Advancing Out-of-Distribution Detection via Local Neuroplasticity
Authors: Alessandro Canevaro
Julian Schmidt
Mohammad Sajad Marvi
Hang Yu
Georg Martius
Julian Jordan
Venue: ICLR 2025 Poster (2025)
Keywords: Out-of-Distribution Detection
Local Neuroplasticity
Kolmogorov-Arnold Networks
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: A novel method leveraging the local neuroplasticity of Kolmogorov-Arnold Networks for OOD detection

Abstract: In the domain of machine learning, the assumption that training and test data share the same distribution is often violated in real-world scenarios, requiring effective out-of-distribution (OOD) detection. 
This paper presents a novel OOD detection method that leverages the unique local neuroplasticity property of Kolmogorov-Arnold Networks (KANs). 
Unlike traditional multilayer perceptrons, KANs exhibit local plasticity, allowing them to preserve learned information while adapting to new tasks. 
Our method compares the activation patterns of a trained KAN against its untrained counterpart to detect OOD samples. 
We validate our approach on benchmarks from image and medical domains, demonstrating superior performance and robustness compared to state-of-the-art techniques. 
These results underscore the potential of KANs in enhancing the reliability of machine learning systems in diverse environments.

Published as a conference paper at ICLR 2025
ADVANCING OUT-OF-DISTRIBUTIIO DETECTION VIA LOCAL NEUROPLASTICITY
Alessandro Canevaro" Julian Schmidt'
Mohammad Sajad Marvi'
Hang Yu' Georg Martius Julian Jordan'
Mercedes- Bercedes-Benz.eeeee AG, Sindelfingen, Germany University of Tübingen, Tübingen, Germany com
alessandro. canevaroemercedee
ABSTRACT
In the domain of machine learning, the assumption that training and test data share the same distribution is often violated in real- wal-world scenarios, requiring effective out-of-distribution (OOD) detection. This paper presents novel OOD detection method that leverages the unique local neuroplasticity property of Kolmogorov- Arnold Networks (KANs). Unlike traditional multilayer perceptrons, KANs ex- hibit local plasticity, allowing them to preserve learned information while adapt- ing to new tasks. Our method compares the activation patterns trained KAN against its untrained counterpart to detect OOD samples. We validate our ap- proach on benchmarks from image and medical domains, demonstrating superior performance and robustness compared to state-of-the off-the-art techniques. These results underscore the potential of KANs in enhancing the reliability machine learning systems in diverse environments.
INTRODUCTION
Most machine learning algorithms operate under the assumption that training and test data share the same distribution. However, this assumption frequently fails in real-world scenarios where models encounter out-of-diste distriibiittinoonn (OOD) data-samples that deviate from the training distribution, such as those belonging to novel categories. This mismatch can significantly impair a model's accuracy and reliability. As result, OOD detection has become critical area of research, aiming to discern when inputs fall outside the scope of the distribution used for training. Effective OOD detection not only enhances a model's robustness by identifying and handling these anomalous inputs but also ensures that the model maintains reliable performance on known, in-distribution data Yangg et al, 2022).
OOD detection poses a significant challenge due to the diverse nature of OOD types. While many O0D) detectors excel when tested against specific OOD datasets, they often struggle maintain high performance across a broad range of OOD samples. As stated by /Zhang et al. (2023a) there no single winner that always outperforms others across multiple datasets. One reason for this inconsistency is that OOD instances can vary widely, from subtle variations near the distribution boundary to completely dissimilar and far-off examples. As result, developing a universal OOD detection method that performs robustly across multiple datasets, spanning near to far OOD samples, remains challenging.
In this paper, we present novel OOD detection method using Kolmogorov-Amol. Networks (KANs) (Liu et al. 2024b). KANs are neural networks with unique architecture that enhances in- terpretability, improves the securacy-to-paramee pared to multilayer perceptrons (MLPs). Our approach takes advantage of KANs' distinctive prop- erty of local neuroplasticity-a characteristic absent in traditional MLPs due to their reliance on shared, non non-trainable activation functions. In contrast, KANs demonstrate local plasticity owing to their spline- based architecture. This characteristic ensures that learning regions of the network activated by the training data, thereby preserving the integrity of distant and unrelated regions.
ratio, and mitigates catastrophic forgetting com-
task impacts only the

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As illustrated in Figure [ method compares the activation patterns of two identically initialized KANs: one trained on In- in-Distribution (InD) data and the other left untrained. OOD samples will predominantly trigger the regions of the trained network that not adapted during the learning phase, thus the samples will produce a response closer to the untrained network.
Conversely, InD samples will mostly engage the neurons that have been trained, resulting in a noticeable difference in the activation between the models.
InD sample
Untrsined KAN
response
A
We tested our method on seven different benchmarks from two different domains: the OpenOOD CIFAR- 10, CIFAR-100, ImageNet-2000 full-spectrum (FS), and ImageNet- 1K FS (Yang al., 2022) for the image do- main, and the Ethnicity, Age, and Synthetic OOD bench- marks for the tabular medical data domain (Azizmalayeri al. 2023). Our experiments demonstrate that the KAN detector outperforms current Otate-Of-The-Art (SOTA) techniques across all seven benchmarks on the overall average AUROC that considers both near and far OOD, Additionally, in contrast to many other SOTA methods, our approach's 's performance does not vary significantly based the number of training samples. This indicates that leveraging KANs leads to highly effective OOD de- tection, underscoring the potential of this novel architecture in developing more robust machine learning systems capable of operating reliably in diverse and unpredictable environments.
OOD sample
Trained KAN
OOD response
Figure Overview of the proposed method: the detector compares the ac- tivation function response of trained KAN model with its untrained counter- part. difference the response in- dicates the sample is InD, a similar re- sponse suggests is OOD.
KAN-BASED OOD DETECTION
This section begins by providing a short background on KANs and their working principle. Next, delve into the core concept underlying our proposed method for OOD detection. Finally, describe the primary limitation of the KAN detector and propose a strategy to enable its deployment in complex real-world scenarios.
2.1 BACKGROUND
KANs are neural network architectures based on the Kolmogorov-Amoo representation theorem. This theorem states that any continuous multivariate function can be represented as a sum of con- tinuous functions of single variable. Hence, KANs approximate high-dimensional functions using simpler, univariate components, effectively addressing the curse of dimensionality in machine learn- ing.
In practice KANs decompose multivariate functions into univariate B-spline functions with learn- able coefficients. Let vp be the p-th component (feature) of the input vector x The and let Yo be the q-th component (feature) of the output vector E I A KAN layer transforms x into using a matrix of univariate functions & { where each óp.q is parameterized by a B- B-spline. Each B-spline consists of a linear combination of + & B-spline basis functions with learnable coefficients Grg.i- The spline order is denoted & (usually 3) and G is the grid size.
