  We present a convolutional neural network that is capable of searching for
continuous gravitational waves, quasi-monochromatic, persistent signals arising
from asymmetrically rotating neutron stars, in $\sim 1$ year of simulated data
that is plagued by non-stationary, narrow-band disturbances, i.e., lines. Our
network has learned to classify the input strain data into four categories: (1)
only Gaussian noise, (2) an astrophysical signal injected into Gaussian noise,
(3) a line embedded in Gaussian noise, and (4) an astrophysical signal
contaminated by both Gaussian noise and line noise. In our algorithm, different
frequencies are treated independently; therefore, our network is robust against
sets of evenly-spaced lines, i.e., combs, and we only need to consider
perfectly sinusoidal line in this work. We find that our neural network can
distinguish between astrophysical signals and lines with high accuracy. In a
frequency band without line noise, the sensitivity depth of our network is
about $\mathcal{D}^{95\%} \simeq 43.9$ with a false alarm probability of $\sim
0.5\%$, while in the presence of line noise, we can maintain a false alarm
probability of $\sim 10\%$ and achieve $\mathcal{D}^\mathrm{95\%} \simeq 3.62$
when the line noise amplitude is $h_0^\mathrm{line}/\sqrt{S_\mathrm{n}(f_k)} =
1.0$. We evaluate the computational cost of our method to be $O(10^{19})$
floating point operations, and compare it to those from standard all-sky
searches, putting aside differences between covered parameter spaces. Our
results show that our method is more efficient by one or two orders of
magnitude than standard searches. Although our neural network takes about
$O(10^8)$ sec to employ using our current facilities (a single GPU of
GTX1080Ti), we expect that it can be reduced to an acceptable level by
utilizing a larger number of improved GPUs.
