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Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…

Transformer-based detection and segmentation methods use a list of learned detection queries to retrieve information from the transformer network and learn to predict the location and category of one specific object from each query. We…

Learning structured representations of visual scenes is currently a major bottleneck to bridging perception with reasoning. While there has been exciting progress with slot-based models, which learn to segment scenes into sets of objects,…

Diffusion Models are popular generative modeling methods in various vision tasks, attracting significant attention. They can be considered a unique instance of self-supervised learning methods due to their independence from label…

The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks…

This is the same version that was previously only on my home page. We give a description of geometric realization which makes it evident that it commutes with products. A similar approach is used to treat cyclic sets. Our approach is…

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This…

The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…

Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We…

This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…

Machine learning and data mining techniques are effective tools to classify large amounts of data. But they tend to preserve any inherent bias in the data, for example, with regards to gender or race. Removing such bias from data or the…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…

Modern machine learning models are complicated. Most of them rely on convoluted latent representations of their input to issue a prediction. To achieve greater transparency than a black-box that connects inputs to predictions, it is…

We introduce a new variant of quantitative Helly-type theorems: the minimal \emph{"homothetic distance"} of the intersection of a family of convex sets to the intersection of a subfamily of a fixed size. As an application, we establish the…

Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

We study intersections of complex Lagrangian in complex symplectic manifolds, proving two main results. First, we construct global canonical perverse sheaves on complex Lagrangian intersections in complex symplectic manifolds for any pair…

Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…