Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
EDLP samples flat modes in discrete spaces using entropy.
problem Sampling flat modes in discrete spaces is challenging.
method EDLP uses a continuous auxiliary variable and local entropy to guide sampling.
result EDLP consistently outperforms traditional methods in various tasks.
Estimates modes and ridges in mixed Euclidean and directional spaces.
problem Estimating local modes and density ridges in product spaces combining Euclidean and directional metrics.
method Extends mean shift algorithm to product spaces, addressing challenges in generalization.
result Established convergence of the proposed methods and demonstrated effectiveness on real-world datasets.
Modified PCA algorithm with continual learning preserves features of previous modes for multimode process monitoring.
problem Catastrophic forgetting of previous modes in monitoring models for successive modes.
method Modified PCA algorithm with elastic weight consolidation (EWC) to preserve features of previous modes.
result PCA-EWC algorithm effectively monitors multimode processes without performance decrease.
cKAM improves adaptive sampling by incorporating a cyclical stepsize scheme.
problem Adaptive Metropolis algorithms can get stuck in local modes.
method cKAM uses a cyclical stepsize scheme to encourage exploration and escape from local modes.
result cKAM successfully escapes local modes and converges to the true posterior distribution.
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
Simple mode exploration methods do not improve performance in neural networks.
problem Improving predictive probabilities in neural networks.
method Exploring local regions around diverse solutions using simple methods.
result Simple mode exploration methods do not improve performance.
An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…
BDMBC clusters data with varying densities using a new PLLS measure.
problem Finding clusters with varying densities in data.
method Bagged k-distance with PLLS for mode estimation. result BDMBC achieves optimal convergence rates for mode and level set estimation.
Proves stability of gravitational instantons, proving operator positivity.
problem Stability of gravitational instantons.
method Riemannian analog of black hole mode stability for Hermitian, non-self-dual gravitational instantons.
result Teukolsky equation is a positive definite operator on Hermitian, non-self-dual gravitational instantons.
Neural networks can learn optimal auction mechanisms and satisfy mode connectivity.
problem Optimal auction design in complex settings.
method Generalized RochetNet and affine maximizer auctions.
result Neural networks (RochetNet and generalized version) satisfy mode connectivity.
Study on mode stability of gravitational instantons of type D.
problem Proving mode stability of gravitational instantons of type D.
method Analogous to Lorentzian case, analyze Weyl curvature scalars satisfying a separable Teukolsky equation.
result Prove mode stability, showing no solutions compatible with regularity and asymptotic flatness.
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose a test based on the bootstrap for the significance of the estimated local modes …
With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the secto…
In this paper, we show that Generative Adversarial Networks (GANs) suffer from catastrophic forgetting even when they are trained to approximate a single target distribution. We show that GAN training is a continual learning problem in which the sequence of changing model distributions is the sequence of tasks to the d…
New geometric approach realizes 5D bulk theories with 4D edge modes.
problem Realizing novel higher-dimensional junctions of theories coupled to localized edge modes.
method M-theory on singular, asymptotically conical G2-holonomy orbifolds.
result Geometric approach shows how bulk generalized symmetries are inherited in the boundary system.
HiSS sampling overcomes local mode traps in rugged discrete spaces.
problem Sampling multimodal discrete distributions with gradient-based methods.
method Integrates Metropolis-within-Gibbs framework with logistic convolution.
result HiSS outperforms alternatives on various tasks, including Ising models and binary neural networks.
Many generative models have to combat missing modes. The conventional wisdom to this end is by reducing through training a statistical distance (such as f-divergence) between the generated distribution and provided data distribution. But this is more of a heuristic than a guarantee. The statistical distanc…
Bayesian taut splines estimate modes in probability densities.
problem Estimating the number of modes in probability density functions.
method Bayesian inference with flexible kernel estimators and compositional splines.
result The new method provides more accurate results than traditional approaches.
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
Proposes neuron alignment to optimize mode connectivity in neural networks.
problem Understanding and optimizing mode connectivity in deep neural networks.
method Introduces neuron alignment to approximate optimal weight permutations and improve mode connectivity.
result Neuron alignment significantly alleviates robust loss barriers and improves model robustness and accuracy.
The paper studies kernel smoothing and mean shift for directional data, deriving convergence rates and mode estimation.
problem Statistical and computational problems of kernel smoothing for directional data.
method Generalization of mean shift to directional data, derivation of convergence rates, and investigation of mode estimation.
result Statistical convergence rates of directional KDE and its derivatives, ascending property of directional mean shift, and mode estimation.
End-to-end training of DBMs with improved gradient estimation.
problem Biased gradient estimation in DBMs, especially with high-dimensional states.
method Unbiased contrastive divergence using MH coupling and local mode initialization.
result End-to-end training of DBMs without greedy pretraining, achieving FID score of 10.33 for MNIST.
