arXiv research

Autoencoder estimates parameters of noisy, multi-component damped signals.

Paper proposes robust LAD estimators for 2D sinusoidal model, proving consistency and normality.

A new neural network improves frequency estimation from noisy signals.

Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8-12 Hz) are known to closely resemble short sinusoids, and thus are revealed by Fouri…

It is well-known that the robustness of artificial neural networks (ANNs) is important for their wide ranges of applications. In this paper, we focus on the robustness of the classification ability of a spiking neural network which receives perturbed inputs. Actually, the perturbation is allowed to be arbitrary styles.…

Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.

WaveQ uses sinusoidal regularization to optimize deep quantization for neural networks, improving both efficiency and accuracy.

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid. Theoretical …

The fundamental frequency (F0) represents pitch in speech that determines prosodic characteristics of speech and is needed in various tasks for speech analysis and synthesis. Despite decades of research on this topic, F0 estimation at low signal-to-noise ratios (SNRs) in unexpected noise conditions remains difficult. T…

This paper explores robust recovery of a superposition of $R$ distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of $2N-1$ dimensional and $R<<2N-1$. This framework covers a large class of signals arising from real applications in biology, automation,…

A new KAN variant uses sinusoidal activations to approximate functions.

Alternative wavelet analysis method for financial signals.

We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…

A new method uses sinusoidal functions to represent timestamps as dense vectors for improving irregularly sampled time series learning.

A multiple classifiers fusion localization technique using received signal strengths (RSSs) of visible light is proposed, in which the proposed system transmits different intensity modulated sinusoidal signals by LEDs and the signals received by a Photo Diode (PD) placed at various grid points. First, we obtain some {\…

Principal component analysis (PCA) is a popular method for projecting data onto uncorrelated components in lower dimension, although the optimal number of components is not specified. Likewise, multiple signal classification (MUSIC) algorithm is a popular PCA-based method for estimating directions of arrival (DOAs) of …

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement uncertainties for arbitrary error models (not just Gaussian) on both the time and signal var…

Deep quantization of neural networks (below eight bits) offers significant promise in reducing their compute and storage cost. Albeit alluring, without special techniques for training and optimization, deep quantization results in significant accuracy loss. To further mitigate this loss, we propose a novel sinusoidal r…

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis (kernel PCA). Kernel trick is to define a kernel function which relies on the inner-…

Paper revises power theory using classical mechanics concepts.

Compressive sensing (CS) has been studied and applied in structural health monitoring for wireless data acquisition and transmission, structural modal identification, and spare damage identification. The key issue in CS is finding the optimal solution for sparse optimization. In the past years, many algorithms have bee…

The paper explores the problem of \emph{spectral compressed sensing}, which aims to recover a spectrally sparse signal from a small random subset of its $n$ time domain samples. The signal of interest is assumed to be a superposition of $r$ multi-dimensional complex sinusoids, while the underlying frequencies can assum…

The study proposes a new interest rate model that captures long-term periodicity in U.S. Treasury yields.

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…

RI-DeepONet learns neural operators from arbitrary sensor data.

Numerical simulations show stability of Type-II singularities in noncompact hypersurfaces.

New method for Transformer models to encode position information without sequential bias.

Paper designs a penalty for model order selection using information criteria.

New algorithm trains deep neural networks without global optimization.

In the recent years Generative Adversarial Networks (GANs) have demonstrated significant progress in generating authentic looking data. In this work we introduce our simple method to exploit the advancements in well established image-based GANs to synthesise single channel time series data. We implement Wasserstein GAN…

In this paper, we introduce a novel method to interpret recurrent neural networks (RNNs), particularly long short-term memory networks (LSTMs) at the cellular level. We propose a systematic pipeline for interpreting individual hidden state dynamics within the network using response characterization methods. The ranked …

Periodic activation functions improve neural network reliability and interpretability.

Learning to infer Bayesian posterior from a few-shot dataset is an important step towards robust meta-learning due to the model uncertainty inherent in the problem. In this paper, we propose a novel Bayesian model-agnostic meta-learning method. The proposed method combines scalable gradient-based meta-learning with non…

Neural networks struggle with periodic functions, a new activation fixes this.

Gradient-EM Bayesian meta-learning accelerates adaptation with reduced computation and improved robustness.

Exploiting the fact that most arrival processes exhibit cyclic behaviour, we propose a simple procedure for estimating the intensity of a nonhomogeneous Poisson process. The estimator is the super-resolution analogue to Shao 2010 and Shao & Lii 2011, which is a sum of $p$ sinusoids where $p$ and the frequency, amplitud…

Paper uses DMD to embed time in spatiotemporal forecasting.

Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.

Time-aware deep learning methods improve spatial downscaling of atmospheric pollutants.

Paper introduces a new method for Transformers with linear complexity.

EmDT generates synthetic fraud data to improve detection accuracy.

Symmetry-regularized Neural ODEs improve model stability and interpretability.

The gauge theory of arbitrage was introduced by Ilinski in [arXiv:hep-th/9710148] and applied to fast money flows in [arXiv:cond-mat/9902044]. The theory of fast money flow dynamics attempts to model the evolution of currency exchange rates and stock prices on short, e.g.\ intra-day, time scales. It has been used to ex…

This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount of training data. Concretely, we consider Kolmogorov-optimal approximation through deep neural networks with the guiding theme being a relat…

The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional sinusoids, while the underlying frequencies can assume any value in the unit disk…

Estimation of functions of $d$ variables is considered using ridge combinations of the form $\textstyle\sum_{k=1}^m c_{1,k} φ(\textstyle\sum_{j=1}^d c_{0,j,k}x_j-b_k)$ where the activation function $φ$ is a function with bounded value and derivative. These include single-hidden layer neural networks, polynomials, …

A new geometry for comparing signals, overcoming traditional limitations.

Paper presents a unique method to recover signals from their bispectrum.