SARGAN uses GANs to fill in missing radar frequency bands.
problem Missing spectral information in low frequency radar bands.
method Generative adversarial network (GAN) trained on paired original and missing band signals.
result Initial results show promise in recovering missing spectral information.
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.
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…
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.
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix i…
Muon outperforms GD in associative memory learning by balancing frequency components.
problem Training dynamics and scaling behavior of Muon in associative memory learning.
method Study of Muon in a linear associative memory model with softmax retrieval and hierarchical frequency spectrum over query-answer pairs.
result Muon achieves exponential speedup over GD in noiseless case and superior scaling efficiency in noisy case.
Random SNNs are stable and simple, with low-frequency Fourier spectra.
problem Stability and robustness of spiking neural networks.
method Boolean function analysis and Fourier spectrum concentration.
result Random LIF-SNNs are stable and biased towards simple functions.
We analyze the frequency spectrum of quantum neural networks using algebraic methods and prove maximality results.
problem Understanding the frequency spectrum and maximality properties of quantum neural networks.
method Using Minkowski sums and algebraic descriptions, we prove maximality results for QNN architectures.
result We establish spectral invariance under area-preserving transformations, showing the frequency spectrum depends only on the area A=RL. The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. A major open issue is to verify the presence of LPPL in price sequences and to estimate the LPPL parameters. Estimation is complicated by the fact that daily LPPL returns are typically orders of magnitude smaller than measured price…
A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph …
While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such a…
Band-limited training reduces resource usage without sacrificing accuracy.
problem Resource constraints in training Convolutional Neural Networks (CNNs).
method Artificially constraining the frequency spectra of convolutional filters during training.
result CNNs can leverage lower-frequency components effectively, reducing resource usage.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.
problem Inconsistent performance of Hayashi-Yoshida estimator in high dimensions.
method Analyzed the limiting spectral distribution of the Hayashi-Yoshida estimator.
result Established the connection between the estimator's spectrum and the true covariance matrix in high dimensions.
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.
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …
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.
LEGO estimates tangent spaces more robustly than LPCA in noisy data.
problem Estimating tangent spaces in high-noise settings.
method Spectral method using graph Laplacian eigenvectors and gradient orthogonization.
result LEGO yields more robust tangent space estimates than LPCA.
Deep models generate images with missing high-frequency details.
problem Malicious use of realistic deep-generated images.
method Analysis of Fourier spectrum discrepancies between real and generated images.
result Detection method achieves up to 99.2% accuracy in classifying real and generated images.
Low frequency perturbations improve model robustness, contrary to high frequency attacks.
problem Improving model robustness against adversarial attacks.
method Systematic control of frequency components in perturbations.
result Low frequency perturbations improve model robustness, especially in white-box and black-box settings.
A new spectrum attention mechanism improves time series classification.
problem Improving robustness and classification accuracy in time series classification.
method Proposes a spectrum attention mechanism (SAM) to filter and highlight important frequency components, using L1 regularization and a tumbling window for segmentation.
result Experimental results show that the proposed SSAM method produces better feature representations and improves classification accuracy.
PhaseDNN speeds up learning of high-dimensional functions across wide frequencies.
problem Training high-dimensional functions at wide frequencies is slow and inefficient.
method Parallel DNNs with frequency-specific training and phase shifts.
result PhaseDNN achieves uniform learning across wide frequencies.
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.
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…
Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.
problem Theoretical properties of quantum machine learning models, particularly their expressive power.
method Investigated how data encoding affects the expressive power of parametrized quantum circuits.
result Quantum models can access increasingly rich frequency spectra by repeating data encoding gates, potentially making them universal function approximators.
Empirical study compares finite- and infinite-width BNNs, revealing performance differences under model mismatch.
problem Comparing BNNs with different widths due to conflicting model properties and inference intractability.
method Empirical comparison of finite- and infinite-width BNNs, analyzing performance under model mismatch.
result Increasing width can hurt BNN performance when the model is mis-specified, and finite-width BNNs generalize better under model mismatch.
Proposes a novel graph signal model using narrowband kernels.
problem Graph signals with multiple concentrated frequency regions.
method Jointly learns graph signal model parameters and coefficients.
result Joint learning improves signal interpolation accuracy.
Deep networks often capture low frequency functions, improving generalization.
problem Understanding deep learning's generalization ability.
method Showed F-Principle holds for various loss functions and applied it to differential equations.
result Deep networks capture low frequency functions, leading to better generalization.
Study on adversarial training's impact on deep neural reinforcement learning policies.
problem Vulnerability of deep neural reinforcement learning policies to imperceptible adversarial perturbations.
method Two parallel approaches: Fourier spectrum analysis and feature sensitivity measurement.
result Adversarially trained policies are more sensitive to low frequency perturbations.
TensorShield defends images from adversarial attacks using tensor decomposition.
problem Adversarial attacks on images can fool deep neural networks.
method Tensor decomposition to find low-rank approximations of images, reducing high-frequency perturbations.
result TensorShield outperforms existing methods like SLQ by 14% against FGSM attacks.
A new convolution method stabilizes GANs by learning coarse structures first.
problem Mode collapse in GANs during training.
method Soft octave convolutions that split filters into high and low frequency parts, shifting weight updates.
result Reduces mode collapse and artifacts in generated images.
Deep neural networks often fit low-frequency functions, contrary to conventional numerical schemes.
problem Understanding the implicit bias of deep neural networks in fitting training data.
method Fourier analysis perspective applied to DNNs training process.
result Deep neural networks tend to fit training data by low-frequency functions, contrary to conventional numerical schemes.
Neural network detects spectrum signals under uncertain parameters.
problem Spectrum sensing under uncertain primary user signal parameters.
method Trained neural network to detect modulated signals robustly.
result Neural network gains robustness under carrier frequency, phase, and symbol time offsets.
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.
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.
For the first time, we apply the wavelet coherence methodology on biofuels (ethanol and biodiesel) and a wide range of related commodities (gasoline, diesel, crude oil, corn, wheat, soybeans, sugarcane and rapeseed oil). This way, we are able to investigate dynamics of correlations in time and across scales (frequencie…
A new neural network separates singing voices more effectively.
problem Separating singing voices from mixed signals with high accuracy.
method MBR-FCN that processes different frequency bands with varying resolutions and filters.
result The MBR-FCN achieves better performance with fewer parameters.
Power spectral density (PSD) maps providing the distribution of RF power across space and frequency are constructed using power measurements collected by a network of low-cost sensors. By introducing linear compression and quantization to a small number of bits, sensor measurements can be communicated to the fusion cen…
We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby, we identify degenerate operators in terms of special 'polynomially growing' solutions of a corresponding static problem, wh…
We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.
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.
MSNet uses high frequency residual learning for efficient multi-scale image classification.
problem Efficient multi-scale image classification for mobile and embedded devices.
method Two network architecture: low resolution for low frequency, high resolution for high frequency residuals.
result MSNet achieves significant accuracy improvements over different base networks.
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.
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance fu…
Two econometric models forecast security volatility using various data sources.
problem Forecasting security volatility using low, high, and option data.
method Proposes two GARCH models integrating low, high, and option data.
result GARCH-Itô-OI and GARCH-Itô-IV models outperform other models in 5-minute high-frequency data.
The study finds that low frequency macroeconomic variables are more important for short-term electricity price forecasting.
problem Improving short-term forecasting of daily electricity prices using macroeconomic variables.
method Developed a Bayesian reverse unrestricted MIDAS model to account for frequency mismatch.
result Inclusion of macroeconomic low frequency variables improves short-term forecasts more than using only surveys or industrial production data.
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.