The paper finds shape modes for vortices in a specific sigma model.
problem Existence of internal modes in CP1 vortices. method Developed a geometric formalism based on the Bogomol'nyi decomposition of the energy functional.
result Proved the existence of at least one shape mode for a general CP1 vortex solution. The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
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…
The paper reveals surprising star-shaped connectivity in neural networks.
problem Understanding mode connectivity in neural network landscapes.
method Fine-grained analysis of connectivity in overparameterized and finite minima cases.
result Star-shaped connectivity exists in neural network landscapes, suggesting near convexity.
Frustration causes buckling-like behavior in tubular foldable mechanisms.
problem Kinematic coupling and geometric confinement in tubular foldable mechanisms.
method Analytical and numerical solutions of exact kinematics.
result Frustration propagates axially as if by buckling in tubular states.
Transformers infer tasks from context via two modes, geometrically shaped task vectors explain their behavior.
problem Understanding how transformers infer tasks from context and the geometric properties of task vectors.
method Synthetic setting to train small transformers, mathematical characterization of task-vector geometry and inference modes.
result Task-vector geometry shapes in-distribution and out-of-distribution behavior of transformers.
U-Net trained to recover acoustic interference striations from distorted data.
problem Recovering acoustic interference striations from distorted signals.
method Training a U-Net using a random mode-coupling matrix model to generate training data.
result U-Net successfully recovers AISs under various conditions.
Hybrid model for multimodal distributions using diffusion and classification.
problem Sampling from multimodal distributions with correct proportions.
method Divide-and-conquer strategy: identify modes, train classifiers, diffusion models, bridge sampling.
result Framework effectively handles multimodal distributions in high dimensions.
New model explains GAN training dynamics and mode collapse.
problem Mode collapse in GANs, where generators fail to reproduce diversity.
method Simplified model using particles in output space, coupled by universal kernel.
result Gradient regularizers can optimally yield convergence through critical damping.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
problem Handling hyperparameters for non-informative limits in multivariate Gaussian conjugate priors.
method Using scaled KL-divergence between multivariate Gaussians to construct Wishart and normal-Wishart conjugate priors.
result Forming non-informative priors without violating Wishart shape parameter restrictions.
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.
We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a n…
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical …
Neural nets improve plasma equilibrium modeling for NSTX-U.
problem Modeling plasma equilibrium and shape control for NSTX-U.
method Developed two neural networks: Eqnet and Pertnet.
result NNs offer faster and more flexible prediction of plasma scenarios.
Meta-CoTGAN improves adversarial text generation by preventing mode collapse.
problem Mode collapse in adversarial text generation.
method Meta-Cooperative Training Paradigm with a language model.
result Meta-CoTGAN effectively slows down mode collapse and improves generation quality and diversity.
The paper introduces flat-topped PDFs for better fitting machine learning models.
problem Improving goodness of fit in machine learning models.
method Developed a new PDF based on the Fermi-Dirac or logistic function for adaptability.
result Flat-topped PDFs enhance model simplicity and fit quality.
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, a…
We consider N-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank appr…
A new distributed clustering framework using distributional kernel.
problem Clustering in distributed networks with arbitrary shapes, sizes, and densities.
method Distributed Clustering based on Distributional Kernel (KDC) using similarity of distributions.
result KDC guarantees equivalent clustering outcomes to centralized methods, reduces runtime, and discovers arbitrary clusters.
VINNAS uses variational inference to avoid mode collapse in neural architecture search.
problem Mode collapse in gradient-based NAS methods, leading to suboptimal architectures.
method Differentiable variational inference with variational dropout and automatic relevance determination.
result State-of-the-art accuracy with up to twice fewer non-zero parameters.
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
In regression tasks, aleatoric uncertainty is commonly addressed by considering a parametric distribution of the output variable, which is based on strong assumptions such as symmetry, unimodality or by supposing a restricted shape. These assumptions are too limited in scenarios where complex shapes, strong skews or mu…
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-…
Procedural content generation via machine learning (PCGML) is typically framed as the task of fitting a generative model to full-scale examples of a desired content distribution. This approach presents a fundamental tension: the more design effort expended to produce detailed training examples for shaping a generator, …
NVA combines variational posteriors, annealing, and natural-gradient learning for multimodal optimization.
problem Finding multiple global and local modes in nonconvex objectives.
method NVA integrates variational posteriors, annealing, and natural-gradient learning.
result NVA outperforms gradient descent and evolution strategies on simulations and real-world problems.
