In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[EX Q]: In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified. INTRODUCTION The quality of a model is typically measured by its ability to generalize from a training set to previously unseen data from the same distribution. In regression tasks generalization essentially boils down to interpolation if the training data is sufficiently dense. As long as models are selected correctly, i. e. in a way to not overfit the data, the regression problem is well understood and can – at least conceptually – be considered solved. However, when working with data from real-world devices, e. g. controlling a robotic arm, interpolation might not be sufficient. It could happen that future data lies outside of the training domain, e. g. when the arm is temporarily operated outside of its specifications. For the sake of robustness and safety it is desirable in such a case to have a regression model that continues to make good predictions, or at least does not fail catastrophically. This setting, which we call extrapolation generalization, is the topic of the present paper. We are particularly interested in regression tasks for systems that can be described by real-valued analytic expression, e. g. mechanical systems such as a pendulum or a robotic arm. These are typically governed by a highly nonlinear function but it is nevertheless possible, in principle, to infer their behavior on an extrapolation domain from their behavior elsewhere. We make two main contributions: 1) a new type of network that can learn analytical expressions and is able to extrapolate to unseen domains and 2) a model selection strategy tailored to the extrapolation setting. The following section describes the setting of regression and extrapolation. Afterwards we introduce our method and discuss the architecture, its training, and its relation to prior art. We present our results in the Section Experimental evaluation and close with conclusions. REGRESSION AND EXTRAPOLATION We consider a multivariate regression problem with a training set {(x1, y1), . . . , (xN , yN )} with x ∈ R, y ∈ R. Because our main interest lies on extrapolation in the context of learning the dynamics of physical systems we assume the data originates from an unknown analytical function (or system of functions), φ : R → R with additive zero-mean noise, ξ, i. e. y = φ(x) + ξ and Eξ = 0. The function φ may, for instance, reflect a system of ordinary differential equations that govern the movements of a robot arm or the like. The general task is to learn a function ψ : R → R that approximates the true functional relation as well as possible in the squared loss sense, i. e. achieves minimal expected error E‖ψ(x) − φ(x)‖2. In practice, we only have particular examples of the function values available and measure the quality of predicting in terms of the empirical error on
[EX A]: EXTRAPOLATION AND LEARNING EQUATIONS

[EX Q]: Reactive (memoryless) policies are sufficient in completely observable Markov decision pro­ cesses (MDPs), but some kind of memory is usually necessary for optimal control of a par­ tially observable MDP. Policies with finite mem­ ory can be represented as finite-state automata. In this paper, we extend Baird and Moore's YAPS algorithm to the problem of learning gen­ eral finite-state automata. Because it performs stochastic gradient descent, this algorithm can be shown to converge to a locally optimal finite­ state controller. We provide the details of the algorithm and then consider the question of un­ der what conditions stochastic gradient descent will outperform exact gradient descent. We con­ clude with empirical results comparing the per­ formance of stochastic and exact gradient de­ scent, and showing the ability of our algorithm to extract the useful information contained in the sequence of past observations to compensate for the lack of observability at each time-step.
[EX A]: Learning Finite-State Controllers for Partially Observable Environments

[EX Q]: In this paper we examine the benefit of performing named entity recognition (NER) and co-reference resolution to an English and a Greek corpus used for text segmentation. The aim here is to examine whether the combination of text segmentation and information extraction can be beneficial for the identification of the various topics that appear in a document. NER was performed manually in the English corpus and was compared with the output produced by publicly available annotation tools while, an already existing tool was used for the Greek corpus. Produced annotations from both corpora were manually corrected and enriched to cover four types of named entities. Co-reference resolution i.e., substitution of every reference of the same instance with the same named entity identifier was subsequently performed. The evaluation, using five text segmentation algorithms for the English corpus and four for the Greek corpus leads to the conclusion that, the benefit highly depends on the segment’s topic, the number of named entity instances appearing in it, as well as the segment’s length.
[EX A]:
Text Segmentation using Named Entity Recognition and Co-reference Resolution in English and Greek Texts