OpEvo automates tensor operator optimization for better efficiency.
problem Manual optimization of tensor operators is inefficient and limited.
method OpEvo uses evolutionary computation with topology-aware mutation.
result OpEvo finds optimal configurations with less effort and variance.
Data-efficient PDE operator learning without expensive simulations.
problem Expensive numerical PDE solutions limit data efficiency in machine learning.
method Unsupervised pretraining and in-context learning.
result Highly data-efficient and more generalizable than conventional models.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
MetaNOR learns common nonlocal kernels for efficient metamaterial modeling.
problem Efficiently modeling wave propagation in new metamaterials.
method Meta-learns a common nonlocal kernel from existing tasks and transfers this knowledge to new tasks with minimal data.
result Substantial improvements in sampling efficiency for new metamaterials.
Study efficient neural operator learning using variation spaces.
problem Operator learning using encoder-decoder neural networks.
method Introduce variation space for nonlinear operators, establish approximation bounds.
result Algebraic approximation and learning rates for polynomially decaying input and output encoding errors.
FNOs learn solution operators of dissipative equations efficiently via spectral methods.
problem Learning and approximation of solution operators for dissipative equations.
method Introducing spectral methods and deriving FNO approximation bounds and sample complexity guarantees.
result Polynomial sample complexity guarantees for FNOs learning solution operators of dissipative equations.
Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow efficient computation of a family of differential operators involving dimension-wise…
Paper introduces a Gaussian Process for operator learning in computational mechanics.
problem Efficient and accurate solutions for large datasets with reliable uncertainty quantification.
method Gaussian Process (GP) embedded in a neural operator framework with stochastic dual descent (SDD) algorithm.
result Improves GP resolution independence and scalability for high-dimensional and non-linear systems.
Covariance is shown as a commutator in random variable calculus.
problem Expressing covariance as a commutator of operators.
method Demonstrated through commutator identities involving expectations and products of functions.
result Revealed the underlying Lie algebraic structure in efficient influence curve calculus.
Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.
problem Quantifying the efficiency of neural operators for solving nonlinear parabolic PDEs.
method Deriving approximation rates by transferring PDEs to integral equations and leveraging Picard's iteration.
result Neural operators can efficiently approximate solution operators of nonlinear PDEs without exponential complexity growth.
New model outperforms Neural ODEs while being more efficient.
problem Stable convergence and existence guarantees for implicit-depth models.
method Developed Monotone Operator Equilibrium Network (monDEQ) based on monotone operator theory.
result MonDEQ models outperform Neural ODEs and are more computationally efficient.
New method uses neural operators for efficient function space optimization.
problem Optimization over function spaces with costly function evaluations.
method Sample-then-optimize approach with neural operator surrogates.
result Better sample efficiency and significant performance gains in experiments.
Woodbury transformations improve deep generative models with efficient invertibility and determinant calculation.
problem Efficiently invertible and determinant-calculable functions for deep generative models.
method Introducing Woodbury transformations that leverage matrix identities for efficient invertibility and determinant calculation.
result Woodbury transformations enable high-dimensional interactions, efficient sampling, and likelihood evaluation, outperforming other flow architectures.
MAD framework learns operators from physics-embedded data efficiently.
problem Data-driven methods require costly labeled datasets and model-driven techniques face efficiency-accuracy trade-offs.
method Integrates physical laws with data-driven learning to generate physics-embedded analytical solutions and synthetic data.
result Eliminates dependence on experimental or simulated training data, enabling efficient operator learning across multi-parameter systems.
AdaKoop efficiently models nonlinear dynamics from nonstationary data streams.
problem Capturing nonlinear dynamics in nonstationary data streams with computational efficiency.
method Koopman operator theory and probabilistic framework for streaming data.
result AdaKoop outperforms state-of-the-art methods in real-time forecasting accuracy and efficiency.
Self-ONNs adapt nodal operators during training for higher diversity and efficiency.
problem Limited network heterogeneity and high computational demand in ONNs.
method Self-organized ONNs with generative neurons that adapt nodal operators during training.
result Self-ONNs achieve utmost heterogeneity and computational efficiency.
Paper establishes convergence rates for learning elliptic pseudo-differential operators.
problem Learning elliptic pseudo-differential operators in partial differential equations.
method Wavelet-Galerkin framework, structured infinite-dimensional regression problem, sparse estimator, matrix compression, nested-support strategy.
result Obtained convergence rates for the estimator and efficient Galerkin solver.
