Beyond the Class Subspace: Teacher-Guided Training for Reliable Out-of-Distribution Detection in Single-Domain Models

Hong Yang; Devroop Kar; Qi Yu; Travis Desell; Alex Ororbia

cs.LGMar 11, 2026

Beyond the Class Subspace: Teacher-Guided Training for Reliable Out-of-Distribution Detection in Single-Domain Models

Authors: Hong Yang, Devroop Kar, Qi Yu, Travis Desell, Alex Ororbia

Organizations: Rochester Institute of Technology, Rochester, NY 14623, USA

Abstract

Out-of-distribution (OOD) detection methods perform well on multi-domain benchmarks, yet many practical systems are trained on single-domain data. We show that this regime induces a geometric failure mode, Domain-Sensitivity Collapse (DSC): supervised training compresses features into a low-rank class subspace and suppresses directions that carry domain-shift signal. We provide theory showing that, under DSC, distance- and logit-based OOD scores lose sensitivity to domain shift. We then introduce Teacher-Guided Training (TGT), which distills class-suppressed residual structure from a frozen multi-domain teacher (DINOv2) into the student during training. The teacher and auxiliary head are discarded after training, adding no inference overhead. Across eight single-domain benchmarks, TGT yields large far-OOD FPR@95 reductions for distance-based scorers: MDS improves by 11.61 pp, ViM by 10.78 pp, and kNN by 12.87 pp (ResNet-50 average), while maintaining or slightly improving in-domain OOD and classification accuracy.

Figures & tables

Figure 1: Per-dataset gains from Teacher-Guided Training on ResNet-50 relative to the CE baseline. Blue bars show effective-rank increase (TGT $-$ CE), and hatched orange bars show FPR@95 reduction (CE $-$ TGT; larger is better). The shown datasets are EuroSAT, Colon, Fashion, Tissue, and Rock (Rock shown in a separate $y$ -region).

Figure 2: EuroSAT out-of-domain OOD (FarOOD) FPR@95 by method across teacher-guidance strengths $\lambda$ , averaged over 5 random splits. The effect of $\lambda$ is method-dependent: for example, ReAct improves at higher $\lambda$ , while SCALE worsens. Many methods also perform poorly at $\lambda=0.5$ .

Appendix figures & tables49 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Tot.	Tr./Wh.	$N_{\text{train}}$	$N_{\text{test}}$	Res.	Domain characteristic
Colon (PathMNIST) [ 34 ]	9	6/3	67,497	22,499	$64\times 64$	Sensor-homogeneous: histopathology tiles
Tissue (TissueMNIST) [ 34 ]	8	5/3	124,099	41,367	$64\times 64$	Sensor-homogeneous: microscopy tissue slices
EuroSAT [ 8 ]	10	7/3	20,250	6,750	$64\times 64$	Sensor-homogeneous: Sentinel-2 satellite
Fashion (FashionMNIST) [ 31 ]	10	7/3	45,000	15,000	$28\times 28$	Sensor-homogeneous: greyscale product images
Food-101 [ 2 ]	101	67/34	75,750	25,250	$224\times 224$	Semantically narrow: food photography
Rock (Rock Gallery) [ 11 ]	7	5/2	1,551	518	$224\times 224$	Semantically narrow: macro rock photography

Appendix

Table S1 : Dataset summary. Tot. : total classes. Tr./Wh. : training classes / withheld classes (withheld classes serve as in-domain OOD targets; values from training config YAMLs).

N_{\text{train}}

and

N_{\text{test}}

are approximate. For datasets not divisible by 3 (Tissue, EuroSAT, Fashion, Rock) the split approximates the

\tfrac{1}{3}

-withheld protocol.

Figure S1 : EuroSAT out-of-domain (FarOOD) FPR@95 by method across teacher-guidance strengths $\lambda$ , averaged over 5 splits. The effect of $\lambda$ is method-dependent: for example, React improves at higher $\lambda$ , while SCALE worsens. Many methods also perform poorly at $\lambda=0.5$ .

	CE			TGT
Dataset	$r_{\mathrm{eff}}$	PR	$\rho_{64}$ (%)	$r_{\mathrm{eff}}$	PR	$\rho_{64}$ (%)
Colon	5.2	5.0	100.0	12.1	6.5	94.6
Tissue	5.3	4.1	99.5	9.9	5.0	95.2
EuroSAT	8.1	6.6	99.9	15.9	7.9	92.6
Fashion	6.2	5.7	100.0	18.0	8.5	93.3
Food	65.3	56.8	98.1	117.1	71.5	85.3

Appendix

Table S2 : Geometry audit: effective rank

r_{\mathrm{eff}}

, participation ratio (PR), and variance concentration in the top-64 PCs (

\rho_{64}

, in %). ResNet-50 backbone (

d{=}2048

Dataset	$C$	$r_{\mathrm{eff}}$ (CE)	$r_{\mathrm{eff}}$ (TGT)	$r_{\mathrm{eff}}/C$ (CE)	DSC severity
Colon	6	5.19	12.09	0.86	Severe
Fashion	7	6.18	17.97	0.88	Severe
Food	67	65.29	117.13	0.97	Severe
Tissue	5	5.32	9.90	1.06	Severe
Yoga	4	4.53	46.97	1.13	Severe
EuroSAT	7	8.07	15.95	1.15	Severe

Appendix

Table S3 : DSC severity characterisation for all 8 benchmarks (CE-trained ResNet-50).

C

is the number of ID training classes;

r_{\mathrm{eff}}

is the effective rank of the learned feature covariance;

\rho_{\mathrm{within}}=\operatorname{tr}(\Sigma_{\mathrm{within}})/\operatorname{tr}(\Sigma)

measures intra-class heterogeneity. Datasets with

r_{\mathrm{eff}}/C\approx 1

exhibit severe DSC; Rock and Garbage (

r_{\mathrm{eff}}/C\gg 1

) serve as within-class-diverse controls.

Dataset	$\rho_{\mathrm{within}}$	$\operatorname{tr}(\Sigma_{\mathrm{within}})$	$\operatorname{tr}(\Sigma_{\mathrm{total}})$	$N_{\mathrm{train}}$
Colon	0.009	0.0067	0.7765	46,650
Food	0.020	0.0173	0.8726	50,250
Fashion	0.028	0.0200	0.7164	31,500
EuroSAT	0.065	0.0520	0.8020	14,625
Tissue	0.072	0.0367	0.5107	108,060
Yoga	0.651	0.4992	0.7665	2,307

Appendix

Table S4 : Within-class variance ratio

\rho_{\mathrm{within}}

for CE-trained ResNet-50 features.

\operatorname{tr}(\Sigma_{\mathrm{within}})

and

\operatorname{tr}(\Sigma_{\mathrm{total}})

are the traces of the weighted within-class and total covariance matrices, respectively. Datasets are sorted by

\rho_{\mathrm{within}}

(ascending); the two datasets with

\rho_{\mathrm{within}}>0.65

(Garbage, Rock) coincide exactly with those showing mild DSC in Table S3 .

Dataset	Regular Acc.	TGT Acc.	Degradation (pp)	Relative Drop (%)
rock	0.665100	0.741600	-7.650000	-11.502000
food	0.529400	0.577800	-4.840000	-9.142000
garbage	0.899700	0.924100	-2.440000	-2.712000
tissue	0.788700	0.790100	-0.140000	-0.178000
colon	0.996800	0.997300	-0.050000	-0.050000
fashion	0.983700	0.983000	0.070000	0.071000

Appendix

Table S5 : Classification accuracy (%) for CE-trained and TGT-trained ResNet-50 on each benchmark.

