New method improves model reconstruction using counterfactuals and polytope theory.
problem Reconstructing models with minimal input changes and avoiding decision boundary shifts.
method Using polytope theory to derive loss functions that treat counterfactuals differently from ordinary instances.
result Improves fidelity between target and surrogate model predictions on multiple datasets.
The paper reconstructs Lorentzian spacetimes from causal sets.
problem Reconstructing Lorentzian spacetimes from causal sets.
method Introduced a concept of isomorphy and three types of convergence.
result Established Gromov's reconstruction theorem in Lorentzian geometry.
Proposes a new approach to learn predicates from data.
problem Predicate invention in relational and deep learning communities.
method Theory reconstruction approach extending autoencoder to relational settings.
result Starts a discussion for a unified framework for predicate invention.
The VAE's reconstruction ability is studied using PAC-Bayes theory.
problem Understanding the performance of VAEs for unseen data.
method PAC-Bayes theory is applied to analyze VAE's reconstruction error.
result Generalization bounds on VAE's reconstruction error are provided.
Unified theory explains and mitigates double descent in data reconstruction.
problem Understanding and mitigating double descent in reduced order modeling.
method Data-Noise Averaging theory, sufficient criteria, detailed risk curve prediction, regularization mechanisms.
result Detailed risk curves predicted at reduced computational cost, instability traced to individual sensors.
Reconstruct spacetime from order and number of points.
problem Reconstruct spacetime from chronological relations and i.i.d. samples.
method Relaxing hypotheses of Gromov reconstruction theorem, using random adjacency matrices and chronological relations.
result Spacetime can be recovered by only knowing 'order' and 'number' of its points.
Belief Propagation outperforms other algorithms in reconstructing binary symmetric channel trees.
problem Reconstructing binary symmetric channel trees with bounded memory.
method Combining recursive reconstruction, information theory, and optimal transport.
result Any recursive algorithm with bounded memory for the reconstruction problem on binary symmetric channel trees has a phase transition strictly below the Belief Propagation threshold.
New method reconstructs hidden structures from noisy data.
problem Resurrecting hidden structures from incomplete or distorted data.
method Integrates Atiyah--Molino framework and Hantjies tensor.
result Exceptional robustness in noisy conditions with error-bounded reconstructions.
The not-quite-Hamiltonian theory of singular reduction and reconstruction is described. This includes the notions of both regular and collective Hamiltonian reduction and reconstruction.
New methods for signal reconstruction using guiding sets and frame-less pathways.
problem Signal reconstruction in Hilbert spaces with specified properties.
method Axiomatic approach involving sample consistent and guiding sets, with reconstruction set defined as a shortest pathway.
result Existence and uniqueness of reconstruction set in Hilbert space, with derived stability and error bounds.
Theory reconstructs network connectivity from event timings.
problem Reconstructing network connectivity from incomplete continuous-time data.
method Linearizes event space mapping to reveal direct influences.
result Reveals synapse presence and inhibitory/activating nature.
Reduces field theories on principal bundles by a subgroup, deriving reduced equations.
problem Hamiltonian field theories on principal G-bundles with invariant densities.
method Lie-Poisson reduction using covariant bracket formulation.
result Derives reduced observables, brackets, and equations of motion for field theories.
New theory for curve-based 3D reconstruction and camera estimation.
problem Challenges in point feature extraction limit traditional methods.
method Differential geometry of general curves for image and space curves.
result Theoretical foundations for curve-based multiview reconstruction.
Algorithm reconstructs conserved networks from flow data.
problem Network reconstruction from flow data.
method Polynomial time algorithm exploiting graph theoretic properties and learning techniques.
result Exact network reconstruction possible for arborescence networks.
Sparse elasticity reconstruction from local displacements reduces error.
problem Reconstructing elasticity from limited data.
method Sparse elasticity reconstruction theory, local clustering, alternating optimization.
result Higher spatial resolution elasticity distribution estimation.
