HyFAD improves time series imputation by combining time and frequency diffusion.
problem Improve time series imputation by handling frequency-sensitive denoising and balancing global and local dynamics.
method HyFAD is a hybrid time-frequency diffusion model with frequency-aware embedding, built on DDPM paradigm.
result HyFAD achieves state-of-the-art performance in time series imputation.
SSMs have a built-in bias towards low-frequency components, which can be adjusted.
problem Frequency bias in SSMs affects their performance on long-range sequences.
method Proposed two mechanisms to tune frequency bias: scaling initialization or applying a Sobolev-norm-based filter.
result Tuning frequency bias improves SSMs' performance on long-range sequence learning tasks.
Geometrically interprets frequency in electric circuits.
problem Conventional frequency definition limitations.
method Introduces a multivector definition of frequency.
result Conventional frequency is a special case of the new framework.
Trading affects grid frequency fluctuations, making them more extreme.
problem Impact of trading on grid frequency stability.
method Analysis of frequency time series from 2011 and 2017.
result Trading modifies frequency fluctuation statistics, making large deviations more likely.
Study on frequencies of non-simple curves in surfaces of large genus.
problem Frequency of non-simple curves in surfaces of large genus.
method Expression for frequency, large genus asymptotics, comparison with previous work.
result Identify most common types of non-simple curves with K intersections.
CNNs show sensitivity to low-frequency signals due to image frequency distribution.
problem Understanding why CNNs are sensitive to low-frequency signals.
method Theoretical analysis of CNN representations in frequency space.
result CNNs sensitivity to low-frequency signals is due to the frequency distribution of natural images.
The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.
problem Understanding the behavior of parabolic frequency under Ricci flow and Ricci-harmonic flow.
method Investigates the monotonicity of parabolic frequency for solutions of linear and heat equations with bounded curvatures.
result Establishes monotonicity results for parabolic frequency under specific curvature conditions.
New method constrains CNN filter frequencies to improve robustness.
problem CNN bias towards low frequency components, leading to poor performance in scenario transformations.
method Frequency domain regularization by constraining filter spectra, training valid frequency range end-to-end.
result Demonstrated effectiveness in defending adversarial perturbations, reducing generalization gap, and improving transfer learning.
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.
Paper extends SI method for detecting CPs in complex systems' frequency domain.
problem Identifying change points in complex systems' frequency domain.
method Extends SI framework to frequency domain using DFT properties and develops valid p-values.
result Reliable detection of genuine CPs with strong statistical guarantees.
The paper defines a frequency for mean curvature flow and proves its monotonicity.
problem Backwards uniqueness for solutions of mean curvature flow.
method Defining and proving monotonicity of a parabolic frequency for mean curvature flows.
result Frequency monotonicity implies backwards uniqueness for mean curvature flow solutions.
Paper defines parabolic frequency for Ricci flow solutions, proving monotonicity and uniqueness.
problem Backwards uniqueness for solutions of parabolic equations on Ricci flows.
method Defines and proves monotonicity of parabolic frequency for Ricci flow solutions.
result Backwards uniqueness for solutions of parabolic equations on Ricci flows.
Proves monotonicity of parabolic frequency on all manifolds without curvature assumptions.
problem Monotonicity of parabolic frequency on manifolds.
method Analyzes parabolic frequency function on manifolds, proving monotonicity without curvature assumptions.
result Monotonicity of parabolic frequency on all manifolds, no curvature assumption needed.
New Fourier-based diffusion model improves high-frequency generation quality.
problem Diffusion models struggle with high-frequency details.
method Analyzed and modified the forward process in Fourier space to equalize noise corruption across frequencies.
result Improved generation quality for high-frequency components.
Proposes a conservative LR estimator for infrequent data near a frequency threshold.
problem Overestimation of likelihood ratios for infrequent data near a frequency threshold.
method Conservative likelihood ratio estimator for frequencies slightly above a threshold.
result Improves prediction accuracy in named entity context prediction.
