GAGA learns a warped metric for geometry-aware data generation and interpolation.
problem Challenges in generating data with meaningful geometry in high-dimensional datasets.
method Combines manifold learning with generative modeling to learn a warped Riemannian metric.
result GAGA improves trajectory inference by 30% in single-cell population-level data.
GH-PID uses guided harmonic paths for efficient SOT with interpretable diagnostics.
problem Efficiently solving Stochastic Optimal Transport with hard terminal distributions and soft costs.
method Guided Harmonic Path-Integral Diffusion (GH-PID) framework with low-dimensional guidance.
result GH-PID generates geometry-aware, cost-reducing trajectories that match terminal distributions.
Geometry-aware noise improves model generalization on complex manifolds.
problem Improving model generalization on highly curved data manifolds.
method Add geometry-aware noise to input space, projecting Gaussian noise onto tangent space of manifold and mapping it via geodesic curve.
result Geometry-aware noise leads to improved generalization and robustness on highly curved manifolds.
Geometry-aware models improve cross-subject EEG decoding accuracy.
problem Strong inter-subject variability in motor imagery decoding.
method Discriminative Congruence Transform (DCT), Deep Linear DCT (DLDCT), Deep DCT-UNet (DDCT-UNet).
result Improves transductive cross-subject accuracy by 2-3%.
ES-VAE models skeletal pose trajectories by removing nuisance factors.
problem Handling camera orientation, subject scale, viewpoint, and execution speed in skeletal data.
method ES-VAE uses TSRVF representation on Kendall's shape manifold to isolate shape dynamics.
result ES-VAE outperforms standard VAEs and sequence modeling baselines in gait cycle prediction and action recognition.
This paper proposes a geometry-aware active learning framework for spatiotemporal dynamic systems.
problem Challenges in modeling complex dynamic systems with 3D geometries and time evolution.
method Geometry-aware spatiotemporal Gaussian Process (G-ST-GP) and adaptive active learning strategy.
result The proposed framework outperforms traditional methods in predicting high-dimensional dynamic behaviors.
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
problem Machine learning methods struggle with geometric data
method Shape space analysis provides a mathematical and computational framework
result Characterizes shape variability, compares geometric objects, and analyzes structural trajectories
Sparse GEMINI selects relevant features for clustering without assumptions.
problem Feature selection in clustering with relevant clusters and variables.
method Discriminative clustering model maximizing GEMINI with l1 penalty.
result Sparse GEMINI selects relevant subsets of variables without prior hypotheses.
This work investigates implicit bias in multiclass separable data using a novel geometry-aware optimizer.
problem Understanding implicit bias in overparameterized models on multiclass separable data.
method Introduces NucGD, a geometry-aware optimizer enforcing low-rank structures through nuclear norm constraints.
result NucGD enables scalable training and characterizes the impact of stochastic optimization dynamics.
OrthoGrad improves neural calibration by constraining gradient updates orthogonally.
problem Overconfidence in neural networks, leading to poor uncertainty estimates.
method Orthogonal gradient updates to optimize for decision boundaries and reduce overconfidence.
result Significant improvements in test loss, predictive entropy, and confidence measures.
Geometry-aware KDE model improves multiclass quantification.
problem Accurately estimating class prevalence for label shift adaptation.
method Log-ratio representations and Aitchison geometry for compositional data, shrinkage regularization.
result Competitive with state-of-the-art quantifiers, often improving over standard KDE-based baselines.
DFR models dynamic distributional data with weighted Fréchet means.
problem Regression of distribution-valued responses over time.
method Dynamic Fréchet Regression (DFR) with index-aware weighting and feature selection.
result Improved predictive accuracy and feature recovery over existing methods.
GeoERM learns shared representations on Riemannian manifolds for multi-task learning.
problem Heterogeneous and adversarial tasks in MTL.
method Geometry-aware MTL framework embedding shared representation on Riemannian manifold, optimizing via manifold operations.
result GeoERM improves estimation accuracy and stability, outperforming alternatives.
Paper introduces geometry-aware normalizing flows for improved causal inference.
problem Disparity between sample and population distributions in causal inference.
method Integrates continuous normalizing flows with parametric submodels, employing Wasserstein gradient flows and optimal transport.
result Significantly reduces parameter estimation bias and variance in finite-sample settings.
