Reliable Neural Collapse Approximation for Open-World Test-Time Adaptation

Jia-Qi Lin; Yuangang Pan; Chang-Dong Wang; Haizhang Zhang; Ivor W. Tsang; Joey Tianyi Zhou

cs.LGAug 20, 2026

Reliable Neural Collapse Approximation for Open-World Test-Time Adaptation

Authors: Jia-Qi Lin, Yuangang Pan, Chang-Dong Wang, Haizhang Zhang, Ivor W. Tsang, Joey Tianyi Zhou

Organizations: Centre for Frontier AI Research, Agency for Science, Technology and Research (A*STAR), Singapore 138632 · School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, China, Key Laboratory of Machine Intelligence and Advanced Computing, Ministry of Education, China, and Guangdong Province Key Laboratory of Computational Science, Guangzhou, China · School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, China

Abstract

Test-Time Adaptation (TTA) methods aim to bridge the domain gap between the source and target domains. However, traditional TTA methods become ineffective when the label distribution shift occurs, a challenge commonly referred to as an open-world scenario. In this paper, we introduce a new method named Reliable Neural Collapse approximation (ReNC) for Open-World Test-Time Adaptation (OWTTA). Specifically, we leverage neural collapse as a structural prior for reliable target-domain adaptation. Guided by this prior, we justify that the pre-trained classifier weights can serve as the prototypes of the source domain. By measuring the similarity between samples and prototypes, we filter out the Out-Of-Distribution~(OOD) samples for reliable updates. Furthermore, we propose a neural collapse approximation mechanism to refine these prototypes, ensuring they can gradually adapt to the target domain while maintaining the neural collapse structure. Extensive experiments on several open-world benchmarks demonstrate the superiority of the proposed method. Our empirical analysis suggests that ReNC better preserves NC-related properties in the target domain, providing useful evidence for explaining reliable OWTTA and offering new insights for model design. Code is available at https://github.com/JiaqiLin-AI/ReNC.

Figures & tables

Panel of Figure 1 — Figure 1: Motivation of ReNC. (a) Existing methods use fixed source-domain prototypes, which may mismatch the target domain. (b) ReNC improves feature-prototype consistency and adapts prototypes toward target-domain neural collapse.

Panel of Figure 2 — Figure 2: Entropy of CIFAR10-C with OOD samples ((a) Gaussian noise and (b) SVHN) pre-trained on CIFAR10. Minimizing entropy facilitates adaptation to the target domain. However, indiscriminately minimizing all entropy in an open-world scenario would degrade the model performance.

Panel of Figure 3 — Figure 3: t-SNE visualization of extracted features on CIFAR10-C with OOD samples ((a) Gaussian noise and (b) SVHN) pre-trained on CIFAR10. Prototypes are generated using the feature class-means of source samples.

Panel of Figure 4 — Figure 4: Similarity scores of CIFAR10-C with OOD samples ((a) Gaussian noise and (b) SVHN) pre-trained on CIFAR10. The differences in the similarity scores between ID and OOD samples provide a basis for their discrimination.

Panel of Figure 5 — Figure 5: Simplex Equiangular Tight Frame (Simplex ETF) with different class numbers.

Datasets	#Images	#Classes	Target Domain
CIFAR10-C	10,000	10	Corruption
CIFAR100-C	10,000	100	Corruption
ImageNet-C	50,000	1,000	Corruption
ImageNet-R	30,000	200	Style Transfer
VisDA-C	55,388	12	Style Transfer

Table 1: In-distribution Datasets Information

CIFAR10-C	Noise			MNIST			SVHN			Tiny			CIFAR100-C
CIFAR10-C	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$
TEST	69.19	99.96	81.78	63.61	91.11	74.92	63.54	90.91	74.80	61.09	77.48	68.32	61.27	76.58	68.07
BN	39.44	60.57	47.77	60.19	69.56	64.54	69.21	80.17	74.29	69.02	75.15	71.95	68.83	73.33	71.01
TENT	42.75	61.99	50.60	63.21	72.80	67.67	70.84	82.92	76.41	69.70	76.23	72.82	69.22	74.07	71.56
SHOT	42.71	60.72	50.15	64.57	73.51	68.75	71.12	84.37	77.18	69.51	77.06	73.09	69.10	74.76	71.82
OSTTA	53.43	13.69	21.80	53.88	36.94	43.83	62.76	41.20	49.74	74.85	32.38	45.20	76.39	29.80	42.87

Table 2: Open-world test-time adaptation results on CIFAR10-C with OOD samples. Best marked in bold, second best underlined.