G+
04 = Σ (p))))p)
with: @pp(Tp)) = Σ cp.. (1p))
(1)
KAN layers can be stacked to construct deeper networks, allowing for complex transformations across multiple stages. Performance is further enhanced by incorporating residual connections, which add flexibility to the spline functions through trainable weights and additional basis func- tions (Liu et al.) 2024b).
Local neuroplasticity KANs facilitated by two key properties. First, each input feature Ip processed independently by its set of activation functions (dp. Vg). Second, during
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backpropagation, only the spline coefficients sample 2p modified, leaving the other areas of the activation function largely unchanged.
2.2 OOD DETECTION WITH KANS
We propose leveraging the local plasticity of KANs for OOD detection. The InD data seen dur- ing training only affects specific regions (spline grid coefficients) of the network. By determining whether region contains InD data and inspecting which regions are activated by each sample, the KAN-based detector can distinguish between InD and OOD samples. This differentiation is achieved by comparing the output of the trained activation functions with their values prior to train- ing. The step-by-step procedure is follows:
Setup: Initialize untrained KAN and create copy. Train one KAN with the InD dataset
while keeping the other untrained.
Detection: Perform a forward pass on both networks with the given sample x, and save the output of the activation functions:
ttained (1pp): p.g
guntrained (Ip)
Vp,
(2)
Compute the difference between the responses:
p.. = trained
(Ip)
P.a
gumtrained
(rp)
(3)
Analyze the difference matrix A. OOD samples will tend to have a higher ratio of the entries in the A matrix close to zero. To obtain a scalar InD score S(x), we aggregate the differences using scoring function F Fscore (detailed in Appendix A.
S(x) Fscurel (A(x).
(4)
To clarify our method's working principle, let rewrite (T.p) using Eq.
Ano(Tp))
Σ trained
untrained
Bx(xp))
(5)
define the locations within the network where InD information is stored, while (x,)) serves as a mask and specify the regions activated by the sample x. Con- sequently, multiplying these two terms provides quantitative measure of the overlap between InD regions and the given sample. This overlap subsequently utilized to compute the InD score.
The terms Ic
cuntrained p.q.
Once the InD score is obtained, it is thresholded classify the sample as InD OOD:
InD, if S(x) > X D(x) OOD, if S(x) X.
(6)
where À is predefined threshold. A test sample with InD score less than À is categorized OOD. Otherwise, it is classified as InD.
Figure 2 illustrates the working principle of the proposed algorithm using modified version of the toy example proposed by Liu et al.) (2024b). The dataset is a one-dimensional regression task featuring five Gaussian peaks. We used two of these peaks the training set and InD test set, while the remaining three peaks are the OOD test set. Here the KAN model is composed of a single layer with one input and one output, i.e. single univariate function á with 200 spline coefficients.
2.3 CAPTURING THE JOINT FEATURE DISTRIBUTION
Like MLPs, KANs are capable of processing multivariate inputs and producing multivariate outputs. However, differently from MLPs where activation functions receive a weighted sum of all inputs, in KANs, each activation function receives only single input. While this characteristic allows the KAN detector to effectively capture the marginal distributions of input features, it also constrains its ability model the joint distribution of features.
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(a) Truin Dataset
(b) Untrained Model
[c] Trained Model
Prodiction Lin
Prediction Sin
(d) Test Dataset
(e) InD Scores
(c) Threshokded Scores
Soure
Figure 2: (a) Visualization of the training dataset, showing the relationship between inputs and targets. (b) Response of the untrained KAN model across the entire input range. (c) Response of the trained KAN model across the entire input range. (d) Test dataset illustrating inputs versus targets, created by combining the training dataset (InD) with three additional Gaussian peaks over the remaining input range (OOD). (e) InD score S(x)Vx E 1- using the median as scoring function (Fscor). (f) Final results after applying threshold (Å 1e 3) to the InD scores: blue regions indicate predicted InD areas and red regions indicate predicted OOD areas.
To overcome this limitation we propose partition the InD dataset and train separate KAN models for each partition. In this way, the complex training distribution is decomposed into smaller parts that can accurately described using only the marginal feature distribution. Various techniques can be employed to partition the dataset. A simple, yet effective approach is split the dataset based on class labels. An alternative approach, which also works when class labels are absent, such as in regression tasks, is to apply clustering algorithm like k-means (Lloyd 1982). Formally, the dataset is partitioned into P non-overlapping subsets D1, D2...., Dp. For each partition D,, we train separate detector, denoted KAN, While the partition D; is different for each KAN,, the training task is always the same (e.g., classification). During inference, we compute the InD score for a sample by aggregating the InD score from each KAN model. Let A (x(x be the difference matrix of KAN,:
(xx) Fage (Fsoore (A (x)), Fscore (x²(x)), Fscore (A Px)).
where Fag. is a suitable aggregation function, such as the maximum function. Since the partitions non-overlapping, for Inl samples, there will be only one model that recognises the sample as InD (high InD score), while the other will flag it as OOD (low InD score).
Through this partitioning, detector is composed of multiple KAN models, and the strategy resembles ensemble methods. Furthermore, if all models are initialized with the same weights, the untrained KAN be shared, reducing the number of forward passes inference time.
To demonstrate the effectiveness of our proposed improvement method, we designed specialized L-shaped dataset where the base KAN detector fails. This dataset consists of 2D points, with the training task being regression to predefined constant. Figure 3 iillusraates the results, showing the performance of the default KAN detector compared to the partitioning method.
EXPERIMENTS
First, we describe the benchmarks, metrics, and implementation details used in our study. The re- sults demonstrate the superior performance of our method, highlighting its key advantages. Finally, a comprehensive ablation study analyzes each hyperparameter and component, elucidating their im- pact performance.
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(a) Default approach
Dateset partitioning
1.6
0.0
0.0
-1.0
1.0
1.6
20
The blue point cloud shows the training distribution and the red points are OOD test samples. The black contour represents the thresholded score function (median) separating InD from OOD samples. (a) Default KAN detector limited by the marginal distribution of Φ and 22. (b) Improved performance by partitioning the training dataset with KMeans clustering (P 2) and Fage. max aggregation function.
Figure 3: 2DD L-shape toy dataset:
3.1 EVALUATION PROTOCOL
Setup. The evaluation of the proposed method is performed on seven different benchmarks from two different domains: OOD detection in images and tabular medical data.
