A Strong Balanced-Softmax Classifier-Retraining Baseline for Long-Tailed Recognition

Juan Terven, Diana Margarita Córdova Esparza, Julio Alejandro Romero Gonzalez, Edgar Arturo Chávez Urbiola, Francisco Javier Willars Rodriguez, Juan Bautista Hurtado Ramos, Alfonso Ramirez Pedraza

Long-tailed recognition methods often modify losses, margins, or representations to reduce the dominance of frequent classes. We ask whether, after Balanced Softmax training, the remaining tail error can be reduced by retraining only the classifier. We evaluate BS-cRT, a two-stage procedure that trains a backbone and cosine classifier with Balanced Softmax, freezes the backbone, and updates only the classifier on balanced episodic batches. The second stage keeps the empirical-prior Balanced Softmax objective and uses raw cosine logits at inference. Across CIFAR-100-LT, CIFAR-10-LT, ImageNet-LT, and Places-LT, this classifier-only step consistently improves Few-shot accuracy over the matched Balanced Softmax checkpoint. At imbalance factor 100, Few-shot gains are +5.15 points on CIFAR-100-LT and +5.83 on CIFAR-10-LT; on ImageNet-LT and Places-LT, gains are +6.92 and +9.78 points, respectively, with a Top-1/Few-shot trade-off on ImageNet-LT. We also analyze Counterfactual Boundary Risk Minimization (CBRM), a boundary-probe extension using prototype-based features near decision boundaries. CBRM identifies two failure modes: scaled-logit cosine margins destabilize training, and corrected hardest-negative probes remain head-class anchored. The results support BS-cRT as a practical classifier-side baseline and indicate that boundary supervision must account for class frequency.