An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analysing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.

We have developed a digital watermarking method that use neural networks to learn embedding and extraction processes that are robust against rotation and JPEG compression. The proposed neural networks consist of a stego-image generator, a watermark extractor, a stego-image discriminator, and an attack simulator. The attack simulator consists of a rotation layer and an additive noise layer, which simulate the rotation attack and the JPEG compression attack, respectively. The stego-image generator can learn embedding that is robust against these attacks, and also, the watermark extractor can extract watermarks without rotation synchronization. The quality of the stego-images can be improved by using the stego-image discriminator, which is a type of adversarial network. We evaluated the robustness of the watermarks and image quality and found that, using the proposed method, high-quality stego-images could be generated and the neural networks could be trained to embed and extract watermarks that are robust against rotation and JPEG compression attacks. We also showed that the robustness and image quality can be adjusted by changing the noise strength in the noise layer.