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.
GANs predict injection molding parts geometry from hot parts images.
problem Predicting final part geometry from early-stage measurements in injection molding.
method Used pix2pix GAN architecture to translate thermographic images to geometry.
result DMD analysis of GAN predictions reveals geometrical parameters.
This paper presents a novel framework for accurate pedestrian intent prediction at intersections. Given some prior knowledge of the curbside geometry, the presented framework can accurately predict pedestrian trajectories, even in new intersections that it has not been trained on. This is achieved by making use of the …
Online distributional prediction with latent cluster geometry
problem Predicting the full data-generating distribution in non-stationary streams
method Representing candidate laws as latent cluster geometry and using Gibbs quasi-posterior
result Achieving sublinear cumulative Wasserstein regret under bounded support and stable latent geometry
Spectral graph sparsification preserves geometry of GNN embeddings.
problem Maintaining geometric properties of graph neural network embeddings during sparsification.
method Proving spectral sparsification preserves squared pairwise distances, class means, and covariance structure in embedding space.
result Spectral sparsification preserves the geometry of learned embeddings in GNNs.
Enhances knowledge graph completion with mixed geometry tensor factorization.
problem Capturing nuanced distributional properties in knowledge graphs.
method Combines Euclidean and hyperbolic geometries for tensor factorization.
result Improves link prediction accuracy with fewer parameters.
The paper examines Bitcoin's nature using fractal geometry and finds it highly persistent, affecting predictability and decentralization.
problem Understanding the nature and predictability of Bitcoin prices.
method Statistical analysis of Bitcoin returns using fractal geometry.
result Bitcoin exhibits high persistence in prices, reducing efficiency but increasing predictability.
The study analyzes neural network predictions of knot invariants and finds that braid representations work best.
problem Understanding and predicting knot invariants using neural networks.
method Investigated different knot representations and invariants, proposed a cosine similarity score.
result Braid representations are best for predicting knot invariants, and some invariants are easier to learn than others.
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
New method uses Cantor embeddings and Wasserstein distances to analyze predictive states in time series data.
problem Analyzing predictive states in stochastic processes using time series data.
method Wasserstein distances for detecting predictive equivalences in symbolic data, using Cantor embeddings for finite-dimensional representation.
result Exploratory analysis of temporal structure in various processes reveals insights.
Mathematical framework using Riemannian geometry for intelligence and consciousness.
problem Lack of a unified mathematical framework for intelligence and consciousness.
method Conceptualizes intelligence as tokens in a high-dimensional space, using Riemannian geometry to describe structure and dynamics.
result Integrates geometric concepts to offer a unified framework for intelligence and consciousness.
Develops information geometry for Lévy processes in finance.
problem Understanding the statistical properties of Lévy processes for financial modeling.
method Deriving α-divergences from Lévy triplets, identifying Fisher information matrix and α-connection. result Identifies statistical implications and differential-geometric structures of Lévy processes.
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
Four geometries govern sequential and distribution-free inference.
problem Sequential and distribution-free inference challenges.
method Four distinct admissibility geometries.
result Four classes of admissible procedures are pairwise non-nested.
Neural network learns from higher-order connections in molecules.
problem Graph neural networks fail to account for local and hidden structures in graphs.
method Developed a neural network that can pass messages and aggregate information across higher-order paths.
result The model improves molecular property prediction.
The paper predicts edge weights in weighted directed networks using metric geometry.
problem Predicting edge weights in weighted directed networks.
method Introducing new types of weighted directed networks (AWDNs), constructing metrics, and proposing modified kNN and SVM methods.
result The proposed methods outperform traditional approaches in predicting edge weights.
Recursive filtering predicts wireless interference levels accurately.
problem Predicting interference in wireless networks.
method Designing a recursive predictor using Kalman filtering and ARMA model.
result Good accuracy of predicted interference values compared to true values.