We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronol…
Deeper neural networks learn lower frequency functions faster, according to a new principle.
problem Understanding why deeper learning is faster.
method Fourier analysis and filtering method to separate and analyze the frequency distribution of neural network outputs.
result Deeper hidden layers in neural networks bias towards lower frequency functions during training.
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
Local convolutions bias neural networks towards high-frequency adversarial examples.
problem High-frequency adversarial examples in neural networks.
method Analysis of different linear and nonlinear architectures, focusing on the impact of local convolution operations.
result Local convolutions induce an implicit bias towards high frequency features, leading to high-frequency adversarial examples.
Study shows neural networks learn low frequencies first, proposing solutions.
problem Frequency bias in neural network learning process.
method Developed a PDE to unravel frequency dynamics, used Fourier Features model.
result Appropriate weight initialization can eliminate or control frequency bias.
Deep neural networks with convolutional layers usually process the entire spectrogram of an audio signal with the same time-frequency resolutions, number of filters, and dimensionality reduction scale. According to the constant-Q transform, good features can be extracted from audio signals if the low frequency bands ar…
In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the network. The PhaseDNN utilizes the fact that many DNN achieves convergence in the low frequency range first, thus, a series of moderately-s…
Complex frequency generalizes eigenvalues in LTI systems.
problem Characterizing dynamics of signals with complex values.
method Geometric frequency interpretation and transformation analysis.
result Complex frequencies in LTI systems match eigenvalues.
The paper studies frequency monotonicity for solutions of nonlinear equations under Ricci flow.
problem Frequency monotonicity for positive solutions of nonlinear equations under Ricci flow.
method Obtained parabolic frequency monotonicity for solutions of two nonlinear parabolic equations with bounded Ricci curvature.
result Established integral type Harnack inequalities using parabolic frequency monotonicity.
Convolutional GANs favor low spatial frequencies, affecting fine detail generation.
problem Understanding GANs' limitations in high spatial frequency learning.
method Proposed method to manipulate GANs' bias against high spatial frequencies.
result Convolutional GANs have a bias against learning high spatial frequencies.
The paper introduces a frequency-domain estimator for low-order systems from noisy data.
problem Estimating frequency responses of low-order systems from noisy measurements.
method Uses a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint.
result Proves a finite-sample error bound and extends it to all frequencies through rational interpolation.
The paper explains how neural networks learn less salient frequency components during training.
problem Understanding the grokking phenomenon in neural networks.
method Empirical frequency analysis of training data.
result Neural networks initially learn less salient frequency components of the test data.
A predictor improves power grid frequency forecasts up to one hour.
problem Improving frequency forecast for better power system stability.
method Developed a weighted-nearest-neighbor (WNN) predictor.
result Forecasts for up to one hour are more precise than averaged daily profiles.
FreSh shifts model's initial frequency spectrum to match target signal, improving neural representation performance.
problem MLPs' low-frequency bias limits capturing high-frequency details accurately.
method FreSh selects embedding hyperparameters to align model's initial output spectrum with target signal's spectrum.
result FreSh improves performance across various neural representation methods and tasks with minimal computational overhead.
Generative networks improve fluid simulation quality by focusing on high frequencies.
problem Low-frequency details missing in fluid simulation reconstructions.
method Frequency-aware loss function for generative networks.
result Improved perceptual quality of fluid simulation results in mid-frequency bands.
This work analyzes how frequency components affect CNN predictions and robustness.
problem Lack of frequency-based explanation for CNNs leading to vulnerabilities.
method Frequency component analysis and quantification of their contribution to CNN predictions.
result Adversarial attacks exploit high-frequency features, while robustness comes from low-frequency associations.
New formula for instantaneous frequency in unbalanced systems.
problem Estimating frequency in unbalanced electrical systems.
method Utilizes affine differential geometry to link frequency and voltage derivatives.
result Proposes a new formula for instantaneous frequency estimation.
Paper introduces Simplet Frequency Distribution (SFD) for SCs.
problem Frequency analysis of simplets in large SCs.
method Developed SFD vector and uniform sampling-based algorithm.
result Validated theoretical bounds with experiments.