\Delta

(pp) is the change from CE to TGT: positive values indicate TGT improves classification accuracy. All values are the best accuracy over 3 seeds.

Dataset	Out-of-domain OOD	In-domain OOD
Colon	0.35	100.00
Tissue	$<0.1$	88.83
EuroSAT	0.19	65.13
Fashion	0.95	63.26
Food	0.67	89.31
Rock	7.20	87.09

Appendix

Table S6 : MDS Teacher Only: per-dataset FPR@95 (%) on frozen DINOv2 features. The teacher achieves near-perfect out-of-domain OOD detection but fails catastrophically on in-domain OOD, confirming the orthogonality of domain-shift and class-boundary signals.

Teacher Guided $\lambda$	Method	FPR@95	AUROC	AUPR_IN	AUPR_OUT	FPR@98
0.5	Mahalanobis (MDS)	37.47	93.17	96.34	88.64	51.36
0.5	Nearest Neigh. (kNN)	44.13	91.31	95.41	84.74	61.56
0.5	Neural Collapse (NCI)	61.06	85.40	90.88	79.08	75.65
0.5	Virtual-Logit (ViM)	31.61	93.88	96.91	88.99	48.06
0.5	Energy-Based (EBO)	47.20	91.22	94.84	85.96	64.30
0.5	MaxSoftmax (MSP)	45.59	91.09	94.96	84.03	63.32

Appendix

Table S7 : EuroSAT in-domain (NearOOD) lambda ablation across teacher-guidance strengths

\lambda

Teacher Guided $\lambda$	Method	FPR@95	AUROC	AUPR_IN	AUPR_OUT	FPR@98
0.5	Mahalanobis (MDS)	2.78	99.38	97.58	99.85	5.62
0.5	Nearest Neigh. (kNN)	8.45	97.71	93.18	99.46	13.93
0.5	Neural Collapse (NCI)	26.85	94.78	81.18	98.76	38.84
0.5	Virtual-Logit (ViM)	3.22	99.33	97.28	99.85	6.31
0.5	Energy-Based (EBO)	21.30	95.52	81.05	98.86	37.79
0.5	MaxSoftmax (MSP)	20.65	95.27	81.42	98.71	36.74

Appendix

Table S8 : EuroSAT out-of-domain (FarOOD) lambda ablation across teacher-guidance strengths

\lambda

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	40.45 +- 16.55	37.18 +- 17.98	50.89 +- 27.50	31.00 +- 15.09	32.03 +- 6.97	40.93 +- 16.56	33.49 +- 11.38	32.85 +- 15.49	38.41 +- 18.35
eurosat	66.84 +- 7.42	36.85 +- 10.06	75.50 +- 9.73	31.71 +- 6.62	72.59 +- 18.61	71.51 +- 8.06	70.78 +- 14.08	35.58 +- 9.73	36.89 +- 9.74
fashion	70.93 +- 8.22	67.59 +- 9.74	65.70 +- 12.19	68.79 +- 13.26	71.06 +- 9.14	72.37 +- 7.14	64.74 +- 12.10	68.54 +- 10.88	66.94 +- 9.82
food	67.91 +- 1.50	76.49 +- 1.55	69.63 +- 1.15	73.32 +- 1.44	67.70 +- 1.69	68.08 +- 1.39	71.05 +- 1.89	68.62 +- 1.43	73.24 +- 1.46
garbage	74.66 +- 11.06	73.12 +- 8.37	77.07 +- 10.50	79.33 +- 12.57	78.28 +- 10.73	76.09 +- 11.81	77.16 +- 9.16	73.33 +- 7.19	73.54 +- 8.07

Appendix

Table S9 : FPR@95 (dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	14.64 +- 18.41	0.06 +- 0.04	13.11 +- 16.71	1.64 +- 1.55	11.39 +- 19.77	12.49 +- 18.35	25.14 +- 22.37	0.07 +- 0.05	0.11 +- 0.07
eurosat	17.85 +- 6.95	4.34 +- 2.34	19.55 +- 7.29	22.54 +- 15.94	14.27 +- 10.40	15.94 +- 5.59	19.29 +- 7.71	3.51 +- 2.01	4.41 +- 2.34
fashion	46.87 +- 15.38	4.86 +- 2.22	52.15 +- 11.54	8.42 +- 3.03	32.85 +- 13.25	40.53 +- 13.99	39.94 +- 16.30	5.57 +- 2.88	5.00 +- 2.29
food	41.13 +- 1.25	37.32 +- 3.21	53.48 +- 1.21	48.72 +- 6.77	42.19 +- 2.13	40.25 +- 1.55	46.06 +- 1.74	37.40 +- 1.31	35.76 +- 2.68
garbage	56.11 +- 9.21	29.38 +- 7.52	58.89 +- 3.81	49.29 +- 4.01	53.95 +- 4.45	54.84 +- 6.90	57.66 +- 11.77	30.46 +- 5.68	29.32 +- 7.52

Appendix

Table S10 : FPR@95 (dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	60.96 +- 34.33	40.56 +- 12.85	59.05 +- 36.10	40.05 +- 23.44	74.51 +- 14.10	39.01 +- 12.14	63.81 +- 29.89	44.68 +- 23.78	42.22 +- 16.30	100.00 +- 0.00
eurosat	42.46 +- 9.93	51.37 +- 17.98	41.32 +- 10.69	49.04 +- 17.78	72.70 +- 6.48	55.47 +- 8.75	43.62 +- 9.39	50.35 +- 17.30	48.76 +- 16.30	65.13 +- 6.37
fashion	77.21 +- 13.39	75.48 +- 10.68	75.61 +- 13.66	79.07 +- 9.33	65.88 +- 15.38	85.12 +- 13.39	76.76 +- 15.27	77.52 +- 13.34	78.91 +- 9.32	63.26 +- 22.24
food	75.21 +- 2.55	76.75 +- 1.65	74.86 +- 2.26	73.42 +- 1.82	80.39 +- 1.24	85.89 +- 1.73	77.47 +- 2.99	75.98 +- 1.63	76.92 +- 1.61	89.31 +- 1.44
garbage	76.96 +- 11.26	57.54 +- 9.34	73.11 +- 13.20	69.51 +- 8.82	69.70 +- 9.73	77.16 +- 11.81	78.13 +- 10.56	58.61 +- 11.67	54.91 +- 9.89	77.98 +- 8.13

Appendix

Table S11 : FPR@95 (resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	70.74 +- 7.43	12.67 +- 14.23	53.01 +- 13.28	13.26 +- 17.17	24.81 +- 12.62	61.22 +- 19.30	71.29 +- 6.78	9.78 +- 9.87	18.69 +- 21.00	0.35 +- 0.10
eurosat	50.09 +- 8.58	13.69 +- 5.05	49.82 +- 9.11	31.37 +- 8.39	57.03 +- 6.99	54.37 +- 11.91	50.42 +- 8.51	17.75 +- 6.40	17.17 +- 5.74	0.19 +- 0.05
fashion	15.78 +- 6.88	6.34 +- 2.23	19.74 +- 8.46	14.88 +- 6.19	38.59 +- 10.31	34.13 +- 22.15	19.86 +- 6.78	8.45 +- 3.46	7.23 +- 2.70	0.95 +- 0.60
food	62.92 +- 2.25	52.22 +- 2.60	63.69 +- 2.04	62.75 +- 2.01	65.41 +- 2.62	71.10 +- 2.23	63.47 +- 2.07	53.58 +- 2.45	52.25 +- 2.47	0.67 +- 0.07
garbage	35.04 +- 30.53	14.49 +- 18.95	34.74 +- 25.39	31.77 +- 7.52	30.41 +- 20.60	36.00 +- 22.90	38.91 +- 29.06	10.95 +- 12.59	12.45 +- 15.74	0.10 +- 0.08