For OOD detection images, the experimental setup adheres to the OpenOOD (Yang et al. 2022) benchmark protocol. We evaluate the KAN detector the CIFAR-10 10 benchmark, using CIFAR- 10 (Krizhevsky et al., b) as the InD dataset. The OOD datasets are categorized into near OOD datasets (CIFAR-ION 100 (Krizhevsky et al., a) and Tiny ImageNet (TIN) (Le & Yangl 2015 ) and far OOD datasets (MNIST (Deng] 2012). SVHN (Netzer et al.) 2011). Textures (Cimpoi et al. 2014), and Places365 (Zhou et al.] (018)). The CIFAR-100 benchmark contains the same datasets as the CIFAR-10 benchmark except for the CIFAR-I0 and CIFAR-100 datasets which have an inverted role (CIFAR-100 as training data and CIFAR-I0 as OOD dataset). To evaluate the scalability of our method. we also tested it on the Ima FS and ImageNet- IK FS benchmarks. Com- pared to CIFAR-10 and CIFAR-100, these benchmarks features five to twenty times more training images, each with size seven times larger. The full-spectrum version increases the detection chal- lenge and, at the same time, makes closer real-world applications by enriching the InD test set with covariate-shifted Inl) samples (Yang et al., 2023). The datasets used in this benchmark are: ImageNet-200 or ImageNet-IK IK (Deng et al. 2009) as training set, ImageNet-V2 V2 (Recht et al., 2019), ImageNet-C (Hendrycks & Dietterich, 2019). ImageNet-R (Hendrycks et al.
(021) as covariate-
shifted InD test set, SSB-hard (Vaze et al. 2022). NINCO (Bitterwolf et al. 2023) as near OOD,
and iNaturalist (Van Hor et al. 2018). Textures, OpenImage-O (Wang et al. 2022) as far OOD.
For OOD detection in tabular medical data, we follow the benchmark proposed by Azizmalayeei let al. (2023). We consider the benchmarks derived from the eICU dataset (Pollard et al.) (018)) which contains clinical data of tens thousands of Intensive Care Unit (ICU) patients in several hospitals. In the near OOD benchmarks, the eICU dataset is divided into InD and OOD according to some features such as ethnicity (Caucasian as InD) or age (older than 70 as InD). The feature used for splitting the dataset then removed. In the synthetic OOD benchmark, the OOD data is generated by scaling single feature from the InD set by factor F. For each factor, the experiment repeated 100 times with different features, to minimize the impact of the chosen feature. By varying the scaling factor, the generated samples range from near to far OOD.
In contrast to training-time regularization methods (e.g., MOS (Huang & Li, 2021). CIDER (Ming et al. 2023)), our detector operates in post-hoc manner and can be seamlessly integrated with any pre-trained classifier, regardless of model architecture, training procedures, or types of OOD data. The backbone is used to perform the classification regression task and in the case of post-hoc methods it is trained independently from the detector. The OOD detector only uses the latent fea- tures of the backbone for InD/OOD classification. The considered OpenOOD benchmarks employ a pre-trained ResNet backbone (He et al.) 2015) for feature extraction, while the tabular medical benchmarks use FT-TTranformmr backbone (Gorishniy et al. 2021).
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Given that the benchmarks we considered are all based classification tasks and require pre- trained backbone network, we conducted additional experiments on regression based datasets, ap- plying the detector directly the data without feature extractor. The results, presented in Appendix A.2 demonstrate that our method also performs well in these scenarios.
Metrics. In all benchmarks, the primary metric used to evaluate the OOD detection performance is the Area Under the Receiver Operating Characteristic curve (AUROC). This threshold-free metric provides a robust assessment of the model's ' ability to distinguish between InD and OOD samples.
In our evaluation, we focus on the average AUROC across all test datasets, including both near and far OOD (for more details on how the overall average computed see Appendix [A.3). This approach is motivated by the desire to develop a method that performs well across diverse datasets, as real-world applications often encounter unknown types of OOD samples. We acknowledge that achieving consistent performance across multiple datasets is challenging, as many methods excel on specific datasets but struggle to generalize.
Following the OpenOOD benchmark guidelines, report the results averaged over three seeds, corresponding to three pre-trained backbones. This does not apply to the ImageNet-IK, FS bench- mark where only one pre-trained backbone is available. The results for the tabular medical data benchmarks. Our approach also introduces some stochasticity due to the KAN initialization. To assess its impact on performance, we initialized the detector with five different seeds for each pre-trained backbone. The results indicate that the stochasticity due to the KAN initialization is lower than the one due the backbone training (see Appendix A.4).
averaged over five seeds
Implementation details. The detectors are trained us- ing the InD dataset. During the evaluation phase, InD scores are calculated for all the test data. All hyperpa- rameters are tuned using the validation set, according to the OpenOOD benchmark guidelines. The tabular medi- cal data benchmarks follow a similar structure.
Fa OOD
oob
Inlt
Density
On all benchmarks, used the median the scoring function and the maximum as the aggregation function. The median is particularly effective due its robustness to outliers, making it reliable for distinguishing between InD and OOD samples, as illustrated in Figure These choices for both (scoring and aggregation) are further mo- tivated in Appendix A.I
Response difference
Figure 4: Distribution of activation's 's differences (A) for three different sam- ples (InD, near and far OOD). The InD sample tends produce bigger values in the A matrix compared to the OOD samples. Using the median as a scor- ing function (vertical dashed lines) ef- fectively separates InD from OOD.
The latent features of the backbones exhibited a highly skewed distribution. To address this skewness and achieve more balanced distribution that fully utilizes the KAN's grid range, we applied histogram normalization.
We leverage information from multiple latent layers of the pre-trained backbone. As demonstrated by Liu et al.) (2024)). this multi-layer integration enriches the feature representation, leading improved detec- tion accuracy. Specifically, the authors claim that the last layer contains predominantly semantic information while including the layers closer the input allows the detector to capture also the covariate information.
3.2 RESULTS
Table presents the results of our experiments on the CI and CIFAR-100 benchmarks, com- paring the KAN detector with several SOTA OOD detection methods (see Appendix [A.5] for list of all the considered baselines). On top the numerous baselines provided by the benchmark we also compare approach to the current best post-hoc method on the CIFAR leaderboard: the NAC [Liu et al. 2024a). The results show that the KAN detector outperforms all previous methods on both benchmarks, demonstrating the effectiveness of leveraging spline- based local activation func- tions for OOD detection. In each column of this and the following tables, we highlight in bold the best-performing method. Where multiple seeds of the backbone are available we also highlight

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any other methods that do not show statistically significant difference from the best best-performing method. Statistical significance is assessed using Welch's t-test with p < 0.05.
Table I: Comparison of OOD detection performance (AUROC) on CIFAR-10 10 and CIFAR-100 benchmarks.
Method
Near OOD
Far OOD
Avg Near
Avg Far
Avg Overall
CIFAR
TIN
MNIST
SVHN
Textures
Places365
CIFAR-10
Benchmark
Mpx
2631
88. 88.32
90.50
89.77
89.58aum
28.63-022
27.6222929
89. 29.622.m.
