Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Exact Gradient Update for training Deep Networks with Very
  Large Sparse Targets   An important class of problems involves training deep neural networks with
sparse prediction targets of very high dimension D. These occur naturally in
e.g. neural language models or the learning of word-embeddings, often posed as
predicting the probability of next words among a vocabulary of size D (e.g. 200
000). Computing the equally large, but typically non-sparse D-dimensional
output vector from a last hidden layer of reasonable dimension d (e.g. 500)
incurs a prohibitive O(Dd) computational cost for each example, as does
updating the D x d output weight matrix and computing the gradient needed for
backpropagation to previous layers. While efficient handling of large sparse
network inputs is trivial, the case of large sparse targets is not, and has
thus so far been sidestepped with approximate alternatives such as hierarchical
softmax or sampling-based approximations during training. In this work we
develop an original algorithmic approach which, for a family of loss functions
that includes squared error and spherical softmax, can compute the exact loss,
gradient update for the output weights, and gradient for backpropagation, all
in O(d^2) per example instead of O(Dd), remarkably without ever computing the
D-dimensional output. The proposed algorithm yields a speedup of D/4d , i.e.
two orders of magnitude for typical sizes, for that critical part of the
computations that often dominates the training time in this kind of network
architecture.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg