Extends orbital integral evaluation to center of enveloping algebra.
problem Evaluate semisimple orbital integrals for arbitrary elements in the center of the enveloping algebra.
method Explicit geometric evaluation of Casimir operator to arbitrary elements in the center of the enveloping algebra.
result Extension of orbital integral evaluation to center of enveloping algebra.
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…
The problem of evaluating heat invariants can be computerized. Geometric symbol calculus of pseudodifferential operators is the main tool of such computerization.
New statistical measures assess group separability in low-dimensional geometrical spaces.
problem Lack of statistical measures to evaluate group separability in low-dimensional geometrical spaces.
method Proposed three statistical measures (PSI-ROC, PSI-PR, PSI-P) based on Projection Separability rationale.
result Statistical-based measures outperform traditional cluster validity indices in evaluating group separability.
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of potential applications including estimating the normal vector and mean curvature …
PackIt creates a virtual space for testing geometric planning skills.
problem Evaluating geometric planning abilities in virtual environments.
method Developed a virtual environment, PackIt, for geometric planning tasks.
result Demonstrated the effectiveness of various methods for geometric planning.
New geometric metrics improve Bayesian optimization performance evaluation.
problem Current metrics lack geometric insights and cannot compare algorithms effectively.
method Proposed four geometric metrics: precision, recall, average degree, and average distance.
result Proposed metrics provide more detailed evaluation of Bayesian optimization.
Active learning (AL) repeatedly trains the classifier with the minimum labeling budget to improve the current classification model. The training process is usually supervised by an uncertainty evaluation strategy. However, the uncertainty evaluation always suffers from performance degeneration when the initial labeled …
Deep learning approximates geometric measures of planar curves.
problem Approximating differential invariants of planar curves.
method Utilizing deep neural networks to estimate geometric measures of planar curves.
result Deep neural networks can learn to overcome instabilities and sampling artifacts.
Raven's Progressive Matrices are one of the widely used tests in evaluating the human test taker's fluid intelligence. Analogously, this paper introduces geometric generalization based zero-shot learning tests to measure the rapid learning ability and the internal consistency of deep generative models. Our empirical re…
We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…
Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.
problem Evaluation of LLM personas via psychometric questionnaires discards within-instance correlation structure.
method Constructed within-instance correlation matrices from IPIP-50 responses and analyzed geometry on SPD manifolds under manipulated question orderings.
result Persona expression comprises two dissociable components: aggregated features (Big Five scores) and geometric features (SPD manifold).
The paper calculates the full asymptotics of analytic torsions for compact orbifolds.
problem Analytic torsions of compact locally symmetric orbifolds.
method Using Selberg's trace formula and geometric localization, the paper evaluates the heat trace and orbital integrals.
result Explicit formula for the asymptotic Ray-Singer analytic torsion of compact orbifolds.
PyTorch Geometric Signed Directed fills the gap for GNNs on signed and directed graphs.
problem Lack of unified software packages for GNNs on signed and directed networks.
method Developed a software package with GNN models, synthetic and real-world data, and evaluation metrics.
result Demonstrates the effectiveness of the implemented methods through experiments.
In this study we model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the p…
CP2 uses geometric information to improve conformal prediction robustness.
problem CP fails under geometric data shifts, losing coverage guarantees.
method Integrates geometric pose information into CP via canonicalization.
result Integrating geometric information with CP ensures robustness under geometric shifts.
This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean curvature surfaces. This differential geometric interpretation provides an impor…
The paper examines geometric invariants near a specific type of singular point.
problem The behavior of geometric invariants near a singular point of a surface or curve.
method Analysis of geometric invariants for surfaces and curves that are suspensions of singular curves.
result Evaluation of the orders of Gaussian and mean curvatures for the studied surfaces and curves.
Unified pipeline detects multi-turn deception using geometric signals.
problem Detecting multi-turn deceptive interactions in LLMs.
method Geometric signaturization via genetic prompt optimization.
result Compact geometric model achieves high recall and F1 scores.
We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convol…
Randomized control methods improve asset pricing and performance analysis.
problem Challenges in drawing inferences from traditional random portfolios in performance evaluation.
method Geometric random walks and Markov chain Monte Carlo methods to construct flexible control groups.
result Captured premia associated with size, value, quality, and momentum in a constrained setting.
Generative model designs highly designable proteins using geometric algebra.
problem Creating proteins with diverse and statistically accurate secondary structures.
method Introduced a geometric algebra flow matching model (FrameFlow) with Clifford Frame Attention (CFA) for protein backbone design.
result Achieved high designability, diversity, and novelty in protein backbone sampling.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
problem Lack of geometric ergodicity study in Riemannian manifold and Lagrangian Monte Carlo methods.
method Investigates a mixture of LMC and RMHMC with MMALA to achieve geometric ergodicity.
result Demonstrates geometric ergodicity in the mixture of LMC and RMHMC with MMALA.
Geometric AD framework simplifies derivative computation in JAX.
problem Efficient and accurate automatic differentiation.
method Jet functors and Weil algebras for geometric analysis.
result Unified view of derivative propagation with algebraic exactness.
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Ou…
Soft geometric bias improves physical dynamics predictions.
problem Learning physical dynamics with exact group equivariance can degrade performance.
method Object-centric world models using geometric algebra neural networks.
result Soft geometric inductive bias leads to better physical fidelity predictions.
