New findings on how convolutional architectures approximate time series data.
problem Understanding the approximation properties of convolutional architectures in time series modeling.
method Mathematical analysis of convolutional architectures applied to time series modeling.
result A new definition of spectrum-based regularity for measuring temporal relationships under convolutional approximation.
New deep learning architecture learns martingales efficiently.
problem Efficiently learning martingales in financial derivatives pricing.
method High-order weak approximation algorithms of Runge-Kutta type.
result Deep neural networks based on this architecture learn martingales effectively.
New neural network architecture with height adds expressive power.
problem Expressiveness of neural networks limited by width and depth.
method Introduces height as a new hyper-parameter in neural network architecture.
result Neural networks with height achieve significantly better approximation of functions.
Paper characterizes and constructs universal approximators for neural networks.
problem Limited understanding of universal approximation in neural networks.
method Characterization, representation, construction method, existence result for any universal approximator.
result Improved capabilities of feed-forward architecture to approximate continuous functions.
New RL algorithm learns state aggregation architecture adaptively.
problem Adapting reinforcement learning value function architectures.
method Adapts state aggregation architecture using state visit frequency feedback.
result Improves RL performance on various test problems.
A new machine learning model uses matrix exponentials for universal approximation.
problem Developing a robust and efficient machine learning model.
method Introduces a novel architecture using matrix exponentials as the only nonlinearity.
result The model achieves universal approximation properties and outperforms other models on benchmark tasks.
Adapts reinforcement learning architectures using state visit frequency.
problem Determining an optimal approximation architecture for reinforcement learning.
method Adapts state aggregation approximation architecture based on state visit frequency.
result Guarantees VF estimate arbitrarily close to zero with large S. Develops approximately equivariant neural processes for better data modeling.
problem Real-world data often breaks exact equivariance; how to model this?
method General approach to creating approximately equivariant architectures, applicable to any model and symmetry group.
result Approximately equivariant neural processes outperform non-equivariant and strictly equivariant models in regression tasks.
POUnets combine partitions of unity and monomials for efficient deep learning.
problem Efficiently approximating functions with deep neural networks in high dimensions.
method Integrates partitions of unity and monomials into neural network architecture.
result POUnets achieve hp-convergence for smooth functions and outperform MLPs for discontinuous functions.
Adapts deep learning with kernel methods for efficient learning.
problem Combining kernel methods and deep learning for efficient learning.
method Nyström approximation of kernel functions in neural networks.
result Performance comparable to standard architectures on datasets like SVHN and CIFAR100.
New study shows deep, skinny networks can't approximate all functions.
problem Limitations of deep, skinny neural networks in approximating functions.
method Examined topological constraints imposed by network architecture.
result Deep, skinny networks are not universal approximators for all functions.
Review of neural network expressivity and architectures.
problem Understanding neural network expressivity across different architectures.
method Comprehensive overview of approximation results for various neural network types.
result Deep neural networks offer advantages over shallow ones for specific function classes.
Paper proposes MCMA architecture for neural approximate computing with higher invocation rate and energy savings.
problem Limited invocation rate of neural approximators leading to suboptimal energy efficiency.
method Introduces MCMA architecture with a multiclass classifier and multiple approximators, sharing hardware resources and efficiently swapping approximators.
result Significantly higher invocation rate and energy savings compared to existing methods.
New conditions ensure deep neural networks can approximate any function on non-Euclidean spaces.
problem Understanding how to modify neural network architectures to approximate functions on non-Euclidean spaces.
method Developed conditions for feature and readout maps that preserve universal approximation capabilities.
result Modified architectures can deterministically approximate any classifier on non-Euclidean spaces.
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
New ADANNs improve PDE approximations.
problem Approximating operators for parametric PDEs.
method Custom ANN architectures and initialization schemes.
result ADANNs significantly outperform existing methods.
Deep neural networks improve modulation recognition accuracy.
problem Improving modulation recognition accuracy in wireless signals.
method Developed and tested deep neural network architectures, including CNN, ResNet, DenseNet, and CLDNN.
result Achieved high accuracy (up to 88.5%) in recognizing wireless signal modulations.
MiLeNAS improves neural architecture search by reducing approximation errors and achieving better accuracy.
problem Improving efficiency and accuracy in neural architecture search (NAS).
method Mixed-level reformulation (MiLeNAS) to optimize efficiently and reliably.
result MiLeNAS achieves lower validation error and higher accuracy than bilevel optimization methods.
