Out-of-Distribution Detection in Continual Learning

Nimeshika Udayangani; Flora D. Salim; Christopher Leckie; Sarah Erfani

cs.LGOct 19, 2026

Out-of-Distribution Detection in Continual Learning

Authors: Nimeshika Udayangani, Flora D. Salim, Christopher Leckie, Sarah Erfani

Organizations: School of Computing and Information Systems, The University of Melbourne, Australia · School of Computer Science Engineering, University of New South Wales, Australia

Abstract

Out-of-distribution detection in continual learning (OOD-CL) is highly challenging, as it requires (i) learning a sequence of tasks without catastrophic forgetting, and (ii) identifying unknown samples (OOD) without access to known (in-distribution (ID)) data from past tasks, where standard confidence-based OOD scores tend to degrade. Existing methods largely rely on a rehearsal buffer of past data or assume closed-world settings, limiting their scalability and reliability in real-world scenarios. In this paper, we propose a novel OOD detection framework for rehearsal-free continual learning, inspired by Kolmogorov-Arnold Networks (KAN), which mitigate catastrophic forgetting via their inherent local neuroplasticity. To better leverage KAN in OOD-CL, we introduce a task-adaptive classifier architecture, TA-KAN, which mitigates recency bias and enhances ID--OOD separability through task-specific control of activation locality. Furthermore, we propose a geometry-guided OOD score that complements TA-KAN classifier confidence without relying on past ID data. Our method significantly improves OOD detection while maintaining strong ID classification performance, achieving state-of-the-art results in OOD-CL.

Figures & tables

Figure 1: FPR of a trained CIL model on ImageNet-R (5-task), evaluated across task-wise ID settings. KAN-Head exhibits significantly higher FPR when older tasks are treated as ID compared to recently learned tasks, revealing a bias toward new-task classes. The proposed TA-KAN mitigates this bias, thereby reducing the average FPR.

Panel of Figure 2 — Figure 2: Relative improvement ( $\Delta$ ) of the KAN head over a linear head in a SOTA CIL model. The improvement in OOD detection is limited compared to ID performance. The proposed TA-KAN significantly improves OOD performance while maintaining comparable ID performance.

Panel of Figure 3 — Figure 3: Comparison of RBF approximations using wide and narrow basis functions. (a) RBF bases with different widths, $1\times s$ (top) and $0.5\times s$ (bottom). (b) Approximation of a target ID activation using wide bases yields a coarse approximation and produces similar responses for both ID and nearby OOD samples. (c) Approximation using narrower bases with similar weights, results a more accurate reconstruction and better captures localized responses.

Method	5 Tasks					10 Tasks					20 Tasks
Method	$FPR_{L}$	$AUC_{L}$	$AUP_{L_{\mathrm{In}}}$	$AUP_{L_{\mathrm{Out}}}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$AUP_{L_{\mathrm{In}}}$	$AUP_{L_{\mathrm{Out}}}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$AUP_{L_{\mathrm{In}}}$	$AUP_{L_{\mathrm{Out}}}$	$ACC_{L}$
Linear-Head [ 48 ]	66.16	79.30	77.08	80.43	73.85	71.93	77.41	74.78	79.64	68.35	67.91	79.56	77.44	81.57	61.69
Cosine-Head [ 21 ]	60.67	84.13	81.20	85.24	80.08	69.40	80.30	76.11	82.12	73.17	63.19	79.14	78.11	80.14	62.24
NCM Readout [ 43 ]	77.21	77.83	73.41	79.96	80.54	78.12	74.19	69.71	76.67	77.13	76.41	76.28	73.32	78.27	81.42
KAN-Head (Baseline) [ 22 ]	59.65	83.48	80.51	84.27	81.55	71.11	80.53	76.69	82.30	78.29	59.69	81.86	81.18	82.93	75.24
ProKT [ 30 ]	65.41	80.85	77.78	81.62	77.39	73.55	77.79	73.78	79.14	71.34	61.61	78.93	79.02	78.92	64.52

Table 1: Results on CUB-200 [ 54 ] dataset under different task settings. Lower FPR is better; higher AUC, AUP and ACC are better.

