The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.
problem Analyzing spatio-temporal and polarimetric fluctuations of radar electromagnetic waves.
method Using statistical mechanics and Information Geometry, the paper defines a Fréchet barycentre and maximum entropy density for radar measurements.
result New tools for describing radar electromagnetic wave fluctuations, including a distance on covariance matrices.
The asymptotic concentration of the Fr{é}chet mean of IID random variables on a Rieman-nian manifold was established with a central limit theorem by Bhattacharya \& Patrangenaru (BP-CLT) [6]. This asymptotic result shows that the Fr{é}chet mean behaves almost as the usual Euclidean case for sufficiently concentrated di…
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …
Study on geometry of Dirichlet distributions using Fisher-Rao metric.
problem Understanding the geometry of Dirichlet distributions.
method Analysis of Fisher-Rao metric on Dirichlet distribution parameter space.
result Geodesic completeness and negative sectional curvature of the space.
New metrics defined for full-rank correlation matrices, ensuring unique operations.
problem No suitable problem statement as the abstract does not describe a problem to be solved.
method New Riemannian metrics defined on full-rank correlation matrices, providing unique operations.
result Unique Riemannian logarithm and Fréchet mean defined for full-rank correlation matrices.
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
problem Computing geodesics and logarithms on Stiefel and flag manifolds.
method Closed-form geodesic formulas, trust-region solver, Fréchet derivatives.
result Efficient computation of geodesic distance and logarithm map.
Constructs supermartingale couplings with full marginals constraints.
problem Optimal transport for supermartingale couplings with multiple marginals.
method Markovian iteration of one-period optimal supermartingale couplings.
result Explicit construction of supermartingale processes solving optimal transport problem.
Proposes Topology Distance for evaluating GANs.
problem Challenges in evaluating GANs' goodness.
method Builds Vietoris-Rips complex on image features and defines TD based on latent manifold comparisons.
result Demonstrates TD's superiority over existing metrics.
FastFID efficiently trains generative models with FID loss.
problem Efficiently training generative models with FID loss.
method Introduces FastFID to train generative models with FID as a loss function.
result Improves FID for GANs using FID as an additional loss.
Hyperbolic GANs improve image generation metrics.
problem Improving image generation quality in neural networks.
method Integrating hyperbolic layers into GAN architectures.
result Hyperbolic GANs achieve better metrics than Euclidean counterparts.
Improves GANs by incorporating class information with a multi-hinge loss.
problem Improving GANs to better respect class information.
method Proposes a multi-class generalization of the Hinge loss for GANs.
result Improves Inception Scores and Frechet Inception Distance on Imagenet.
FID misaligns with human judgment due to reliance on ImageNet classes.
problem FID metric's reliance on ImageNet classes causes discrepancies with human evaluation.
method Investigated and visualized the feature space of FID and its relation to ImageNet classes.
result Aligning histograms of Top-N ImageNet classifications can reduce FID without improving quality. Paper proposes evaluation methods for climate change illustrations.
problem Lack of metrics to compare realism in conditional generative models.
method Adapted and assessed several existing metrics, including FID.
result FID with Inception-V3 embeddings correlates best with human realism.
Improved GAN training speed and quality with FastGAN.
problem Slower convergence and less expressive models in GAN training.
method Adversarial training with FastGAN algorithm.
result Better generation quality with less training time.
Improved sampling quality with RBM-Flow and D-Flow models.
problem Efficient sampling of complex data distributions using invertible flows.
method Implement RBM-Flow and D-Flow models with discrete latent variables.
result Significant improvement in sampling quality over baseline models.
Let G be a compact connected simple Lie group and let $M=G^{\bb{C}}/P=G/K$ be a generalized flag manifold. In this article we focus on an important invariant of G/K, the so called $\fr{t}$-root system $R_{\fr{t}}$, and we introduce the notion of symmetric $\fr{t}$-triples, that is triples of $\fr{t}$-roots $ξ, ζ, η…
Inception v3 model classifies face shapes with high accuracy.
problem Face shape classification using deep learning.
method Retraining Inception v3 model on face shape dataset.
result Inception v3 outperforms other classifiers.
We study the impact of input noise dimension on GAN performance.
problem Challenges in GANs like mode collapse and unstable training.
method Quantitative analysis using FID and IS on different image datasets.
result The optimal input noise dimension varies by dataset and architecture.
LOGAN optimizes GAN training by improving adversarial dynamics.
problem Training GANs is challenging due to delicate adversarial dynamics and potential divergence.
method Integrates natural gradient-based latent optimisation into CS-GAN.
result Significant improvement in GAN training performance, achieving state-of-the-art results.
We propose a rejection sampling scheme using the discriminator of a GAN to approximately correct errors in the GAN generator distribution. We show that under quite strict assumptions, this will allow us to recover the data distribution exactly. We then examine where those strict assumptions break down and design a prac…
We consider in this paper the FRS-deformations of a family of space curves with codimension ≤3. Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.
Paper tackles GAN instability in audio and speech signals using a new similarity metric.
problem Improving stability of LS-GANs for audio and speech signals.
method Proposes a new similarity metric in unitary space of Schur decomposition for 2D audio and speech representations.
result Enhanced stability in training with less mode collapse compared to baseline GANs.
A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
Spider GAN accelerates GAN training with a new approach.
problem Stable training of Generative adversarial networks (GANs).
method Spider GAN leverages a novel approach to identify closely related datasets (friendly neighborhoods) and uses a new measure (signed inception distance) to accelerate GAN training.
result Spider GAN achieves faster convergence and state-of-the-art FID values with one-fifth of the training iterations.
Study shows splitting schemes can approximate WFR flows faster than the exact flow.
problem Improving sampling efficiency in Wasserstein-Fisher-Rao gradient flows.
method Investigates operator splitting techniques to numerically approximate WFR flows.
result A judicious choice of step size and operator ordering can lead to faster convergence of split schemes to the target distribution.
Recent work (Pennington et al, 2017) suggests that controlling the entire distribution of Jacobian singular values is an important design consideration in deep learning. Motivated by this, we study the distribution of singular values of the Jacobian of the generator in Generative Adversarial Networks (GANs). We find th…
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
Generative adversarial networks (GANs) are recently highly successful in generative applications involving images and start being applied to time series data. Here we describe EEG-GAN as a framework to generate electroencephalographic (EEG) brain signals. We introduce a modification to the improved training of Wasserst…
Discriminator optimizes to approximate optimal transport for better image generation.
problem Improving the quality of generated images using GANs.
method Trains discriminator to optimize a lower bound of Wasserstein distance, approximating optimal transport.
result Trained discriminator improves inception score and FID metrics.
Phishing as one of the most well-known cybercrime activities is a deception of online users to steal their personal or confidential information by impersonating a legitimate website. Several machine learning-based strategies have been proposed to detect phishing websites. These techniques are dependent on the features …
We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approxim…
Generative models improved with smoothed score functions for better sample quality.
problem Improving generative models for better sample quality.
method Smoothed score functions based on factorial Gaussian kernels.
result Single noise level achieved 14.15 Fréchet inception distance on CIFAR-10.
The problem of video frame prediction has received much interest due to its relevance to many computer vision applications such as autonomous vehicles or robotics. Supervised methods for video frame prediction rely on labeled data, which may not always be available. In this paper, we provide a novel unsupervised deep-l…
FR-Train improves fair and robust AI training by detecting and reducing poisoned data.
problem Training AI models that are fair and robust in the presence of data bias and poisoning.
method Mutual information-based adversarial training with an additional discriminator.
result FR-Train maintains fairness and accuracy even in the presence of poisoned data.
In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modi…
Proves FR-NGD optimally approximates evolutionary dynamics and continuous Bayesian inference.
problem Optimizing continuous time replicator equations and continuous Bayesian inference.
method Fisher-Rao natural gradient descent (FR-NGD) and its correspondence with evolutionary dynamics.
result FR-NGD optimally approximates continuous time replicator equations and continuous Bayesian inference.
FR-LUX optimizes portfolio management by learning cost-aware policies robust to market conditions.
problem Transaction costs and regime shifts cause failure in live trading portfolios.
method Integrates three ingredients: microstructure-consistent execution model, trade-space trust region, and explicit regime conditioning.
result Achieves top average Sharpe ratio, maintains flat cost-performance slope, and superior risk-return efficiency.
The paper improves interpolation in generative models by using specific base distributions.
problem Unexpected side effects in linear interpolations of normalizing flows.
method Enforces a specific manifold using Dirichlet and von Mises-Fisher base distributions.
result Superior performance in terms of bits per dimension, FID, and KID scores for interpolation.
Generative models of natural images have progressed towards high fidelity samples by the strong leveraging of scale. We attempt to carry this success to the field of video modeling by showing that large Generative Adversarial Networks trained on the complex Kinetics-600 dataset are able to produce video samples of subs…
Consider an anchored bundle (E,ρ), i.e. a vector bundle E→M equipped with a bundle map ρ:E→TM covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid FR(E)⊃E. We …
Introduces a new geometric framework for field theories.
problem Developing a rigorous mathematical framework for field theories.
method Introduces supergeometric homotopy theory to physics.
result Classical bosonic field theories fit naturally into smooth sets.
A new GAN loss function based on cumulant generating functions improves stability and robustness.
problem Improving the stability and performance of GANs.
method Cumulant GAN loss function based on variational R{é}nyi divergence.
result Cumulant GAN achieves linear convergence to Nash equilibrium and superior performance in image generation.
Automatically evaluates image quality based on human judgment.
problem Difficulty in rigorously evaluating generated image quality.
method Generative model embeddings, human labels regression, and statistical matching.
result 66% accuracy in predicting human scores of image realism.
We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are equivalent, and thus describe the same classes of 3-manifolds. This makes the p…
This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
problem Sampling techniques struggle to traverse between modes in non-convex potential functions.
method Explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
result The convergence rate to π is independent of the potential function.
Unified and extended precision-recall metrics for generative models.
problem Evaluation of generative models using scalar metrics like FID and IS.
method Unified various precision-recall approaches under a common framework.
result Recovered entire precision-recall curves and exposed metric pitfalls.
Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal. To this end, we train Generative Adversarial Networks at the largest scale yet attempted, and study the instabilities specific to such scale. We …
We study geodesics of the form γ(t)=π(exp(tX)exp(tY)), $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces G/K, where π:G→G/K is the natural projection. These curves naturally generalise homogeneous geodesics, that is orbits of one-parameter subgroups of G (i.e. γ(t)=π(exp(tX)), $X\in …