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Recently, Neural Turing Machine and Memory Networks have shown that adding an external memory can greatly ameliorate a traditional recurrent neural network's tendency to forget after a long period of time. Here we present a new design of an external memory, wherein memories are stored in an Euclidean key space R n. An LSTM controller performs read and write(More)
In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes A = B especially when A is known to be a subset of B. In this paper we introduce a homological theory of functions that can be used to establish complexity separations, while also providing other(More)
External neural memory structures have recently become a popular tool for algo-rithmic deep learning (Graves et al., 2014; Weston et al., 2014). These models generally utilize differentiable versions of traditional discrete memory-access structures (random access, stacks, tapes) to provide the storage necessary for computational tasks. In this work, we(More)
  • Greg Yang
  • 2015
The ǫ-logic (which is called ǫE-logic in this paper) of Kuyper and Terwijn is a variant of first order logic with the same syntax, in which the models are equipped with probability measures and in which the ∀x quantifier is interpreted as " there exists a set A of measure ≥ 1 − ǫ such that for each x ∈ A,. .. . " Previously, Kuyper and Terwijn proved that(More)
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