Appendix

Table S12 : FPR@95 (resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	68.94 +- 15.61	28.09 +- 13.97
eurosat	72.75 +- 18.75	34.13 +- 14.70
fashion	76.45 +- 13.05	58.80 +- 12.89
food	95.20 +- 0.73	65.82 +- 4.33
garbage	90.13 +- 5.26	84.71 +- 9.80

Appendix

Table S13 : FPR@95 (simclr backbone). Per-dataset in-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	4.09 +- 2.28	21.98 +- 12.18
eurosat	13.95 +- 3.87	20.67 +- 4.70
fashion	6.61 +- 2.16	23.15 +- 4.84
food	89.89 +- 3.88	44.07 +- 3.30
garbage	6.11 +- 2.41	70.73 +- 8.56

Appendix

Table S14 : FPR@95 (simclr backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	49.27 +- 29.23	23.98 +- 13.76	40.55 +- 26.52	24.40 +- 9.83	48.25 +- 21.83	49.83 +- 27.22	48.90 +- 20.43	24.60 +- 15.28	24.02 +- 13.65
eurosat	32.28 +- 11.54	37.05 +- 13.26	37.03 +- 13.37	38.93 +- 15.85	35.77 +- 11.88	32.42 +- 11.37	35.29 +- 12.09	26.56 +- 7.26	36.66 +- 12.89
fashion	56.81 +- 18.77	57.68 +- 17.61	58.14 +- 19.17	56.97 +- 17.44	57.51 +- 18.00	57.29 +- 19.10	70.15 +- 24.19	55.15 +- 19.47	57.43 +- 18.00
food	65.68 +- 1.87	74.09 +- 1.53	67.24 +- 2.06	72.19 +- 1.69	65.32 +- 2.12	65.70 +- 1.93	69.98 +- 2.34	66.20 +- 1.94	70.80 +- 1.84
garbage	74.15 +- 10.58	64.02 +- 2.72	75.95 +- 10.16	75.62 +- 9.78	78.29 +- 6.70	77.26 +- 14.13	75.76 +- 7.65	61.96 +- 7.56	63.72 +- 2.74

Appendix

Table S15 : FPR@95 (tra_dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	5.01 +- 4.82	0.03 +- 0.03	4.57 +- 4.96	1.08 +- 0.96	3.05 +- 2.84	4.38 +- 4.79	9.69 +- 10.61	0.07 +- 0.05	0.04 +- 0.04
eurosat	17.44 +- 12.77	8.36 +- 7.43	18.68 +- 12.44	12.70 +- 10.33	18.48 +- 15.56	16.74 +- 12.83	18.20 +- 11.82	7.46 +- 6.08	8.36 +- 7.43
fashion	12.10 +- 5.68	4.58 +- 1.42	19.02 +- 9.01	10.51 +- 3.89	12.43 +- 6.85	11.82 +- 5.69	11.38 +- 3.50	5.07 +- 2.20	4.56 +- 1.43
food	37.56 +- 2.49	36.48 +- 4.14	50.70 +- 2.61	46.42 +- 5.29	37.56 +- 2.97	36.97 +- 2.78	40.43 +- 4.77	34.94 +- 2.68	34.53 +- 3.94
garbage	48.56 +- 7.01	23.66 +- 8.63	53.89 +- 6.69	48.29 +- 8.41	46.23 +- 5.06	47.37 +- 6.04	46.67 +- 9.87	22.23 +- 5.78	23.74 +- 8.64

Appendix

Table S16 : FPR@95 (tra_dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	51.85 +- 32.56	26.37 +- 15.99	51.57 +- 32.47	30.06 +- 14.11	75.81 +- 8.21	60.42 +- 25.38	54.66 +- 32.66	32.96 +- 14.45	28.10 +- 17.04
eurosat	39.36 +- 14.59	43.45 +- 9.39	36.51 +- 9.20	47.99 +- 4.39	40.21 +- 25.57	49.49 +- 21.68	41.01 +- 17.05	27.80 +- 7.58	43.64 +- 9.08
fashion	73.33 +- 13.59	64.35 +- 13.02	71.21 +- 14.81	61.19 +- 15.98	71.23 +- 10.34	70.32 +- 15.47	70.29 +- 20.73	62.64 +- 12.74	64.12 +- 13.57
food	70.84 +- 1.22	74.40 +- 0.65	71.29 +- 1.36	71.12 +- 1.42	70.73 +- 1.01	82.66 +- 4.92	80.85 +- 10.34	71.49 +- 0.74	73.72 +- 0.70
garbage	68.00 +- 8.49	53.21 +- 12.01	64.46 +- 9.51	74.10 +- 8.80	69.47 +- 4.07	70.61 +- 13.95	68.10 +- 8.50	55.07 +- 8.06	49.40 +- 9.16

Appendix

Table S17 : FPR@95 (tra_resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	25.82 +- 22.98	0.73 +- 0.77	21.60 +- 22.98	2.25 +- 1.31	5.91 +- 8.80	27.21 +- 3.98	30.03 +- 24.21	0.90 +- 1.08	0.75 +- 0.83
eurosat	10.31 +- 1.83	1.80 +- 1.01	11.42 +- 2.27	4.73 +- 1.39	14.23 +- 11.44	28.68 +- 21.87	10.19 +- 1.94	2.27 +- 1.26	1.81 +- 1.02
fashion	53.68 +- 31.32	2.66 +- 2.23	53.70 +- 29.21	8.45 +- 5.85	8.98 +- 2.51	23.81 +- 14.44	55.54 +- 30.18	2.51 +- 2.06	2.49 +- 2.12
food	51.86 +- 3.62	35.16 +- 4.33	56.13 +- 2.84	50.50 +- 3.47	49.95 +- 3.05	47.79 +- 5.02	52.50 +- 2.47	35.93 +- 4.96	35.11 +- 4.37
garbage	33.45 +- 34.16	17.93 +- 33.96	34.98 +- 29.15	29.16 +- 19.62	33.26 +- 19.17	32.95 +- 24.25	33.75 +- 34.20	12.34 +- 11.50	11.48 +- 20.70

Appendix

Table S18 : FPR@95 (tra_resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	89.27 +- 6.85	91.12 +- 4.52	87.50 +- 7.47	91.78 +- 4.78	92.12 +- 2.73	89.23 +- 6.76	92.15 +- 2.71	92.45 +- 3.78	90.65 +- 4.77
eurosat	85.27 +- 2.73	91.22 +- 2.38	84.56 +- 3.79	92.05 +- 1.84	84.78 +- 4.69	84.78 +- 3.51	83.25 +- 5.07	91.66 +- 2.37	91.17 +- 2.39
fashion	70.03 +- 10.97	79.29 +- 6.20	73.55 +- 9.92	80.09 +- 7.45	71.55 +- 12.12	72.24 +- 9.24	75.09 +- 11.15	78.32 +- 7.46	79.44 +- 6.15
food	71.21 +- 0.57	66.82 +- 0.47	69.19 +- 0.72	68.40 +- 0.83	71.22 +- 0.66	71.20 +- 0.52	70.24 +- 0.83	70.55 +- 0.66	68.19 +- 0.43
garbage	70.59 +- 8.45	71.72 +- 7.33	69.28 +- 7.44	62.54 +- 14.76	68.06 +- 8.75	70.53 +- 8.57	70.16 +- 8.28	73.30 +- 7.03	71.71 +- 7.32

