CL-CLIP: CLIP-Based Continual Learning Framework with Cost-Volume Category Decoupling for Object Detection

Continual Object Detection (COD) requires a detector to acquire new categories over time while preserving previously learned ones. This goal is closely related to open-vocabulary detection, since both settings require reasoning over categories that are not fully covered by the annotations available at the current training stage. Recent CLIP-based open-vocabulary detectors have shown strong zero-shot generalization, and frameworks such as F-ViT demonstrate that vision-language pretraining can provide powerful zero-shot detection ability for unseen categories. However, real-world deployments cannot remain purely zero-shot: once these detectors are continually updated on newly introduced categories, they suffer severe catastrophic forgetting and quickly lose their previously calibrated detection ability. We therefore propose CL-CLIP, a CLIP-based COD framework that equips open-vocabulary detectors with better continual learning ability through cost-volume-guided category decoupling. Specifically, following CAT-Seg, we compute a CLIP image-text similarity cost volume, defined as dense category-wise response maps between visual tokens and class text embeddings. This zero-shot spatial prior decomposes shared region features into class-specific pathways, which are then processed by a Multi-Expert RoI head. Extensive experiments on PASCAL VOC and MS-COCO show that CL-CLIP substantially improves the F-ViT baseline under continual fine-tuning and achieves competitive performance with existing continual object detectors, especially in adapting to newly introduced categories while preserving competitive base-class performance.

On the minimal teaching sets of two-dimensional threshold functions

It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane.