arXiv research

Paper introduces a new time separation function for $C^0$ spacetimes.

Spectral analysis shows neural networks separate from linear methods in approximating functions.

Single-microphone, speaker-independent speech separation is normally performed through two steps: (i) separating the specific speech sources, and (ii) determining the best output-label assignment to find the separation error. The second step is the main obstacle in training neural networks for speech separation. Recent…

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

The article finds conditions for separating filling pairs on surfaces and constructs a Morse function.

Study on size and depth of neural networks for approximating benign functions, showing barriers and explicit results.

PPG separates policy and value function training phases for better reinforcement learning efficiency.

This paper proposes RAS, a novel unsupervised loss function for speech separation.

Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.

We give effective proofs of residual finiteness and conjugacy separability for finitely generated nilpotent groups. In particular, we give precise asymptotic bounds for a function introduced by Bou-Rabee that measures how large the quotients that are need to separate non-identity elements of bounded length from the ide…

TSL learns separable models to avoid signal cancellation and off-support extrapolation.

We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $ε:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$ for which $|f(x)-g(x)|\leqε(x)$ and $g'(x)\neq 0$ for all $x\in X$ (that is, $g$ has no…

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separab…

This paper extends depth separation results to piece-wise oscillatory functions.

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $ε:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leqε(p)$ for every …

Existing depth separation results for constant-depth networks essentially show that certain radial functions in $\mathbb{R}^d$, which can be easily approximated with depth $3$ networks, cannot be approximated by depth $2$ networks, even up to constant accuracy, unless their size is exponential in $d$. However, the func…

Study on self-similar sets on Riemannian manifolds with new separation conditions.

New algorithms reduce slate bandit regret for large slates, outperforming existing methods.

While there has been much recent progress using deep learning techniques to separate speech and music audio signals, these systems typically require large collections of isolated sources during the training process. When extending audio source separation algorithms to more general domains such as environmental monitori…

Sound source separation has attracted attention from Music Information Retrieval(MIR) researchers, since it is related to many MIR tasks such as automatic lyric transcription, singer identification, and voice conversion. In this paper, we propose an intuitive spectrogram-based model for source separation by adapting U-…

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring…

Proves depth 2 neural networks can't approximate certain functions as well as depth 3 networks.

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting challenging. For example, Gaussian graphical models have recently been extended to the…

In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard splitting, we show that an incompressible subsurface of the Heegaard splitting can be found, by decomposing the 3-manifold along the separating …

In this paper, we propose a two-step training procedure for source separation via a deep neural network. In the first step we learn a transform (and it's inverse) to a latent space where masking-based separation performance using oracles is optimal. For the second step, we train a separation module that operates on the…

Speech separation refers to extracting each individual speech source in a given mixed signal. Recent advancements in speech separation and ongoing research in this area, have made these approaches as promising techniques for pre-processing of naturalistic audio streams. After incorporating deep learning techniques into…

Develops large-sample theory for non-stationary source separation.

Introduces Soft-SVM for binary classification bridging logistic and SVM.

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of nodes in networks with two hidden layers such that linear separabili…

Enhances CNN feature extractors' separation capacity analysis.

Diffusion models can memorize training data, limiting their creativity and privacy.

New findings on depth vs. width in neural networks, showing depth can improve learnability.

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

New indices for determining cluster compactness and separability.

The paper introduces toric separable geometries and finds new extremal metrics.

The paper uses deep neural networks to estimate economic models without separability restrictions.

The Stone-Weierstrass theorem aids in solving inverse problems on specific manifolds.

Among all $C^\infty$-algebras we characterize those which are algebras of smooth functions on smooth separable Hausdorff manifolds.

New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.

DDICA separates nonlinear mixed signals robustly.

Classifies polynomial growth solutions to drift-harmonic equations on asymptotically paraboloidal manifolds.

Paper calculates distances between strata in Teichmüller space, proving a constant separation.

Classifies zero mean curvature surfaces in Lorentz-Minkowski space.

Gradient descent converges with arbitrary stepsize for separable data under Fenchel-Young losses.

We propose a new blind source separation algorithm based on mixtures of alpha-stable distributions. Complex symmetric alpha-stable distributions have been recently showed to better model audio signals in the time-frequency domain than classical Gaussian distributions thanks to their larger dynamic range. However, infer…

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both funct…

This work introduces sequential neural beamforming, which alternates between neural network based spectral separation and beamforming based spatial separation. Our neural networks for separation use an advanced convolutional architecture trained with a novel stabilized signal-to-noise ratio loss function. For beamformi…