RGC: a radio AGN classifier based on deep learning. I. A semi-supervised multiclass model for VLA images

Bent radio active galactic nuclei (RAGNs) -- wide-angle tails (WATs) and narrow-angle tails (NATs) -- trace dense environments in galaxy groups and clusters, yet no multiclass classifier simultaneously separates them from straight Fanaroff--Riley types (sFRI, sFRII) using visually inspected labels and unlabelled data. We release FIRST-2060, a four-class labelled dataset of 2060 RAGNs (sFRI, sFRII, WAT, NAT) constructed from three publicly available catalogues through multi-tier visual inspection, together with the semi-supervised RGC 1.0 model that leverages 20,000 unlabelled sources. We benchmark RGC against five supervised baselines. FIRST-2060 is provided in two preprocessing variants: R_{L1}, which retains spurious sources, and R_{L2}, from which they are removed. The RGC model integrates the self-supervised framework BYOL (Bootstrap Your Own Latent) with an E(2)-equivariant steerable CNN (E2CNN) encoder, pre-trained on the unlabelled data and fine-tuned on the labelled sets. All six models are evaluated with 5-fold cross-validation, Grad-CAM attention analysis, and controlled class-imbalance experiments. ConvNeXT (M_1) and RGC (M_2) form a top tier at macro-F_1 0.80\pm0.02 and 0.79\pm0.02 respectively, a difference within one standard deviation. M_2 is the only model whose Grad-CAM contours consistently trace the morphological structure of RAGNs -- lobes, jets, and bends -- rather than defaulting to compact blobs or diffuse patterns. The four-class scheme introduced here enables WAT/NAT-resolved catalogues that can serve as environment probes and progenitor classifications for diffuse cluster radio emission. The complementary strengths of M_1 and M_2 -- in cross-type and within-type discrimination respectively -- suggest that an ensemble approach may offer a practical framework for survey-scale morphological catalogues.