Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network’s success, usually done in a manual manner. As a straightforward strategy, large, mostly fully connected architectures are selected, thereby relying on a good optimization strategy to find proper weights while at the same time avoiding overfitting. However, large parts of the final network are redundant. In the best case, large parts of the network become simply irrelevant for later inferencing. In the worst case, highly parameterized architectures hinder proper optimization and allow the easy creation of adverserial examples fooling the network. A first step in removing irrelevant architectural parts lies in identifying those parts, which requires measuring the contribution of individual components such as neurons. In previous work, heuristics based on using the weight distribution of a neuron as contribution measure have shown some success, but do not provide a proper theoretical understanding. Therefore, in our work we investigate game theoretic measures, namely the Shapley value (SV), in order to separate relevant from irrelevant parts of an artificial neural network. We begin by designing a coalitional game for an artificial neural network, where neurons form coalitions and the average contributions of neurons to coalitions yield to the Shapley value. In order to measure how well the Shapley value measures the contribution of individual neurons, we remove low-contributing neurons and measure its impact on the network performance. In our experiments we show that the Shapley value outperforms other heuristics for measuring the contribution of neurons.

Crowdsourcing has emerged as a promising approach for obtaining services and data in a short time and at a reasonable budget. However, the quality of the output provided by the crowd is not guaranteed, and must be controlled. This quality control usually relies on worker screening or contribution reviewing at the cost of additional time and budget overheads. In this paper, we propose to reduce these overheads by leveraging the system history. We describe an offline learning algorithm that groups tasks from history into homogeneous clusters and learns for each cluster the worker features that optimize the contribution quality. These features are then used by the online targeting algorithm to select reliable workers for each incoming task. The proposed method is compared to the state of the art selection methods using real world datasets. Results show that we achieve comparable, and in some cases better, output quality for a smaller budget and shorter time.

The inferences of a machine learning algorithm are naturally limited by the available data. In many real-world applications, the provided internal data is domain-specific and we use external background knowledge to derive or add new features. Semantic networks, like linked open data, provide a largely unused treasure trove of background knowledge. This drives a recent surge of interest in unsupervised methods to automatically extract such semantic background knowledge and inject it into machine learning algorithms. In this work, we describe the general process of extracting knowledge from semantic networks through vector space embeddings. The locations in the vector space then reflect relations in the original semantic network. We perform this extraction for geographic background knowledge and inject it into a neural network for the complicated real-world task of credit-card fraud detection. This improves the performance by 11.2%.

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The tame case, where the characteristic of Fq does not divide n = deg f, is fairly well-understood, and we have reasonable bounds on the number of decomposables of degree n. Nevertheless, no exact formula is known if n has more than two prime factors. In order to count the decomposables, one wants to know, under a suitable normalization, the number of collisions, where essentially different components (g, h) yield the same f. In the tame case, Ritt's Second Theorem classifies all collisions of two such pairs.

We present counting methods for some special classes of multivariate polynomials over a finite field, namely, the reducible ones, the $s$-powerful ones (divisible by the $s$th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, and another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.

A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one wants to know the number of equal-degree collisions of the form f = g o h = g* o h* with (g, h) ≠ (g*, h*) and deg g = deg g*. Such collisions only occur in the wild case, where the field characteristic p divides deg f. Reasonable bounds on the number of decomposables over a finite field are known, but they are less sharp in the wild case, in particular for degree p2.

The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f = g o h in Fq[x] is well understood in many cases, but quite poorly when the degrees of both components are divisible by the characteristic p. This work investigates the decomposition of polynomials whose degree is a power of p. An (equal-degree) i-collision is a set of i distinct pairs (g, h) of polynomials, all with the same composition and deg g the same for all (g, h). Abhyankar (1997) introduced the projective polynomials xn+ ax + b, where n is of the form (rm -- 1)/(r -- 1) and r is a power of p. Our first tool is a bijective correspondence between i-collisions of certain additive trinomials, projective polynomials with i roots, and linear spaces with i Frobenius-invariant lines.