ARFF reduces spectral bias in SGD-trained neural networks.
problem Spectral bias in two-layer neural networks.
method Comparison of SGD and ARFF on spectral bias and robustness.
result ARFF yields a closer to zero spectral bias compared to SGD.
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48 results for “Spectral Bias”
Study reveals how spectral bias affects learnability on real-world data.
problem Understanding how well complex datasets can be learned using kernel methods.
method Use eigenvalues and eigenfunctions from idealized data to reveal spectral bias on real-world data.
result Bound learnability on real-world data using symmetries of realistic kernels.
Efficiently scales continuous kernels with sparse Fourier domain learning.
problem High computational and memory demands, spectral bias in continuous kernels.
method Sparse learning in the Fourier domain.
result Efficient scaling of continuous kernels, reduced computational and memory requirements, mitigated spectral bias.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
FFN addresses spectral bias in neural value approximation, improving reinforcement learning performance.
problem Spectral bias in neural value approximation, leading to slow convergence and poor performance.
method Proposes Fourier feature networks (FFN) to overcome spectral bias by using a composite neural tangent kernel.
result FFN achieves state-of-the-art performance on challenging continuous control domains with faster convergence and better stability.
An intriguing phenomenon observed during training neural networks is the spectral bias, which states that neural networks are biased towards learning less complex functions. The priority of learning functions with low complexity might be at the core of explaining generalization ability of neural network, and certain ef…
Spectral decoupling improves neural network generalization in medical imaging.
problem Poor generalization of neural networks trained on medical imaging data.
method Spectral decoupling, a regularization technique that encourages learning more features.
result Spectral decoupling increases network robustness and performance on external datasets.
Deep neural networks can generalize by reducing high-frequency noise over time, not always following a monotonic learning bias.
problem Understanding the learning dynamics and generalization of over-parameterized DNNs.
method Experimental analysis of deep double descent, focusing on the spectral bias of DNNs.
result The high-frequency components of DNNs diminish over training, leading to a second descent in test error.
Analyzes how diffusion models learn, revealing a spectral bias in structure mastery.
problem Understanding the learning dynamics and bias in diffusion models.
method Developed an analytical framework using a Gaussian-equivalence principle to solve gradient-flow dynamics and integrate probability-flow ODEs.
result Exposes a universal inverse-variance spectral law: high-variance structure is mastered faster than low-variance detail.
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
problem Estimating invariant subspaces across heterogeneous multiple networks.
method Bias-corrected joint spectral embedding algorithm that recursively calibrates diagonal bias and iteratively updates the subspace estimator.
result Established entrywise subspace perturbation bound and entrywise eigenvector central limit theorem for the algorithm.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
problem Optimizing spectral risk measures for learning systems.
method Developed stochastic algorithms to optimize spectral risk measures by characterizing their subdifferential and addressing challenges like biasedness of subgradient estimates and non-smoothness.
result Our approach outperforms out-of-the-box stochastic subgradient and dual averaging methods in optimizing spectral risk measures.
Spectral regularization simplifies sequence models by focusing on grammatical simplicity.
problem Sequence modeling challenges in learning tasks.
method Introduces spectral regularization based on Hankel matrices and trace norm, addressing bi-infinite matrices with an unbiased estimator.
result Demonstrates spectral regularization's potential benefits on Tomita grammars.
Extended Gauss-Markov theorem for linear estimation with bounded bias.
problem Linear estimation with bounded bias operator.
method Derive optimal estimator formulas for Nuclear and Spectral norms, analyze generalization error.
result Cross-validated Nuclear and Spectral regressors outperform Ridge regression in simulations.
New framework explains neural network bias in solving differential equations.
problem Understanding and controlling the bias in PINNs for differential equations.
method Deriving an integro-differential equation from PINNs and GPR equivalence.
result PINN predictions are influenced by a kernel term reflecting architecture choices.
Study reveals class disparities in balanced datasets through spectral imbalance.
problem Class disparities in balanced datasets are overlooked despite model performance gaps.
method Developed a theoretical framework and studied 11 encoders to diagnose spectral imbalance.
result Identified spectral imbalance as a source of class disparities in balanced datasets.
