BSD is a Bayesian framework for analyzing neural spectral data.
problem Challenges in statistical analysis and group-level comparisons of neural power spectra.
method Bayesian Spectral Decomposition (BSD) for parametric models of neural spectra.
result BSD outperforms existing methods in model selection and parameter estimation.
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.
problem Limited real observations in Raman and CARS spectroscopy.
method Log-Gaussian Gamma Processes and Bayesian Neural Networks.
result Trained Bayesian neural networks provide accurate estimates of Raman and CARS spectra with uncertainty quantification.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
problem Mie scattering obscures biochemically relevant spectral information in FTIR spectra of biological samples.
method Deep neural networks to approximate the preprocessing function that removes Mie scattering.
result The model is faster and more generalizable across different tissue types.
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.
problem Understanding how neural network performance scales with key factors like data size and model complexity.
method Statistical mechanics techniques applied to one-pass stochastic gradient descent in a student-teacher framework.
result Derivation of analytical expressions for generalization error under power-law data spectra and identification of conditions for power-law scaling.
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.
problem Eigenvalue distributions of neural kernels in linear-width networks.
method Asymptotic analysis of Conjugate Kernel and Neural Tangent Kernel under random initialization and approximate orthogonality.
result Eigenvalue distributions converge to deterministic limits, described by recursive fixed-point equations.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
problem High-dimensional and incomplete tensor completion.
method Spectra-Guided Neural Tucker Factorization (SG-NTF) with Spatio-Temporal Co-Gating (STCG).
result Maintains competitive completion accuracy with parameter efficiency.
spectra2pix generates nanostructure images from spectra using DNN.
problem Designing nanostructures is complex and relies on intuition.
method Trained a DNN to infer nanostructure images from spectra.
result spectra2pix successfully designs unseen nanostructures.
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.
Investigates spectral properties of neural networks, showing invariance under certain conditions.
problem Understanding the spectral evolution and invariance in linear-width neural networks.
method Empirical and theoretical analysis of spectra of weight matrices in high-dimensional settings.
result Spectra of weight matrices are invariant under certain training conditions, with implications for feature learning.
INNs improve acceptance rates in electron spectra analysis.
problem Analyzing electron spectra from near-critical laser-plasmas.
method Invertible Neural Networks (INNs) for forward and inverse modeling.
result INNs significantly increase acceptance rates up to a factor of 10.
DeepHybrid uses radar data to classify objects accurately.
problem Challenges in classifying objects using automotive radar sensors.
method Combines radar signal processing and Deep Learning; uses neural architecture search.
result Improves object classification performance compared to models using only spectra.
SGD's training dynamics align with Hessian and gradient spectra in high-dimensional classification tasks.
problem Understanding the spectra of Hessian and gradient matrices in high-dimensional classification tasks.
method Rigorous analysis of SGD dynamics and spectra of Hessian and gradient matrices.
result SGD trajectory and emergent outlier eigenspaces align with a common low-dimensional subspace in multi-class high-dimensional mixtures and neural networks.
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.
problem Understanding the point spectra of vector fields.
method Define and study point spectra, prove properties under isometries, and analyze compactly supported fields.
result Point spectra are well-behaved under isometries and trivial for compactly supported fields.
Machine learning models simulate molecular spectra and reactions in solvents.
problem Accurate simulation of molecular spectra and reactions in solvent environments.
method Introduced FieldSchNet, a deep neural network for modeling molecular interactions with external fields.
result Demonstrated significant lowering of Claisen rearrangement reaction activation barrier using FieldSchNet.
Khovanov spectra are shown to be functorial under certain conditions.
problem Understanding functoriality of Khovanov spectra.
method Proving functoriality up to homotopy and sign for Khovanov spectra.
result Khovanov spectra are functorial under specific 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…
Method calculates spectra of Rarita-Schwinger operator on symmetric spaces.
problem Calculating spectra of the Rarita-Schwinger operator on compact symmetric spaces.
method Using Weitzenböck formulas, Laplace operator, Casimir operator, Freudenthal's formula, and branching rules.
result Obtained spectra on the sphere, complex projective space, and quaternionic projective space.
Paper presents a method to detect out-of-distribution spectra in intra-operative functional imaging.
problem Detecting out-of-distribution (OoD) spectra in multispectral optical imaging during surgery.
method Information theory-based approach using WAIC with an ensemble of INNs.
result The method is effective in detecting OoD spectra, improving the reliability of functional imaging.
Proves spectra equivalence for Riemannian manifolds.
problem Equivalence of Almgren-Pitts and phase-transition half-volume spectra.
method Proof of spectra equivalence for Riemannian manifolds.
result Confirms conjecture about spectra equivalence.
We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.
Paper resolves decades-old problem about L-spectra.
problem Identifying L-spectra local information with geometric data. method Proved equivalence of L-orientations and characteristic classes. result Levitt-Ranicki's theory equivalent to Brumfiel-Morgan's classes.
Study calculates spectra of minimal hypersurfaces in hyperbolic space.
problem Computing Laplacian spectra of minimal hypersurfaces.
method Analyzes hypersurfaces in hyperbolic space with specific asymptotic data.
result Obtains spectra and extremal properties of the bottom of the spectrum.
New metrics compare rational spectra using optimal transport.
problem Comparing rational spectra efficiently and accurately.
method Optimal transport and linear-systems theory.
result Established connection to Wasserstein distance.
Study how bottom of spectra changes with Riemannian coverings.
problem Behavior of bottom of spectra under Riemannian coverings.
method Analysis of scalar Schrödinger operators on Riemannian manifolds.
result Changes in the bottom of spectra observed under coverings.
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.
problem Inaccurate separation of sources with temporal autocorrelations and mixed spectra.
method Estimates spectral density functions and line spectra using cubic splines and indicator functions, then maximizes the Whittle likelihood function.
result Outperforms existing ICA methods in simulations and EEG data applications.
Jones-Wenzl projectors lifted to Khovanov spectra, proving knot conjectures.
problem Understanding Jones-Wenzl projectors in Khovanov spectra.
method Constructing and studying lifted projectors via maps and polynomial actions.
result Complete computation of 3-colored Khovanov spectrum of the unknot, proving conjectures.
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.
problem Computing Khovanov spectra for diagrams without alternating pairs.
method Functor from cube to Burnside 2-category, decomposition into simplicial complexes.
result Homotopy type of almost-extreme Khovanov spectra computed.
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.
problem Constructing the Bauer--Furuta invariant without finite-dimensional approximations.
method Using sheaves of spectra and Borel--Moore homology, avoiding approximations.
result Defines the shriek functors and Thom spectra for index calculations.
Study on sine-cones' spectra and stability under Ricci-de Turck flow.
problem Analyzing stability and rigidity of sine-cones.
method Computed spectra of specific operators on sine-cones.
result Conditions for sine-cones' dynamic stability and rigidity.
We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…
The paper proves geometric and spectral alignment for deep neural networks.
problem Understanding the singular spectra of deep neural network layers.
method Proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors.
result Exact power-law spectra form a trace-normalized Cartan orbit under Frobenius normalization.
The paper describes correlations of spectra for higher rank Anosov representations.
problem Understanding correlations of spectra for Anosov representations of higher rank groups.
method Relates correlation problem to counting projections in truncated hypertubes.
result Extends previous work on rank one representations to higher rank.
Formulas for spectra of higher spin operators on sphere subbundles.
problem Finding spectra of higher spin operators on specific subbundles of spinor-valued tensors.
method Explicit formulas derived for spectra in both even and odd dimensions.
result Spectra formulas for higher spin operators and their squares.
Study bottom of spectra on orbifolds via coverings.
problem Behavior of bottom of spectra under orbifold coverings.
method Analysis of scalar Schrödinger operators on orbifolds.
result Results apply to geometrically finite and conformally compact orbifolds.
Integrally splits L-spectra of integers into simpler components.
problem Understanding the homotopy type of L-spectra of integers.
method Using Anderson duality and splitting into simpler spectra.
result 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…