88. :5:44
ODIN
82.18+187
83.55
95.24
84,58
26,94=226
85,07=124
82.87=185
87.96=06:
86.26
MDS
83.59
84.81
90.10a241
91.18
92.69
84,90
84.90=254
84.20=2.0
89.72
87. 87.88
MDSEns
61.29+003
59,57=033
99.17=0.11
66. 66.56.203
77.40=028
52.47=0.15
60.43-0026
73.90=0027
69.41
RMDS
88.83
90.76
91.84 93.222+0.0
92.23:0:3
=1.51=0.11
89, 39:80=022
92.20=n22
91.40=:0.0
Gram
58.3314449
18.9
72.64.12.4
91.52
62.34:822
20.44
68.66
71.73::320
67.377.15.4
ReAct
85.932085
88. 2:44
92.81 #100
89. 12:112
89, 89,38 4s
90.35
87, 17.11 2001
90.422a141
89.31
VIM
87.75+028
89. 622323
94. 24.36
24.50
95.15=034
89, -9,49=0.39
88, 68:688
93.48=0244
91.88+0037
KNN
89.731014
91.5611976
94, 26..6.
92.67
93.162024
91.77.003
90.64.0000
92.96.0144
92. 19
ASH
74.11
76.44
83. 16:446
73.4626.11
77.45=239
79. =9.89=309
75.27=1 04
78,49=255
77 77.42
SHE
80.31
82.764043
90.43
86.38
81.57=121
82.89=12:
81.54=0.51
85.32=1.4
84.06+2.16
GEN
87.21
89:20
93.83-22.4
91.97
90.14:006
89.46:005
88.20:0.0
91.35
90.30
NAC
89.83+0.9
92.02=aazo
14.337
96.06
95.64:045
91.85=025
90.93=022
94.60 04.60=0.5
93.37:00.44
KAN
90.06
91.926:022
97.86 20.73
97.39
95
91.64:099
90.99
95.69 :0.22
94.12
CIFAR-100 Benchmark
Mpe
24.3
78. 1804
76.01 1::30
82.07
80.56:0m
29.29
76.41:0025
79.48:041
78 78.46.
ODIN
78.18+014
81.63+00e
83.79+1.31
74.54=0.76
79.33=1.08
79.45=022
79.90=0.11
79,28
79.49:0077
MDS
55.87
61 61.50
67.47:
70.68
76.26:00m
63.15 15.
58. 28.69
69. 69.39
65 82:
MDSFns
43.85
48.78 19
48.21
53.762167
69.75.114
42.27
46.31
66.00=0e
59 1004
RMDS
77.75=am
82. 52.55
79. 7.424.4
84, =4.8
83.65
83.40 20.4
80. 15:0.1
82.92.a02
82.00=1115
Grum
53.91 49.41=0.5
80.71
95.55=0000
70.79=1.22
46.38 =6
51.66=077
73.36=1.0
66. 12::188
ReAct
78.65
82. 88
78.37
83.01 2097
80. 15:
80.03
80.77
80,39
800.52.0099
VIM
72.21
77. 77.76=0.6
81.89+1.02
13.14
=5.91
75.8 00.35
74.98=0.13
81.70=002
79.46=1142
KNN
77.02+0a5
83.34:016
82.36
84.15
83,66:083
79.43=..47
18.18
82,40=0.17
81.66 :037
ASH
76.48.2.3
79.92..00
77.23
85.6021.0
80.72:0.0
78.76_0016
78, 78.20:0015
80.58.006
79.79
SHE
78.15
79.7440336
76.76+1.07
80.97=3.9
73.64=128
76.30=0.5:
78.95=0018
76.92=1.16
77.59+1.78
GEN
79.38:.0.x
83.25
78.29
81.41
08874
80.28
81.31
79.68
80.23 1:10
NAC
72.02...
79.8611975
93.2611134
92.60g114
89.36_054
73.06-007
10.9
87.07
83.3610044
KAN
72.97=007
81.37
92.29=1.85
87.16:4436
89,43-039
77.42=0035
77.17
86,57
83.44
The KAN detector ranks first on both ImageNet-200 FS and ImageNet- 1K FS benchmarks as shown in Table 2 and it consistently ranks in the top three across all tabular medical data benchmarks as reported in Tables 3 and
In Appendix A.6 we report the results with all the baselines available in the benchmarks for the AUROC and HPR @95 metrics.
Moreover, our method demonstrates significant robustness to variations in the number of training samples. Table[Banalyse this phenomenon on the CIFAR-10 and CIFAR-100 benchmarks, compar- ing the performance of the three previously best-performing methods and our approach by evaluating all methods with different dataset sizes only. Unlike other methods that achieve peak performance only with an optimal number of training samples, our approach consistently performs well across different dataset sizes. The performance of VIM and KNN is closely tied to the size of the InD dataset, while NAC achieves its best results when only 2% of the training samples are used. con- trast, the KAN detector maintains high performance across wide range of training dataset sizes, with only a minor decrease observed in the extreme case of five samples per class. Robustness to variations in training dataset sizes is crucial in real-world scenarios where the number of training samples may be insufficient to capture the underlying distribution's characteristics. Additionally, this property is advantageous when scaling to large datasets. We attribute the strong performance of our approach across all considered benchmarks also to this key characteristic.
3.3 ABLATION STUDY
Parameter analysis. The main hyperparameters that regulate the performance of the proposed method are the number of partitions P. and the grid size G. Table 7 illustrates the variations in AUROC performance as a function of the number of partitions obtained through k-means clustering. Increasing P enhances the detector's ability capture the joint distribution of features, resulting
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Table 2: Comparison of OOD detection performance (AUROC) on ImageNet-200 FS and ImageNet- 1K FS benchmarks.
Method
Near OOD
Far OOD
Avg Near
Avg Far
Avg Overall
SSB-hard
NINCO
INaturalist
Textures
OpenImage-O
ImageNet-200
Benchmark
Ope
47.64=030
15.15
72.44+082
69.1240.6
62.31
50.89
67.96
G1.13
ODIN
14.31=0m
52.36:00
70.
67.10
61.48an31
48.33=a0s
66.25
59.09
28.59
56.65189
68.25
73784
61,901a57
52.62.099
68.00gea7
61. 61.855a
MDSEns
34.22:044
41.58
43.63
67.54
48.38+036
37.90=0020
53.18:6.39
47.07
RMDS
56.24=062
60.95
71.71
64.61
63.52
58.59
66.62+11.1
63.41
59.12-071
63.35
78.42.1975
75
61.5
61.23
65.2611031
63.65
ReAct
47.25=055
53.84
39.45
71.45
62.30+238
50.55
67.73
60.86
VIM
45.34=0.72
1m.
