107,400 research outputs found
Fast Single-Class Classification and the Principle of Logit Separation
We consider neural network training, in applications in which there are many
possible classes, but at test-time, the task is a binary classification task of
determining whether the given example belongs to a specific class, where the
class of interest can be different each time the classifier is applied. For
instance, this is the case for real-time image search. We define the Single
Logit Classification (SLC) task: training the network so that at test-time, it
would be possible to accurately identify whether the example belongs to a given
class in a computationally efficient manner, based only on the output logit for
this class. We propose a natural principle, the Principle of Logit Separation,
as a guideline for choosing and designing losses suitable for the SLC. We show
that the cross-entropy loss function is not aligned with the Principle of Logit
Separation. In contrast, there are known loss functions, as well as novel batch
loss functions that we propose, which are aligned with this principle. In
total, we study seven loss functions. Our experiments show that indeed in
almost all cases, losses that are aligned with the Principle of Logit
Separation obtain at least 20% relative accuracy improvement in the SLC task
compared to losses that are not aligned with it, and sometimes considerably
more. Furthermore, we show that fast SLC does not cause any drop in binary
classification accuracy, compared to standard classification in which all
logits are computed, and yields a speedup which grows with the number of
classes. For instance, we demonstrate a 10x speedup when the number of classes
is 400,000. Tensorflow code for optimizing the new batch losses is publicly
available at https://github.com/cruvadom/Logit Separation.Comment: Published as a conference paper in ICDM 201
The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods
The short--time self diffusion coefficient of a sphere in a suspension of
rigid rods is calculated in first order in the rod volume fraction. For low rod
concentrations the correction to the Einstein diffusion constant of the sphere
is a linear function of the rod volume fraction with the slope proportional to
the equilibrium averaged mobility diminution trace of the sphere interacting
with a single freely translating and rotating rod. The two--body hydrodynamic
interactions are calculated using the so--called bead model in which the rod is
replaced by a stiff linear chain of touching spheres. The interactions between
spheres are calculated numerically using the multipole method. Also an
analytical expression for the diffusion coefficient as a function of the rod
aspect ratio is derived in the limit of very long rods. We show that in this
limit the correction to the Einstein diffusion constant does not depend on the
size of the tracer sphere. The higher order corrections depending on the
applied model are computed numerically. An approximate expression is provided,
valid for a wide range of aspect ratios.Comment: 11 pages, 6 figure
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