CIFAR100-C	Noise			MNIST			SVHN			Tiny			CIFAR10-C
CIFAR100-C	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$
TEST	25.30	99.99	40.38	24.76	46.81	32.39	26.34	91.65	40.92	26.20	86.68	40.24	25.79	87.86	39.88
BN	21.22	93.29	34.58	26.09	93.21	40.77	30.60	95.42	46.34	31.41	89.69	46.53	31.95	89.93	47.15
TENT	24.45	95.75	38.95	27.50	91.49	42.29	32.05	95.17	47.95	31.33	89.64	46.43	32.08	89.93	47.29
SHOT	25.98	96.62	40.95	28.26	87.36	42.71	32.42	95.14	48.36	31.18	89.71	46.28	32.07	90.10	47.30
OSTTA	12.20	40.58	18.76	17.97	46.56	25.93	33.33	62.59	43.50	36.81	52.15	43.16	42.75	43.67	43.21

Table 3: Open-world test-time adaptation results on CIFAR100-C with OOD samples. Best marked in bold, second best underlined.

ImageNet-C	Noise			MNIST			SVHN
ImageNet-C	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$
TEST	11.79	40.85	18.30	11.33	59.57	19.04	11.62	82.04	20.36
BN	9.73	66.50	16.98	15.20	74.24	25.23	16.24	77.93	26.88
TENT	9.31	68.49	16.39	15.26	72.67	25.22	17.28	78.79	28.34
SHOT	9.70	64.57	16.87	14.76	71.69	24.48	17.70	79.63	28.96
OSTTA	13.90	65.34	22.92	20.54	57.34	30.25	21.93	59.43	32.04

Table 4: Open-world test-time adaptation results on ImageNet-C with OOD samples. Best marked in bold, second best underlined.

ImageNet-R	Noise			MNIST			SVHN
ImageNet-R	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$
TEST	24.71	100.00	39.63	23.60	99.81	38.17	22.46	98.89	36.61
BN	16.38	89.76	27.70	18.70	82.97	30.52	19.03	86.08	31.17
TENT	16.87	93.23	28.57	19.81	84.72	32.11	20.09	87.99	32.71
SHOT	17.27	96.24	29.28	19.70	81.43	31.72	20.44	89.61	33.29
OSTTA	25.46	58.59	35.50	22.46	49.67	30.93	25.66	58.02	35.58

Table 5: Open-world test-time adaptation results on ImageNet-R with OOD samples. Best marked in bold, second best underlined.

VisDA-C	Noise			MNIST			SVHN
VisDA-C	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$	$ACC_{I}$	$ACC_{O}$	$ACC_{H}$
TEST	41.27	100.00	58.43	43.12	97.41	59.78	42.06	99.46	59.12
BN	45.48	99.64	62.45	42.06	79.96	55.12	42.80	88.77	57.75
TENT	51.57	100.00	68.05	41.50	79.96	54.64	44.57	88.40	59.26
SHOT	42.39	99.94	59.53	42.69	68.08	52.48	43.45	72.69	54.33
OSTTA	39.60	54.33	45.81	46.41	29.81	36.30	44.91	45.55	45.23

Table 6: Open-world test-time adaptation results on VisDA-C with OOD samples. Best marked in bold, second best underlined.

CIFAR10		CIFAR100		ImageNet		VisDA
$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$
0.1712	0.2466	0.7541	0.6235	2.3275	1.1968	0.3031	0.5146

Table 7:

\mathcal{NC}_{1}

and

\mathcal{NC}_{3}

on each training dataset. Lower values indicate closer to the neural collapse state.

Dataset	CIFAR10	CIFAR100	ImageNet	VisDA
Ratio	$1.526\times 10^{-2}$	$7.693\times 10^{-3}$	$1.116\times 10^{-3}$	$1.873\times 10^{-3}$

Table 8: The ratio

\mathbf{b}

\langle\mathbf{w},\mathbf{c}\rangle

quantifies their relative influence. Lower values imply that the bias term is increasingly negligible in the neural collapse state.

