Related papers: SVarM: Linear Support Varifold Machines for Classi…

Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric…

This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…

Humans naturally possess the spatial reasoning ability to form and manipulate images and structures of objects in space. There is an increasing effort to endow Vision-Language Models (VLMs) with similar spatial reasoning capabilities.…

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…

Merging the two cultures of deep and statistical learning provides insights into structured high-dimensional data. Traditional statistical modeling is still a dominant strategy for structured tabular data. Deep learning can be viewed…

Instruction following is crucial in contemporary LLM. However, when extended to multimodal setting, it often suffers from misalignment between specific textual instruction and targeted local region of an image. To achieve more accurate and…

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

Machine learning in materials science faces challenges due to limited experimental data, as generating synthesis data is costly and time-consuming, especially with in-house experiments. Mining data from existing literature introduces issues…

Deep learning models have great potential in medical imaging, including orthodontics and skeletal maturity assessment. However, applying a model to data different from its training set can lead to unreliable predictions that may impact…

Visual place recognition (VPR) remains challenging due to significant viewpoint changes and appearance variations. Mainstream works tackle these challenges by developing various feature aggregation methods to transform deep features into…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…

Graph representation learning methods are highly effective in handling complex non-Euclidean data by capturing intricate relationships and features within graph structures. However, traditional methods face challenges when dealing with…

Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…

We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Visual explanation maps enhance the trustworthiness of decisions made by deep learning models and offer valuable guidance for developing new algorithms in image recognition tasks. Class activation maps (CAM) and their variants (e.g.,…