We present the Lyα Continuum Analysis Network (LyCAN), a convolutional neural network that predicts the unabsorbed quasar continuum within the rest-frame wavelength range of 1040-1600 Å based on the red side of the Lyα emission line (1216-1600 Å). We developed synthetic spectra based on a Gaussian mixture model representation of nonnegative matrix factorization (NMF) coefficients. These coefficients were derived from high-resolution, low-redshift (z < 0.2) Hubble Space Telescope/Cosmic Origins Spectrograph (COS) quasar spectra. We supplemented this COS-based synthetic sample with an equal number of DESI Year 5 mock spectra. LyCAN performs extremely well on testing sets, achieving a median error in the forest region of 1.5% on the DESI mock sample, 2.0% on the COS-based synthetic sample, and 4.1% on the original COS spectra. LyCAN outperforms principal component analysis (PCA) and NMF-based prediction methods using the same training set by 40% or more. We predict the intrinsic continua of 83,635 DESI Year 1 spectra in the redshift range of 2.1 ≤ z ≤ 4.2 and perform an absolute measurement of the evolution of the effective optical depth. This is the largest sample employed to measure the optical depth evolution to date. We fit a power law of the form τ ( z ) = τ 0 ( 1 + z ) γ to our measurements and find τ 0 = (2.46 ± 0.14) × 10−3 and γ = 3.62 ± 0.04. Our results show particular agreement with high-resolution, ground-based observations around z = 2, indicating that LyCAN is able to predict the quasar continuum in the forest region with only spectral information outside the forest.