Related papers: Sparse Tiling through Overlap Closures for Termina…
Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
Selective rationalization aims to produce decisions along with rationales (e.g., text highlights or word alignments between two sentences). Commonly, rationales are modeled as stochastic binary masks, requiring sampling-based gradient…
Traditionally a tiling is defined with a finite number of finite forbidden patterns. We can generalize this notion considering any set of patterns. Generalized tilings defined in this way can be studied with a dynamical point of view,…
Text Simplification improves the readability of sentences through several rewriting transformations, such as lexical paraphrasing, deletion, and splitting. Current simplification systems are predominantly sequence-to-sequence models that…
We consider overlap splines that are defined by connecting the patches of piecewise functions via common values at given finite sets of nodes, without using any partitions of the computational domain. It is shown that some classical finite…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
We present the stellar resolution, a "flexible" tile system based on Robinson's first-order resolution. After establishing formal definitions and basic properties of the stellar resolution, we show its Turing-completeness and to illustrate…
We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by…
Sparsity is regarded as a desirable property of representations, especially in terms of explanation. However, its usage has been limited due to the gap with dense representations. Most NLP research progresses in recent years are based on…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…
We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…