1..
82754
65,70
51.22=0.6
73.19
64,40=1.0
44.05=004z
54.51
71.53
19.881
12:129
49.28:a051
71, 21.84
62.82.amm
ASH
50.96=091
1805
77.9611
79.394081
69.09;a71
54.74:074
75.48:10.5
68.18
SHE
52.82:0a5
56.64=aam
72.20+2.65
74.27
64,95
54.73=005
70.47=1.39
64.18+1441
48.33=027
44.85
68.944.0.3
66.5840477
60.87:a02
51.59
65,46.0.44
59.91
NAC
45.42-011
53.80
65,8311.22
74.41
60.79
29.6
67.01
60.05g9
KAN
58.37=0047
61.10+a.a
84.13
83,30 +0.35
70.40:n26
59.74:0045
79.28 20.18
71.46 #0.40
ImageNet-11 FS Benchmark
OpenMax
53.79
60.28
80,30
73.54
$7.03
75.24
67.96
ODIN
54.22
60.59
77.43
76.04
73.40
57.41
75.62
68.34
MDS
39.22
52.83
54.06
86.26
60.75
46.02
67.02
58.62
MDSEns
37.13
53,32
$2.98
RMDS
56.61
67.50
73.48
74.25
72.13
62.06
73.29
68.79
Gram
51.93
60.63
71.36
84.83
69,40
56.28
75.20
67.63
ReAct
VIM
45.88
59.12
72.22
93.09
75.01
52.50
80.10
69.06
KNN
43.78
59.86
67.79
90.29
69,98
51.82
76.02
66.34
ASH
54,66
66.38
89.23
89.53
81.47
60.52
86.75
76.25
SHE
58.15
64.27
84.71
87.48
76.92
61.21
83,04
74.31
GEN
52.95
62.73
78.47
71.82
72.62
57.84
74.31
67.72
NAC
52.48
66.49
88,92
92.77
80.76
59.48
87.48
76.28
KAN
55.88
69,55
91.55
93,45
82.15
62.71
89.05
78.52
Table 3: Tab. Med.
Table 4: Tab. Med.
Table 5: Tab. Med. Feature multiplication (AUROC metric).
Caucasian Eth. as InD
70 y.o. as InD
(AUROC metric).
(AUROC metric).
Method
eICU Eth.
Method
eICU Age
Method
eICU Synthetic OOD
Avg Overall
MDS
58,5
MDS
50.8
1000
RMDS
51.6115
RMDS
48.31u7
MDS
59.9:14
79.5
87.5
75.63-1.5
KNN
55.8
KNN
49.62a2
RMDS
51.5113
57.8.14
64.0gm5
57.77
VIM
57.3+23
VIM
48.82n1
KNN
57.3
75.4
86.5115
73.07:118
SHE
50.5
SHE
50.4207
VIM
57.9=15
77.6=13
88.3407
74.60=1.25
KLM
51.622.1
KLM
51.0=a7
KLM
55.7213
54.1a08
63.1=11
71.2=39
80.4116
72.1
63. 63.10-215
69.10=235
OpenMax
48.7
OpenMax
48.1
OpenMax
$1.0=07
71.4432
59.50=245
KAN
61.4331
KAN 50.5
KAN
64.6233
83.0
89.8
79.13:331
Table 6: The effect of training dataset sizes on AUROC performance.
Method
CIFAR-10 benchmark
CIFAR-100 benchmark
100%
10%
1
0.1
100%
10%
1%
VIM
91
91.69
88.67+1.29
76.38=188
79.46
78.8 18.83
67.06+243
KNN
29
91.7240.18
88.9410.0
8.15..3
81.66
80.05
27.03-1111
NAC
87.05-114
89.7440.0
93.09
89.29=a77
80.80=006
81.72+0.99
80,97410
KAN
94.12-0.0
93.95
93.90
93.21
83.44:199
83.11
81.44+1a1
in higher AUROC values. However, there is upper limit beyond which further increasing the number partitions does not lead to performance improvements. The choice of k-means clustering over other methods is justified by its simplicity and excellent scaling performance. Additionally, empirical evidence, as reported in Appendix A..]] demonstrates that the choice of the clustering algorithm does not significantly affect detection performance.
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According the authors of KAN (Liu al. 2024b), varying the grid size has similar effect to varying the width and depth of a traditional MLP. A fine ome-grained grid (higher G) should improve the accuracy of the network. In the case of our detector, reported in Table increasing the density of the grid above a certain threshold does not result in higher OOD detection performance.
Splines' smoothing operation. KANs incorporate splines that perform an essen- tial smoothing operation. which cru- cial given the continuous nature of the in- put space. To demonstrate the superior- ity of the KAN detector, implemented a baseline histogram method by replac- ing all the univariate functions Φn. in KAN with simple histograms that record the presence of InD samples in a binary manner. The histogram method achieves an overall AUROC of 85.29% which approximately 9% lower than that of the KAN detector, clearly demonstrating the superiority of the KAN's splines approach.
Table 7:
KAN detector performance w.r. different datasets partitions and grid sizes over CIFAR-10.
Partitions (P)
AUROC
Grid size (G)
AUROC
P
46,08
k
87.2011.52
p
90.3912778
$ 10
91.72.1..4
p 10
94.12
& 50
93.9220.40
P 20
94.10
100
14.12:1..0
P 30
94.0510053
200
94.0311.49
Partitioning alternatives. To capture the joint feature distribution, the partitioning method is not the only solution. Another approach is to augment the input features with new features that are combinations of the original ones. This can be efficiently achieved using techniques like Principal Component Analysis (PCA) or autoencoders. PCA provides features that are linear combinations of the original ones, while autoencoders generate features that are non-lineat combinations, Although this technique worked well on toy L-shaped dataset (Appendix AA8)) it did not yield the desired results on high-dimensional feature spaces in other benchmarks. It resulted in a lower AUROC compared to the partitioning method.
Influence of the training task. Since KANs are differentiable, they can be trained similarly to conventional MLPs using backpropagation. our approach, the KAN trained with latent features extracted from the backbone as inputs, and the training task mirrors that of the backbone network, specifically multi-class classification. For more details on used training parameters see Appendix A.9 Importantly, the training task does not need to directly relate to the OOD detection problem. Similar to the histogram baseline, our primary objective is to register all imput samples within the correct spline coefficients. Any training task that adjusts the spline coefficients in the vicinity of the InD samples can yield a valid OOD detector.