CIFAR10-C	Noise		MNIST		SVHN		Tiny		CIFAR100-C
CIFAR10-C	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$
TEST	0.7386	0.3548	0.7386	0.3548	0.7386	0.3548	0.7386	0.3548	0.7386	0.3548
BN	1.5176	0.4034	0.8026	0.3637	0.6209	0.3189	0.6052	0.3204	0.5970	0.3193
TENT	1.4132	0.3917	0.7314	0.3497	0.5924	0.3151	0.5946	0.3179	0.5884	0.3179
SHOT	1.3871	0.3914	0.7057	0.3461	0.5815	0.3147	0.5914	0.3180	0.5863	0.3185
OSTTA	1.4157	0.4056	0.7922	0.3633	0.6154	0.3194	0.5944	0.3212	0.5852	0.3203

Table 9:

\mathcal{NC}_{1}

and

\mathcal{NC}_{3}

on CIFAR10-C and CIFAR100-C with OOD samples. Best results are marked in bold, second best are underlined. The gray background indicates the highest

ACC_{S}

ImageNet-C	Noise		MNIST		SVHN
ImageNet-C	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$
TEST	3.7824	1.2762	3.7824	1.2762	3.7824	1.2762
BN	7.6031	1.2733	6.0601	1.2620	6.7761	1.2581
TENT	7.4605	1.2755	5.6129	1.2635	6.3444	1.2574
SHOT	7.6685	1.2759	5.8075	1.2610	6.3542	1.2557
OSTTA	6.0655	1.2586	4.1373	1.2554	4.1407	1.2557

Table 10:

\mathcal{NC}_{1}

and

\mathcal{NC}_{3}

on ImageNet-C with OOD samples. Best results marked in bold, second best underlined. The gray background indicates the highest

ACC_{S}

ImageNet-R	Noise		MNIST		SVHN
ImageNet-R	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$
TEST	20.6384	1.0441	20.6384	1.0441	20.6384	1.0441
BN	30.1058	1.0541	28.6891	1.0577	27.8901	1.0540
TENT	27.4597	1.0478	27.5288	1.0549	26.6687	1.0507
SHOT	26.1513	1.0437	27.2900	1.0539	25.9399	1.0480
OSTTA	25.8711	1.0483	24.8492	1.0584	24.3873	1.0555

Table 11:

\mathcal{NC}_{1}

and

\mathcal{NC}_{3}

on ImageNet-R with OOD samples. Best results marked in bold, second best underlined. The gray background indicates the highest

ACC_{S}

VisDA-C	Noise		MNIST		SVHN
VisDA-C	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$	$\mathcal{NC}_{1}$	$\mathcal{NC}_{3}$
TEST	1.8591	0.8081	1.8591	0.8081	1.8591	0.8081
BN	1.3001	0.7268	1.2937	0.7217	1.2915	0.7126
TENT	1.1664	0.7034	1.3417	0.7287	1.1755	0.7005
SHOT	1.0559	0.6944	1.1516	0.7098	1.1388	0.7003
OSTTA	1.4202	0.7503	1.2309	0.748	1.2792	0.7308

Table 12:

\mathcal{NC}_{1}

and

\mathcal{NC}_{3}

on VisDA-C with OOD samples. Best results marked in bold, second best underlined. The gray background indicates the highest

ACC_{S}

CIFAR10-C				Noise	MNIST	SVHN	Tiny	CIFAR100-C
$\mathcal{L}_{e}^{+}$	$\mathcal{L}_{d}$	$\mathcal{L}_{s}$	U.P.	$ACC_{H}$	$ACC_{H}$	$ACC_{H}$	$ACC_{H}$	$ACC_{H}$
✓				86.05	78.60	82.10	69.25	68.04
✓	✓			86.07	78.56	82.06	69.27	68.00
✓	✓	✓		86.05	78.62	82.06	69.27	68.00
		✓	✓	88.02	89.21	83.22	73.77	72.13
✓		✓	✓	88.07	89.24	83.30	73.42	71.47

Table 13: Ablation study on the CIFAR10-C and CIFAR100-C with OOD samples. Best results marked in bold, second best underlined.

