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.
This work examines curvature effects on empirical mean in Riemannian and affine manifolds for small samples.
problem Understanding curvature effects on empirical mean in small samples on Riemannian and affine manifolds.
method Established Taylor expansions for the first and second moments of the empirical mean, showing curvature impacts.
result Explicit formulas for bias and modulation of empirical mean's covariance matrix due to curvature.
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.
Improved action recognition in live videos with hybrid FR-DL method.
problem High computational costs and lack of temporal information in conventional action recognition.
method Automated selection of representative frames, feature extraction, background subtraction, HOG, deep neural network, LSTM, Softmax-KNN classifier.
result Significant improvement in accuracy and speed compared to state-of-the-art methods.
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.
Generative model produces high-fidelity video samples.
problem Generating high-fidelity videos from complex datasets.
method Large GAN trained on Kinetics-600 dataset, using a computationally efficient discriminator.
result Achieved state-of-the-art metrics in video synthesis and prediction.
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…
New metric for video generation models, addressing quality, coherence, and diversity.
problem Lack of metrics for evaluating generative models of video.
method Proposed Fréchet Video Distance (FVD) and StarCraft 2 Videos (SCV) benchmark.
result FVD correlates well with human judgment of generated videos.
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.
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.
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.
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.
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.
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.
Fuzzy Rough Set selects key features for phishing detection.
problem Efficient feature selection for phishing detection.
method Fuzzy Rough Set (FRS) theory for feature selection.
result Maximum F-measure of 95% using Random Forest.
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.
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.
The extension of image generation to video generation turns out to be a very difficult task, since the temporal dimension of videos introduces an extra challenge during the generation process. Besides, due to the limitation of memory and training stability, the generation becomes increasingly challenging with the incre…
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.
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…
Universal construction for Lie algebroids from anchored bundles with connections.
problem Creating a universal framework for Lie algebroids from anchored bundles with connections.
method Adapting Kapranov's construction to anchored bundles with arbitrary connections, showing compatibility with Lie algebroid structure.
result Universal connection ildeabla on FR(E) compatible with Lie algebroid structure, turning (FR(E),ildeabla) into a Cartan-Lie algebroid. 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 …
Paper proposes FR algorithm to solve minimax optimization locally.
problem Gradient descent fails to find local minimax in minimax optimization.
method Follow-the-Ridge (FR) algorithm, addressing rotational behavior of gradient dynamics.
result FR algorithm provably converges to local minimax.
Paper introduces DACAL for high-resolution photo and video enhancement.
problem Photo and video enhancement with weak supervision.
method Divide-and-conquer adversarial learning approach with hierarchical decomposition.
result State-of-the-art performance in high-resolution photo and video enhancement.
Self-supervised method estimates distances on fisheye cameras for autonomous driving.
problem Accurate Euclidean distance estimation on fisheye cameras for autonomous driving.
method Self-supervised scale-aware framework for monocular fisheye videos.
result State-of-the-art results on KITTI dataset, comparable to other methods.
We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces M=G/K whose isotropy representation decomposes into a direct sum of three submodules m=m1⊕m2⊕m3, satisfying the relations $[\fr…
This article follow the article {http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the author characterize the fact of being of finite volume for a convex projective surface. We show here that the moduli space βf(Σg,p) of the convex projective structure on the surface Σg,p of genius g with p pun…
A new category generates 1D tangle invariants.
problem Developing a new category for 1D tangles.
method Proving a new (∞,1)-category has universal mapping property. result The new category generates link invariants.
New method improves fairness of facial recognition systems.
problem Facial recognition systems exhibit bias across different demographic groups.
method Optimizes centroid-based scores to reduce bias in pre-trained models.
result Demonstrates significant improvement in fairness with minimal loss in accuracy.
Person re-identification (Re-ID) aims at matching images of the same person across disjoint camera views, which is a challenging problem in multimedia analysis, multimedia editing and content-based media retrieval communities. The major challenge lies in how to preserve similarity of the same person across video footag…
A method learns to imitate from a single video demonstration using contrastive training and Siamese networks.
problem Learning to imitate from video demonstrations without direct access to state or action information.
method Contrastive training with Siamese recurrent neural networks to learn rewards and an RL policy to minimize distance.
result The method significantly improves policy learning and outperforms current techniques in various environments.
GeoIB uses information geometry to control compression in deep learning models.
problem The indirect and biased nature of traditional IB implementations in deep learning.
method GeoIB uses Fisher-Rao and Jacobian-Frobenius terms to control information compression directly.
result GeoIB achieves better trade-off between accuracy and compression than traditional IB methods.
Person Re-Identification (person re-id) is a crucial task as its applications in visual surveillance and human-computer interaction. In this work, we present a novel joint Spatial and Temporal Attention Pooling Network (ASTPN) for video-based person re-identification, which enables the feature extractor to be aware of …
This paper introduces a new Urban Point Cloud Dataset for Automatic Segmentation and Classification acquired by Mobile Laser Scanning (MLS). We describe how the dataset is obtained from acquisition to post-processing and labeling. This dataset can be used to learn classification algorithm, however, given that a great a…
We introduce \texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Pytho…
Study reveals centralization in Bitcoin transactions involving retail users.
problem Centralization and bias in Bitcoin transaction data.
method Heuristic classification of Bitcoin users, weekly activity pattern analysis.
result Most real transactions involve Frequent Receivers, centralizing the ecosystem.
Conditional COT-GAN predicts sequences using past data and kernel smoothing.
problem Predicting sequences given past data.
method Conditional COT-GAN with kernel smoothing.
result Improved convergence results for sequence prediction.
We construct examples of finitely generated groups L that have non-trivial actions on R-trees but which cannot act, without fixing a vertex, on any simplicial tree. Moreover, any finitely presented group mapping onto L does have a fixed point-free action on some simplicial tree.
Cross-domain visual data matching is one of the fundamental problems in many real-world vision tasks, e.g., matching persons across ID photos and surveillance videos. Conventional approaches to this problem usually involves two steps: i) projecting samples from different domains into a common space, and ii) computing (…
Unified framework for discrete diffusion modeling with flexible noising processes.
problem Efficient modeling of large discrete state spaces with arbitrary corruption dynamics.
method Generalized Discrete Diffusion from Snapshots (GDDS) framework that supports uniformization for fast noising and snapshot-based ELBO for reverse process.
result GDDS outperforms existing discrete diffusion methods in training efficiency and generation quality.
Motivation: Prediction of ligands for proteins of known 3D structure is important to understand structure-function relationship, predict molecular function, or design new drugs. Results: We explore a new approach for ligand prediction in which binding pockets are represented by atom clouds. Each target pocket is compar…
New algorithm for multi-armed bandits with delayed, partially observed rewards.
problem Sequential decision-making with delayed feedback.
method Proposed multi-armed bandits with generalized temporally-partitioned rewards, introducing β-spread property.
result Upper bound on performance of TP-UCB-FR-G algorithm improves state of the art.
Ground-A-Video edits videos without training, preserving intended changes.
problem Complex multi-attribute video editing with omitted or wrong changes.
method Grounding-guided video-to-video translation with Cross-Frame Gated Attention.
result Zero-shot multi-attribute video editing with improved accuracy and frame consistency.
CB-GLNs learn video data's complex dependencies via graph representation.
problem Capturing complex dependency structures in sequential data like videos.
method Represent video data as a graph, find compositional dependencies via graph-cut and message passing.
result CB-GLNs efficiently learn video data's semantic compositional structure.
A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspa…