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.
BSD is a Bayesian framework for analyzing neural spectral data.
This paper proposes a new loss using short-time Fourier transform (STFT) spectra for the aim of training a high-performance neural speech waveform model that predicts raw continuous speech waveform samples directly. Not only amplitude spectra but also phase spectra obtained from generated speech waveforms are used to c…
Proposes a method for training Bayesian neural networks using synthetic data from Raman and CARS spectra.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
Are neural networks biased toward simple functions? Does depth always help learn more complex features? Is training the last layer of a network as good as training all layers? How to set the range for learning rate tuning? These questions seem unrelated at face value, but in this work we give all of them a common treat…
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
When confronted with a substance of unknown identity, researchers often perform mass spectrometry on the sample and compare the observed spectrum to a library of previously-collected spectra to identify the molecule. While popular, this approach will fail to identify molecules that are not in the existing library. In r…
Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects -- typically neglected by conventional quan…
Study eigenvalue distributions of neural kernels for linear-width networks.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
Neural networks learn simpler features first, then more complex ones; Fourier analysis reveals this pattern.
Investigates spectral properties of neural networks, showing invariance under certain conditions.
INNs improve acceptance rates in electron spectra analysis.
DeepHybrid uses radar data to classify objects accurately.
SGD's training dynamics align with Hessian and gradient spectra in high-dimensional classification tasks.
We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology is very flexible: adapting to different signal and noise models only requires m…
Investigates point spectra of vector fields and their properties.
Machine learning models simulate molecular spectra and reactions in solvents.
Khovanov spectra are shown to be functorial under certain conditions.
In this work a novel method to quantify spectral ergodicity for random matrices is presented. The new methodology combines approaches rooted in the metrics of Thirumalai-Mountain (TM) and Kullbach-Leibler (KL) divergence. The method is applied to a general study of deep and recurrent neural networks via the analysis of…
As in many other scientific domains, we face a fundamental problem when using machine learning to identify proteins from mass spectrometry data: large ground truth datasets mapping inputs to correct outputs are extremely difficult to obtain. Instead, we have access to imperfect hand-coded models crafted by domain exper…
The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural networks (DNNs), we reveal their characteristic scale dependence on the network width, …
We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's funct…
Proves spectra equivalence for Riemannian manifolds.
We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.
Study calculates spectra of minimal hypersurfaces in hyperbolic space.
Paper resolves decades-old problem about -spectra.
New metrics compare rational spectra using optimal transport.
In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compar…
Tomova, along with results of Bachman and Schleimer, showed that any high distance knot has a stair-step bridge spectrum. In this paper, we compute the bridge spectra and distance of generalized Montesinos knots. In particular, we produce the first example of a class of knots which attain the stair-step bridge spectra …
New ICA method for sources with mixed spectra.
Jones-Wenzl projectors lifted to Khovanov spectra, proving knot conjectures.
We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using the Freudenthal's f…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…
Functor decomposes Khovanov spectra for non-alternating diagrams.
Convolutional neural networks (CNNs) attained a good performance in hyperspectral sensing image (HSI) classification, but CNNs consider spectra as orderless vectors. Therefore, considering the spectra as sequences, recurrent neural networks (RNNs) have been applied in HSI classification, for RNNs is skilled at dealing …
Novel construction of Bauer--Furuta invariant using sheaves of spectra.
Study on sine-cones' spectra and stability under Ricci-de Turck flow.
We prove explicit upper and lower bounds for the -moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds in ambient Riemannian spaces . We assume that and both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…
The paper proves geometric and spectral alignment for deep neural networks.
The paper describes correlations of spectra for higher rank Anosov representations.
Formulas for spectra of higher spin operators on sphere subbundles.
Study bottom of spectra on orbifolds via coverings.
Integrally splits L-spectra of integers into simpler components.
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…
The design of the nanostructures that are used in the field of nano-photonics has remained complex, very often relying on the intuition and expertise of the designer, ultimately limiting the reach and penetration of this groundbreaking approach. Recently, there has been an increasing number of studies suggesting to app…
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
Manifold methods improve amino acid classification in LIBS spectra.