Appendix

Table S19 : AUROC (dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	96.98 +- 3.88	99.98 +- 0.02	96.67 +- 3.64	99.59 +- 0.41	97.35 +- 4.28	97.29 +- 3.84	94.42 +- 5.02	99.98 +- 0.01	99.97 +- 0.03
eurosat	95.64 +- 1.34	99.10 +- 0.46	94.16 +- 1.83	94.80 +- 3.50	96.13 +- 3.51	96.23 +- 1.04	95.35 +- 1.35	99.26 +- 0.38	99.08 +- 0.47
fashion	84.61 +- 6.98	98.67 +- 0.68	80.12 +- 4.25	97.69 +- 1.04	90.30 +- 5.77	87.62 +- 6.29	87.81 +- 7.40	98.65 +- 0.72	98.64 +- 0.70
food	86.21 +- 1.44	87.99 +- 1.90	78.64 +- 1.17	83.22 +- 3.32	85.37 +- 1.36	86.82 +- 1.16	83.16 +- 2.40	87.47 +- 1.45	88.55 +- 1.68
garbage	78.75 +- 6.24	91.67 +- 3.70	75.97 +- 2.18	82.11 +- 3.44	79.48 +- 1.83	79.49 +- 4.77	78.15 +- 7.50	91.26 +- 3.00	91.65 +- 3.70

Appendix

Table S20 : AUROC (dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	84.74 +- 12.53	89.28 +- 5.48	85.03 +- 12.46	89.43 +- 8.11	68.30 +- 16.17	86.31 +- 8.03	84.16 +- 11.98	88.74 +- 6.68	89.42 +- 5.89	28.55 +- 13.85
eurosat	89.63 +- 3.65	88.40 +- 5.81	89.35 +- 3.42	88.28 +- 4.44	80.10 +- 4.71	86.00 +- 5.06	89.14 +- 3.59	88.42 +- 4.61	88.95 +- 4.28	76.10 +- 2.74
fashion	73.15 +- 19.71	75.59 +- 8.09	73.78 +- 17.00	75.15 +- 9.59	75.99 +- 10.19	64.91 +- 19.97	70.47 +- 19.44	75.26 +- 9.20	74.28 +- 8.98	78.47 +- 10.96
food	66.90 +- 1.29	66.80 +- 0.91	66.44 +- 1.17	66.58 +- 1.06	65.65 +- 0.93	64.83 +- 0.93	66.72 +- 1.19	65.91 +- 0.52	66.82 +- 0.91	58.91 +- 2.03
garbage	75.21 +- 6.08	78.70 +- 6.44	76.71 +- 5.98	70.57 +- 4.30	75.09 +- 5.66	70.46 +- 9.19	74.72 +- 5.51	80.19 +- 3.72	80.29 +- 3.96	72.67 +- 6.90

Appendix

Table S21 : AUROC (resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	86.74 +- 2.44	96.25 +- 4.28	90.91 +- 1.58	96.80 +- 3.61	95.14 +- 2.46	78.59 +- 10.29	86.51 +- 2.24	97.21 +- 2.80	95.07 +- 5.73	99.87 +- 0.04
eurosat	89.59 +- 2.44	97.31 +- 1.05	89.10 +- 2.64	92.87 +- 2.38	84.16 +- 3.62	87.86 +- 3.32	89.06 +- 2.68	96.72 +- 1.25	96.75 +- 1.14	99.95 +- 0.01
fashion	96.05 +- 1.60	98.49 +- 0.58	93.42 +- 2.33	96.26 +- 1.55	90.63 +- 2.16	90.57 +- 6.56	94.78 +- 1.64	97.87 +- 0.91	98.31 +- 0.70	99.75 +- 0.16
food	75.51 +- 2.09	84.18 +- 2.31	74.10 +- 1.76	74.15 +- 1.71	73.34 +- 1.54	74.79 +- 1.95	75.39 +- 1.77	82.59 +- 1.20	84.30 +- 2.22	99.74 +- 0.03
garbage	87.84 +- 15.00	94.72 +- 8.82	87.30 +- 10.27	90.17 +- 4.26	90.17 +- 9.35	87.70 +- 12.85	86.95 +- 14.29	97.29 +- 3.13	96.12 +- 6.01	99.98 +- 0.03

Appendix

Table S22 : AUROC (resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	77.48 +- 10.66	93.41 +- 3.26
eurosat	60.65 +- 16.45	92.03 +- 3.08
fashion	65.90 +- 7.75	83.19 +- 7.75
food	47.97 +- 2.16	72.87 +- 1.95
garbage	58.82 +- 7.91	58.89 +- 17.24

Appendix

Table S23 : AUROC (simclr backbone). Per-dataset in-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	99.28 +- 0.37	93.71 +- 4.47
eurosat	96.88 +- 1.16	94.73 +- 1.30
fashion	97.65 +- 1.02	92.27 +- 1.67
food	59.35 +- 3.69	83.36 +- 2.07
garbage	98.48 +- 0.58	71.62 +- 10.34

Appendix

Table S24 : AUROC (simclr backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	91.50 +- 5.35	94.21 +- 3.15	92.56 +- 4.26	94.50 +- 2.78	91.66 +- 3.98	91.35 +- 5.15	91.55 +- 4.00	94.90 +- 2.82	94.25 +- 3.14
eurosat	93.29 +- 1.76	90.67 +- 3.32	91.15 +- 2.98	91.20 +- 3.90	92.49 +- 2.28	93.29 +- 1.87	92.94 +- 2.00	93.69 +- 1.75	90.83 +- 3.25
fashion	80.67 +- 12.75	78.96 +- 9.66	78.90 +- 11.77	79.48 +- 11.13	81.07 +- 11.99	80.53 +- 13.19	77.39 +- 13.19	81.12 +- 11.03	79.06 +- 9.71
food	72.61 +- 0.82	67.80 +- 1.34	70.48 +- 0.91	69.50 +- 1.47	72.59 +- 0.83	72.63 +- 0.74	71.21 +- 1.19	71.44 +- 1.10	69.23 +- 1.30
garbage	73.32 +- 6.58	78.27 +- 3.17	71.86 +- 8.12	68.09 +- 5.86	69.57 +- 7.01	71.89 +- 7.80	73.61 +- 7.17	78.57 +- 5.02	78.29 +- 3.18

Appendix

Table S25 : AUROC (tra_dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	98.56 +- 1.44	99.99 +- 0.02	98.42 +- 1.74	99.73 +- 0.23	99.20 +- 0.70	98.74 +- 1.43	97.50 +- 2.60	99.98 +- 0.02	99.99 +- 0.03
eurosat	96.02 +- 2.88	98.27 +- 1.48	94.83 +- 3.23	97.41 +- 2.09	95.69 +- 3.91	96.20 +- 2.91	95.91 +- 2.50	98.42 +- 1.30	98.28 +- 1.47
fashion	96.71 +- 1.90	98.69 +- 0.43	92.41 +- 4.25	97.16 +- 1.16	96.53 +- 2.31	96.79 +- 1.91	97.03 +- 1.03	98.63 +- 0.59	98.70 +- 0.43
food	87.40 +- 1.03	86.36 +- 3.45	79.44 +- 0.70	81.13 +- 3.29	87.11 +- 0.98	87.80 +- 1.09	85.44 +- 2.92	87.46 +- 1.75	87.36 +- 3.10
garbage	83.60 +- 2.81	92.69 +- 3.13	78.41 +- 3.22	83.39 +- 3.72	82.69 +- 4.00	83.95 +- 2.75	84.62 +- 3.12	93.58 +- 1.93	92.68 +- 3.13