A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
problem Inconsistent starting cycles and series length issues in Fourier-based methods.
method Fourier Basis Mapping (FBM) method that integrates time-frequency features through Fourier basis expansion and mapping.
result FBM addresses inconsistencies and preserves temporal characteristics, achieving SOTA performance.
Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-of-the-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is …
A new method for modeling insurance claim frequencies using random proportions.
problem Inaccurate fitting of classical distributions to insurance claim frequency data.
method Modeling claim frequencies using random proportions of insurance contracts and applying goodness-of-fit tests.
result A new statistical approach for better modeling insurance claim frequencies.
Deep network improves electrical tomography across multiple frequencies.
problem Nonlinear multi-frequency electrical impedance tomography (mfEIT) for tissue conductivity estimation.
method Integrates graph neural networks (GNNs) into the iterative Proximal Regularized Gauss Newton (PRGN) framework to reconstruct tissue concentrations accurately.
result Accurate reconstruction of overlapping tissue fraction concentrations across multiple frequencies.
Optical DNNet boosts accuracy with multiple frequency-channels.
problem Improving the accuracy of optical neural networks.
method Developed a novel optical diffractive deep neural network with multiple frequency-channels.
result Multiple frequency-channels significantly increase network accuracy.
The paper proposes a mixed-frequency quantile regression model for VaR and ES forecasting.
problem Forecasting VaR and ES with mixed-frequency data.
method Mixed-frequency quantile regression model to estimate VaR and ES.
result The proposed model outperforms other models in VaR and ES backtesting tests.
FAL improves formation resistivity prediction from cased boreholes with noise resistance.
problem Noise and high-frequency disaster in predicting formation resistivity from cased boreholes.
method Frequency-aware framework and temporal anti-noise block for LSTM.
result FAL achieves a 24.3% improvement in R2 over LSTM, reaching R2=0.91.
SPGD improves adversarial training efficiency and accuracy.
problem Improving adversarial training efficiency and accuracy with fewer steps.
method Adversarial-sample generation from a frequency domain perspective, extending PGD to the frequency domain.
result SPGD achieves greater adversarial accuracy compared to PGD with fewer attack steps.
Method improves clarity in forecasting spatio-temporal data.
problem Forecasting spatio-temporal data with clarity and interpretability.
method Supervised semi-nonnegative matrix factorization with frequency regularization.
result Method offers clearer interpretability in forecasting spatio-temporal data.
Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal signal from a finite number of noisy samples. A recent machine-learning approach u…
Study non-parametric frequency-domain system identification from finite samples.
problem Frequency-domain system identification from limited data.
method Empirical Transfer Function Estimate (ETFE) under sub-Gaussian colored noise and stability assumptions.
result ETFE estimates are concentrated around true values with a finite-sample rate of Ntot−1/3 for all frequencies in the H∞ norm. Study describes frequencies of geodesics on hyperbolic surfaces as genus grows.
problem Large genus asymptotic behaviors of geodesic frequencies on hyperbolic surfaces.
method Proof of conjecture involving separating and nonseparating geodesics.
result Explicit function $f( rac{n}{g})$ for frequency ratio given.
Stochastic methods improve data assimilation with high-frequency sensor data.
problem Computational challenges in data assimilation with high-frequency sensor data.
method Adapted stochastic approximation methods to handle high-frequency observations.
result Produces high-quality estimates using all observations without compromising statistical accuracy.
Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.
problem Understanding and classifying system operating conditions based on electric quantity waveform distortions.
method Demonstrates equivalence between geometric frequency and Lagrange derivative through numerical examples.
result Identifies components of Lagrange derivative that relate to geometric frequency and waveform distortions.
FredNormer improves time series forecasting by adapting to frequency domain patterns.
problem Current normalization methods struggle with non-stationary time series due to their time-domain approach.
method FredNormer analyzes frequency components, adapts weights, and improves robustness.
result FredNormer boosts forecasting accuracy by 33.3% on ETTm2 dataset.