Related papers: Sculptures in Concurrency
Computation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the lambda-calculus. However, recent…
Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension d is equal to the…
We explore the question of which shape a manifold is compelled to take when immersed in another one, provided it must be the extremum of some functional. We consider a family of functionals which depend quadratically on the extrinsic…
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…
Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…
Linear sketches are powerful algorithmic tools that turn an n-dimensional input into a concise lower-dimensional representation via a linear transformation. Such sketches have seen a wide range of applications including norm estimation over…
In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited…
Words are not created equal. In fact, they form an aristocratic graph with a latent hierarchical structure that the next generation of unsupervised learned word embeddings should reveal. In this paper, justified by the notion of…
In the era of foundation models and Large Language Models (LLMs), Euclidean space is the de facto geometric setting of our machine learning architectures. However, recent literature has demonstrated that this choice comes with fundamental…
Robotic fabric manipulation is challenging due to the infinite dimensional configuration space, self-occlusion, and complex dynamics of fabrics. There has been significant prior work on learning policies for specific deformable manipulation…
Unsupervised learning of a generalizable model of the visual appearance of humans from video data is of major importance for computing systems interacting naturally with their users and others. We propose a step towards automatic behavior…
Human bodies exhibit various shapes for different identities or poses, but the body shape has certain similarities in structure and thus can be embedded in a low-dimensional space. This paper presents an autoencoder-like network…
Constructing accurate model-agnostic explanations for opaque machine learning models remains a challenging task. Classification models for high-dimensional data, like images, are often inherently complex. To reduce this complexity,…
Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly…
Vector bundles and double vector bundles, or $2$-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these…
Hyperdimensional Computing (HDC) is a brain-inspired computing paradigm that represents and manipulates information using high-dimensional vectors, called hypervectors (HV). Traditional HDC methods, while robust to noise and inherently…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled n-cube, in exactly one way. The main ingredient is the non-functorial…
Deformable object manipulation remains a key challenge in developing autonomous robotic systems that can be successfully deployed in real-world scenarios. In this work, we explore the challenges of deformable object manipulation through the…
Physics-based simulation is essential for developing and evaluating robot manipulation policies, particularly in scenarios involving deformable objects and complex contact interactions. However, existing simulators often struggle to balance…