROM error by singular-value tail sums and problem-specific constants.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
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A Multi-Order Extension of Fractional HBVMs (FHBVMs)
Extension of FHBVMs to multi-order fractional differential equations with a Matlab implementation for two orders.
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A Block-Shifted Cyclic Reduction Algorithm for Solving a Class of Quadratic Matrix Equations
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Adaptive hyperviscosity stabilisation for the RBF-FD method in solving advection-dominated transport equations
An adaptive hyperviscosity stabilization for RBF-FD is proposed that sets the constant from the spectral radius of the evolution matrix, supports general nodes, and is demonstrated on linear advection and Burgers' equation with limited dissipation.
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Isogeometric Topology Optimization Based on Topological Derivatives
An isogeometric topology optimization approach using topological derivatives and level-set methods in an immersed framework enables seamless geometry updates without remeshing and benefits from higher-order basis functions for solution accuracy.
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Neural operators for solving nonlinear inverse problems
Tikhonov regularization is analyzed using neural operators as learned surrogates for ill-posed nonlinear operator equations, with error balancing and approximation results extended to Sobolev and Lebesgue spaces.
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Some new properties of an Active flux type scheme: PamPa
Active Flux/PamPa schemes incorporate discontinuous Galerkin methods as a building block, possess intrinsic bound-preserving properties illustrated numerically, and satisfy the summation-by-parts property in one dimension.
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An Adaptive Subdomain Coupling Approach in Domain Decomposition for Multiphase Porous Media Flow
Presents an adaptive subdomain coupling approach in domain decomposition for multiphase porous media flow, with new strategies and initial guesses to improve nonlinear solver convergence and parallel scalability.
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A Cartesian grid-based boundary integral method for moving interface problems
A boundary integral method on Cartesian grids is introduced for moving interface problems, using θ-L variables for stable evolution and fast solvers for efficiency, demonstrated on complex fingering and solidification cases.
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Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
Develops energy-stable asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation via SBP operators and IMEX Runge-Kutta methods guided by relative-energy error estimates.
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Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces
Defines trace-based metric and Bures-Wasserstein distance for PSD tensors, derives spectral eigenvalue bounds, and analyzes dependence on PSD condition with examples and complexity.
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Parallel matching-based AMG preconditioners for elliptic equations discretized by IgA
Matching-based AMG preconditioners deliver robust and scalable performance for solving large ill-conditioned systems from IgA discretizations in parallel HPC settings.
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Effect of different clustering approaches on the multilevel fast multipole method for the Helmholtz equation
Clustering approaches significantly affect the stability and efficiency of the multilevel fast multipole method for the Helmholtz equation, with poor choices causing instabilities on non-uniform meshes.
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