Related papers: Sparse Tiling through Overlap Closures for Termina…
Let $T$ be a tile in $\mathbb{Z}^n$, meaning a finite subset of $\mathbb{Z}^n$. It may or may not tile $\mathbb{Z}^n$, in the sense of $\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\mathbb{Z}^d$…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
In text classification, the problem of overfitting arises due to the high dimensionality, making regularization essential. Although classic regularizers provide sparsity, they fail to return highly accurate models. On the contrary,…
We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for…
In this thesis we discuss machine learning methods performing automated variable selection for learning sparse predictive models. There are multiple reasons for promoting sparsity in the predictive models. By relying on a limited set of…
Sparse coding or sparse dictionary learning has been widely used to recover underlying structure in many kinds of natural data. Here, we provide conditions guaranteeing when this recovery is universal; that is, when sparse codes and…
An integral self-affine tile is the solution of a set equation $\mathbf{A} \mathcal{T} = \bigcup_{d \in \mathcal{D}} (\mathcal{T} + d)$, where $\mathbf{A}$ is an $n \times n$ integer matrix and $\mathcal{D}$ is a finite subset of…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
String analysis is the problem of reasoning about how strings are manipulated by a program. It has numerous applications including automatic detection of cross-site scripting (XSS). A popular string analysis technique includes symbolic…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
We introduce a novel parsing concept called local lexing. It integrates the classically separated stages of lexing and parsing by allowing lexing to be dependent upon the parsing progress and by providing a simple mechanism for constraining…
In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and…
Word embeddings are a powerful natural language processing technique, but they are extremely difficult to interpret. To enable interpretable NLP models, we create vectors where each dimension is inherently interpretable. By inherently…
For a large class of tilings, including the Penrose tiling in two dimension as well as the icosahedral ones in 3 dimension, the continuous hull of such a tiling inherits a minimal lamination structure with flat leaves and a transversal…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…