New method speeds up learning of complex dynamical systems.
problem Efficiently learning large-scale dynamical systems from finite data.
method Random projections (sketching) to boost kernel-based Koopman operator estimators.
result The proposed estimators maintain accuracy while significantly reducing computation time.
Study shows neural operators can efficiently solve complex reaction-diffusion systems.
problem Efficiently solving nonlinear reaction-diffusion systems using neural operators.
method Laplacian-based neural operators applied to a generalized Gierer-Meinhardt system.
result Explicit approximation error bounds established for neural operators in terms of network parameters.
New method solves high-dimensional Bayesian inverse problems efficiently.
problem Efficiently solving high-dimensional Bayesian inverse problems with limited data.
method Physics-informed Neural Operators with RealNVP architecture for invertibility and differentiability.
result Accurate approximations of the full posterior without additional forward solves or sampling.
This work proposes a method to learn sparse representations that are more efficient for large-scale data retrieval.
problem Efficient retrieval of high-dimensional representations from large databases is computationally challenging.
method The approach minimizes the number of floating-point operations (FLOPs) by learning sparse embeddings with uniform non-zero entries.
result The proposed method achieves a similar or better speed-vs-accuracy tradeoff compared to existing baselines.
Improved DeepONet variants using Transformer cross-conditioning enhance PDE solution efficiency.
problem Solving partial differential equations efficiently and accurately.
method Transformer-inspired DeepONet variants with bidirectional cross-conditioning.
result Improved efficiency and accuracy compared to modified DeepONet, with variant effectiveness tied to PDE characteristics.
New algorithm improves PPS for multi-object matching.
problem Efficiently synchronize partial permutations for multi-object matching.
method Proposed CEMP-Partial algorithm for partial permutation synchronization (PPS). Uses sparse matrix operations and nonconvex weighted projected power method.
result Proves CEMP-Partial can exactly classify corrupted and clean partial permutations under adversarial corruption.
Smoothed top-k operator improves model training efficiency.
problem Discontinuous top-k operation makes models untrainable end-to-end.
method SOFT top-k operator approximates top-k as EOT solution.
result Improved performance in k-nearest neighbors and beam search.
Proposes glocal hypergradient estimation for hyperparameter optimization.
problem Combining reliability and efficiency in hyperparameter optimization.
method Uses Koopman operator theory to approximate global hypergradients from local ones.
result Achieves both reliability and efficiency in hyperparameter optimization.
New diagonal move simplifies knots and links efficiently.
problem Efficiently unknotting knots and links.
method Introduces diagonal move, proving its effectiveness for classical and welded knots.
result Diagonal move reduces any knot or link to the unknot or unlink with fewer operations.
Enhances neural operators with physics knowledge for more accurate simulations.
problem Improving accuracy and generalization of neural operators for physical systems.
method Jointly learns from original PDEs and simplified forms, incorporating fundamental physics.
result Significant improvement in nRMSE across various PDE problems.
State-space models improve dynamical system predictions efficiently and accurately.
problem Challenges in predicting dynamical systems, including long-time integration and long-range dependencies.
method State-space models implemented in Mamba, addressing limitations of existing architectures.
result Mamba outperforms other models in interpolation and challenging extrapolation tasks.
Latent-IMH improves Bayesian inference for expensive operators.
problem Efficient sampling from posterior distributions in inverse problems with computationally expensive operators.
method Metropolis-Hastings independence sampler using approximate and exact operators.
result Latent-IMH outperforms existing methods in computational efficiency.
SCOPE-FE improves feature engineering efficiency for high-dimensional datasets.
problem Expanding and reducing feature space in tabular learning becomes computationally expensive with increased dimensionality.
method SCOPE-FE controls the search space by regulating operator and feature-pair spaces, using OperatorProbing and FeatureClustering.
result SCOPE-FE reduces feature engineering time while maintaining competitive predictive performance.
