103,957 research outputs found

    Fast Single-Class Classification and the Principle of Logit Separation

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    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

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    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

    Self-gravity in thin discs and edge effects: an extension of Paczynski's approximation

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    As hydrostatic equilibrium of gaseous discs is partly governed by the gravity field, we have estimated the component caused by a vertically homogeneous disc, with a special attention for the outer regions where self-gravity classically appears. The accuracy of the integral formula is better than 1%, whatever the disc thickness, radial extension and radial density profile. At order zero, the field is even algebraic for thin discs and writes −4πGΣ(R)fedge(R)- 4 \pi G \Sigma(R) f_{edge} (R) at disc surface, thereby correcting Paczynski's formula by a multiplying factor fedge≳1/2f_{edge} \gtrsim 1/2, which depends on the relative distance to the edges and the local disc thickness. For very centrally condensed discs however, this local contribution can be surpassed by action of mass stored in the inner regions, possibly resulting in fedge≫1f_{edge} \gg 1. A criterion setting the limit between these two regimes is derived. These result are robust in the sense that the details of vertical stratification are not critical. We briefly discuss how hydrostatic equilibrium is impacted. In particular, the disc flaring should not reverse in the self-gravitating region, which contradicts what is usually obtained from Paczynski's formula. This suggests that i) these outer regions are probably not fully shadowed by the inner ones (important when illuminated by a central star), and ii) the flared shape of discs does not firmly prove the absence or weakness of self-gravity.Comment: Accepted for publication in A&
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