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We present a new catalog of $9318$ Ly$\alpha$ emitter (LAE) candidates at $z = 2.2$, $3.3$, $4.9$, $5.7$, $6.6$, and $7.0$ that are photometrically selected by the SILVERRUSH program with a machine learning technique from large area (up to $25.0$ deg$^2$) imaging data with six narrowband filters taken by the Subaru Strategic Program with Hyper Suprime-Cam (HSC SSP) and a Subaru intensive program, Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS). We construct a convolutional neural network that distinguishes between real LAEs and contaminants with a completeness of $94$% and a contamination rate of $1$%, enabling us to efficiently remove contaminants from the photometrically selected LAE candidates. We confirm that our LAE catalogs include $177$ LAEs that have been spectroscopically identified in our SILVERRUSH programs and previous studies, ensuring the validity of our machine learning selection. In addition, we find that the object-matching rates between our LAE catalogs and our previous results are $\simeq 80$-$100$% at bright NB magnitudes of $\lesssim 24$ mag. We also confirm that the surface number densities of our LAE candidates are consistent with previous results. Our LAE catalogs will be made public on our project webpage., Comment: 19 pages, 10 figures, accepted for publication in ApJ. Our LAE catalogs will become available at http://cos.icrr.u-tokyo.ac.jp/rush.html