Related papers: Morphisms of Neural Codes
It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Selfridge, along with Sutherland and Marr provided some of the earliest proposals for how to program computers to recognize shapes. Their emphasis on filtering for contour features, especially the orientation of boundary segments, was…
To remain useful for their users, software systems need to continuously enhance and extend their functionality. Nevertheless, in many object-oriented applications, features are not represented explicitly. The lack of modularization is known…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
This paper proposes a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agent-based microsimulations. The definition makes it almost trivial to define morphisms to transform and…
Mathematical morphology is a theory concerned with non-linear operators for image processing and analysis. The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.…
Two of the most useful tools in topological combinatorics are the nerve lemma and discrete Morse theory. In this note we introduce a theorem that interpolates between them and allows decompositions of complexes into non-contractible pieces…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of…
Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with…
Non-negative sparse coding is a method for decomposing multivariate data into non-negative sparse components. In this paper we briefly describe the motivation behind this type of data representation and its relation to standard sparse…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural…
Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…