Method	5 Tasks			10 Tasks			20 Tasks			40 Tasks
Method	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
Linear-Head [ 48 ]	42.74	85.44	77.96	45.69	86.26	76.51	53.49	85.28	73.90	53.21	81.57	68.80
Cosine-Head [ 21 ]	41.87	84.62	80.73	42.32	86.73	79.22	45.64	85.50	77.91	50.17	83.27	74.01
NCM Readout [ 43 ]	43.33	85.38	77.98	45.43	85.36	77.32	47.26	84.59	76.86	49.37	83.19	74.38
KAN-Head (Baseline) [ 22 ]	42.52	84.81	79.25	43.04	85.64	78.76	44.00	85.40	77.42	44.80	84.63	73.95
ProKT [ 30 ]	48.59	81.26	72.82	50.18	81.63	71.72	52.19	80.52	69.15	51.94	80.91	65.97

Table 2: Results on ImageNet-R [ 17 ] dataset under different task settings. Lower FPR is better; higher AUC and ACC are better.

Method	$FPR_{L}$	$FPR_{A}$	$AUC_{L}$	$AUC_{A}$	$ACC_{L}$	$ACC_{A}$
MLP-Head	77.46	64.09	71.16	77.72	54.82	70.49
Linear-Head	68.67	59.17	78.76	82.40	67.96	79.42
Linear-Head+Guidance	67.03	60.81	79.06	82.54	67.96	79.42
KAN-Head (Baseline)	63.48	56.00	81.96	85.16	78.36	85.37
KAN-Head $\alpha_{\min}$	60.12	54.28	82.27	85.80	76.11	84.52
KAN-Head trainable $\sigma$	64.69	56.30	81.53	85.04	78.16	85.36

Table 3: Ablation study of different components. Results are averaged over all task settings on CUB-200 dataset.

$\alpha$	Method	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
1	KAN	59.65	83.48	81.55
1	KAN+Guidance	54.64	84.18	81.55
0.75	KAN	58.07	83.87	81.54
	KAN+Guidance	54.31	84.47	81.54
	TA-KAN	55.78	84.61	81.47
	TA-KAN+Guidance	51.46	85.28	81.47

Table 4: Effect of

\alpha

on KAN and TA-KAN on the CUB-200 dataset. Lower FPR and higher AUC/ACC are better.

Panel of Figure 4 — Figure 4: Simplified illustration of KAN [ 35 ] and MLP [ 20 ] architectures. (a) MLP uses globally shared weights with fixed activation functions, where all parameters are equally updated across all tasks, resulting in updates on irrelevant regions during new task learning. (b) In contrast, KAN employs learnable activation functions, enabling localized responses where only input-relevant regions are activated and updated, thereby preventing impact on other regions and mitigating catastrophic forgetting.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Method	5 Tasks			10 Tasks			20 Tasks
Method	$FPR_{L}\downarrow$	$AUC_{L}\uparrow$	$ACC_{L}\uparrow$	$FPR_{L}\downarrow$	$AUC_{L}\uparrow$	$ACC_{L}\uparrow$	$FPR_{L}\downarrow$	$AUC_{L}\uparrow$	$ACC_{L}\uparrow$
Linear-Head [ 48 ]	36.45	90.67	88.71	41.58	89.30	86.55	49.92	86.27	82.96
KAN-Head (Baseline) [ 22 ]	37.28	89.73	87.92	42.79	88.34	86.71	45.06	86.84	84.83
ProKT [ 30 ]	45.91	86.44	83.72	52.97	83.62	79.27	64.20	77.43	72.54
MORE [ 24 ]	36.95	89.17	85.67	48.10	86.94	85.43	51.32	79.24	74.27
MSP-BC-CE [ 15 ]	33.96	92.22	87.92	41.77	89.98	86.71	46.53	87.34	84.83

Appendix

Table 5: Results on CIFAR-100 [ 28 ] dataset under different task settings.Lower FPR is better; higher AUC and ACC are better.