Jeffreys Flow improves robustness of Boltzmann generators for rare event sampling.
problem Rare events and metastable trapping in sampling physical systems with rough energy landscapes.
method Introduces Jeffreys Flow, a robust generative framework using Parallel Tempering distillation and symmetric Jeffreys divergence to mitigate mode collapse and improve mode coverage.
result Minimizing Jeffreys divergence suppresses mode collapse and corrects inaccuracies in multi-modal distributions.
Study reveals issues with neural autoregressive models and proposes mode recovery cost.
problem Unreasonable affinity of neural autoregressive models to short and long sequences.
method Investigates modes of ground-truth, empirical, and decoding-induced distributions via mode recovery cost.
result Mode recovery cost varies depending on ground-truth distribution and impacts decoding-induced distribution.
Neurons predict future scalar inputs by learning top modes of lag vectors.
problem Predicting future scalar inputs with physiological delays.
method Normal Mode Decomposition to extract independently evolving modes.
result Temporal filters of neurons correspond to left eigenvectors of a generalized eigenvalue problem.
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
Sampling from posterior distributions using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations, particularly when the posterior is multi-modal as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC…
We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the η invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set o…
The Generative Adversarial Networks (GANs) have demonstrated impressive performance for data synthesis, and are now used in a wide range of computer vision tasks. In spite of this success, they gained a reputation for being difficult to train, what results in a time-consuming and human-involved development process to u…
A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.
problem Learning principal variations of random probability measures under Wasserstein geometry.
method Introducing a new dynamical formulation of log-PCA as a variational approach.
result Deriving a general statistical convergence rate for empirical WT-PCA.
Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the…
We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring Cq[SL2] at odd roots of unity and with its standard 4-dimensional differential structure. We find that H1 and H3 have three additional modes beyond the generic q-case where they are 1-dimensional, while $H…
Periodic surfaces have a limited number of bending modes, equal to their membrane modes.
problem Understanding the limitations of bending modes in periodic surfaces.
method Analyzing deformation modes of periodic, piecewise smooth, simply connected surfaces.
result Effective membrane modes and bending modes are orthogonal, limiting the total number of modes to 3.
Detrended fluctuation analysis (DFA) is a simple but very efficient method for investigating the power-law long-term correlations of non-stationary time series, in which a detrending step is necessary to obtain the local fluctuations at different timescales. We propose to determine the local trends through empirical mo…
Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range and distribution of weights in the current-mode design, it is shown that any we…
Unsupervised domain adaptation methods aim to alleviate performance degradation caused by domain-shift by learning domain-invariant representations. Existing deep domain adaptation methods focus on holistic feature alignment by matching source and target holistic feature distributions, without considering local feature…
SPECTRE uses spectral conditioning to generate larger graphs without mode collapse.
problem Overcoming expressivity and mode collapse in one-shot graph generators.
method SPECTRE generates graph Laplacian spectrum and eigenvectors to model graph structure.
result SPECTRE outperforms state-of-the-art deep autoregressive generators in fidelity and speed.
Proves a function's locally least gradient property if its level sets are minimal laminations.
problem Understanding the relationship between 1-harmonic functions and minimal laminations.
method Analyzes minimal laminations and their convergence properties, then applies to 1-harmonic functions.
result Proves a function is 1-harmonic if its level sets are minimal laminations.
Analyzes how diffusion models learn, revealing a spectral bias in structure mastery.
problem Understanding the learning dynamics and bias in diffusion models.
method Developed an analytical framework using a Gaussian-equivalence principle to solve gradient-flow dynamics and integrate probability-flow ODEs.
result Exposes a universal inverse-variance spectral law: high-variance structure is mastered faster than low-variance detail.
Encouraging sustainable mobility patterns is at the forefront of policymaking at all scales of governance as the collective consciousness surrounding climate change continues to expand. Not every community, however, possesses the necessary economic or socio-cultural capital to encourage modal shifts away from private m…
Proposes a method to sample from flat basins of posterior distributions in Bayesian deep learning.
problem Sampling from multi-modal posterior distributions leads to overfitting due to trapping in bad modes.
method Introduces an auxiliary guiding variable to bias MCMC sampling towards flat basins of the energy landscape.
result The method converges faster and outperforms existing methods in sampling from flat basins of the posterior.
Mode connectivity is a recently introduced frame- work that empirically establishes the connected- ness of minima by finding a high accuracy curve between two independently trained models. To investigate the limits of this setup, we examine the efficacy of this technique in extreme cases where the input models are trai…
Proposes an automatic cyclical scheduling for gradient-based discrete sampling.
problem Gradient-based sampling in high-dimensional models can get stuck in local modes.
method Cyclical step size and balancing schedules with automatic hyperparameter tuning.
result Proves non-asymptotic convergence and inference guarantees for general discrete distributions.
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or modal-sets, of any bounded shape or dimension, including usual point-modes. In practice, modal-…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…
Characterizes neutral deformation modes of minimal surfaces.
problem Understanding the energy content of deformation modes of minimal surfaces.
method Analyzes the energy content of stretching, drilling, and bending modes of minimal surfaces.
result All isometries of a minimal surface are globally neutral and give rise to soft elasticity.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.