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.
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.
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
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.
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.
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.
Ill-posed inverse problems in imaging remain an active research topic in several decades, with new approaches constantly emerging. Recognizing that the popular dictionary learning and convolutional sparse coding are both essentially modeling the high-frequency component of an image, which convey most of the semantic in…
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.
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 …
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.
FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.
problem Effective representation and learning of high-frequency features in neural networks.
method Introduces FMMNN with sine-type activations and multi-component, multi-layer structure.
result FMMNN achieves strong accuracy and favorable convergence on oscillatory function-approximation benchmarks.
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.
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.
Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable charac…
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.
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.
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.
This paper analyzes the multi-armed bandit problem using frequency-domain methods.
problem The exploration-exploitation trade-off in sequential decision-making.
method Proposes a frequency-domain analysis framework, reformulating the bandit process as a signal processing problem.
result Confidence bound term in UCB algorithm is equivalent to a time-varying gain in frequency domain.
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.
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.
New DMEM models forecast volatility combining low- and high-frequency data.
problem Modeling realized volatility with both short- and long-term features.
method Doubly Multiplicative Error (DMEM) models combining daily and long-term data.
result DMEM models outperform existing GARCH-type models in forecasting.
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…
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
In this paper, we study the adversarial attack and defence problem in deep learning from the perspective of Fourier analysis. We first explicitly compute the Fourier transform of deep ReLU neural networks and show that there exist decaying but non-zero high frequency components in the Fourier spectrum of neural network…
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most important feature is the ability to take into account lead-lag relations …
In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid's Stock Exchange IBEX35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum which is most likely caused by its long memory. Our findings also show that this lo…
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.
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.
Robustly detects jumps in high-frequency CIR and CKLS models.
problem Jump detection in high-frequency jump-diffusion processes.
method MDPDE-based robust estimators for drift and diffusion coefficients.
result Maximum of normalized residuals converges to Gumbel distribution.
This paper presents a learning method for convolutional autoencoders (CAEs) for extracting features from images. CAEs can be obtained by utilizing convolutional neural networks to learn an approximation to the identity function in an unsupervised manner. The loss function based on the pixel loss (PL) that is the mean s…
Paper proposes a risk index combining frequency and severity of abnormal driving patterns.
problem Assessing driver risk based on telematics data.
method Combines frequency of abnormal driving patterns with severity quantified through tail rarity.
result Developed a risk index that enables reliable discrimination and ranking of drivers.
GNIs induce a regulariser that penalizes high-frequency components in neural network activations.
problem Understanding the regularizing effect of Gaussian noise injections on neural network activations.
method Deriving the explicit regularizer by marginalizing out injected noise and analyzing its effect in the Fourier domain.
result GNIs induce a regularizer that produces calibrated classifiers with large margins.
MPTE uses Transformer attention to estimate mixed-frequency factor models.
problem Estimating factor models in panel datasets with mixed frequencies and nonlinear signals.
method Mixed-Panels-Transformer Encoder (MPTE) with attention mechanisms.
result MPTE achieves competitive performance in nonlinear forecasting environments.
The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of these filters and data, called band-limiting, during training. The frequency dom…
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of DNNs. In this work, for both real and synthetic datasets, we empirically find that a…
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.
Explicitly taking into account the risk incurred when borrowing at a shorter tenor versus lending at a longer tenor ("roll-over risk"), we construct a stochastic model framework for the term structure of interest rates in which a frequency basis (i.e. a spread applied to one leg of a swap to exchange one floating inter…
We present a novel high frequency residual learning framework, which leads to a highly efficient multi-scale network (MSNet) architecture for mobile and embedded vision problems. The architecture utilizes two networks: a low resolution network to efficiently approximate low frequency components and a high resolution ne…
Study reveals how neural network biases align with adversarial attack frequencies.
problem Correlation between neural network biases and adversarial attacks.
method Fourier transform analysis of network implicit bias and adversarial perturbations.
result Network bias and adversarial attack frequencies are highly correlated.
Proposes a deep spectral Q-learning for mobile health data.
problem Personalized treatment assignment for patients with time-varying covariates.
method Integrates PCA with deep Q-learning for mixed frequency data.
result Mean return converges to optimal under estimated optimal policy.
Calibrates carbon futures option pricing using high-frequency data.
problem Estimating equity and variance risk premia for carbon futures options.
method Multifactor stochastic volatility framework with jumps, employing indirect inference.
result Provides insights into carbon futures and option dynamics.
FreDN separates trends and periodicities in non-stationary time series forecasts.
problem Spectral entanglement and computational burden in frequency-domain methods for non-stationary time series.
method FreDN introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain, and uses a ReIm Block to reduce complexity.
result FreDN outperforms state-of-the-art methods by up to 10% on long-term forecasting benchmarks.
This paper proposes a method for generating speech from filterbank mel frequency cepstral coefficients (MFCC), which are widely used in speech applications, such as ASR, but are generally considered unusable for speech synthesis. First, we predict fundamental frequency and voicing information from MFCCs with an autoreg…
Novel method separates astrophysical components from noisy data.
problem Separating and reconstructing astrophysical components from noisy data.
method Latent-space field tension for automated component separation.
result High accuracy in reconstructing astrophysical components.
Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work, we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased…
SKI speeds up Toeplitz Neural Networks by avoiding explicit decay bias and using frequency response.
problem Efficiently compute and update Toeplitz matrices in neural networks.
method Sparse plus low-rank decomposition, asymmetric SKI, frequency response modeling.
result Achieved significant speedup with minimal performance loss.
FRA-Attack improves adversarial transferability for closed-source MLLMs by aligning visual focus across models.
problem Improving adversarial transferability for closed-source MLLMs, especially with high accuracy.
method Unified frequency-domain regularization approach: high-pass DCT objective for feature alignment and Frequency-domain Gradient Regularization (FGR) for gradient optimization.
result FRA-Attack achieves superior cross-model transferability, especially on GPT-5.4, Claude-Opus-4.6, and Gemini-3-flash.
Model-based reinforcement learning has been empirically demonstrated as a successful strategy to improve sample efficiency. In particular, Dyna is an elegant model-based architecture integrating learning and planning that provides huge flexibility of using a model. One of the most important components in Dyna is called…