Nyström approximation for scalable operator learning
problem Scalability of operator learning for large datasets
method Nyström subsampling with operator learning
result Minimax-optimal convergence rates for functional outputs
The new generation of machine learning processors have evolved from multi-core and parallel architectures that were designed to efficiently implement matrix-vector-multiplications (MVMs). This is because at the fundamental level, neural network and machine learning operations extensively use MVM operations and hardware…
Paper presents efficient algorithms for convolutional neural networks using Winograd minimal filtering.
problem Resource-efficient implementation of convolutional neural networks.
method Winograd minimal filtering trick applied to M-tap filters (M=3,5,7,9,11) for parallel hardware implementation.
result Approximately 30% reduction in multipliers for fully parallel hardware implementation.
Neural operators solve families of 2BSDEs efficiently.
problem Solving infinite families of 2BSDEs on bounded domains.
method Introduces a mild generative neural operator model to approximate solutions.
result Solution operators can be approximated by neural operators with polynomial parameters.
Koopman operator theory simplifies complex systems analysis.
problem Analyzing nonlinear dynamical systems and complex networks.
method Estimating Koopman operator from data to reveal system properties.
result Koopman operators provide insights into system characteristics.
VIDON learns operators with variable sensors, overcoming sensor limitations.
problem Fixed sensor locations restrict operator learning applicability.
method Variable-Input Deep Operator Network (VIDON) with random, varying sensors.
result VIDON efficiently approximates operators in PDEs and is robust to sensor permutations.
MCNO learns PDE solution operators using Monte Carlo sampling.
problem Learning solution operators for PDEs efficiently and flexibly.
method Directly learns kernel function using Monte Carlo sampling of input-output pairs.
result Competitive accuracy with efficient computational cost on 1D PDE benchmarks.
Transformers learn functionals from distributions without losing information.
problem Lack of rigorous mathematical theory supporting Transformer performance.
method Proposed a Transformer learning framework, attention operator, and distribution regression.
result Transformers can compress distributions into function representations without loss of information.
We investigate the relationship between market efficiency of rice futures transaction in Osaka and the Japanese government intervention in rice distributions by directly buying and selling rice during the interwar period, from the middle 1910s to 1939, considering the context of "discretion versus rules." We use a time…
This study approximates distances between Gaussian processes and covariance operators using RKHS.
problem Approximating distances between Gaussian processes and covariance operators from finite samples.
method Using reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators, the study shows how to consistently and efficiently estimate Sinkhorn divergence from finite samples.
result Convergence rates are dimension-independent and of the same order as Hilbert-Schmidt distance.
Random sampling improves DeepONet training efficiency without sacrificing accuracy.
problem Training DeepONet models with high computational and memory costs.
method Random sampling of inputs in the trunk network of DeepONet.
result Significant reduction in training time with comparable accuracy.
Paper introduces FNM framework for learning finite-dimensional parametrized models.
problem Efficiently learning finite-dimensional parametrized models from limited data.
method Fourier Neural Mappings (FNMs) framework for operator learning.
result End-to-end learning of PtO maps can be less data-efficient than learning the solution operator first.
Proposes SCD-split for CP to balance interpretability and efficiency.
problem Difficult interpretation of disconnected subintervals in CP prediction sets.
method Incorporates smoothing operations into CP framework.
result SCD-split balances interval length and subinterval number, theoretically provable.
Efficient algorithm for evaluating hierarchical classification methods at multiple operating points.
problem Evaluating hierarchical classification methods at multiple operating points.
method Efficient algorithm to produce operating characteristic curves for any method that assigns scores to every class in the hierarchy.
result Top-down classifiers are dominated by a naive flat softmax classifier across the entire operating range.
CoLA automates efficient numerical linear algebra for complex matrix structures.
problem Efficiently solving large-scale linear algebra problems with complex matrix structures.
method Combining linear operator abstraction with compositional dispatch rules.
result Automatic and efficient numerical algorithms for various linear algebra operations.
Enhances neural architecture search efficiency and prevents performance collapse.
problem Improving memory efficiency and preventing performance collapse in neural architecture search.
method Employing continuous relaxation strategy and gradient-based optimization for over-parameterized BCNN construction, introducing Confident Learning Rate and partial channel connections.
result NAS-v2 delivers state-of-the-art search efficiency on CIFAR-10 and ImageNet.
New neural operators learn structured patterns efficiently.
problem Learning and representing complex, structured patterns in data.
method Sparse autoencoder neural operators (SAE-NOs) parameterize concepts as functions, enabling efficient and structured representation.
result SAE-FNOs learn localized patterns and generalize across different scales and discretizations.
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…