New method speeds up neural kernel computations for various activations.
problem Inefficient computation of neural kernels for general activations.
method Fast sketching method using truncated Hermite expansion.
result 106x speedup for approximate CNTK computation on CIFAR-10.
Characterizes neural kernel and NNGP for various activations.
problem Understanding neural kernels and NNGP for non-RELU activations.
method Characterization of RKHS for various activation functions.
result Broad class of non-infinitely smooth activations generate equivalent RKHSs at different depths.
New active learning method for kernel selection improves efficiency and accuracy.
problem Real-world applications where acquiring true labels is costly or time-consuming.
method Active Multiple Kernel Learning (AMKL) with adaptive kernel selection (AMKL-AKS).
result AMKL-AKS achieves optimal sublinear regret and better performance with fewer labeled data.
The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.
problem Understanding how neural networks transform input data across layers.
method Theoretical framework for the evolution of the kernel sequence, using mean-field regime and Hermite polynomials.
result For nonlinear activations, the kernel sequence converges globally to a unique fixed point.
Active data collection improves convergence rates in operator learning.
problem Improving convergence rates in operator learning with linear target and stochastic input.
method Active data collection strategies with mean-zero stochastic process and continuous covariance kernels.
result Achieves arbitrarily fast error convergence rates with eigenvalue decay of covariance kernels.
Kafnets introduces flexible neural network activation functions based on kernels.
problem Lack of flexible activation functions in neural networks.
method Kernel-based non-parametric activation functions (KAFs).
result KAFs can approximate any mapping and are smooth, linear in parameters, and regularizable.
Study on deep neural networks using branching processes and Mehler's formula.
problem Understanding the mathematical role of activation functions in compositional neural networks.
method Connection between compositional kernels and branching processes via Mehler's formula; new random features algorithm.
result Explicit formulas for eigenvalues of compositional kernels quantify complexity.
New activation functions improve neural network stability and generalize well.
problem Proving theoretical generalization of non-parametric activation functions.
method Stability analysis of non-convex models trained with SGD.
result Neural networks with kernel activation functions generalize well with SGD.
New method uses neural tangent kernel for efficient active learning.
problem Efficiently approximating deep learning's look-ahead selection criteria.
method Approximates retraining with neural tangent kernel for active learning.
result Approximation works asymptotically and enables sequential active learning.
Improved neural network accuracy with multi-Kernel activation functions.
problem Designing effective activation functions for neural networks.
method Developed multi-Kernel activation functions (multi-KAF) combining multiple kernel models.
result Multi-KAFs enhance convolutional networks' accuracy on handwritten Latin OCR tasks.
Predicts atomization energy with high accuracy using graph kernels and active learning.
problem Predicting molecular atomization energy with high accuracy.
method Gaussian process regression with marginalized graph kernel, active learning.
result Achieves mean absolute error of 0.62 +- 0.01 kcal/mol with 2000 training samples.
Optimal kernel learning improves GP regression for high-dimensional inputs.
problem High computational costs and low prediction accuracy in GP models with many inputs.
method Approximates GP covariance with a convex combination of kernel functions, identifying active variables.
result Improves prediction accuracy and correctly identifies active input variables.
Deep learning fuses multiple kernels for improved data characterization.
problem Combining multiple kernels for effective data characterization.
method Creates dense embeddings using kernel similarities, then uses a deep neural network to fuse them. Introduces kernel dropout regularization and expanded composition kernels.
result Achieves state-of-the-art performance in kernel fusion.
A framework and benchmark for deep batch active learning in neural networks.
problem Efficiently acquiring labels for neural network regression.
method Framework of base kernels, transformations, and selection methods; use of sketched finite-width neural tangent kernels and clustering.
result Proposed method outperforms state-of-the-art on benchmark, scales to large data sets.
Paper discusses optimal selection of neuron non-linearities using kernel expansions.
problem Optimizing neuron non-linearities in deep neural networks.
method Inspired by classic regularization arguments, the paper uses kernel expansions to represent the best activation function.
result Kernel-based activation functions effectively capture long-term dependencies in recurrent networks.
New approach for active learning in overparameterized models.
problem Efficiently labeling datasets in machine learning.
method MaxiMin Active Learning for nonparametric or overparameterized models.
result Automatically identifies decision boundaries and data clusters.