Appendix

Table S26 : AUROC (tra_dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	89.49 +- 7.51	94.75 +- 3.21	89.60 +- 7.34	93.76 +- 3.51	81.58 +- 7.48	83.34 +- 4.78	89.11 +- 7.54	93.42 +- 3.51	94.44 +- 3.52
eurosat	93.15 +- 1.59	89.34 +- 6.05	92.92 +- 1.02	90.86 +- 1.63	91.19 +- 6.15	89.50 +- 6.59	92.87 +- 1.90	94.54 +- 1.10	89.41 +- 5.95
fashion	78.12 +- 10.48	80.22 +- 7.03	78.37 +- 9.55	79.95 +- 9.67	77.12 +- 7.37	74.59 +- 16.40	79.54 +- 12.33	81.00 +- 6.91	80.26 +- 7.17
food	69.74 +- 1.27	68.08 +- 0.66	69.23 +- 1.16	69.98 +- 1.10	69.77 +- 1.11	65.41 +- 2.56	67.47 +- 2.84	69.67 +- 0.59	68.37 +- 0.68
garbage	78.28 +- 7.73	81.53 +- 7.71	78.39 +- 5.99	67.28 +- 7.31	75.52 +- 5.79	75.08 +- 10.08	78.43 +- 7.23	80.69 +- 6.49	83.43 +- 5.58

Appendix

Table S27 : AUROC (tra_resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	94.87 +- 4.37	99.80 +- 0.21	95.38 +- 4.27	99.30 +- 0.40	98.67 +- 1.53	93.06 +- 3.12	94.83 +- 4.05	99.75 +- 0.29	99.79 +- 0.24
eurosat	97.60 +- 0.53	99.57 +- 0.21	96.92 +- 0.71	98.76 +- 0.47	97.27 +- 2.12	93.91 +- 4.92	97.59 +- 0.55	99.50 +- 0.23	99.56 +- 0.22
fashion	84.77 +- 9.40	99.32 +- 0.57	84.49 +- 7.91	96.92 +- 2.54	96.70 +- 1.74	91.83 +- 6.49	83.39 +- 10.47	99.41 +- 0.50	99.36 +- 0.55
food	81.43 +- 2.71	89.14 +- 1.80	78.37 +- 2.28	84.68 +- 2.51	82.92 +- 2.30	86.31 +- 3.05	84.06 +- 2.01	91.15 +- 1.44	89.31 +- 1.76
garbage	87.83 +- 16.83	94.82 +- 9.88	88.15 +- 10.46	90.45 +- 8.77	89.58 +- 7.35	89.94 +- 9.60	87.47 +- 17.29	97.20 +- 1.94	96.74 +- 5.93

Appendix

Table S28 : AUROC (tra_resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	93.50 +- 4.94	95.02 +- 3.34	91.28 +- 7.23	95.68 +- 3.03	95.75 +- 1.90	93.57 +- 4.96	95.54 +- 1.56	95.85 +- 2.66	94.72 +- 3.56
eurosat	91.04 +- 1.55	95.61 +- 1.72	90.44 +- 2.68	96.15 +- 1.31	89.70 +- 4.20	90.29 +- 2.22	89.18 +- 4.35	95.81 +- 1.69	95.59 +- 1.73
fashion	85.06 +- 5.89	89.29 +- 3.12	87.10 +- 6.00	89.24 +- 4.50	85.41 +- 6.40	85.88 +- 4.86	87.71 +- 5.66	88.45 +- 4.23	89.39 +- 3.05
food	84.55 +- 0.46	81.08 +- 0.49	83.39 +- 0.56	82.44 +- 0.71	84.59 +- 0.53	84.54 +- 0.43	83.54 +- 0.54	84.22 +- 0.48	82.40 +- 0.44
garbage	79.99 +- 6.61	81.99 +- 4.44	79.46 +- 5.95	75.55 +- 9.09	78.37 +- 6.14	79.68 +- 7.05	79.84 +- 6.10	83.12 +- 4.52	82.01 +- 4.44

Appendix

Table S29 : AUPR_IN (dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	94.39 +- 6.79	99.98 +- 0.02	94.96 +- 5.97	99.47 +- 0.54	95.63 +- 7.00	95.28 +- 6.50	90.39 +- 8.40	99.98 +- 0.02	99.96 +- 0.03
eurosat	87.45 +- 3.87	97.11 +- 1.52	86.12 +- 4.78	85.13 +- 10.69	89.59 +- 8.48	88.54 +- 3.29	86.38 +- 3.52	97.61 +- 1.33	97.05 +- 1.52
fashion	73.60 +- 9.91	96.64 +- 1.90	69.13 +- 6.64	95.10 +- 2.24	82.38 +- 7.09	77.57 +- 8.91	77.86 +- 10.29	96.02 +- 2.29	96.60 +- 1.94
food	83.82 +- 1.04	86.16 +- 1.97	75.86 +- 1.04	79.61 +- 4.12	83.08 +- 1.29	84.51 +- 0.91	80.50 +- 1.88	85.75 +- 0.87	86.81 +- 1.58
garbage	32.96 +- 9.56	59.61 +- 6.79	28.54 +- 4.60	41.13 +- 4.48	34.72 +- 5.25	33.76 +- 8.73	32.41 +- 12.82	58.06 +- 4.17	59.52 +- 6.77

Appendix

Table S30 : AUPR_IN (dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	86.42 +- 12.85	94.07 +- 3.91	86.68 +- 12.83	93.65 +- 5.67	79.10 +- 15.77	92.18 +- 5.26	86.16 +- 11.97	92.92 +- 5.75	93.82 +- 4.50	52.93 +- 7.78
eurosat	94.58 +- 2.06	93.52 +- 3.84	94.54 +- 1.97	93.75 +- 3.32	87.78 +- 3.45	92.35 +- 3.29	94.36 +- 2.03	93.77 +- 3.10	94.05 +- 2.92	88.17 +- 2.19
fashion	83.74 +- 13.18	86.27 +- 5.03	84.14 +- 12.28	85.24 +- 5.93	87.62 +- 5.77	78.38 +- 12.29	82.23 +- 13.66	85.61 +- 5.55	85.08 +- 5.50	88.99 +- 5.74
food	80.76 +- 1.21	80.88 +- 0.86	80.64 +- 1.12	81.31 +- 0.88	79.02 +- 0.82	77.39 +- 0.98	80.48 +- 1.14	80.63 +- 0.70	80.87 +- 0.87	73.52 +- 1.27
garbage	83.00 +- 3.02	87.68 +- 2.64	84.45 +- 3.03	82.43 +- 1.36	84.05 +- 1.90	80.22 +- 5.74	82.31 +- 3.02	88.06 +- 1.97	88.48 +- 2.03	80.38 +- 7.65

