A new method normalizes activations to match batch normalization without batch dependence.
problem Performance degradation with batch-independent normalization techniques.
method Proxy-Normalizing Activations
result Proxy-Normalization technique emulates batch normalization's behavior and performance.
Improves NF for complex data distributions with multiple modes.
problem Difficulty in handling data distributions with multiple isolated modes.
method Proposes a new framework using variational latent representation to improve NF.
result Significantly more powerful for generating data distributions with multiple modes.
FlowVAT improves variational inference for multi-modal distributions.
problem Mode-seeking behavior and collapse in variational inference for complex posteriors.
method Conditional tempering approach for normalizing flow variational inference.
result FlowVAT outperforms traditional and adaptive annealing methods in multi-modal distributions, finding more modes and achieving better ELBO values.
Normalization methods are a central building block in the deep learning toolbox. They accelerate and stabilize training, while decreasing the dependence on manually tuned learning rate schedules. When learning from multi-modal distributions, the effectiveness of batch normalization (BN), arguably the most prominent nor…
Study shows annealing with adaptive schedule reduces mode collapse in NFs for parameter estimation.
problem Mode collapse in normalizing flows for multimodal distributions.
method Annealing with an adaptive schedule based on effective sample size (ESS).
result Our approach reduces mode collapse and converges marginal likelihood faster than MCMC methods.
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.
Theoretical work on mode collapse in variational inference models.
problem Mode collapse in variational inference models, where models focus on a few modes instead of all possible ones.
method Theoretical investigation of mode collapse in Gaussian mixture models, identifying key low-dimensional statistics and equations governing their evolution.
result Mode collapse is present even in favorable scenarios, driven by mean alignment and vanishing weight mechanisms.
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
problem Understanding the properties of two-component bivariate normal mixtures.
method Classification via A-equivalence and statistical analysis. result Three distinct types of mappings with specific geometric and statistical properties, and upper bounds for the number of modes.
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative perodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular we prove that under appropriate hypothes…
We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we signific…
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
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.
This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.
problem Analyzing the distribution of genera in 2-bridge knots.
method Proving asymptotic normality through median, mode, and variance calculations.
result The distribution of genera of 2-bridge knots is asymptotically normal.
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.
Proves analyticity of quasinormal modes in Kerr and Kerr-de Sitter spacetimes.
problem Analyticity of quasinormal modes in extreme Kerr and Kerr-de Sitter spacetimes.
method Observation of stable radial point source/sink structure in bicharacteristic flow; recent microlocal analysis result by Galkowski and Zworski.
result Quasinormal modes are real analytic in subextremal Kerr and Kerr-de Sitter spacetimes.
Develops an oblique projection technique to approximate a foliation for non-normal dynamics.
problem Modeling dynamics far from a primary Spectral Submanifold (SSM) in non-normal systems.
method Oblique projection technique based on experimental data.
result Approximates a stable invariant foliation for non-normal dynamics efficiently.
Proves wave equation solutions in Kerr-de Sitter spacetime have specific asymptotic expansions.
problem Analyzing solutions to wave equations in Kerr-de Sitter spacetime.
method Developed a Fredholm setup for quasinormal modes and analyzed trapping of lightlike geodesics.
result Proves asymptotic expansions of wave equation solutions up to a decay order.
NS-GAN mode collapse due to sample weighting inversion, solved with MM-nsat.
problem Mode collapse in GANs due to sample weighting inversion.
method Preserves MM-GAN sample weighting while avoiding saturation by rescaling gradients.
result MM-nsat improves mode coverage, stability, and FID on MNIST and CIFAR-10.
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 method trains neural samplers without simulation, but fails due to mode collapse.
problem Training neural samplers without simulation.
method Time-dependent normalizing flow with Langevin preconditioning.
result Langevin preconditioning is crucial for avoiding mode collapse.
