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.

Example Input: 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.
Example Output: Representing Objects, Relations, and Sequences

Example Input: A perfectly rational decision-maker chooses the best action with the highest utility gain from a set of possible actions. The optimality principles that describe such decision processes do not take into account the computational costs of finding the optimal action. Bounded rational decision-making addresses this problem by specifically trading off information-processing costs and expected utility. Interestingly, a similar trade-off between energy and entropy arises when describing changes in thermodynamic systems. This similarity has been recently used to describe bounded rational agents. Crucially, this framework assumes that the environment does not change while the decision-maker is computing the optimal policy. When this requirement is not fulfilled, the decision-maker will suffer inefficiencies in utility, that arise because the current policy is optimal for an environment in the past. Here we borrow concepts from non-equilibrium thermodynamics to quantify these inefficiencies and illustrate with simulations its relationship with computational resources.
Example Output: Bounded Rational Decision-Making in Changing Environments

Example Input: In this paper, we describe our autonomous bidding agent, RoxyBot, who emerged victorious in the travel division of the 2006 Trading Agent Competition in a photo finish. At a high level, the design of many successful trading agents can be summarized as follows: (i) price prediction: build a model of market prices; and (ii) optimization: solve for an approximately optimal set of bids, given this model. To predict, RoxyBot builds a stochastic model of market prices by simulating simultaneous ascending auctions. To optimize, RoxyBot relies on the sample average approximation method, a stochastic optimization technique.
Example Output:
RoxyBot-06: Stochastic Prediction and Optimization in TAC Travel