Terahertz (THz) communications have emerged as a key technology for escalating data rates in future generation wireless networks. However, severe propagation losses at THz frequencies pose significant challenges, which can be mitigated via ultra-massive multiple-input multiple-output (UM-MIMO) systems employing highly directional transmissions. To this end, codebook-based analog beamforming constitutes a realistic solution, eliminating the need for explicit channel estimation. However, in UM-MIMO systems, the use of extremely narrow beams makes beam training and alignment increasingly challenging, leading to a substantial increase in the number of codewords to be tested and, thus, to high computational complexity. In this paper, a novel artificial neural network architecture for low-complexity beam training in UM-MIMO THz systems is presented, which does not require a constant feedback link between transmitter and receiver to obtain the best beamformer and combiner pair. An inception and residual network, which is trained based on the received signal powers using the transmit and receive codewords generated from predefined hierarchical codebooks, is designed. Our numerical investigations demonstrate that the proposed machine learning approach significantly reduces the complexity of UM-MIMO transmit and receive beamforming design, as compared to the standard exhaustive and hierarchical beam searching methods.