GOAL: Geometrically Optimal Alignment for Continual Generalized Category Discovery

Jizhou Han; Chenhao Ding; SongLin Dong; Yuhang He; Shaokun Wang; Qiang Wang; Yihong Gong

cs.CVFeb 23, 2026

GOAL: Geometrically Optimal Alignment for Continual Generalized Category Discovery

Authors: Jizhou Han, Chenhao Ding, SongLin Dong, Yuhang He, Shaokun Wang, Qiang Wang, Yihong Gong

Organizations: National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, National Engineering Research Center for Visual Information and Applications, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · School of Software Engineering, Xi’an Jiaotong University · Shenzhen University of Advanced Technology · Harbin Institute of Technology, Shenzhen

Abstract

Continual Generalized Category Discovery (C-GCD) requires identifying novel classes from unlabeled data while retaining knowledge of known classes over time. Existing methods typically update classifier weights dynamically, resulting in forgetting and inconsistent feature alignment. We propose GOAL, a unified framework that introduces a fixed Equiangular Tight Frame (ETF) classifier to impose a consistent geometric structure throughout learning. GOAL conducts supervised alignment for labeled samples and confidence-guided alignment for novel samples, enabling stable integration of new classes without disrupting old ones. Experiments on four benchmarks show that GOAL outperforms the prior method Happy, reducing forgetting by 16.1% and boosting novel class discovery by 3.2%, establishing a strong solution for long-horizon continual discovery.

Figures & tables

Figure 1: Conceptual illustration of the Continual Generalized Category Discovery (C-GCD) task and classifier design strategies. (a) Overview of the C-GCD task: a model is trained on labeled base classes and incrementally discovers novel categories from unlabeled data in subsequent sessions. (b) Prior studies typically use learnable prototypes or classifier weights. (c) Our method adopts a fixed optimal geometric structure, ensuring better alignment and generalization across continual sessions.

Figure 2: Overview of the GOAL framework. In the base session, labeled features are aligned to fixed ETF prototypes via supervised training. In incremental sessions, high-confidence unlabeled samples are aligned to unallocated prototypes with unsupervised learning. This maintains geometric consistency for continual discovery and retention.

Datasets	Methods	S-0	Stage-1			Stage-2			Stage-3			Stage-4			Stage-5			1-5 Stages Avg
Datasets	Methods	All	All	Old	New	All	Old	New	All	Old	New	All	Old	New	All	Old	New	All	Old	New
C100	VanillaGCD †	90.8	72.3	78.5	41.4	67.0	72.5	34.3	58.0	62.3	28.1	56.6	59.5	33.0	51.4	53.7	30.3	61.1	65.3	33.4
	SimGCD †	90.4	73.4	86.4	8.0	62.6	72.4	3.3	54.2	61.6	2.1	47.6	53.4	1.6	43.5	47.9	4.6	56.2	64.3	3.9
	SimGCD+ †	90.4	75.9	87.0	20.4	67.1	75.3	17.5	58.4	64.3	17.3	54.3	58.7	19.1	50.5	53.9	19.8	61.3	67.9	18.8
	FRoST †	90.4	76.9	79.6	63.3	65.3	68.9	43.9	58.0	61.1	36.5	49.3	50.9	36.2	48.0	48.2	46.8	59.5	61.7	45.3
	GM †	90.4	76.6	79.8	60.5	71.1	74.5	50.6	63.5	68.2	31.0	59.7	62.5	37.6	54.1	54.7	48.4	65.0	68.0	45.6

Table 1: Performance of C-GCD on four benchmarks. Here †denotes results reported by Happy .

Methods	CIFAR100		CUB-200		TinyImageNet		ImageNet-100		All Datasets Avg
Methods	$\mathcal{M}_{f}\downarrow$	$\mathcal{M}_{d}\uparrow$	$\mathcal{M}_{f}\downarrow$	$\mathcal{M}_{d}\uparrow$	$\mathcal{M}_{f}\downarrow$	$\mathcal{M}_{d}\uparrow$	$\mathcal{M}_{f}\downarrow$	$\mathcal{M}_{d}\uparrow$	$\mathcal{M}_{f}\downarrow$	$\mathcal{M}_{d}\uparrow$
FRoST (ECCV 2022)	42.19	45.34	55.14	31.30	43.13	34.96	29.80	55.92	42.57	41.88
GM (NeurIPS 2022)	35.62	45.62	35.86	37.51	35.24	28.52	24.44	61.88	32.79	43.38
MetaGCD (CVPR 2023)	32.35	37.76	39.24	47.27	34.04	33.68	26.65	50.42	33.07	42.28
Happy (NeurIPS 2024)	29.40	51.36	29.77	53.13	29.20	43.38	17.09	72.88	26.37	55.19
GOAL (Ours)	11.82	53.97	14.36	58.57	11.66	47.88	3.24	73.08	10.27	58.38