Method	5 Tasks			10 Tasks			20 Tasks
Method	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
Linear-Head [ 48 ]	$42.74\pm 1.29$	$85.44\pm 0.39$	$77.96\pm 0.26$	$45.69\pm 2.71$	$86.26\pm 0.71$	$76.51\pm 0.32$	$53.49\pm 6.59$	$85.28\pm 1.63$	$73.90\pm 0.32$
KAN-Head (Baseline) [ 22 ]	$42.52\pm 1.28$	$84.81\pm 0.32$	$\textbf{79.25}\pm 0.38$	$43.04\pm 3.06$	$85.64\pm 0.28$	$\textbf{78.76}\pm 0.26$	$44.00\pm 7.79$	$85.40\pm 1.17$	$\textbf{77.42}\pm 0.30$
MSP-BC-CE [ 15 ]	$40.65\pm 1.52$	$85.50\pm 0.21$	$79.25\pm 0.38$	$42.12\pm 2.91$	$\underline{86.84}\pm 0.74$	$78.76\pm 0.26$	$44.88\pm 7.04$	$85.78\pm 1.21$	$77.42\pm 0.30$
TA-KAN	$\underline{40.07}\pm 1.18$	$\underline{85.77}\pm 0.29$	$78.83\pm 0.22$	$\underline{40.25}\pm 3.00$	$86.76\pm 0.48$	$77.76\pm 0.49$	$\underline{42.57}\pm 8.16$	$\underline{85.99}\pm 1.38$	$77.03\pm 0.10$
TA-KAN + Guidance	$\textbf{39.72}\pm 1.35$	$\textbf{85.92}\pm 0.35$	$\underline{78.83}\pm 0.22$	$\textbf{39.98}\pm 2.90$	$\textbf{86.87}\pm 0.48$	$\underline{77.76}\pm 0.49$	$\textbf{42.61}\pm 8.39$	$\textbf{86.10}\pm 1.55$	$\underline{77.03}\pm 0.10$

Appendix

Table 6: Results on ImageNet-R [ 17 ] under different task settings (mean ± standard deviation over random trials). Lower FPR is better; higher AUC and ACC are better.

$\alpha_{\min}$	$FPR_{L}$	$FPR_{A}$	$AUC_{L}$	$AUC_{A}$	$ACC_{L}$	$ACC_{A}$
1	59.65	53.84	83.48	86.37	81.55	87.18
1 + Guidance	54.64	51.89	84.18	86.80	81.55	87.18
0.75	55.78	53.11	84.61	86.90	81.47	87.10
0.75 + Guidance	51.46	49.40	85.28	87.42	81.47	87.10
0.5	52.11	52.19	85.86	87.53	80.86	86.80
0.5 + Guidance	48.73	48.52	86.42	88.06	80.86	86.80

Appendix

Table 8: Results on CUB-200 dataset for different

\alpha_{\min}

values. Lower FPR is better; higher AUC and ACC are better.

Method	Score	5 tasks			10 tasks			20 tasks
Method	Score	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
Linear-Head	MSP [ 18 ]	66.16	79.30	73.85	71.93	77.41	68.35	67.91	79.56	61.69
	MaxLogit [ 16 ]	59.36	84.16		66.41	80.91		70.71	78.08
	Energy [ 33 ]	59.66	83.75		66.13	79.90		76.89	73.42
	Entropy [ 4 ]	64.43	82.40		68.34	81.49		65.02	80.63
	KL [ 16 ]	60.53	82.89		67.56	78.73		78.43	72.71

Appendix

Table 9: Results on the CUB-200 [ 54 ] dataset using various post-hoc OOD scoring methods across task settings. Lower FPR is better; higher AUC and ACC are better. Values in parentheses denote changes relative to the corresponding Linear-Head scores.

