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: Vector Symbolic Architectures (VSAs) are high-dimensional vector representations of objects (eg., words, image parts), relations (eg., sentence structures), and sequences for use with machine learning algorithms. They consist of a vector addition operator for representing a collection of unordered objects, a Binding operator for associating groups of objects, and a methodology for encoding complex structures. We first develop Constraints that machine learning imposes upon VSAs: for example, similar structures must be represented by similar vectors. The constraints suggest that current VSAs should represent phrases ("The smart Brazilian girl") by binding sums of terms, in addition to simply binding the terms directly. We show that matrix multiplication can be used as the binding operator for a VSA, and that matrix elements can be chosen at random. A consequence for living systems is that binding is mathematically possible without the need to specify, in advance, precise neuron-to-neuron connection properties for large numbers of synapses. A VSA that incorporates these ideas, MBAT (Matrix Binding of Additive Terms), is described that satisfies all Constraints. With respect to machine learning, for some types of problems appropriate VSA representations permit us to prove learnability, rather than relying on simulations. We also propose dividing machine (and neural) learning and representation into three Stages, with differing roles for learning in each stage. For neural modeling, we give "representational reasons" for nervous systems to have many recurrent connections, as well as for the importance of phrases in language processing. Sizing simulations and analyses suggest that VSAs in general, and MBAT in particular, are ready for real-world applications.

Answer: Representing Objects, Relations, and Sequences

Question: Data can be acquired, shared, and processed by an increasingly larger number of entities, in particular people. The distributed nature of this phenomenon has contributed to the development of many crowdsourcing projects. This scenario is prevalent in most forms of expert/non-expert group opinion and rating tasks (including many forms of internet or on-line user behavior), where a key element is the aggregation of observations-opinions from multiple sources.

Answer: Evaluating Crowdsourcing Participants in the Absence of Ground-Truth

Question: For high level path planning, environments are usually modeled as distance graphs, and path planning problems are reduced to com puting the shortest path in distance graphs. One major drawback of this modeling is the inability to model uncertainties, which are of ten encountered in practice. In this paper, a new tool, called U-graph, is proposed for environment modeling. A U-graph is an ex tension of distance graphs with the ability to handle a kind of uncertainty. By model ing an uncertain environment as a U-graph, and a navigation problem as a Markovian decision process, we can precisely define a new optimality criterion for navigation plans, and more importantly, we can come up with a general algorithm for computing optimal plans for navigation tasks.

Answer:
High Level Path Planning with Uncertainty