We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT). The computational cost of VAT is relatively low. For neural networks, the approximated gradient of virtual adversarial loss can be computed with no more than two pairs of forward- and back-propagations. In our experiments, we applied VAT to supervised and semi-supervised learning tasks on multiple benchmark datasets. With a simple enhancement of the algorithm based on the entropy minimization principle, our VAT achieves state-of-the-art performance for semi-supervised learning tasks on SVHN and CIFAR-10.

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This paper reports the two-photon absorbing and orange-red fluorescence emitting properties of a series of new 2,1,3-benzothiadiazole (BTD)-based D-pi-A-pi-D-type and star-burst-type fluorescent dyes. In the D-pi-A-pi-D-type dyes 1-6, a central BTD core was connected with two terminal N,N-disubstituted amino groups via various pi-conjugated spacers. The star-burst-type dyes 8 and 10 have a three-branched structure composed of a central core (benzene core in 8 and triphenylamine core in 10) and three triphenylamine-containing BTD branches. All the BTD-based dyes displayed intense orange-red color fluorescence in a region of 550-689 nm, which was obtained by single-photon excitation with good fluorescent quantum yield up to 0.98 as well as by two-photon excitation. Large two-photon absorption (TPA) cross-sections (110-800 GM) of these BTD dyes were evaluated by open aperture Z-scan technique with a femtosecond Ti/sapphire laser. The TPA cross-sections of D-pi-A-pi-D-type dyes 2-6 with a benzene, thiophene, ethene, ethyne, and styrene moiety, respectively, as an additional pi-conjugated spacer are about 1.5-2.5 times larger than that of 1c with only a benzene spacer. The TPA cross-sections significantly increased in three-branched star-burst-type BTDs 8 (780 GM) with a benzene core and 10 (800 GM) with a triphenylamine core, which are about 3-5 times larger than those of the corresponding one-dimensional sub-units 9 (170 GM) and 11 (230 GM), respectively. The ratios of sigma/e(pi) between three-branched and one-dimensional dyes were 6.5:3.8 (for 8 and 9) and 6.0:4.0 (for 10 and 11), which are larger than those predicted simply on the basis of the chromophore number density (1:1), according to a cooperative enhancement of the two-photon absorbing nature in the three-branched system.