PENs learn summary statistics for ABC using invariant neural architectures.
problem Learning summary statistics for approximate Bayesian computation (ABC).
method Partially exchangeable networks (PENs) that are invariant to block-switch transformations.
result PENs provide more reliable posterior samples with less training data.
This work proposes searching for optimal operation distribution in neural architecture search.
problem Finding optimal neural architecture with specific operations and connections.
method Search for the optimal operation distribution, providing a stochastic and approximate solution.
result Operation distribution holds enough discriminating power to reliably identify a solution and is easier to optimise than traditional encodings.
Aims to find efficient neural architectures under resource constraints.
problem Resource constraints in neural architecture search.
method Lamarckian Evolutionary Algorithm for Multi-objective Neural Architecture Search.
result Found models that are competitive with both hand-crafted and automatically-designed networks.
Paper bounds NAS function approximation, showing computational limits.
problem NAS function approximation problem.
method Reformulated FA problem, showed computational infeasibility, described a-ASP.
result NAS cannot solve FA for all functions to zero error.
New method selects neural network architectures without needing data.
problem Choosing efficient deep neural network architectures.
method Developed the deep frame potential to quantify network capacity.
result Deep frame potential correlates with generalization error.
New Zap Q-learning accelerates reinforcement learning with neural networks.
problem Accelerate convergence of reinforcement learning algorithms.
method Introduces a new framework for analysis of stochastic approximation algorithms, proving consistency under non-degeneracy assumption.
result Zap Q-learning with neural network function approximation converges quickly and is robust to function approximation architecture choice.
TCNs can approximate complex input-output maps with limited memory.
problem Approximating complex input-output maps with limited memory.
method Proved TCNs can approximate a wide class of input-output maps with arbitrary error tolerance.
result Deep ReLU TCNs can approximate input-output maps with finite memory to arbitrary error.
This work maps Boltzmann distributions to ARNNs for better physics-based model approximations.
problem Approximating Boltzmann distributions of binary systems.
method Exact mapping of Boltzmann distribution to autoregressive neural network architecture.
result New ARNN architectures derived from physical models show superior performance.
Pruned neural networks' error scales predictably with architecture and task.
problem Understanding the predictability of pruning across different scales and architectures.
method Functionally approximated the error of pruned networks, showing it is predictable in terms of invariant tying width, depth, and pruning level.
result The error of pruned networks follows a scaling law with interpretable coefficients that depend on architecture and task.
New CFNN architecture approximates functions with machine accuracy.
problem Function approximation with high precision.
method Chebyshev Feature Neural Network (CFNN) with learnable frequencies.
result Achieves machine accuracy in function approximation.
New neural network architecture preserves gradient norms to approximate Lipschitz functions.
problem Training neural networks with strict Lipschitz constraints to ensure robustness and generalization.
method Identified gradient norm preservation as a necessary property, combined with norm-constrained weight matrices and GroupSort activation function.
result Norm-constrained GroupSort architectures can approximate Lipschitz functions and achieve tighter Wasserstein distance estimates.
This study uncovers how neural architectures and weights interact in classification tasks.
problem Understanding the role of neural architecture and weights in classification performance.
method Developed a novel method to find optimal task-specific architectures as binary networks with {0, 1}-valued weights, using approximate gradient descent.
result Well-trained architectures may not require fine-tuning of weights, highlighting the importance of structure over weights.
New architectures improve KANs, making them more interpretable and accurate.
problem Improving Kolmogorov-Arnold networks while maintaining interpretability.
method Overprovisioned architectures combined with sparsification, deep supervision, and depth selection, optimized with a minimum description length objective.
result Combining sparsification with depth selection achieves competitive or superior accuracy while discovering smaller models.
Sumformer simplifies Transformers to handle long sequences efficiently.
problem Quadratic complexity of Transformers limits their use with long sequences.
method Introducing Sumformer, a simple architecture that universally approximates equivariant sequence-to-sequence functions.
result Sumformer achieves the first universal approximation results for Linformer and Performer.
New algorithm for non-Markovian optimal stopping problems using Brownian motion.
problem Optimal stopping time problems for non-Markovian state processes.
method Longstaff-Schwartz-type algorithm based on statistical learning theory.
result Error estimates for approximation architecture spaces with finite Vapnik-Chervonenkis dimension.