New framework uses geometry of embeddings to predict robustness.
problem Monitoring robustness in models without OOD labels.
method Constructs graphs from embeddings, measures spectral complexity and curvature.
result Representation geometry predicts robustness reliably.
Atiyah-Singer theorem links math fields, predicts topological insights.
problem Understanding the interplay between analysis, geometry, and topology.
method Analyzes and generalizes topological invariants in differential geometry.
result Predicts the index of elliptic operators based on topology.
Model financial dynamics using 2-manifold geometries, revealing the torus as best for cyclical data.
problem Financial forecasting using complex market data.
method Embedding market data onto 2-manifolds (S2, R2, H2, T) guided by uniformization theorem, inferring latent curvature.
result The torus geometry best predicts cyclical financial data, aligning with IS-LM theory.
Develops a data-driven model for porous media flow simulations.
problem Capturing flow field and permeability in digital porous media.
method Data-driven approach using Lattice Boltzmann simulation data.
result Accurately predicts flow solutions with reduced computational time.
Framework predicts melt pool geometry with AI, improving manufacturing quality.
problem Achieving consistent product quality in Metal Additive Manufacturing.
method Surprise-guided sequential learning framework integrating CTGAN for limited data.
result Enhanced predictive accuracy for melt pool dimensions.
TabPFN's internal geometry topology correlates with dataset reliability.
problem Understanding TabPFN's behavior on structurally difficult tabular geometries.
method Using zigzag persistent homology, studying TabPFN's internal representations on synthetic tabular tasks with known topology.
result Topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability.
E2M predicts metric space outputs using deep learning.
problem Predicting non-Euclidean outputs like distributions and matrices.
method Weighted Fréchet means over learned weights.
result E2M achieves state-of-the-art performance across various outputs.
Enhances neural rendering with geometry-aware attention.
problem Efficiently modeling complex 3D scenes.
method Introduces Epipolar Cross Attention (ECA) for non-local operations.
result Significant improvement in Generative Query Networks (GQN) performance.
A new model uses Lorentz-Finsler geometry to predict wave propagation.
problem Modeling wave propagation in anisotropic and rheonomic media.
method Identifying wave trajectories as lightlike pregeodesics of a specific Lorentz-Finsler metric, solving ODE systems.
result Wave trajectories can be easily computed in real time.
Discrete Flow Maps bypass sequential prediction limits for parallel text generation.
problem Sequential autoregressive prediction limits large language model speed.
method Flow Maps compress generative trajectories into single-step mappings.
result Discrete Flow Maps surpass previous state-of-the-art results in discrete flow modeling.
We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The…
We present an unsupervised approach for learning to estimate three dimensional (3D) facial structure from a single image while also predicting 3D viewpoint transformations that match a desired pose and facial geometry. We achieve this by inferring the depth of facial keypoints of an input image in an unsupervised manne…
Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.
problem Efficiently dealing with distributions of covariance matrices in M/EEG multivariate time series.
method Defines a Sliced-Wasserstein distance for symmetric positive definite matrices and applies it to brain-age prediction and Brain Computer Interface applications.
result Demonstrates computational efficiency and strong theoretical guarantees for the proposed distance.
Higher-order geometry modifies Newtonian dynamics and predicts anomalies in spacecraft motion.
problem Observing and understanding higher-order effects in general relativity.
method Generalizing the Einstein-Hilbert action to include higher-order infinitesimals and studying field equations and cosmologies.
result Higher-order corrections predict anomalies like the Pioneer and flyby effects.
Study develops machine learning model to predict component movement during reflow in SMT.
problem Inaccurate self-alignment of components during reflow process in SMT leads to defects.
method Experimental data analysis followed by advanced machine learning models (SVR, NN, RFR) to predict component shift in x, y, and rotational directions.
result Random forest regression (RFR) model predicts component shift with high accuracy and low error.
New framework certifies robustness for regression models.
problem Certifying robustness for regression models is challenging.
method Derives a prediction-centered certificate that exploits local geometry.
result Gradient information yields tighter robustness certificates.
Wi-GATr learns to simulate wireless signals with high accuracy and speed.
problem Inaccurate wireless signal propagation models limit modern communication system design.
method Wi-GATr uses a Geometric Algebra Transformer to learn from scene primitives.
result Wi-GATr achieves more accurate predictions than existing methods.
Unified approach combines prediction-powered inference and variance reduction for semi-supervised optimization.
problem Scarcity of labeled data in semi-supervised optimization.
method PPI-SVRG, combining PPI and SVRG methods.
result Unified convergence bound with improved performance under label scarcity.
This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix.…
CSHT predicts financial returns from news using a novel transformer model on a sphere.
problem Financial forecasting from news and sentiment.
method Granger-causal hypergraph structure, Riemannian geometry, causally masked Transformer attention.
result CSHT outperforms baselines in return prediction, regime classification, and asset ranking.
New algorithm reduces regret and constraint violation in online convex optimization with predictions.
problem Online convex optimization with time-varying constraints and predictions.
method Primal-dual algorithm combining Follow-The-Regularized-Leader with adaptive steps.
result Achieves O(T43−β) regret and O(T21+β) constraint violation bounds. Unified mathematical theory for analyzing biomolecular geometry and flexibility.
problem Lack of a unified mathematical theory for analyzing biomolecular geometry and flexibility.
method Introducing de Rham-Hodge theory, Helmholtz-Hodge decomposition, and discrete exterior calculus.
result Unified framework for predicting macromolecular flexibility and natural modes.
Introduces TPV to analyze model robustness without labels.
problem Analyzing post-training robustness of machine learning models.
method Parameter perturbations and test prediction variance (TPV) as a unifying framework.
result TPV connects various perturbations under a single lens, providing insights into model stability.
Review of mathematical representations for biomolecular data.
problem Complexity and high dimensionality of biomolecular datasets hinder ML applications.
method Developed low-dimensional and scalable mathematical representations using algebraic topology, differential geometry, and graph theory.
result Mathematical representations improve protein-ligand binding predictions and other biomolecular applications.
A new framework for structured prediction on non-vectorial spaces.
problem Structured prediction on non-vectorial output spaces.
method Defining a suitable geometry for implicit loss functions.
result Efficient algorithmic framework with sharp statistical analysis.
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…
The Fisher information metric is an important foundation of information geometry, wherein it allows us to approximate the local geometry of a probability distribution. Recurrent neural networks such as the Sequence-to-Sequence (Seq2Seq) networks that have lately been used to yield state-of-the-art performance on speech…
Bayesian models for networks are often misspecified, leading to overconfident inference.
problem Real-world networks violate assumptions of geometry and link function in latent space models.
method Proposes a generalized posterior framework for random geometric graphs, using Link-Sequential R-SafeBayes to adaptively tune posterior regularization.
result Improved calibration and better link prediction performance demonstrated on synthetic and real-world networks.
GeoHNN models physics laws for stable, accurate predictions.
problem Violations of physical principles in machine learning models.
method Explicitly encodes geometric priors in inertia and phase space.
result Significantly outperforms existing models in long-term stability and accuracy.
The study uses machine learning to analyze office floor plans and predict function based on geometry.
problem Lack of formalisms to describe spatial affordance in automated floor-plan generation tools.
method Supervised and unsupervised data mining techniques, including J48 algorithm, were used to analyze office floor plans.
result J48 algorithm can predict class performance on unseen examples up to 79.5% for office dataset.
Foundation models fail to preserve continuous geometry, identified as the Geometric Alignment Tax.
problem Continuous geometry is lost in foundation models due to discrete categorical bottlenecks.
method Controlled ablations on synthetic systems and evaluation of 14 biological models using rate-distortion theory and MINE.
result Replacing cross-entropy with a continuous head reduces geometric distortion by up to 8.5x.