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Traditionally, gravitational waves are detected with techniques such as matched filtering or unmodeled searches based on wavelets. However, in the case of generic black hole binaries with non-aligned spins, if one wants to explore the whole parameter space, matched filtering can become impractical, which sets severe restrictions on the sensitivity and computational efficiency of gravitational-wave searches. Here, we use a novel combination of machine-learning algorithms and arrive at sensitive distances that surpass traditional techniques in a specific setting. Moreover, the computational cost is only a small fraction of the computational cost of matched filtering. The main ingredients are a 54-layer deep residual network (ResNet), a Deep Adaptive Input Normalization (DAIN), a dynamic dataset augmentation, and curriculum learning, based on an empirical relation for the signal-to-noise ratio. We compare the algorithm's sensitivity with two traditional algorithms on a dataset consisting of a large number of injected waveforms of non-aligned binary black hole mergers in real LIGO O3a noise samples. Our machine-learning algorithm can be used in upcoming rapid online searches of gravitational-wave events in a sizeable portion of the astrophysically interesting parameter space. We make our code, AResGW, and detailed results publicly available at https://github.com/vivinousi/gw-detection-deep-learning .