Appendix

Table S31 : AUPR_IN (resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	68.47 +- 3.94	93.87 +- 6.63	76.05 +- 3.94	93.71 +- 7.40	91.51 +- 3.57	70.42 +- 12.73	68.10 +- 3.68	95.24 +- 4.66	91.20 +- 10.09	99.86 +- 0.05
eurosat	61.75 +- 5.50	90.70 +- 4.21	61.64 +- 5.82	79.27 +- 6.60	55.39 +- 7.93	58.67 +- 7.87	61.36 +- 5.47	88.28 +- 4.79	88.39 +- 4.22	99.84 +- 0.03
fashion	92.31 +- 3.06	96.68 +- 0.88	89.59 +- 4.06	92.67 +- 3.00	80.55 +- 4.61	81.75 +- 12.42	90.04 +- 3.20	95.91 +- 1.49	96.28 +- 1.17	99.04 +- 0.57
food	68.77 +- 1.89	77.65 +- 2.32	67.82 +- 1.55	69.28 +- 1.59	66.76 +- 1.59	64.52 +- 1.48	68.56 +- 1.58	76.57 +- 1.53	77.69 +- 2.25	99.67 +- 0.03
garbage	51.82 +- 25.89	79.07 +- 20.33	52.54 +- 24.05	57.96 +- 8.65	59.16 +- 20.39	50.58 +- 20.58	46.27 +- 24.97	81.06 +- 17.13	81.24 +- 18.24	99.81 +- 0.11

Appendix

Table S32 : AUPR_IN (resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	86.16 +- 6.69	96.50 +- 1.80
eurosat	79.29 +- 10.01	95.81 +- 1.44
fashion	82.45 +- 5.17	91.33 +- 3.79
food	65.31 +- 1.57	85.46 +- 1.36
garbage	69.44 +- 10.63	72.48 +- 9.91

Appendix

Table S33 : AUPR_IN (simclr backbone). Per-dataset in-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	99.04 +- 0.50	90.39 +- 5.74
eurosat	91.46 +- 2.60	81.85 +- 4.38
fashion	93.49 +- 2.09	87.55 +- 2.40
food	47.82 +- 4.01	80.98 +- 1.64
garbage	85.93 +- 4.28	18.68 +- 5.97

Appendix

Table S34 : AUPR_IN (simclr backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	93.17 +- 5.82	96.85 +- 2.36	94.30 +- 4.92	97.16 +- 1.66	93.81 +- 4.42	93.16 +- 5.60	94.01 +- 3.87	96.91 +- 2.44	96.87 +- 2.35
eurosat	96.49 +- 1.32	95.60 +- 1.59	95.39 +- 1.98	95.59 +- 1.98	95.96 +- 1.77	96.52 +- 1.30	96.26 +- 1.29	97.06 +- 0.88	95.69 +- 1.55
fashion	89.98 +- 7.60	89.62 +- 6.15	89.21 +- 7.60	89.95 +- 6.56	90.24 +- 6.91	89.83 +- 8.05	86.29 +- 9.68	90.35 +- 7.31	89.68 +- 6.20
food	85.43 +- 0.53	82.04 +- 0.88	84.29 +- 0.67	83.11 +- 0.95	85.50 +- 0.57	85.47 +- 0.52	84.09 +- 0.75	84.92 +- 0.66	83.30 +- 0.84
garbage	81.25 +- 6.13	86.17 +- 4.15	81.33 +- 5.33	79.53 +- 6.48	79.55 +- 4.20	79.80 +- 7.02	81.40 +- 5.72	86.53 +- 3.78	86.19 +- 4.15

Appendix

Table S35 : AUPR_IN (tra_dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	97.96 +- 2.11	99.98 +- 0.03	98.00 +- 2.41	99.56 +- 0.49	98.84 +- 1.14	98.23 +- 2.10	96.36 +- 3.89	99.97 +- 0.03	99.98 +- 0.02
eurosat	88.03 +- 8.56	94.52 +- 4.67	87.12 +- 8.92	92.02 +- 6.33	87.00 +- 11.02	88.52 +- 8.76	87.56 +- 7.65	95.01 +- 3.93	94.54 +- 4.66
fashion	94.36 +- 2.65	97.39 +- 0.69	89.90 +- 5.06	94.74 +- 1.44	94.09 +- 3.38	94.45 +- 2.71	94.51 +- 1.51	97.44 +- 0.73	97.40 +- 0.68
food	85.34 +- 1.70	85.45 +- 2.93	77.25 +- 1.71	79.52 +- 3.37	85.27 +- 1.67	85.78 +- 1.87	83.28 +- 2.81	86.27 +- 1.75	86.45 +- 2.68
garbage	39.44 +- 8.95	67.53 +- 9.62	33.02 +- 8.86	42.73 +- 6.19	41.45 +- 4.25	40.53 +- 8.52	42.38 +- 11.22	69.97 +- 6.50	67.47 +- 9.62

Appendix

Table S36 : AUPR_IN (tra_dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	91.44 +- 7.28	96.84 +- 2.62	91.57 +- 7.16	96.31 +- 2.79	87.32 +- 5.38	90.00 +- 3.55	90.91 +- 7.57	96.02 +- 2.92	96.61 +- 2.94
eurosat	95.64 +- 1.60	94.53 +- 3.07	95.79 +- 1.16	95.15 +- 0.83	94.95 +- 3.80	94.17 +- 3.40	95.38 +- 1.93	97.27 +- 0.46	94.57 +- 3.03
fashion	86.74 +- 7.99	89.77 +- 4.11	87.31 +- 7.33	89.88 +- 5.52	87.83 +- 3.82	86.39 +- 7.90	87.28 +- 9.40	90.31 +- 3.82	89.81 +- 4.15
food	83.29 +- 0.72	82.02 +- 0.45	83.03 +- 0.69	83.47 +- 0.66	83.26 +- 0.62	78.53 +- 2.46	79.38 +- 4.06	83.25 +- 0.41	82.26 +- 0.46
garbage	85.27 +- 4.48	88.86 +- 4.63	85.87 +- 3.57	79.33 +- 6.25	84.22 +- 1.71	83.36 +- 6.62	85.34 +- 4.27	88.27 +- 3.70	90.19 +- 3.21

Appendix

Table S37 : AUPR_IN (tra_resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	85.70 +- 10.97	99.59 +- 0.44	87.64 +- 11.61	98.92 +- 0.66	97.63 +- 2.72	90.35 +- 2.16	85.13 +- 10.64	99.52 +- 0.59	99.56 +- 0.52
eurosat	90.00 +- 2.33	98.45 +- 0.69	89.31 +- 2.66	95.89 +- 1.36	90.08 +- 6.99	79.81 +- 14.50	90.10 +- 2.35	98.12 +- 0.71	98.44 +- 0.70
fashion	68.09 +- 18.97	98.40 +- 1.17	68.19 +- 17.40	95.19 +- 3.41	93.32 +- 1.54	87.15 +- 7.94	67.41 +- 19.07	98.27 +- 1.02	98.46 +- 1.12
food	77.09 +- 2.87	84.94 +- 2.43	74.00 +- 2.32	79.15 +- 2.80	78.54 +- 2.37	78.99 +- 2.99	76.71 +- 1.25	85.98 +- 2.08	85.09 +- 2.39
garbage	58.17 +- 30.04	78.03 +- 35.48	57.05 +- 26.93	61.52 +- 18.36	55.22 +- 20.04	55.37 +- 22.92	57.94 +- 30.02	79.11 +- 19.32	83.04 +- 26.66