We experimentally verified hypothesis by training the KAN using different loss function and an unrelated task, namely regression to a constant value. The results from this regression task demonstrate that the detector effectively distinguishes between InD and OOD samples. Compared to the KAN trained on the classification task, we observed an improvement of approximately 0.2% in AUROC performance on the image benchmarks. However, the tabular data benchmarks, the performance decreased by approximately 3%. These findings indicate that while modifying the training task of the detector can still yield satisfactory performance, the extent of this effect appears to be benchmark-dependden
4 RELATED WORK
This section reviews recent advancements in OOD detection, provides overview of the latest in- novations to enhance KAN performance, and explores the diverse sectors where KANs have demon- strated successful applications.
4.1 DUTT-OI-DISTRIUUTION DETECTION
OOD detection focuses identifying instances with semantic shifts, special of distribu- tional shift. OOD detection methods can be broadly classified into the following categories (Yang
al. 2024). Classification-Dasee methods use the output of classification models, such as softmax

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scores, to distinguish between InD and OOD samples. Examples include Maximum Softmax Prob- ability (MSP) (Hendrycks & Gimpel, 2017). which uses the softmax score of the predicted class as confidence score, and ODIN Liang et al., 2018), which applies temperature scaling and input perturbations to enhance the separability of InD and OOD samples. More recent methods that fall in this category are SCALE (Xu et al. 2024a), ASH (Djurisic al. (023). VIM (Wang et al.) 2022). and KNN {Sun et al. (022). ). Gradient- based methods also belong to this category. Examples include GradNorm (Huang et al. (021) and NAC (Liu et al. (0244), which use gradients calculated from the KL divergence between the model's output and a uniform probability distribution. Density-based methods model the probability distribution of the training data to identify deviations. This is often achieved using Gaussian mixture model (Zong et al. 2018) or normalizing flows (Zisselman & methods typically use autoencoders to re- construct input samples and measure the reconstruction error as a signal for OOD detection (Jiang ctt al. 2023 Zhou| 2022). Distance-based methods rely on distance metrics in the feature space to identify OOD samples. The Mahalanobis distance-based detector (Lee et al. 2018) first models the feature distribution with a class-conditional Gaussian distribution and then it derives the InD score using the Mahalanobis distance between the InD centroids and the input sample. fDBD (Liu & Qqn 2024) measures the distance between the latent feature of the sample and the class decision boundaries. Our method also falls into this category, as it computes the InD score by measuring the distance between the network's 's regions activated during training (InD regions) and those activated by the test sample.
Tamar 2020 Jiang et al., 2022). Reconstruction-
4.2 KOLMOCOROV-ARNOLD NETWORKS
The recently introduced KAN (Hou & Zhang 2024 represents significant advancement in neural network architectures, offering a potential alternative to traditional MLPs by not only enhancing accuracy but also leading to more interpretable models. As result, numerous studies have tried to innovate and refine KANs further. For example, many articles replace the spline architecture with more efficient or accurate alternatives such as Chebyshev polynomials (SS et al. 2024). wavelet- based structures (Bozorgasl & Chen 2024), sinusoidal functions (Reinhardt et al. 2024), and ra- dial basis functions (Li) 2024). Others try to replicate advanced neural network architectures using KAN's characteristics. This includes convolutional neural networks (Bodner et al. 2024) and graph neural networks (Kiamari al., [024 Bresson et al. [2024] Zhang & Zhang] 2024). ) further demon- strating the versatility and potential of KANs. Applications of KANs have rapidly expanded across various domains, including time series analysis (Vaca-Rubio
al., 2024 Xu al. 2024b), solving
ordinary and partial differential equations (Koenig et al., 2024 Wang et al. 2024). hyperspectral image classification (Seydi 2024 Jamali et al.] 2024), and computer vision (Azam & Akhtar 2024
Li et al. 2024; Cheon 2024). Additionnlly, KANs have recently been applied to fields similar to OOD detection, such as abnormality detection (Huang et al. 2024) and Al-generated image detec- tion (Anon & Emon, 2024). These studies leverage the superior accuracy and interpretability of KANs (Liu et al. (2024b) to uncover more complex patterns in the data. While their work focuses on developing robust models that demonstrate KANs' capacity to generalize effectively to unseen samples, they do not address the detection of these samples. In contrast, we present a novel OOD detection method that leverages the unique local plasticity property of KANs, applicable to any backbone architecture.
CONCLUSIONS
This paper introduces a novel approach to OOD detection using KANs, capitalizing on their unique local neuroplasticity property. Our method effectively differentiates between InD and OOD samples by comparing the activation patterns of a trained KAN against its untrained counterpart. The exper- imental results show that our KAN-based detector reaches SOTA performance across seven bench- marks from two different domains. Importantly, our experiments show that the previous methods suffer from a non-optimal InD dataset size, while our method is unaffected by these perturbations. This makes the KAN detector a robust and versatile method that maintain high performance across diverse and unpredictable data distributions. Future work will further explore the effect of different training tasks on detection performance.
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ACKNOWLEDGMENTS
This work is result of the joint research project STADT:up (19A220060). The project is supported by the German Federal Ministry for Economic Affairs and Climate Action (BMWK), based on decision of the German Bundestag. The authors are solely responsible for the content of this publication.
The authors would like to express their sincere gratitude Pavel Kolev, Niklas Hansclmann, and Shuxiao Ding for their invaluable assistance in proofreading and providing insightful feedback on this manuscript.
REPRODUCIBILITY STATEMENT
Our implementation adheres rigorously to the benchmark guidelines. Detailed information on the hardware and software utilized is provided in Appendix [A. while the inference time performance of our method is discussed in Appendix(A.11 The settings and hyperparameters for each benchmark are reported in Appendix A.12 Our code is publicly available at the following link: https:
//githab. com/ wtwpa/lllssadooooooooo ceneddo--cnevarree KANN-ONN
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A
APPENDIX
A.1
SCORING AND AGGREGATION FUNCTIONS
The trainable coefficients of the detector networks are initialized randomly. As result, it may occasionally oceur that some these coefficients are initialized the exact values they would attain post-training. Consequently, the training procedure does not modify these coefficients, as they are already optimal. This phenomenon can lead to false positives in detection, as both the trained and untrained networks might exhibit the same response to an InD sample. This issue can be mitigated using a scoring function that is more robust to outliers, such as the median. This hypothesis is experimentally validated in Table 8
The use the maximum function for aggregation allows us to select the detector closest to the test sample, which intuitively possesses the best information for decision-making This approach is experimentally verified in Table
Table 8: AUROC performance variation the CIFAR-10 10 benchmark for different scor- ing F functions.
Table 9: AUROC performance variation the CIFAR-I0 benchmark for different ag- gregation F Fage. functions.
Scoring
Fscore
AUROC
Aggregation Fuge.