While matrix factorisation models are ubiquitous in large scale recommendation and search, real time application of such models requires inner product computations over an intractably large set of item factors. In this manuscript we present a novel framework that uses the inverted index representation to exploit struct…
Hybrid method improves SABR implied volatility approximation.
problem Improving SABR implied volatility approximation.
method Combining analytical structure with machine learning, using geometric features and residual correction.
result Hybrid model improves accuracy and robustness compared to analytical and neural-network approaches.
PSLR classifies functional data with scalar covariates using path signatures.
problem Classical functional logistic regression models have limitations in capturing nonlinear and cross-channel dependencies.
method PSLR uses truncated path signatures to create a basis-free representation of functional data.
result PSLR outperforms traditional functional classifiers in accuracy and robustness, especially under non-uniform sampling.
The lack of proper class discrimination among the Hyperspectral (HS) data points poses a potential challenge in HS classification. To address this issue, this paper proposes an optimal geometry-aware transformation for enhancing the classification accuracy. The underlying idea of this method is to obtain a linear proje…
Develops a curvature-corrected tangent space method for manifold-valued data.
problem Generalizing real-valued data approximation to manifold-valued data.
method Systematic approach to developing global-geometry aware, computationally feasible approximation schemes.
result Proposes CC-tHOSVD for low-rank approximation of manifold-valued data.
CDC-FM improves generative model quality-generalization tradeoff by regularizing with geometry-aware noise.
problem Tradeoff between high sample quality and memorization in deep generative models.
method Introduces Carré du champ flow matching (CDC-FM) that replaces homogeneous noise with anisotropic Gaussian noise capturing latent data manifold geometry.
result CDC-FM consistently offers better quality-generalization tradeoff across diverse datasets and architectures.
A new algorithm improves sampling for graph learning models.
problem Euclidean proposals struggle near the boundary of PSD matrices.
method ConeMALA, a geometry-aware Langevin algorithm.
result ConeMALA achieves higher ESS/sec and stable diagnostics.
Persistent homology provides a new, efficient molecular descriptor for protein dynamics.
problem Designing effective molecular descriptors for high-dimensional MD trajectories.
method Introduced masked Flood complex, a protein-tailored modification of simplicial complexes, for persistent homology.
result Persistent homology-based descriptors are competitive across protein dynamics tasks, including frame-level observable regression and MSM estimation.
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
GTA improves transformer-based NVS models by encoding geometric structure.
problem Suboptimal positional encoding for 3D vision tasks.
method Geometry-aware attention mechanism encoding geometric structure of tokens.
result GTA improves learning efficiency and performance of NVS models.
This paper introduces GEMINI, a new mutual information metric for unsupervised neural network training.
problem The mutual information (MI) as a clustering objective does not lead to satisfactory clusters.
method The authors generalised MI by changing its core distance, introducing GEMINIs that do not require regularizations and can automatically select the number of clusters.
result GEMINIs can automatically select the number of clusters without requiring a priori knowledge of the number of clusters.
New algorithms improve neural architecture search with faster convergence.
problem Improving efficiency and accuracy of neural architecture search.
method Geometry-aware gradient algorithms to optimize continuous relaxation of discrete search spaces.
result Exceeds state-of-the-art results on CIFAR and ImageNet benchmarks.
New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.
problem Intrinsic dimension estimation and Wasserstein distance estimation in large-scale OT.
method Introduces novel estimators for intrinsic dimension and Wasserstein distance.
result Simple, tuning-free estimator of OT and fast intrinsic dimension estimator.
Proposes a geometry-aware VAE for better latent space modeling.
problem Lack of meaningful latent space structure in VAEs for small datasets.
method Introduces a Riemannian Hamiltonian VAE with a learned metric.
result Improves latent space structure leading to better interpolations and data generation.
Non-Euclidean BPM extends optimization theory to non-Euclidean norms.
problem Extending BPM's convergence theory to non-Euclidean norms.
method Iteratively minimizing over norm balls in non-Euclidean geometry.
result Most BPM guarantees carry over to non-Euclidean norms.
CWGD measures gradient diversity weighted by curvature, improving SGD convergence.
problem Gradient noise in high-curvature directions is underestimated by standard methods.
method CWGD weights gradient diversity by the inverse square root of the Hessian.
result CWGD-Cosine reduces optimization error by up to 20% compared to standard cosine annealing.