Appendix

Table S38 : AUPR_IN (tra_resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	83.45 +- 7.44	84.75 +- 5.08	80.42 +- 7.07	83.82 +- 7.70	85.67 +- 3.43	83.35 +- 7.26	86.22 +- 4.63	86.94 +- 4.64	83.92 +- 5.34
eurosat	76.90 +- 3.55	82.87 +- 3.69	74.09 +- 5.39	83.63 +- 2.80	76.69 +- 5.03	76.72 +- 4.30	75.04 +- 4.91	83.60 +- 3.48	82.77 +- 3.68
fashion	52.19 +- 13.80	63.18 +- 11.84	51.13 +- 11.15	65.68 +- 13.70	54.44 +- 16.85	55.13 +- 13.24	58.52 +- 15.83	63.90 +- 12.63	63.34 +- 11.99
food	49.47 +- 0.66	45.56 +- 0.71	47.67 +- 0.39	46.72 +- 0.90	49.41 +- 0.62	49.47 +- 0.56	48.78 +- 0.94	48.31 +- 0.63	46.47 +- 0.66
garbage	55.20 +- 12.67	56.39 +- 12.81	53.55 +- 12.37	48.08 +- 17.89	53.45 +- 15.04	55.40 +- 13.08	54.84 +- 13.28	58.19 +- 13.02	56.37 +- 12.82

Appendix

Table S39 : AUPR_OUT (dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	97.98 +- 2.45	99.98 +- 0.02	97.22 +- 2.65	99.62 +- 0.34	98.16 +- 2.79	98.14 +- 2.47	96.39 +- 3.08	99.98 +- 0.02	99.96 +- 0.03
eurosat	98.76 +- 0.28	99.76 +- 0.12	98.04 +- 0.47	98.62 +- 0.90	98.82 +- 1.04	98.94 +- 0.18	98.70 +- 0.34	99.80 +- 0.09	99.75 +- 0.12
fashion	91.39 +- 4.72	99.53 +- 0.31	87.62 +- 3.22	98.67 +- 0.63	94.67 +- 4.25	93.17 +- 4.34	93.25 +- 5.02	99.56 +- 0.35	99.48 +- 0.31
food	87.16 +- 1.40	88.12 +- 1.62	80.54 +- 0.86	85.08 +- 2.38	86.17 +- 1.47	87.50 +- 1.37	83.85 +- 2.59	87.53 +- 1.56	88.62 +- 1.55
garbage	98.80 +- 0.19	99.51 +- 0.34	98.64 +- 0.21	98.89 +- 0.39	98.77 +- 0.20	98.86 +- 0.11	98.79 +- 0.25	99.49 +- 0.30	99.51 +- 0.34

Appendix

Table S40 : AUPR_OUT (dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	83.21 +- 10.61	81.60 +- 6.93	82.98 +- 10.41	84.71 +- 8.98	65.76 +- 11.75	79.28 +- 8.87	82.63 +- 10.21	81.25 +- 6.09	83.35 +- 6.13	27.39 +- 5.06
eurosat	81.28 +- 5.94	81.16 +- 7.08	79.09 +- 5.15	79.18 +- 4.99	68.83 +- 6.15	77.73 +- 6.67	79.68 +- 6.07	80.20 +- 4.99	81.39 +- 5.32	54.21 +- 5.06
fashion	59.02 +- 18.86	61.58 +- 12.66	56.67 +- 14.74	61.15 +- 12.97	57.52 +- 12.03	51.54 +- 17.26	54.77 +- 18.19	61.11 +- 13.89	60.28 +- 13.71	60.87 +- 17.12
food	45.53 +- 1.29	45.40 +- 0.86	45.21 +- 1.13	45.33 +- 1.00	44.91 +- 0.88	44.73 +- 1.15	45.64 +- 1.17	44.18 +- 0.51	45.47 +- 0.87	40.29 +- 2.47
garbage	61.22 +- 12.17	63.15 +- 12.92	61.77 +- 10.97	51.54 +- 9.93	61.16 +- 11.73	56.24 +- 14.29	60.77 +- 11.54	66.22 +- 8.27	65.60 +- 9.02	62.71 +- 10.07

Appendix

Table S41 : AUPR_OUT (resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening	mds_teacher
ID Dataset
colon	93.27 +- 1.47	97.92 +- 2.58	95.21 +- 1.01	98.19 +- 1.93	97.00 +- 1.65	85.13 +- 8.20	93.20 +- 1.33	98.32 +- 1.82	97.39 +- 3.04	99.84 +- 0.05
eurosat	97.22 +- 0.63	99.23 +- 0.28	96.93 +- 0.69	97.94 +- 0.60	95.78 +- 0.91	96.78 +- 0.90	97.00 +- 0.75	99.11 +- 0.32	99.11 +- 0.30	99.99 +- 0.00
fashion	97.65 +- 0.88	99.08 +- 0.41	95.39 +- 1.49	97.83 +- 0.81	94.44 +- 1.49	94.94 +- 3.01	96.89 +- 0.91	98.73 +- 0.62	99.03 +- 0.47	99.96 +- 0.02
food	77.68 +- 1.72	87.51 +- 1.59	76.47 +- 1.45	76.92 +- 1.36	76.20 +- 1.22	77.75 +- 1.63	77.74 +- 1.50	86.06 +- 0.84	87.70 +- 1.52	99.70 +- 0.06
garbage	99.34 +- 0.85	99.67 +- 0.59	99.28 +- 0.59	99.44 +- 0.29	99.48 +- 0.48	99.36 +- 0.71	99.30 +- 0.80	99.89 +- 0.12	99.79 +- 0.34	100.00 +- 0.00

Appendix

Table S42 : AUPR_OUT (resnet backbone). Per-dataset out-of-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	65.70 +- 16.26	87.58 +- 5.54
eurosat	42.49 +- 15.86	83.71 +- 5.73
fashion	43.64 +- 9.77	66.92 +- 12.25
food	32.22 +- 1.48	51.28 +- 1.89
garbage	46.05 +- 3.62	46.46 +- 17.10

Appendix

Table S43 : AUPR_OUT (simclr backbone). Per-dataset in-domain OOD results.

method_display	Mahalanobis (MDS)	Nearest Neigh. (kNN)
ID Dataset
colon	99.36 +- 0.31	95.82 +- 2.10
eurosat	99.05 +- 0.38	98.51 +- 0.22
fashion	99.58 +- 0.20	94.46 +- 1.24
food	72.20 +- 2.17	83.07 +- 3.80
garbage	99.92 +- 0.03	98.42 +- 0.63

Appendix

Table S44 : AUPR_OUT (simclr backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	88.84 +- 5.38	88.70 +- 4.04	88.52 +- 3.99	89.56 +- 4.38	88.57 +- 4.27	88.59 +- 5.22	88.18 +- 4.30	91.12 +- 3.49	88.77 +- 4.01
eurosat	87.55 +- 2.61	80.49 +- 6.69	81.50 +- 5.52	83.62 +- 7.06	86.32 +- 2.97	87.53 +- 2.84	87.21 +- 3.01	86.44 +- 3.87	80.79 +- 6.61
fashion	63.52 +- 15.76	59.65 +- 13.58	58.60 +- 13.88	60.80 +- 15.51	64.41 +- 15.21	63.48 +- 15.54	61.87 +- 16.44	63.34 +- 14.36	59.76 +- 13.62
food	50.60 +- 0.83	46.19 +- 1.37	48.83 +- 0.71	48.09 +- 1.58	50.73 +- 0.65	50.60 +- 0.60	49.60 +- 1.52	49.03 +- 1.30	47.22 +- 1.39
garbage	60.22 +- 11.49	65.30 +- 7.54	56.20 +- 12.00	52.04 +- 9.63	54.93 +- 12.69	59.20 +- 12.13	60.67 +- 12.43	65.91 +- 9.43	65.29 +- 7.55