This paper presents a novel adaptive resonance theory (ART)-based modular architecture for unsupervised learning, namely the distributed dual vigilance fuzzy ART (DDVFA). DDVFA consists of a global ART system whose nodes are local fuzzy ART modules. It is equipped with the distinctive features of distributed higher-ord…
The complete part of the earthquake frequency-magnitude distribution (FMD), above completeness magnitude mc, is well described by the Gutenberg-Richter law. The parameter mc however varies in space due to the seismic network configuration, yielding a convoluted FMD shape below max(mc). This paper investigates the shape…
Randomized fiber projections enhance neural network accuracy.
problem Improving neural network performance with limited resources.
method Training neural networks on randomized speckled images from multi-mode fiber projectors.
result Classification accuracy is higher with randomized fiber data than with direct images.
Gating units in GRUs and LSTMs create slow modes and control phase-space complexity.
problem Training challenges in RNNs due to exploding or vanishing gradients.
method Random matrix theory and mean-field theory applied to GRUs and LSTMs.
result Gates in GRUs and LSTMs lead to accumulation of slow modes and control phase-space complexity.
AMF-VI uses adaptive mixtures of flows for robust VI across diverse distributions.
problem Inconsistent behavior of single-flow models across different distributions.
method Sequential expert training of individual flows and adaptive global weight estimation via likelihood-driven updates.
result AMF-VI achieves lower negative log-likelihood and stable gains in transport metrics across various posterior families.
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.
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.
Selective clustering annotated using modes of projections (SCAMP) is a new clustering algorithm for data in Rp. SCAMP is motivated from the point of view of non-parametric mixture modeling. Rather than maximizing a classification likelihood to determine cluster assignments, SCAMP casts clustering as a searc…
Language models fail to process hallucinated responses, and this study diagnoses the failure.
problem Language models fail to process hallucinated responses, leading to over-concentration or diffuse attention.
method The study uses forced scoring of benchmark-labeled responses to compute attention shapes and analyze the symmetric component of the degree-normalized attention operator.
result The study proves that every transpose-invariant spectral diagnostic of the attention operator is orientation-blind and bounds the sensitivity of any Lipschitz diagnostic by the asymmetry coefficient \(G\).
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…
We characterize stationary solutions to McKean-Vlasov equations on the circle.
problem Stationary solutions of McKean-Vlasov equations on the circle.
method Exact equivalence to an infinite-dimensional quadratic system of equations over Fourier coefficients, leading to explicit characterization of stationary states.
result Analytic expressions for the emergence, form, and shape of bifurcations involving multiple Fourier modes, and connections with discontinuous phase transitions.
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.
Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.
problem Mode collapse in variational inference for multimodal distributions.
method Analyzed annealing strategies for Gaussian mixtures, derived formulas, and tested on neural networks.
result Appropriately chosen annealing schemes can robustly prevent mode collapse.
We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even better performance can in general be achieved by sampling finite temperature (T) …
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
The outcome of Jacobian singular values regularization was studied for supervised learning problems. It also was shown that Jacobian conditioning regularization can help to avoid the ``mode-collapse'' problem in Generative Adversarial Networks. In this paper, we try to answer the following question: Can information abo…
Geodesics connect model modes in neural network loss landscapes.
problem Connecting modes in neural network loss landscapes.
method Reframed mode connectivity in Information Geometry, hypothesized geodesics as mode-connecting paths, proposed algorithm to approximate geodesics.
result Geodesics achieve mode connectivity in neural networks.
A new, efficient k-modes algorithm improves clustering of categorical data.
problem Clustering categorical data using existing methods like k-means is inefficient. method Developed a novel k-modes algorithm called OTQT, which improves on existing methods. result OTQT finds more accurate clusters per iteration and is faster overall.
Multimodal clustering is an unsupervised technique for mining interesting patterns in n-adic binary relations or n-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…
The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements and generalizations, as well as deep theoretical analysis mainly focused on its …
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering wh…
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.
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.