S-GAI initializes MLPs using spectral geometry from data, improving performance.
problem Lack of guidance on initial weights encoding data geometry.
method S-GAI uses SVD to estimate spectral class geometry, initializing MLPs from training data.
result S-GAI-initialized MLPs start from a more informative hidden state and achieve comparable accuracy.
New framework improves experimental design using integral probability metrics.
problem Challenges in Bayesian Optimal Experimental Design (BOED) with KL divergence.
method Integrates integral probability metrics (IPMs) for stability and flexibility.
result IPM-based designs yield more robust and accurate credible sets.
GABI learns geometry from diverse systems to improve Bayesian inference.
problem Bayesian inversion of physical systems with varying geometries.
method Geometric Autoencoders for Bayesian Inversion (GABI) learns geometry-aware priors from large datasets.
result GABI yields comparable predictive accuracy to deterministic methods and well-calibrated uncertainty quantification.
This paper tackles high-dimensional Bayesian optimization by projecting a manifold into a lower space.
problem High-dimensional optimization of expensive functions with limited labeled data.
method Random linear projection of a manifold embedded in high-dimensional space, combined with semi-supervised learning of the manifold's geometry.
result Our approach outperforms existing high-dimensional BO methods in various synthetic and real-world applications.
Understanding the 3-dimensional structure of the world is a core challenge in computer vision and robotics. Neural rendering approaches learn an implicit 3D model by predicting what a camera would see from an arbitrary viewpoint. We extend existing neural rendering to more complex, higher dimensional scenes than previo…
We study the problem of discriminative sub-trajectory mining. Given two groups of trajectories, the goal of this problem is to extract moving patterns in the form of sub-trajectories which are more similar to sub-trajectories of one group and less similar to those of the other. We propose a new method called Statistica…
We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities between them. This concept was originally introduced in theoretical ecology to study the diversity of ecosystems. Based on this notion of entropy, we introduce geometry-aware count…
Paper uses deep imitation learning to predict aircraft trajectories accurately.
problem Inefficient and costly Air Traffic Management system limits predictability.
method Generative Adversarial Imitation Learning framework with trajectory clustering and classification.
result Accurate predictions for entire trajectory stages, pre- and tactical.
Pattern ensembling fills in missing or inaccurate trajectory data.
problem Incompleteness, missing information, and inaccuracies in geolocation data.
method Probabilistically ensemble similar trajectory patterns from the vicinity.
result Reconstructs missing or unreliable trajectory segments effectively.
New method aligns brain data across individuals for better brain decoding.
problem Inter-individual variability in brain response patterns limits decoder generalization.
method SpectralOT method that embeds cortical geometry into Laplace-Beltrami eigenmodes.
result SpectralOT strikes balance between aligning functional features and preserving anatomical structure.
Study shows magnetic trajectories in Berger spheres are homogeneous.
problem Homogeneity of contact magnetic trajectories in Berger spheres.
method Proved every contact magnetic trajectory is a product of a homogeneous geodesic and a charged Reeb flow.
result Contact magnetic trajectories in Berger spheres are homogeneous.
Improved trajectory prediction for team sports using sparse outputs.
problem Challenging to train deep learning models for player trajectory prediction.
method Sparse trajectory prediction and constant acceleration interpolation.
result Interpolation improves performance for all tested models.
WS-II algorithm segments trajectories with high accuracy.
problem Trajectory segmentation for diverse data sources.
method Supervised learning with sliding window analysis.
result WS-II outperforms other methods in all datasets.
A framework clusters vehicle motion trajectories efficiently.
problem Costly manual annotation of vehicle motion data.
method Five-stage framework: align, embed, extract, embed, cluster.
result Framework achieves promising results on real-world dataset.
In this paper we propose a new parameter-free method for trajectory classification which finds the best trajectory partition and dimension combination for robust trajectory classification. Preliminary experiments show that our approach is very promising.
Generative model learns vehicle trajectory distributions for better data generalization.
problem Data sparsity and privacy issues in urban vehicle trajectory analysis.
method Generative adversarial imitation learning framework for urban vehicle trajectory generation.
result TrajGAIL model produces synthetic trajectories similar to real ones, achieving significant performance gains.
Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction and optimization. Interestingly, most all prior work in imitation and reinforcemen…