AaSP improves audio self-supervised learning by addressing aliasing issues.
problem Alias issues in audio spectrogram transformers.
method AaSP combines aliasing-aware patch representation, teacher-student masked modeling, cross-attention predictor, and contrastive regularization.
result AaSP learns more stable representations that integrate high-frequency cues.
We present techniques for effective Gaussian process (GP) modelling of multiple short time series. These problems are common when applying GP models independently to each gene in a gene expression time series data set. Such sets typically contain very few time points. Naive application of common GP modelling techniques…
Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrica…
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains.…
We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance kernels, the core of our proposal is to model power spectral densities through a rect…
This paper presents a deep learning method for faster magnetic resonance imaging (MRI) by reducing k-space data with sub-Nyquist sampling strategies and provides a rationale for why the proposed approach works well. Uniform subsampling is used in the time-consuming phase-encoding direction to capture high-resolution im…
We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured b…
Decreasing magnetic resonance (MR) image acquisition times can potentially reduce procedural cost and make MR examinations more accessible. Compressed sensing (CS)-based image reconstruction methods, for example, decrease MR acquisition time by reconstructing high-quality images from data that were originally sampled a…
Abstract: A new approach to technical indicators without lag.
problem Defining classical technical indicators as bounded operators for lag-free trading.
method Using linear algebra to redefine technical indicators as bounded operators in l∞(N) space. result Demonstrated the no-lag versions of technical indicators are simpler and more effective.
Conventional approaches of sampling signals follow the celebrated theorem of Nyquist and Shannon. Compressive sampling, introduced by Donoho, Romberg and Tao, is a new paradigm that goes against the conventional methods in data acquisition and provides a way of recovering signals using fewer samples than the traditiona…
We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated from the mixture. The problem is well-studied in the parametric setting, i.e., w…
Have you ever felt miserable because of a sudden whipsaw in the price that triggered an unfortunate trade? In an attempt to remove this noise, technical analysts have used various types of moving averages (simple, exponential, adaptive one or using Nyquist criterion). These tools may have performed decently but we show…
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three approximate algorithms are presented: a binary quadratic programming (BQP) algorit…
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.
Observations of astrophysical objects such as galaxies are limited by various sources of random and systematic noise from the sky background, the optical system of the telescope and the detector used to record the data. Conventional deconvolution techniques are limited in their ability to recover features in imaging da…
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.
This work introduces uncertainty principles to mitigate Maximal Extractable Value in blockchain systems.
problem Maximal Extractable Value (MEV) in decentralized systems due to transaction submission privacy and monopolist power.
method Unified approaches via uncertainty principles, akin to harmonic analysis and physics, to quantify trade-offs between transaction flexibility and user economic payoff.
result Demonstrates a quantitative trade-off between transaction flexibility and user economic payoff, analogous to the Nyquist-Shannon sampling theorem.
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.
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.
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.
We prove monotonicity of a parabolic frequency on manifolds. This is a parabolic analog of Almgren's frequency function. Remarkably we get monotonicity on all manifolds and no curvature assumption is needed. When the manifold is Euclidean space and the drift operator is the Ornstein-Uhlenbeck operator this can been see…
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.