Method	Score	5 tasks			10 tasks			20 tasks
Method	Score	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
Linear-Head	MSP [ 18 ]	42.74	85.44	77.96	45.69	86.26	76.51	53.49	85.28	73.90
	MaxLogit [ 16 ]	47.13	87.36		53.63	87.09		63.64	84.24
	Energy [ 33 ]	48.04	87.27		55.12	86.43		66.65	82.06
	Entropy [ 4 ]	41.98	87.21		44.95	87.95		52.62	86.52
	KL [ 16 ]	52.69	86.51		59.11	84.98		68.95	80.76

Appendix

Table 10: Results on the ImageNet-R [ 17 ] dataset using various post-hoc OOD scoring methods across task settings. Lower FPR is better; higher AUC and ACC are better. Values in parentheses denote changes relative to the corresponding Linear-Head scores.

Method	$FPR_{L}$	$FPR_{A}$	$AUC_{L}$	$AUC_{A}$	$ACC_{L}$	$ACC_{A}$
MSP	53.50	50.80	85.70	87.61	81.41	86.97
KNN	85.33	71.43	57.16	69.47	81.41	86.97
NNGuide	55.16	51.69	86.01	87.89	81.41	86.97
Guidance (Ours)	50.30	47.21	86.20	88.15	81.41	86.97

Appendix

Table 11: Comparison of different geometry-based scoring methods on the CUB-200 dataset. Lower FPR is better; higher AUC and ACC are better.

Method	CUB-200			ImageNet-R
Method	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$	$FPR_{L}$	$AUC_{L}$	$ACC_{L}$
Linear-Head	79.15	76.60	70.43	50.84	83.16	72.62
KAN-Head (Baseline)	71.81	80.16	79.28	46.93	83.30	74.34
TA-KAN	67.09	81.86	79.51	46.43	84.12	75.10
TA-KAN+Guidance	62.83	80.67	79.51	44.98	84.80	75.10

Appendix

Table 12: Results on the CUB-200 and ImageNet-R datasets on 10-tasks setting using DualPrompt as the backbone prompt-based model. Lower FPR is better; higher AUC and ACC are better.

Method	$FPR_{L}\downarrow$	$AUC_{L}\uparrow$	Train Time / Epoch (s) $\downarrow$	Inference Time / Sample (ms) $\downarrow$
Linear-Head	66.16	79.30	11.6062	4.5659
KAN-Head	59.65	83.48	11.6449	4.5895
TA-KAN	52.11	85.86	11.6838	4.5887

Appendix

Table 13: Performance–efficiency comparison on the CUB-200 5-task setting.

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TOOD: Task-Aware Out-of-Distribution Score Calibration for Continual Learners

Mostafa ElAraby, Samer B. Nashed, Liam Paull

DIRO, Mila - Quebec AI Institute · Universit´e de Montr´eal · Montreal, Canada+1

Continual Learning OOD Detection

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The primary challenge of continual learning (CL) systems is to learn new tasks while remaining performant on previously learned tasks. A similarly important though less well-studied aspect of CL systems is their ability to distinguish inputs that are unlikely to come from within the set of tasks the system has already encountered, often called out-of-distribution (OOD) detection. This paper presents several findings related to the dynamics of OOD detection in CL systems, causes of performance degradation over time which we call OOD forgetting (OODF), and proposed mitigation strategies for this degradation. Chiefly, we find the unintuitive result that OODF is only weakly anti-correlated with classification performance on previous tasks, suggesting that the underlying mechanisms producing OODF are distinct. Moreover, this effect is observed for both energy-based and feature-based OOD detection methods. Energy-based detectors suffer a drop in logit scale as additional tasks are learned, which we term the Confidence Gap, while feature-based detectors also degrade under a complementary effect we call Manifold Crowding. Motivated by these observations, we propose TOOD, a training-free post-hoc method that decomposes logits into per-task energy scores and re-calibrates them using replay-buffer statistics. Experiments on CIFAR-10, CIFAR-100, and a 100-task ImageNet-1K stream show that TOOD improves OOD detection performance over uncalibrated energy in most settings and ranks first or second in nine of ten CIFAR configurations, with the largest gains when the confidence gap is most severe. These results suggest that a substantial portion of OOD deterioration in continual learning arises from score miscalibration rather than from a complete loss of discriminative structure.

Abstract

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