We introduce PyTorch Geometric, a library for deep learning on irregularly structured input data such as graphs, point clouds and manifolds, built upon PyTorch. In addition to general graph data structures and processing methods, it contains a variety of recently published methods from the domains of relational learnin…
In this paper, we investigate the geometric structure of activation spaces of fully connected layers in neural networks and then show applications of this study. We propose an efficient approximation algorithm to characterize the convex hull of massive points in high dimensional space. Based on this new algorithm, four…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation which relates constant mean curvature surfaces and time-invariant pressure distri…
We introduce a method for evaluating integrals in geometric calculus without introducing coordinates, based on using the fundamental theorem of calculus repeatedly and cutting the resulting manifolds so as to create a boundary and allow for the existence of an antiderivative at each step. The method is a direct general…
This study evaluates handwriting features to diagnose Parkinson's disease.
problem Diagnosing Parkinson's disease through handwriting analysis.
method Kinematic, geometrical, and non-linear features were evaluated using K-nearest neighbors, support vector machines, and random forest classifiers.
result Up to 93.1% accuracy in classifying Parkinson's disease and healthy subjects.
Introduces q-paths for generalizing geometric annealing paths in machine learning.
problem Limited applicability of existing path methods in machine learning.
method Develops a family of paths derived from a generalized mean, including geometric and arithmetic mixtures.
result Empirical gains in Bayesian inference and generative model evaluation.
Graph Neural Networks improve financial time series forecasting accuracy.
problem Forecasting univariate financial time series with statistical significance.
method Introducing the Time-Geometric model combining geometric and temporal patterns.
result Statistically significant improvements in forecasting accuracy through geometric patterns.
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex polytopes. This interpretation combined with novel structural insights from our geom…
Geometric analysis on real analytic manifolds using seminorms.
problem Characterizing operations on real analytic manifolds and vector bundles.
method Using seminorms and geometric decompositions of jet bundles.
result New characterizations of real analytic mappings and operations.
Geometric Capsule Autoencoders group 3D points into parts and objects.
problem Learning object representations from 3D point clouds.
method Geometric capsules with pose and feature components, Multi-View Agreement voting mechanism.
result Learned representations enable object identification and canonical pose recovery.
GDB bridges geometric states with improved accuracy and generality.
problem Challenges in predicting geometric state evolution in complex systems.
method Geometric Diffusion Bridge (GDB) framework using equivariant diffusion bridges.
result GDB surpasses existing methods in accurately bridging geometric states.
Lectures introduce evaluation of SL(3) foams and link homology.
problem Categorification of quantum sl3 web and link invariant. method Introduction and review of SL(3) foams and their evaluation. result Categorification of Kuperberg quantum sl3 web and link invariant. Geometric method improves uncertainty estimation in real-time.
problem Improving uncertainty estimation in machine learning models.
method Geometric distance from training inputs for uncertainty estimation, post-hoc calibration.
result Method yields better uncertainty estimations than existing approaches.
Researchers use LLMs to judge other LLMs, but this study provides a new geometric perspective to understand when it works.
problem The challenge of evaluating LLMs using other LLMs as judges, considering both aleatoric and epistemic uncertainties.
method A geometric perspective on ranking LLM candidates using probability simplices, analyzing conditions for identifiable rankings and designing Bayesian priors.
result Geometric analysis reveals that rankings based on LLM judges are robust in many but not all datasets, emphasizing the importance of modeling epistemic uncertainty.
Two new algorithms solve high-dimensional optimization problems without gradients.
problem Optimizing complex, high-dimensional functions without gradient information.
method GradientLess Descent (GLD) algorithms that use evaluations at adaptively chosen inputs.
result Converges within an ε-ball of the optimum with a number of evaluations that is poly-logarithmic in dimensionality.
Geometric framework for portfolio analysis detects financial crises and evaluates performance.
problem Detecting financial crises and evaluating portfolio performance in volatile markets.
method Geometric framework, copula models, statistical computing.
result Automated crisis detection and new portfolio score for performance evaluation.
A framework for generating 3D shapes by sequentially assembling primitives.
problem Combinatorial complexity in generating 3D shapes.
method Bayesian optimization for efficient exploration and exploitation of feasible combinations.
result Successfully generates realistic combinatorial 3D shapes.
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.
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.
The paper proposes a method to determine the geometric priors of relational data.
problem Identifying geometric structure in heterogeneous, high-dimensional data.
method Combinatorial approach analyzing nearest-neighbor structures and local neighborhood growth rates.
result The method can identify the geometric priors of suitable embedding spaces for relational data.
We initiate the study of classical knots through the homotopy class of the n-th evaluation map of the knot, which is the induced map on the compactified n-point configuration space. Sending a knot to its n-th evaluation map realizes the space of knots as a subspace of what we call the n-th mapping space model for knots…
Geometric observables detect financial regime shifts with high accuracy.
problem Detecting regime shifts in financial markets.
method Extracted four geometric observables from equity-index returns and evaluated them against various baseline methods.
result The Berry Phase Rate achieves an unbiased out-of-sample median Cohen's d of 0.72, significantly reducing false alarms.