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that …
This work analyzes how different layers in deep neural networks contribute to generalization error.
problem Understanding the role of each layer in deep neural networks for generalization.
method Spectral analysis, Neural Tangent Kernel, Hermite polynomials, Spherical Harmonics.
result Initial layers in deep neural networks have a larger bias towards high-frequency functions.
Study spectral density of neural networks using resolvent method.
problem Investigate spectral density of neural networks with random feature matrices.
method Use resolvent method from random matrix theory, cumulant expansion.
result Impossible to preserve singular value distribution with additive bias.
Adaptive spectral RL method enhances RL performance and interpretability.
problem Balancing interpretability and performance in reinforcement learning.
method Spectral based linear RL approach with adaptive regularization.
result Near-optimal bounds for parameter estimation and generalization error.
New model learns graph spectra accurately, outperforming existing methods.
problem Graph diffusion models struggle to distinguish certain graph families and their spectra.
method Leveraged random matrix theory to analytically extract spectral properties, introducing Dyson Diffusion Model.
result Dyson Diffusion Model learns graph spectra accurately and outperforms existing models.
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
SEDA improves RLDA for high-dimensional data.
problem Inconsistent performance of RLDA in high-dimensional scenarios.
method Developed a non-asymptotic approximation of misclassification rate, derived new theoretical results on eigenvectors, and proposed SEDA algorithm.
result SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.
Understanding and inverse design of implicit bias in stochastic learning: a geometric perspectivecs.LG
Geometric framework explains and controls implicit bias in machine learning.
problem Understanding and controlling the selection of solutions in overparameterized models.
method Developed a theoretical and constructive framework based on geometric corrections induced by gradient noise and continuous symmetries of the loss.
result Computed the induced bias across various architectures and enabled inverse design to shape the bias.
This work analyzes PINNs for advection-diffusion equations using NTK theory.
problem Understanding and resolving the training difficulties of PINNs for advection-diffusion equations.
method Neural Tangent Kernel (NTK) analysis of PINNs for the linear advection-diffusion equation (LAD).
result PINNs struggle due to spectral bias and convergence rate disparity, especially in advection-dominated and diffusion-dominated regimes.
Gradient descent with small random init mimics spectral methods for low-rank matrix recovery.
problem Reconstructing a low-rank matrix from few measurements.
method Gradient descent with small random initialization followed by a few iterations.
result Gradient descent from small random init converges to a well-generalizing solution.
The paper explains generalization in kernel regression and deep neural networks using spectral bias and task-model alignment.
problem Understanding generalization in machine learning models, especially deep neural networks.
method Analytical expression for generalization error derived from statistical mechanics, applied to various kernels and data distributions.
result Spectral bias and task-model alignment explain generalization in kernel regression and deep neural networks.
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
SPQR improves Q-ensemble diversity in reinforcement learning.
problem Overestimation bias in Q-learning for complex tasks.
method Introduces SPQR for Q-ensemble independence regularization.
result SPQR outperforms baseline algorithms in online and offline RL benchmarks.
A hybrid model combines diffusion and neural operator methods for stress prediction in hyperelastic materials.
problem Challenges in predicting stress fields in hyperelastic materials with complex microstructures.
method A hybrid surrogate framework combining a conditional denoising diffusion probabilistic model (cDDPM) and a modified DeepONet.
result The hybrid model consistently outperforms traditional methods by one to two orders of magnitude.
High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularizationstat.ML
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.
problem Statistical limits of learning mappings between infinite-dimensional function spaces.
method Minimax optimal regularization and multilevel training.
result Multilevel kernel operator learning achieves optimal learning rate.
Gaussian process models simplify neural network behavior for easier understanding.
problem Understanding and predicting the behavior of deep learning systems.
method Constructing surrogate models using Gaussian processes from finite neural networks.
result Surrogate models capture phenomena like spectral bias and predict generalization well.
Study shows momentum-based optimizers like Muon and MomentumGD bias towards KKT points in smooth homogeneous models.
problem Understanding the implicit bias of momentum-based optimizers on smooth homogeneous models.
method Analysis of Muon, MomentumGD, Signum, and Adam optimizers under decaying learning rate schedules.
result Momentum-based optimizers approximate steepest descent trajectories and bias towards KKT points of margin maximization problems.