ImageNet-C				Noise	MNIST	SVHN
$\mathcal{L}_{e}^{+}$	$\mathcal{L}_{d}$	$\mathcal{L}_{s}$	U.P.	$ACC_{H}$	$ACC_{H}$	$ACC_{H}$
✓				33.11	34.96	36.56
✓	✓			33.25	35.00	36.47
✓	✓	✓		32.27	35.33	36.44
		✓	✓	52.84	52.10	52.45
✓		✓	✓	51.67	51.23	51.53

Table 14: Ablation study on the ImageNet-C, ImageNet-R and VisDA-C with OOD samples. Best results marked in bold, second best underlined.

Running Time	CIFAR10-C	CIFAR100-C	ImageNet-C	ImageNet-R	VisDA-C
TEST	0.000623	0.000626	0.001139	0.001188	0.001165
BN	0.000632	0.000658	0.001163	0.001242	0.001203
TENT	0.003121	0.003208	0.005682	0.005821	0.005640
SHOT	0.002406	0.002496	0.004015	0.003910	0.003733
OSTTA	0.001202	0.001230	0.002643	0.002656	0.003850
EATA	0.001726	0.001830	0.002824	0.002860	0.003195

Table 15: Per-sample running time (in seconds) across all datasets, measured with Noise OOD samples.

Panel of Figure 6 — Figure 6: Parameter analysis of the optimal balance parameter $\lambda$ in Eq. ( 10 ).

Panel of Figure 7 — Figure 7: Open-world test-time adaptation results of ReNC at different OOD sample ratios.

$t\xrightarrow{\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt\hskip 8.24454pt}$
CIFAR10-C	Noise	MNIST	SVHN	Tiny	CIFAR100-C	Average
TEST	81.78	75.10	74.85	68.38	68.07	73.64
BN	47.77	64.19	74.18	71.72	71.32	65.83
TENT	50.60	67.37	76.44	72.75	71.76	67.78
SHOT	50.15	67.74	77.16	72.97	71.89	67.98
OSTTA	21.80	43.70	46.89	48.22	47.47	41.62

Table 16: Continual OWTTA results on CIFAR10-C with OOD samples. Best marked in bold, second best underlined.

CIFAR10-C	Noise	MNIST	SVHN	Tiny	CIFAR100-C
TEST	92.99	91.04	90.40	86.16	81.60
BN	91.81	90.57	87.89	84.80	80.34
TENT	89.15	92.47	90.89	86.23	82.12
SHOT	93.61	92.37	90.36	86.21	82.11
OSTTA	37.21	44.75	49.78	50.36	50.60
EATA	90.26	89.55	88.94	85.55	81.12

Table 17: OWTTA results under ViT backbone, evaluated by

ACC_{H}

. Best marked in bold, second best underlined.

ImageNet-R	Noise	MNIST	SVHN
TEST	39.63	38.17	36.61
BN	27.70	30.52	31.17
TENT	28.57	32.11	32.71
SHOT	29.28	31.72	33.29
OSTTA	35.50	30.93	35.58
EATA	27.55	31.07	31.21

Table 18: Comparison of vision-language model extensions on ImageNet-R with OOD samples, evaluated by

ACC_{H}

. Best marked in bold, second best underlined.

Figure 8: Nemenyi post-hoc analysis of all the baselines.

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Back to Source: Open-Set Continual Test-Time Adaptation via Domain Compensation

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Test-Time Adaptation (TTA) aims to mitigate distributional shifts between training and test domains during inference time. However, existing TTA methods fall short in the realistic scenario where models face both continually changing domains and the simultaneous emergence of unknown semantic classes, a challenging setting we term Open-set Continual Test-Time Adaptation (OCTTA). The coupling of domain and semantic shifts often collapses the feature space, severely degrading both classification and out-of-distribution detection. To tackle this, we propose DOmain COmpensation (DOCO), a lightweight and effective framework that robustly performs domain adaptation and OOD detection in a synergistic, closed loop. DOCO first performs dynamic, adaptation-conditioned sample splitting to separate likely ID from OOD samples. Then, using only the ID samples, it learns a domain compensation prompt by aligning feature statistics with the source domain, guided by a structural preservation regularizer that prevents semantic distortion. This learned prompt is then propagated to the OOD samples within the same batch, effectively isolating their semantic novelty for more reliable detection. Extensive experiments on multiple challenging benchmarks demonstrate that DOCO outperforms prior CTTA and OSTTA methods, establishing a new state-of-the-art for the demanding OCTTA setting.

Abstract

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