Gradient-based explanations can reveal model structure.
problem Tension between secrecy and model explanations.
method Algorithm to learn a two-layer ReLU network using gradient queries.
result The number of gradient queries is nearly optimal and independent of model size.
Reconstructs Shelstad's character identity using index theory.
problem Classifying group representations via the Langlands program.
method Geometric proof using index theory of elliptic operators in K-theory. result Evidence that index theory can be used in representation classification.
New connection found between shape reconstruction methods and persistent homology.
problem Connecting shape reconstruction methods with persistent homology.
method Wrap complexes and lexicographic optimal homologous cycles.
result Lexicographically optimal homologous cycles are supported on Wrap complexes.
We investigate the reduction process of a k-symplectic field theory whose Lagrangian is invariant under a symmetry group. We give explicit coordinate expressions of the resulting reduced partial differential equations, the so-called Lagrange-Poincare field equations. We discuss two issues about reconstructing a solutio…
The paper extends lossy coding to nonlinear latent representations.
problem Learning finite-dimensional coding schemes with nonlinear reconstruction maps.
method Generalizes Maurer--Pontil framework to nonlinear maps, connects to generative modeling, and provides generalization bounds.
result Established a connection to approximate generative modeling and presented generalization bounds.
The paper analyzes privacy leakage in federated learning using linear algebra and optimization theory.
problem Privacy leakage in federated learning despite its promise for data privacy.
method Theoretical analysis from linear algebra and optimization theory perspectives.
result Derives sufficient conditions to prevent data reconstruction attacks and establishes an upper bound on privacy leakage.
SDSR reconstructs species trees from genetic markers efficiently.
problem Challenges in reconstructing species trees from genetic data.
method Spectral divide-and-conquer approach based on graph theory.
result SDSR achieves up to 10-fold faster runtime with comparable accuracy.
Measures time-delay embedding for noisy, sparse data.
problem Applying Takens' embedding theorem to real-world, noisy data.
method Formulated a measure-theoretic generalization of the embedding theorem, using optimal transport.
result Reconstructed full state of dynamical systems from time-lagged partial observations robust to noise and sparsity.
IFT reformulates AI and ML tasks using field theory.
problem Signal reconstruction and non-parametric inverse problems.
method Reformulate inference in IFT as GNN training.
result IFT-based GNNs can operate without pre-training.
Kernel Dynamic Mode Decomposition reconstructs dynamical systems using Laplacian kernel.
problem Reconstructing spatial-temporal dynamics of complex systems.
method Kernel Dynamic Mode Decomposition with Laplacian kernel.
result Laplacian kernel allows for the closability of Koopman operators in RKHS, enabling reconstruction.
Improves deep network generalization for image sequence reconstruction.
problem Improving generalization of deep networks for inverse image reconstruction.
method Proposes a network optimized by a variational approximation of the information bottleneck principle with stochastic latent space.
result Demonstrates improved generalization ability of inverse reconstruction networks through stochasticity and information bottleneck.
Defines precise general manifolds from gluing data.
problem Formalizing the concept of general manifolds.
method Formalized definition using gluing data, equivalence-partially ordered set (e-pos), and natural relations.
result Reconstruction theorems allow reconstructing manifolds and their morphisms from gluing data.
This work provides statistical guarantees for VAEs using PAC-Bayesian theory.
problem Theoretical properties of VAEs remain open questions.
method PAC-Bayesian theory to derive statistical guarantees.
result Upper bounds on Wasserstein distance between input and generative model.
New method improves signal reconstruction with nonconvex penalties and parameter control.
problem Reconstructing sparse signals with nonconvex penalties and nonconvexity control.
method Introduces nonconvex penalties (SCAD, MCP) with nonconvexity parameters and controls them to guide AMP trajectory.
result Achieves perfect reconstruction for relatively dense signals with small nonconvexity parameters.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three parts and we show how the integral curves of the original system can be reconstructe…
New DG method minimizes barycentric alignment and reconstruction loss.
problem Improving domain generalization in machine learning.
method Introduces a new upper bound and WBAE algorithm.
result WBAE outperforms state-of-the-art DG algorithms.