New insights into neural network kernels for rectified MLPs.
problem Understanding the behavior of weight distributions in rectified MLPs.
method Deriving equivalent kernels for MLPs with ReLU or Leaky ReLU activations under various weight distributions.
result Kernels corresponding to layers with certain weight distributions are asymptotically universal and well approximated by Gaussian kernels.
m-arcsinh improves SVM and MLP reliability and speed in scikit-learn.
problem Improving SVM and MLP reliability and speed in scikit-learn.
method Modified arcsinh function for kernel and activation in SVM and MLP.
result Competitive classification performance and reliability of SVM and MLP with m-arcsinh.
Efficiently identifies users from walking activity data using kernel-based DTW.
problem Identifying users from walking activity data streams.
method Learning a kernel to approximate DTW for efficient analysis of streaming data from wearable sensors.
result The proposed approach reduces computational burden compared to traditional DTW.
Generalizes NTK for surrogate gradient learning in neural networks.
problem Lack of theoretical foundation for surrogate gradient learning.
method Generalizes neural tangent kernel (NTK) for surrogate gradient learning (SGL).
result Surrogate gradient NTK provides a good characterization of SGL.
Improved RNNs with flexible gates using kernel activation functions.
problem Modeling long-term dependencies in sequential data.
method Designed a more flexible architecture with adaptable parameters using kernel activation functions.
result Improved accuracy with negligible computational cost and speed-up in training iterations.
This work challenges the Neural Tangent Kernel's role in overparameterized neural networks, especially with large width and depth.
problem The Neural Tangent Kernel's behavior in overparameterized neural networks with large width and depth is unclear.
method Experimental and theoretical analysis of ReLU networks with large width and depth.
result The aggregate norm of hidden neuron deviations does not vanish in infinitely-wide ReLU networks, indicating non-trivial behavior.
New algorithm reduces neural net error in contextual bandits.
problem Neural contextual bandits with general activation functions.
method Proposed an efficient algorithm with sublinear regret bound.
result Demonstrated provably sublinear regret bound in finite regime.
Enhanced GCNs with non-parametric activation functions outperform baselines.
problem Simple activation functions in GNNs limit model flexibility.
method Extended kernel activation function for GCNs, regularizable and smooth.
result Significant improvement over baseline GCNs with similar depth/size.
The paper analyzes the role of ReLU gates in deep learning networks.
problem Understanding the role of gates in deep learning networks.
method Developed neural path features (NPF) and neural path values (NPV) to characterize the active sub-networks during training.
result The neural path kernel associated with NPFs is a fundamental quantity that characterizes the information stored in the gates of a DNN.
Analyzes feature learning in neural networks using a self-consistent dynamical field theory.
problem Feature learning in infinite-width neural networks.
method Constructs deterministic dynamical order parameters as inner-product kernels for hidden unit activations and gradients.
result Reveals the hidden layer activation distribution, neural tangent kernel evolution, and output predictions.
Ahpatron improves online kernel learning with tighter mistake bounds.
problem Improving mistake bounds in online kernel learning with budget constraints.
method Introducing Ahpatron, a new model that uses an aggressive updating rule and a budget maintenance mechanism to approximate AVP.
result Ahpatron achieves tighter mistake bounds compared to previous models.
SANs use sparse activation functions to compress data representations.
problem Learning meaningful features without considering compression.
method Introduce φ metric, define activation functions, and present SANs.
result SANs achieve small description length and interpretable kernels.
The paper uses Banach spaces to analyze neural networks.
problem Understanding the function spaces of neural networks.
method Theory of reproducing kernel Banach spaces.
result Representer theorem for wide class of Banach spaces.
SANs use sparse activation functions to minimize model complexity.
problem Model complexity in unsupervised learning.
method Introduce φ metric, define activation functions, present Sparsely Activated Networks (SANs).
result SANs with selected activation functions have small description length and interpretable kernels.
Study shows depth improves trainability of neural networks by improving kernel conditioning.
problem Improving trainability of neural networks with random initialization and overparameterization.
method Analyzes the role of depth in training neural networks, proving that depth improves conditioning of kernel matrices.
result General result showing depth improves trainability of neural networks by improving the conditioning of kernel matrices.
This paper analyzes convergence rates of neural networks in the deep learning regime.
problem Understanding convergence rates of neural networks in the deep learning regime.
method Analyzing the Neural Tangent Kernel (NTK) convergence rates in the large depth limit.
result Quantifies the impact of initialization and activation function on NTK convergence rates.