Appendix

Table S45 : AUPR_OUT (tra_dino backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	98.89 +- 0.90	99.97 +- 0.07	98.76 +- 0.92	99.79 +- 0.16	99.34 +- 0.50	99.02 +- 0.86	98.08 +- 1.96	99.97 +- 0.05	99.97 +- 0.07
eurosat	98.89 +- 0.74	99.54 +- 0.40	98.36 +- 0.89	99.32 +- 0.54	98.82 +- 1.04	98.94 +- 0.75	98.86 +- 0.62	99.57 +- 0.37	99.54 +- 0.40
fashion	97.88 +- 1.36	99.36 +- 0.32	94.30 +- 3.39	98.33 +- 1.01	97.75 +- 1.64	97.93 +- 1.36	98.18 +- 0.75	99.21 +- 0.52	99.36 +- 0.32
food	88.19 +- 1.00	86.52 +- 3.40	81.19 +- 1.27	82.27 +- 2.77	87.67 +- 1.37	88.46 +- 0.69	86.07 +- 3.31	87.35 +- 1.67	87.42 +- 3.03
garbage	99.05 +- 0.27	99.61 +- 0.18	98.73 +- 0.28	99.04 +- 0.27	98.95 +- 0.36	99.07 +- 0.28	99.13 +- 0.23	99.66 +- 0.12	99.60 +- 0.17

Appendix

Table S46 : AUPR_OUT (tra_dino backbone). Per-dataset out-of-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	86.84 +- 7.64	91.75 +- 3.68	86.57 +- 7.42	89.81 +- 4.20	77.80 +- 9.06	73.58 +- 8.91	86.63 +- 7.53	89.69 +- 3.97	91.43 +- 3.90
eurosat	89.02 +- 1.47	80.14 +- 12.46	86.76 +- 0.69	83.69 +- 3.29	86.34 +- 7.75	84.32 +- 9.53	88.63 +- 1.62	89.69 +- 2.20	80.33 +- 12.22
fashion	64.14 +- 12.88	66.56 +- 10.80	61.63 +- 12.02	64.99 +- 14.39	61.41 +- 10.84	62.62 +- 17.84	67.47 +- 12.74	66.64 +- 11.39	66.51 +- 11.09
food	47.90 +- 1.21	46.97 +- 0.53	47.70 +- 1.13	48.72 +- 1.15	48.26 +- 1.15	45.61 +- 1.64	47.96 +- 1.73	48.39 +- 0.71	47.21 +- 0.57
garbage	65.26 +- 13.86	67.70 +- 14.79	64.21 +- 11.16	49.28 +- 9.45	61.81 +- 12.34	61.95 +- 15.12	65.48 +- 12.99	66.88 +- 10.17	70.71 +- 10.58

Appendix

Table S47 : AUPR_OUT (tra_resnet backbone). Per-dataset in-domain OOD results.

method_display	Energy-Based (EBO)	Mahalanobis (MDS)	MaxSoftmax (MSP)	Nearest Neigh. (kNN)	Neural Collapse (NCI)	ReAct	SCALE	Virtual-Logit (ViM)	whitening
ID Dataset
colon	97.68 +- 1.36	99.90 +- 0.09	97.80 +- 1.27	99.54 +- 0.26	99.13 +- 0.98	95.08 +- 3.12	97.65 +- 1.29	99.86 +- 0.16	99.89 +- 0.11
eurosat	99.39 +- 0.17	99.87 +- 0.05	99.15 +- 0.16	99.66 +- 0.14	99.32 +- 0.52	98.51 +- 1.28	99.38 +- 0.17	99.86 +- 0.06	99.88 +- 0.05
fashion	91.79 +- 4.64	99.62 +- 0.32	90.71 +- 4.31	97.86 +- 1.82	97.64 +- 1.66	94.71 +- 4.01	91.18 +- 5.01	99.74 +- 0.24	99.65 +- 0.31
food	82.06 +- 2.23	91.64 +- 1.05	79.47 +- 1.85	87.50 +- 2.14	84.39 +- 2.08	88.82 +- 3.38	87.15 +- 2.36	93.57 +- 1.07	91.75 +- 1.03
garbage	99.35 +- 0.97	99.69 +- 0.62	99.37 +- 0.63	99.51 +- 0.45	99.47 +- 0.43	99.48 +- 0.58	99.33 +- 1.01	99.87 +- 0.08	99.85 +- 0.29

Appendix

Table S48 : AUPR_OUT (tra_resnet backbone). Per-dataset out-of-domain OOD results.

OOD Detection

Out-of-distribution (OOD) detection identifies inputs unlike a model’s training data so systems can flag uncertainty, reject inputs, or adapt safely.

See all 222 papers

Geometry over Density: Few-Shot Cross-Domain OOD Detection
May 5, 2026Shawn Li, You Qin, Jiate Li +4Diffusion-Based OOD Detection Distribution Shift Detection
University of Southern California · National University of Singapore · Amazon
Unified Multi-Layer Subspace Modeling for Cross-Domain OOD Detection
Sep 6, 2026Gerhard Krumpl, Henning Avenhaus, Horst PosseggerOOD Detection
Institute of Visual Computing, Graz University of Technology, Austria · KESTRELEYE GmbH, Austria
Component-Based Out-of-Distribution Detection
Apr 23, 2026Wenrui Liu, Hong Chang, Ruibing Hou +2Distribution Shift Detection OOD Detection
The State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China · The University of Chinese Academy of Sciences, Beijing 100049, China

May 5, 2026J/K move · Enter open · S save

Geometry over Density: Few-Shot Cross-Domain OOD Detection

Shawn Li, You Qin, Jiate Li, Charith Peris+3

University of Southern California · National University of Singapore · Amazon

Diffusion-Based OOD Detection Distribution Shift Detection Cross-Domain Generalization OOD Detection

Open paper AskPDF arXiv

Out-of-distribution (OOD) detection identifies test samples that fall outside a model's training distribution, a capability critical for safe deployment in high-stakes applications. Standard OOD detectors are trained on a specific in-distribution (ID) dataset and detect deviations from that single domain. In contrast, we study few-shot cross-domain OOD detection: given a single pre-trained model, can we perform OOD detection on arbitrary new ID-OOD task pairs using only a handful of ID samples at inference time, with no additional training? We propose UFCOD, a unified framework that achieves this goal through information-geometric analysis of diffusion trajectories. Our key insight is that diffusion noise predictions are score functions (gradients of log-density), and we extract two energy features: Path Energy (integrated score magnitude) and Dynamics Energy (score smoothness), that form a discrete Sobolev norm capturing how samples interact with the learned diffusion process. The central contribution is a train-once, deploy-anywhere paradigm: a diffusion model trained on a single dataset (e.g., CelebA) serves as a universal feature extractor for OOD detection across semantically unrelated domains (e.g., CIFAR-10, SVHN, Textures). At deployment, each new task requires only

\sim

100 unlabeled ID samples for inference: no retraining, no fine-tuning, no task-specific adaptation. Using 100 ID samples per task, UFCOD achieves 93.7% average AUROC across 12 cross-domain benchmarks, competitive with methods trained on 50k--163k samples, demonstrating

\sim

500

\times

improvement in sample efficiency. See our code in https://github.com/lili0415/UFCOD.

Abstract

OOD Detection

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