Despite excellent progress in recent years, mode collapse remains a major unsolved problem in generative adversarial networks (GANs).In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. Theoretical analysis shows that the optimal …
New methods show quasinormal modes can be defined using various stationary Killing vectors.
problem Proving asymptotic expansions for wave equations in Kerr-de Sitter spacetimes.
method New definition of quasinormal modes using different stationary Killing vectors.
result Horizon Killing vector fields work for analysis, simplifying the problem.
Deep convolutional neural networks are known to be unstable during training at high learning rate unless normalization techniques are employed. Normalizing weights or activations allows the use of higher learning rates, resulting in faster convergence and higher test accuracy. Batch normalization requires minibatch sta…
Deep generative models provide powerful tools for distributions over complicated manifolds, such as those of natural images. But many of these methods, including generative adversarial networks (GANs), can be difficult to train, in part because they are prone to mode collapse, which means that they characterize only a …
The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamical system analysis, the extracted dynamic modes are a generalization of global stability modes. We a…
A new method improves Bayesian inference for multimodal posteriors.
problem Insensitivity to well-separated modes in multimodal posteriors.
method Weighted Kernel Stein Discrepancy method.
result Significantly improved mode sensitivity compared to standard KSD-Bayes.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
problem Training invertible linear layers during optimization with gradient-based methods is challenging.
method Train rank-one perturbations and add them to weight matrices infrequently, keeping track of inverses and determinants.
result Invertible linear layers improve mixing and mode separation in normalizing flows.
Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hu…
Method uses normalizing flows to efficiently sample from complex target densities.
problem Sampling from complex target densities with zero values in regions of transformation.
method Normalizing flows to address exploding reverse Kullback-Leibler divergence.
result Demonstrated efficient sampling from multi-mode complex density function.
We analyze architectural features of Deep Neural Networks (DNNs) using the so-called Neural Tangent Kernel (NTK), which describes the training and generalization of DNNs in the infinite-width setting. In this setting, we show that for fully-connected DNNs, as the depth grows, two regimes appear: "order", where the (sca…
Differentiable sorting and rank normalization are incompatible, with specific conditions for admissibility.
problem Incompatibility between differentiable sorting and rank normalization.
method Formalized admissibility through monotone invariance, batch independence, and rank-space stability conditions.
result Different gap-sensitive and batchwise relaxations of rank normalization violate the conditions for admissibility.
This article presents differential equations and solution methods for the functions of the form Q(x)=F−1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed an…
Spectral normalization stabilizes GANs by controlling gradient explosion and vanishing.
problem Stability and sample quality issues in GAN training.
method Spectral normalization controls gradient explosion and vanishing, improving GAN training stability and sample quality.
result Bidirectional Scaled Spectral Normalization (BSSN) outperforms standard spectral normalization in sample quality and training stability.
DDSME outperforms SME in estimating multimodal distributions.
problem Efficiency of score matching in multimodal distributions.
method Diffusion-based denoising score matching (DDSME) compared to vanilla score matching (SME).
result DDSME avoids the error bound deterioration of SME with increasing mode separation.
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.
Flow AIS Bootstrap improves flow training by generating samples in hard-to-reach regions.
problem Training flows with high variance and mode-seeking behavior.
method Augment flows with AIS and minimize α-divergence with α=2. result FAB learns Boltzmann distribution of alanine dipeptide without MD samples.
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.
Develops MENT for interpreting and detecting changes in network trajectories.
problem Distortion of network geometry and invalidation of temporal comparisons in dynamic network analysis.
method Develops Multiscale Euclidean Network Trajectories (MENT) framework based on second-moment geometry.
result Validates and interprets network trajectories through isotropic normalization and orthogonal transformations.
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…
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…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of variables formula. Such behavior is desirable in multivariate structured predicti…
Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-ba…
Generative adversarial networks (GANs) are a class of deep generative models which aim to learn a target distribution in an unsupervised fashion. While they were successfully applied to many problems, training a GAN is a notoriously challenging task and requires a significant number of hyperparameter tuning, neural arc…
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…
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.
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.
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.