AUROC
min
90.8 8..
min
91.55=0.7
92.04
91.99-2.10
median
94.12:t0.59
median
90.31
max
=2.02
max
94.12=0.59
A.2 DETECTION ON REGRESSION DANSIONN--BSDDDDD DATASETS
As the standard benchmarks used in OOD detection mainly focus on classification tasks, we test our method on three additional regression-based datasets: the California Housing dataset (Kelley Pace & BBrry 1997). the Wine Quality dataset (Cortez et al. 2009), and the Friedman synthetic dataset (Friedman) 199I). To generate the InD and OOD partitions and ensure that the OOD samples are semantically different from the InD ones, we thresholded the regression (output) value. The KAN then directly applied to the raw dataset features, highlighting that the method is not only effective on regression-basee tasks but also in the absence of feature extractor backbone network. This is not possible for other methods such as NAC that require the gradients of the backbone network for detection. Thus, Section 3.2, is one of the best approaches across all benchmarks. Table 10 reports the detection results in terms of AUROC on the three datasets, showing that the KAN detector outperforms the KNN baseline on all of them.
baseline detector method,
used KNN, which, according to the results in
Table 10: Detection (AUROC) results for regression-based datasets.
Method
California Housing
Wine Quality
Friedman
KNN
68.73
68.69
67.30
KAN
70.53
71.32
69.42
On the California Housing and Wine Quality datasets, we used only one partition (P) for the KAN detector because a value greater than one did not improve performance. This indicates that either the partitioning method does not work well on regression-bast separability of data clusters, or these datasets do not require the detector to capture the joint feature distribution effectively separate InD and OOD samples. To investigate this observation further, we also tested our method on the Friedman dataset. Here, the regression output is generated by the following non-line non-linear function of the inputs:
datasets, possibly due to poor internal
xxx 10 -inn(T 20 11) + 20 (x2 0.5) 10 23 5.24 +N(00 a).
(8)
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Given this non-linearity, it is ensured that the samples not separable using only the marginal feature distribution. this case, peak performance is achieved with minimum of four partitions, shown in Table IT This shows that even for regression-basee datasets method can capture the joint feature distribution.
Table 11: AUROC performance as a function of the number of partitions (P) in the Friedman dataset.
Partitions (P)
4
AUROC
52.11
64.15
63.83
69.42
A.3 AVERAGE OVERALL METRIC
Many benchmarks (including the OpenOOD CIFAR-I0 and CIFAR-100) assess OOD detection performance on multiple OOD datasets. However, they lack overall average that gives holistic overview the methods' performance. In our experiments, we additionally evaluate our method on the following overall metric:
Moverall
His
Goverall
(9)
where P4. are the mean and standard deviation of dataset i calculated over multiple seeds.
A.4 EFFECT OF KAN STOCHASTICITY
All benchmarks average results over multiple seeds to address the inherent randomness associated with weight initialization in the backhone model. Our method introduces additional layer of randomness due to the KAN initialization process. To illustrate that the variability introduced by our detector is significantly lower than that stemming from the backbone initialization, we conducted the following experiment.
We repeated the CIFAR-10 benchmark using five distinct KAN initialization seeds (N 5). For each KAN initialization seed i, we recorded the mean and standard deviation (μ4, o²:) of the exper- iment conducted on the three pre-trained backbones specified in the benchmark. The results are summarized in Table [2]
Table 12: CIFAR-10 benchmark results across different KAN initializations.
KAN seed (i)
AUROC (μ + a.)
94.12
94.02+0.58
14.11
94.17
94.06=0.39
We compute the overall standard deviation attributable to the backbone initialization (ox) and that of our detector (aa) as follows:
N
N 14 = 94.10 (10)
1
0, Σ 1=1
0.53,
Σ o0 -2 0.05 with 14b
1 N
N
N
The calculated standard deviations db and da differ by approximately an order of magnitude, indi- cating that the randomness introduced by our detector has negligible effect on the overall results.
A.5 BASELINES METHODS
The baselines used in the banchmarks are: OpenMax (Bendale & Boult 2016), MSP (Hendrycks & Gimpel. 2017), TempScale (Guo et al. 2017). ODIN (Liagg et al. 2018), MDS (Lee et al. 2018).
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MDSEns (eee et al. 2018). RMDS (Ren al.
2021), Gram (Sastry & Oore 2020). EBO (Liu al.
2020
OpenGAN KKng & Ramanan 2021).
GradNorm (Huang et al. (021). ReAct (Sun et al.
2021
MLS (Hendrycks et al. [002)) KLM (Hendrycks al. (022)) VIM (Wang et al. 2022
KNN
Sun al. 2022). DICE (Sun & Li
2022), RankFeat (Song et al.
2022).
ASH (Djurisic et al.
2023
SHE (Zhang et al. 2023b), GEN
Liu al. 2023), and NAC (Liu al. 2024a).
A.6
FULL BENCHMARK RESULTS
In Table 17 we present the AUROC results for all officially available baselines on the CIFAR- 10 and CIFAR- 100 benchmarks. Table 22 provides the results for the same set of baselines and benchmarks using the 95 metric. Similarly, Tables (aan the AUROC and FPR @PR@9 95 results respectively for all the available baselines
the ImageNet-2000 FS and ImageNet-1K FS benchmarks. The same metrics are reported for all the available baselines for the tabular medical for FPR @95.
benchmarks in Tables 19 20 21 for AUROC and 24
25 26
A.7 INFLUENCE OF CLUSTERING METHOD
This experiment analyzes the effect of different clustering methods on detection performance. We considered five popular clustering approaches alternatives k-means: spectral (Ng al. 200T), agglomerative (Murtagh & Legendre (0144), bisecting k-means (Rohilla et al. 2019). BIRCH
(Zhang et al. 1996), and DBSCAN (Ester al. 1996). Table 13 presents the experimental results for the CIFAR- 10 benchmark.
Table 13: Detection performance with different clustering algorithms the CIFAR-10 benchmark.
k-means
spectral
agglomerative
bisecting k-means
BIRCH
DBSCAN
AUROC
94.11
94.12+0.9
94.10=0.57
94.12
89.822464
The results show that the choice of clustering method has negligible impact on detection perfor- mance, except for DBSCAN, which yields an approximate 4% drop. One reason for this behavior is that DBSCAN is the only algorithm among those considered that does not necessarily assign clus- ter to all samples. In our implementation, these unclustered samples are grouped into an additional cluster. However, the samples in this extra cluster do not share common characteristics and can belong to different and distant regions semantically meaningful clusters, aim to divide the InD samples into smaller regions that can be effectively processed by a KAN. The leftover samples cluster in DBSCAN has counterproductive effect, as it span wide region of the input space, making it difficult for the KAN handle effectively.
input space. Although we are not focused on obtaining
A.8 CAPTURING THE JOINT FEATURE DISTRIBUTION
An alternative approach to the partitioning method for capturing the joint feature distribution is to expand the input features with additional values. We applied this technique to the 2D L-shaped toy dataset, illustrated in Figure 5 In this scenario, the input features concatenated with the latent features derived from a variational autoencoder trained on the two original features, resulting in an augmented input space of size 2 64.
