Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

Theory of Thermal Conductivity in High-Tc Superconductors below Tc: Comparison between Hole-Doped and Electron-Doped Systems

In hole-doped high-Tc superconductors, thermal conductivity increases drastically just below Tc, which has been considered as a hallmark of a nodal gap. In contrast, such a coherence peak in thermal conductivity is not visible in electron-doped compounds, which may indicate a full-gap state such as a (d+is)-wave state. To settle this problem, we study the thermal conductivity in the Hubbard model using the fluctuation-exchange (FLEX) approximation, which predicts that the nodal d-wave state is realized in both hole-doped and electron-doped compounds. The contrasting behavior of thermal conductivity in both compounds originates from the differences in the hot/cold spot structure. In general, a prominent coherence peak in thermal conductivity appears in line-node superconductors only when the cold spot exists on the nodal line.Comment: 5 pages, to be published in J. Phys. Soc. Jpn. Vol.76 No.

On partial derivatives of multivariate Bernstein polynomials

It is shown that Bernstein polynomials for a multivariate function converge to this function along with partial derivatives provided that the latter derivatives exist and are continuous. This result may be useful in some issues of stochastic calculus