Related papers: Adaptive Geometric Multiscale Approximations for I…

While retrieval-augmented generation (RAG) has been shown to enhance factuality of large language model (LLM) outputs, LLMs still suffer from hallucination, generating incorrect or irrelevant information. A common detection strategy…

Representational similarity analysis (RSA) has been shown to be an effective framework to characterize brain-activity profiles and deep neural network activations as representational geometry by computing the pairwise distances of the…

Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

We propose a deep learning algorithm for seismic interface and pocket detection with neural networks trained by synthetic high-frequency displacement data efficiently generated by the frozen Gaussian approximation (FGA). In seismic imaging…

We present a Python implementation for RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression). The method builds representations of multivariate functions with lower-dimensional terms, either as an…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the…

When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…

This work presents a novel, fully Riemannian framework for Low-Rank Adaptation (LoRA) that geometrically treats low-rank adapters by optimizing them directly on the fixed-rank manifold. This formulation eliminates the parametrization…

This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the…

Attention is a general reasoning mechanism than can flexibly deal with image information, but its memory requirements had made it so far impractical for high resolution image generation. We present Grid Partitioned Attention (GPA), a new…

Accurate modeling and explaining geospatial tabular data (GTD) are critical for understanding geospatial phenomena and their underlying processes. Recent work has proposed a novel transformer-based deep learning model named GeoAggregator…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…