Table 2: Forgetting and discovery performance on four datasets. We report forgetting rate (

\mathcal{M}_{f}

) and final discovery rate (

\mathcal{M}_{d}

Datasets	Methods	S-0	S-1	S-2	S-3	S-4	S-5	S-6	S-7	S-8	S-9	S-10	1-10-stages Avg			$M_{f}$ $\downarrow$
Datasets	Methods	All	All	All	All	All	All	All	All	All	All	All	All	Old	New	$M_{f}$ $\downarrow$
C100	MetaGCD	90.82	81.07	76.55	74.26	67.64	64.45	61.58	59.13	60.13	56.91	56.51	65.82	68.49	31.82	32.81
	Happy	90.36	85.62	81.88	79.82	74.01	71.81	68.46	64.05	62.14	61.38	57.81	70.70	71.89	52.34	31.00
	GOAL (Ours)	90.60	87.22	84.50	83.20	77.66	75.55	73.72	70.07	68.04	66.48	63.06	74.95	82.63	62.62	11.86
Improv. over Happy		+0.24	+1.60	+2.62	+3.38	+3.65	+3.74	+5.26	+6.02	+5.90	+5.10	+5.25	+4.25	+10.74	+10.28	+19.14
Tiny	MetaGCD	84.20	68.87	65.48	62.92	60.81	58.21	56.16	54.56	52.48	50.57	48.92	57.90	59.91	30.76	34.35

Table 3: C-GCD performance with 10 incremental stages on CIFAR100 and TinyImageNet.

Sup ETF Alignment	Unsup ETF Alignment	CUB			CIFAR100			TinyImageNet			ImageNet-100			Avg
Sup ETF Alignment	Unsup ETF Alignment	All	Old	New	All	Old	New	All	Old	New	All	Old	New	All	Old	New
✗	✗	64.8	73.1	49.9	69.6	79.9	47.5	63.3	72.5	44.2	80.1	87.9	68.0	69.5	78.4	52.4
✓	✗	64.7	77.5	51.1	70.4	83.7	46.2	63.4	73.7	44.7	82.3	94.3	68.7	70.2	82.3	52.7
✗	✓	67.9	73.8	57.3	71.2	81.2	52.4	65.6	72.8	46.1	84.7	89.5	72.1	72.4	79.3	57.0
✓	✓	69.9	77.2	58.6	72.1	83.2	54.0	67.1	78.1	47.9	85.9	94.1	73.1	73.8	83.2	58.4
Improv. over baseline		+5.1	+4.1	+8.7	+2.5	+3.3	+6.5	+3.8	+5.6	+3.7	+5.8	+6.2	+5.1	+4.3	+4.8	+6.0

Table 4: Ablation study on the effect of supervised and unsupervised ETF alignment.

Figure 3: Accuracy trend across different values of $\alpha$ on CIFAR100.

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Virtual Category-Guided Continual Generalized Category Discovery

Jiahui Xiong, Qiuxia Lai, Hongsong Wang

School of Computer Science and Engineering, Southeast University, Nanjing 210096, China · State Key Laboratory of Media Convergence and Communication, Communication University of China, Beijing 100024, China · Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China

Generalized Category Discovery

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Continual Generalized Category Discovery (C-GCD) aims to incrementally identify novel categories from sequential unlabeled data while preserving recognition of known classes, which is an essential capability for open-world visual learning. A major bottleneck lies in ambiguous unlabeled samples that cannot be confidently assigned to known classes nor reliably grouped as novel ones, making pseudo-labeling brittle and often biasing learning toward familiar categories. In this work, we introduce Virtual Category-Guided Continual Generalized Category Discovery by adapting Virtual Category Learning (VCL) to the continual setting. Our method identifies uncertain samples and assigns them to temporary virtual categories, enabling safe and informative learning from unlabeled streams without injecting noisy labels, while improving unlabeled data utilization and mitigating prediction bias. To further stabilize discovery across sessions and enhance class separation, we augment VCL with Expanded Neighborhood Contrastive Learning (ENCL), which exploits extended neighborhood relations and an adaptive margin to learn more discriminative and well-separated representations for both old and emerging classes. Extensive experiments on CIFAR-100, Tiny ImageNet, and ImageNet-100 demonstrate that our approach consistently outperforms state-of-the-art methods, establishing a scalable and effective solution for C-GCD.

Abstract

Generalized Category Discovery

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