A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the paper is to extend the scattering network to allow the use of higher order nonlinear…
Neural networks learn simpler features first, then more complex ones; Fourier analysis reveals this pattern.
problem Understanding the learning dynamics of neural networks, especially with natural image data.
method Fourier analysis of translation-invariant and power-law spectra to study feature learning.
result Simple neural networks first rely on amplitude information, then phase information, and power-law spectra can accelerate learning phase information.
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…
Time-frequency (TF) representations provide powerful and intuitive features for the analysis of time series such as audio. But still, generative modeling of audio in the TF domain is a subtle matter. Consequently, neural audio synthesis widely relies on directly modeling the waveform and previous attempts at unconditio…
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
Study explores how neural networks and Transformers learn modular arithmetic with multiple inputs.
problem Understanding how neural networks and Transformers learn modular arithmetic with multiple inputs.
method Analytical characterization of features learned by neural networks and Transformers, focusing on margin maximization and Fourier spectra.
result Neural networks and Transformers require a minimum neuron count of \( m \geq 2^{2k-2} \cdot (p-1) \) to solve modular addition problems with \( k \) inputs and modulus \( p \).
In this paper, we present a reverberation removal approach for speaker verification, utilizing dual-label deep neural networks (DNNs). The networks perform feature mapping between the spectral features of reverberant and clean speech. Long short term memory recurrent neural networks (LSTMs) are trained to map corrupted…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…
The staircase property aids deep learning by guiding hierarchical feature learning.
problem Understanding how hierarchical structure influences deep learning performance.
method Defined and proved the staircase property for Boolean hypercube functions, and showed its learnability by layerwise stochastic coordinate descent.
result Staircase functions can be learned in polynomial time using layerwise stochastic coordinate descent on regular neural networks.
Recent advances in deep learning motivate the use of deep neural networks in Internet-of-Things (IoT) applications. These networks are modelled after signal processing in the human brain, thereby leading to significant advantages at perceptual tasks such as vision and speech recognition. IoT applications, however, ofte…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
We show that the error probability of reconstructing kernel matrices from Random Fourier Features for the Gaussian kernel function is at most O(R2/3exp(−D)), where D is the number of random features and R is the diameter of the data domain. We also provide an information-theoretic method-independen…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic bounds which are at odds with the empirical results. We tackle these problems an…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large datasets often make modelling periodicity untenable for otherwise powerful non-pa…
Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but…