How to move efficiently is an optimal control problem, whose computational complexity grows exponentially with the horizon of the planned trajectory. Breaking a compound movement into a series of chunks, each planned over a shorter horizon can thus reduce the overall computational complexity and associated costs while limiting the achievable efficiency. This trade-off suggests a cost-effective learning strategy: to learn new movements we should start with many short chunks (to limit the cost of computation). As practice reduces the impediments to more complex computation, the chunking structure should evolve to allow progressively more efficient movements (to maximize efficiency). Here we show that monkeys learning a reaching sequence over an extended period of time adopt this strategy by performing movements that can be described as locally optimal trajectories. Chunking can thus be understood as a cost-effective strategy for producing and learning efficient movements.
Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent searching, statistical characterization, and meaningful classification. Latent Dirichlet allocation (LDA) is the state of the art in topic modeling. Here, we perform a systematic theoretical and numerical analysis that demonstrates that current optimization techniques for LDA often yield results that are not accurate in inferring the most suitable model parameters. Adapting approaches from community detection in networks, we propose a new algorithm that displays high reproducibility and high accuracy and also has high computational efficiency. We apply it to a large set of documents in the English Wikipedia and reveal its hierarchical structure.
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