Deep networks can be biased to learn top eigenfunctions of the kernel outside the training set.
problem Spectral bias of deep networks in the kernel regime.
method Quantitative bounds on difference between finite-width and infinite-width network trajectories.
result Deep networks learn top eigenfunctions of the Neural Tangent Kernel over the entire input space, not just the training set.
Quantum computers can enhance spectral methods in machine learning.
problem Spectral methods are fundamental but challenging for classical models.
method Utilizing quantum Fourier Transform for spectral manipulations.
result Quantum computing can offer more efficient spectral design.
New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.
problem Optimality gap estimation bias in risk-averse stochastic programs.
method Two independent samples, each estimating a different component of the optimality gap.
result Our method reduces bias in estimating optimality gaps for risk-averse problems.
Muon replaces matrix gradient with polar factor, optimizing flat spectrum updates
problem Optimization bias in matrix updates
method Using polar factor of gradient
result Muon update maximizes entropy among bounded updates
A new algorithm reduces bias and variance in distributionally robust optimization.
problem Distributionally robust optimization with bias and variance issues.
method Prospect, a stochastic gradient-based algorithm that reduces hyperparameter tuning.
result Prospect achieves linear convergence and 2-3x faster convergence on various benchmarks.
Quantum kernels offer potential speed-ups but require encoding problem-specific knowledge.
problem Generalization difficulty in high-dimensional feature spaces.
method Analysis of spectral properties of quantum kernels and their RKHS.
result Quantum advantage is expected if RKHS is low-dimensional and contains hard-to-compute functions.
Unified framework explains why overfitting is benign in interpolating learning.
problem Understanding why overfitting is benign in highly overparameterized models.
method Spectral-transport stability framework.
result Sharp benign-overfitting criterion and explicit phase-transition rates.
TopoNTK kernel captures higher-order interactions in simplicial complexes.
problem Graph neural networks miss higher-order interactions in relational systems.
method Introduces TopoNTK, an infinite-width kernel for simplicial message passing.
result TopoNTK captures topology invisible to graph kernels, improving expressivity and interpretability.
PolyNSD improves Neural Sheaf Diffusion with polynomial operators and spectral rescaling.
problem Limitations of common Neural Sheaf Diffusion implementations, including scalability and stability issues.
method Introduces Polynomial Neural Sheaf Diffusion (PolyNSD) with a degree-K polynomial propagation operator and spectral rescaling.
result PolyNSD achieves state-of-the-art results on both homophilic and heterophilic benchmarks with reduced runtime and memory requirements.
Frequency bias affects neural network training on non-uniform data.
problem Understanding how frequency bias impacts neural networks trained on non-uniformly distributed data.
method Used the Neural Tangent Kernel (NTK) model to explore the effect of variable density on training dynamics.
result Convergence time for learning a pure harmonic function depends on the local density at a point.
MASC balances dataset representation using affinity clustering and distribution discrepancies.
problem Representation bias in datasets due to group imbalance.
method MASC uses affinity clustering and pairwise distribution discrepancies to balance non-protected and protected groups.
result MASC effectively debiases target datasets, comparable to existing methods.
Transformers are less sensitive to input perturbations compared to other models.
problem Understanding the inductive biases of transformers and distinguishing them from other architectures.
method Identified token-wise sensitivity as a metric to explain transformers' inductive biases across different data modalities.
result Transformers have lower sensitivity than MLPs, CNNs, ConvMixers, and LSTMs, across vision and language tasks.
Spectral convergence of diffusion maps: improved error bounds and an alternative normalisationmath.ST
Improved spectral convergence bounds for diffusion maps on tori.
problem Weak theoretical error bounds for diffusion maps.
method Spatial Hardy space estimates, PDE spectral stability, Sinkhorn weights.
result Matched pointwise error bounds for spectral data and operator convergence.
Recent work has shown that tight concentration of the entire spectrum of singular values of a deep network's input-output Jacobian around one at initialization can speed up learning by orders of magnitude. Therefore, to guide important design choices, it is important to build a full theoretical understanding of the spe…