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.
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Question: There are already quite a few tools for solving the Satisfiability Modulo Theories (SMT) problems. In this paper, we present VolCE, a tool for counting the solutions of SMT constraints, or in other words, for computing the volume of the solution space. Its input is essentially a set of Boolean combinations of linear constraints, where the numeric variables are either all integers or all reals, and each variable is bounded. The tool extends SMT solving with integer solution counting and volume computation/estimation for convex polytopes. Effective heuristics are adopted, which enable the tool to deal with high-dimensional problem instances efficiently and accurately.

Answer: A Tool for Computing and Estimating the Volume of the Solution Space of SMT(LA) Constraints


Question: We envision a machine learning service provider facing a continuous stream of problems with the same input domain, but with output domains that may differ. Clients present the provider with problems implicitly, by labeling a few example inputs, and then ask the provider to train models which reasonably extend their labelings to novel inputs. The provider wants to avoid constraining its users to a set of common labels, so it does not assume any particular correspondence between labels for a new task and labels for previously encountered tasks. To perform well in this setting, the provider needs a representation of the input domain which, in expectation, permits effective models for new problems to be learned efficiently from a small number of examples. While this bears a resemblance to settings considered in previous work on multitask and lifelong learning, our non-assumption of inter-task label correspondence leads to a novel algorithm: Lifelong Learner of Discriminative Representations (LLDR), which explicitly minimizes a proxy for the intra-task small-sample generalization error. We examine the relative benefits of our approach on a diverse set of real-world datasets in three significant scenarios: representation learning, multitask learning and lifelong learning.

Answer: Lifelong Learning of Discriminative Representations


Question: Abstract. We study the learning algorithm corresponding to the incremental gradient descent defined by the empirical risk over an infinite dimensional hypotheses space. We consider a statistical learning setting and show that, provided with a universal step-size and a suitable early stopping rule, the learning algorithm thus obtained is universally consistent and derive finite sample bounds. Our results provide a theoretical foundation for considering early stopping in online learning algorithms and shed light on the effect of allowing for multiple passes over the data.

Answer:
REGULARIZATION BY EARLY STOPPING FOR ONLINE LEARNING ALGORITHMS