INNs can approximate diverse functions despite layer restrictions.
problem Can INNs approximate sufficiently diverse functions?
method Developed a theoretical framework based on differential geometry to simplify the approximation problem of diffeomorphisms.
result INNs have the universal approximation property.
New Transformers maintain Lipschitz continuity for robustness.
problem Ensuring robustness in Transformers for safety-sensitive applications.
method Introducing gradient-descent-type in-context Transformers with explicit Euler steps of negative gradient flows.
result Universal approximation theorem for Lipschitz continuous Transformers.
This paper explores a novel sparse shortcut topology in neural networks.
problem Understanding the effectiveness and characteristics of shortcut connections in neural networks.
method Investigates a novel sparse shortcut topology, demonstrating its expressivity and generalizability.
result The proposed topology enables a one-neuron-wide deep network to approximate any univariate continuous function and shows excellent generalizability.
Paper proposes a technique to reduce deep neural network parameters without sacrificing accuracy.
problem Designing smaller networks that approximate the operation of larger, more powerful networks.
method Randomized tensor sketching technique applied to convolutional and fully connected layers.
result Smaller networks trained with sketching technique achieve comparable accuracy to original networks.
Near-optimal rates for multi-task learning with shared representations.
problem Approximation and statistical complexity of learning multiple operators.
method Multiple Neural Operators (MNO) architecture and comparison with DeepONet.
result Near-optimal upper and lower bounds for approximation and generalization.
ESAC improves reinforcement learning by lookahead and intuition.
problem Designing efficient reinforcement learning architectures for intelligent agents.
method Integrates selector, tuner, model-learner, estimator, and lookahead into ESAC.
result ESAC outperforms other architectures in optimizing policies.
Bayesian approach fixes overconfidence in ReLU networks, even slightly.
problem Overconfidence in ReLU networks far from training data.
method Theoretical analysis of approximate Gaussian distributions on ReLU weights, and empirical validation.
result Even a simplistic Bayesian approximation fixes overconfidence issues.
Presented are two neural network architectures for convex functions, demonstrating competitive performance.
problem Approximating convex functions efficiently and accurately.
method Developed two neural network architectures: one based on linear-by-part representation and the other on cubic splines.
result Cubic ICKAN networks produce results similar to classical ICNNs in solving convex approximation problems.
Proposes a new neural network architecture combining MLP and basis functions.
problem Function approximation and operator learning in scientific machine learning.
method Combines robust MLP inner functions with flexible basis functions outer functions.
result KKAN outperforms MLPs and KANs in function approximation and operator learning tasks.
Method improves developability of B-spline surfaces for architectural design.
problem Developability of B-spline surfaces for architectural freeform surfaces.
method Algorithm to thin the Gauss image by increasing planarity of neighborhoods, allowing for paneling with specific developable types.
result Enforced developable panels for architectural design, reducing manufacturing costs.
Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.
problem Understanding the expressive power of Graph Neural Networks (GNNs).
method Theoretical framework comparing invariant and equivariant GNNs, proving approximation guarantees for practical architectures.
result Folklore Graph Neural Networks (FGNN) are the most expressive architectures for a given tensor order.
This work analyzes how deep neural networks' expressiveness increases with depth and width.
problem Understanding the expressiveness of deep neural networks (DNNs) based on their Lipschitz constants.
method Leveraging random matrix theory, the study characterizes the expressiveness of DNNs by their Lipschitz constant, showing exponential and polynomial increases with depth and width, respectively.
result The expressiveness of DNNs increases exponentially with depth and polynomially with width, consistent with function approximation benefits.
Optimal function approximation with Relu neural networks achieves minimal error.
problem Finding the minimal error in approximating convex functions with Relu networks.
method Established necessary and sufficient conditions for optimal approximations, presented neural network architectures, and proposed an algorithm for convergence.
result Proved the convergence of the proposed algorithm and validated it with experimental results.
New kernel connects deep learning to optimization, improving generalization.
problem Understanding why deep neural networks generalize well at over-parameterization.
method Established Neural Optimization Kernel (NOK) linking deep NN to optimization problems.
result New generalization bound for deep structured approximated NOK architecture.
Deep ReLU networks approximate as well as shallow ones in kernel regimes.
problem Understanding the limitations of kernel methods for deep ReLU networks.
method Characterizing eigenvalue decays of kernels derived from deep ReLU networks.
result Deep ReLU networks and shallow two-layer networks have equivalent approximation properties in kernel regimes.