New kernels from ELU and GELU networks reveal non-trivial fixed points.
problem Understanding fixed-point dynamics in deep neural networks with ELU and GELU activations.
method Deriving covariance functions and analyzing fixed-point dynamics of ELU and GELU networks.
result ELU and GELU networks exhibit non-trivial fixed-point dynamics, explaining implicit regularization in overparameterized models.
Develops EFT for ResNets, revealing limitations of kernel-only approach.
problem Limitations of kernel-only approach in deep neural networks.
method Collective kernel EFT for pre-activation ResNets based on G-only closure hierarchy. result Numerical findings show V4 equation residual accumulates to an O(1) error. Deep neural networks and Gaussian processes are shown to be equivalent through activation functions.
problem Understanding the relationship between neural networks and Gaussian processes.
method Developing an equivalence theory based on activation functions and kernels.
result Models can be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased accuracy.
This paper improves active learning for Gaussian process regression to handle distributional uncertainty.
problem Active learning for Gaussian process regression does not guarantee accurate predictions for target distributions.
method Proposes two methods to reduce worst-case expected error for Gaussian process regression.
result Shows an upper bound of the worst-case expected squared error, suggesting finite data labels can achieve arbitrarily small error.
Wide residual networks generalize well with uniform convergence to RNTK as width increases.
problem Understanding the generalization ability of wide residual networks.
method Uniform convergence of residual network kernel to residual neural tangent kernel (RNTK).
result Generalization error converges to kernel regression error with respect to RNTK.
Proposes LAMA for principled SVDD hyperparameter estimation.
problem Estimating SVDD hyperparameters is difficult and heuristic methods are unreliable.
method LAMA (Local Active Min-Max Alignment) using active learning and kernel alignment.
result LAMA provides evidence-based estimates for SVDD hyperparameters with quality scores.
The paper connects neural networks to physics using probability theory.
problem Creating neural networks that follow physical laws.
method Applying the central limit theorem and Gaussian process theory to neural networks.
result Neural networks can be designed to obey physical laws by choosing appropriate activation functions.
Procedure removes training data dependency from deep networks, improving generalization.
problem Removing dependency on training data in deep networks for better generalization.
method Deterministic and stochastic parts to ensure forgetting, leveraging activation and weight dynamics.
result New bound on information extraction from black-box networks, ensuring forgetting in activations.
The paper develops a multi-kernel method with sparsity constraint for regression.
problem Developing a robust regression method with sparsity constraints.
method Banach-space formulation, generalized total-variation regularization, multi-kernel expansion, adaptive kernel positions, ℓ1 penalty on coefficients. result The method achieves sparsity in the kernel coefficients, reducing the number of active kernels to the number of data points.
Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.
problem Modeling equity index and spot volatility with path-dependent features and general kernels.
method Proved existence and uniqueness of a continuous solution to a Stochastic Volterra Equation (SVE) with non-convolutional, non-bounded kernels and non-Lipschitz coefficients.
result Positivity of the volatility process under certain conditions on the kernels.
GP CaKe models causal brain connectivity using Gaussian processes.
problem Understanding how one brain region drives activity in another.
method Integro-differential equations and causal kernels learned via Gaussian process regression.
result Demonstrated efficacy on simulations and MEG data.
New method preserves privacy while improving machine learning accuracy.
problem Privacy-preserving machine learning for daily data.
method Compressive Privacy and multi-kernel method.
result Improved utility classification accuracy with privacy preservation.
New active learning methods use statistical leverage scores to select examples efficiently.
problem Efficiently selecting labeled examples for high model accuracy with limited labeled data.
method Proposes ALEVS and DBALEVS methods based on statistical leverage scores.
result DBALEVS selects diverse, representative examples efficiently.
New framework establishes positivity of DNTK for PINNs.
problem Establishing positivity of NTK for PINNs with multiple differential operators.
method Proposed Differential Neural Tangent Kernel (DNTK) for PINNs.
result Positivity of infinite width DNTK for various activation functions and differential operators.
The paper provides recovery guarantees for CNNs with multiple kernels under polynomial sample and computational complexities.
problem Parameter recovery for non-overlapping CNNs with multiple kernels.
method Showed local strong convexity of squared loss for most popular activations, used tensor methods for initialization, and proved convergence of gradient descent.
result Gradient descent following tensor initialization converges to the global optimal with polynomial time complexity.
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.