RepGAN learns a disentangled representation for reconstruction, generation, and clustering.
problem Learning a disentangled representation for reconstruction, generation, and clustering.
method RepGAN learns a disentangled representation through a symmetric adversarial process that minimizes the upper bound of conditional entropy loss.
result RepGAN achieves high unsupervised classification accuracy and low reconstruction error on MNIST.
Reconstructs fundamental groups from liquid local systems.
problem Reconstructing fundamental groups from category of liquid local systems.
method Theory of liquid vector spaces and liquid quasicoherent sheaves.
result Reconstructs topological fundamental group and twisted fundamental groupoids.
A new tensor decomposition method that minimizes KL divergence.
problem Tensor reconstruction accuracy.
method Legendre decomposition, based on information geometry.
result Minimizes KL divergence and improves tensor reconstruction accuracy.
Reconstructing signature features from randomized vector fields in differential equations.
problem Reconstructing signature features from controlled differential equations with random vector fields.
method Using controlled ordinary differential equations driven by continuous bounded variation curves, the study explores the extent to which signature features can be reconstructed from the non-linear flow of these equations.
result The number of signature features that can be reconstructed from the non-linear flow of controlled ordinary differential equations with random vector fields is exponential in the hidden dimension, under certain conditions.
Paper improves deep learning models for cardiac potential reconstruction.
problem Improving generalization of sequence models for cardiac potential reconstruction.
method Constrained stochasticity and global aggregation of temporal information in latent space.
result Improved generalization of inverse reconstruction networks.
Improved β-VAE learns disentangled representations without sacrificing reconstruction accuracy.
problem Learning disentangled representations in variational autoencoders (VAEs).
method Modified β-VAE training regime that increases latent code information capacity over training. result Improved β-VAE robustly learns disentangled representations without sacrificing reconstruction accuracy. Simplifies VAE for anomaly detection using rate-distortion theory.
problem Anomaly detection in unsupervised learning systems.
method Revisit VAE from information theory, incorporate model uncertainty.
result Competitive performance on benchmark datasets.
Proposes a method to estimate discrete curvatures for image reconstruction.
problem Image reconstruction challenges due to non-convex, non-smooth, and highly non-linear first-order optimal conditions.
method Estimates discrete curvatures (mean and Gaussian) locally using differential geometry theory. Solves a weighted total variation minimization problem efficiently with ADMM.
result Demonstrates the effectiveness and superiority of the proposed variational models for various image reconstruction tasks.
Method reconstructs missing wind farm data using graph theory and nearest neighbors.
problem Missing data in wind farm records due to sensor failures.
method Combines spectral graph theory and k-Nearest Neighbors to estimate missing data.
result Significant improvement in data reconstruction over existing methods.
We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the ca…
This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichmüller theory, the mapping class groups, SL(2,C) representation variety of surface groups, and Thurston's theory o…
Quantum groups created from disk configuration space homologies.
problem Creating quantum groups from algebraic structures.
method Reconstructing quantum groups from homologies of configuration spaces of disks.
result New combinatorics and actual submanifolds of configuration spaces.
Random Fourier Features reduce kernel matrix reconstruction error without dimensionality dependence.
problem Error reduction in kernel matrix reconstruction for high-dimensional data.
method Random Fourier Features with theoretical error bounds.
result Error probability is independent of data dimensionality.
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tai…
Explains various PCA and SPCA methods with theory and applications.
problem No specific problem stated; focuses on explaining methods.
method Explains PCA, SPCA, kernel PCA, and kernel SPCA methods with theory and applications.
result Comprehensive coverage of PCA and SPCA methods with theory and applications.
New deep learning methods improve CT image quality from few projections.
problem Sparse-view CT images suffer from streaking artifacts due to limited projections.
method Inspired by deep convolutional framelets, propose new U-Net variants that satisfy the frame condition.
result New U-Net variants provide better reconstruction performance for sparse-view CT.