This method demonstrates promising results, comparable to those achieved with the partitioning method. However, its applicability to high-dimensional input spaces remains uncertain. We hypoth- esize that the number of required features would become excessively large, leading to computational inefficiencies.
A.9 TRAINING PARAMETERS
Finding the optimal training hyperparameters for KANs can initially be challenging, as they may not follow the same intuitions as MI.Ps and other networks (Liu et al. 2024b).
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(a) Default approsch
Feature angmentation
1.6
0.0
1.00
1.0
Figure 5: 2D L-shape toy dataset: The blue point cloud shows the training distribution and the red points are OOD test samples. The black contour represents the thresholded score function (median) separating InD from OOD samples. (a) Default KAN detector limited by the marginal distribution of z and (b) Improved performance by concatenating the input features with the latent features of variational autoencoder.
In our experiments, we use learning rate of 0.1 and limit the training to a single epoch. With these settings, the trained KAN achieved classification accuracy the CIFAR-10 dataset of approxi- mately 94.50%, comparable to the one of the ResNet-18 of 95.06%.
To enhance memory efficiency, employed the AdamW optimizer (Loshchilov & Hutter 2019) instead of the LBFGS optimizer (Liu & Nocedal 1989) originally suggested by the KAN authors.
A.10 SOFTWARE AND HARDWARE
All experiments are performed on a single NVIDIA GeForce GTX 1080Ti GPU. For testing larger models and accelerating the hyperparameter optimization, we leveraged cloud computing platform with an NVIDIA A100 GPU.
We used Python version 3.10 together with PyTorch 2.3.1 as the deep learning framework and lever- aged CUDA 11.8 for GPU accelcration.
A.11 INFERENCE, TIME AND SCALABILITY ANALYSIS
Inference time. Table 14 reports the inference time of a single sample for various methods. The measurements are averaged over 1000 samples, using 100 extra samples GPU warmup. The results show a positive correlation between the inference time and the overall AUROC performance.
Although the KAN method is currently the slowest among the tested ones, it is important to em- phasize that the KAN architecture has just been developed recently. In just a few months since its release, its performance has been steadily improving thanks to many architecture refinements (c.g., replacing splines with Gaussian radial basis functions improves forward speed by approximately a factor of 3.3 (Li 2024 ) We believe that in the future, KANs will achieve efficiency comparable to MLPs. Furthermore, it is worth considering that inference time is not always a critical concern in various applications, particularly in medical contexts. In such scenarios, the enhanced detection performance offered by our method positions it as a more advantageous choice compared to faster alternatives.
Table 14: Inference time of single sample compared to the overall AUROC on CIFAR10.
Method
Inference time (ms)
Overall AUROC
VIM
0.271
91.88
KNN
0.175
92.19
NAC
0.681
93.37
KAN
2.216
94.12
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Setup time. In Table 15
report the setup time of our detector for different training dataset sizes
and various numbers of partitions (P), using the KNN method as a reference baseline.
Table 15: Setup time in seconds for different training dataset sizes and number of partitions.
Method
10K
100K
1M
KAN
2.84
17.49
165.86
KAN p=
2.82
17.44
166.45
KAN 100
3.19
18.24
172.66
KNN
3.27
15.51
141.75
The results indicate that the biggest factor influencing setup time (which includes inference the backbone model, the partitioning method and the training of the KANs) is the dataset size; however, method shows comparable speeds to the KNN baseline. On the other hand, varying the number of partitions seems to have a smaller influence, likely due to GPU parallelization.
Further considerations. The number of parameters in the KAN network is determined by the product of three factors: the number of inputs, the number of outputs, and the grid size. The grid size depends on the specific benchmark, and our experiments indicate that does not correlate with the benchmark's s complexity. For instance, on CIFAR-10 10 the optimal value is 100, while on CIFAR- 100 it is 50. Scalability to larger images, or more generally to large input spaces, is typically not an issue as our detector is applied to the latent space of the backbone model, which is usually much smaller than the inputs. For example, ImageNet- dimensions, but it is compressed by the backbone into a latent space of just 512 features. Lastly, our preliminary results presented in Section 333 demonstrate that changing the training task of the KAN detector can lead to similar performance. This required by the KAN model, further improving scalability. For example, in the ImageNet- K FS benchmark, we employed class-based partitioning, resulting in 1000 clusters and, consequently, 1000 models. However, we reduced the number of outputs for each model from 1000 to 10 classes by randomly grouping labels together. This adjustment is motivated by the fact that with 1000 clusters, the problem tackled by each model is greatly reduced, and thus the model's capacity can also be reduced. As a result, the training time per sample of our model slightly lower than that for the ImageNet-2000 200 FS benchmark: approximately 1.6ms per sample compared to 1.9 1.9ms per sample for ImageNet-200 FS. This indicates that our method remains efficient and robust even with large number of clusters.
has an input space of roughly 150k
be used to reduce the number of outputs
A.12 HYPERPARAMETERS
Table 16 reports all hyperparameters and settings for the five benchmarks. The search space of each hyperparameter follows: [10, 200] for the grid size, [1, 200] for the partitions, [0.0001, 0.1] for the learning rate, [1, 100] for the epochs, and [1, 100] for the histogram bins.
Table 16: Hyperparameters.
Parameter
OpenOOD
Tab/edd
CIFARI0
CIFARI00
ImaggeNet-200 FS
ImsageNet-IK ES
Ethnicity
Synthetic
Partitions
100
200
1000
30
10
Train Size
100%
100%
100%
100%
100%
100%
100%
Epochs
Partisioning method
k-means
class based
class-based yes
class based
class- bass--bsed
k-means
S-means
k means
Histogram
yes
yes
Histogram bins
Backbone
ResNet-18 R8sNNtt118 yes
ResNeet118 yes
ResNet-00
FT-Tranffonee
Fi-Transfommer
Pro Trained backbone
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Table 17: AUROC performance on CIFAR-10 and CIFAR-100 benchmarks.
Method
Near 0OD
Far OOD
Avg Near
Avg Far
Avg Overall
CIFAR
TIN
MNIST
SVHN
Textures
Places365
CIFAR-10
Benchmark
OpenMax
86,9 -6
88.3 38
90.50_n44
89.77an25
89.58aneo
88.632a78
87.62.10
89.62.n
88.95
MSP
87.19 17.19-035
88.87=0.9
92.63-155
91.46:0.0
89.89
88.92+047
88.03-025
90.73=043
89. 89.83+076
TempScale
87. m
89.00.am
93. 93.11
91. 66
90.01
89. 113
88.09
90.97.0
90.01
ODIN
18-18
83.55=154
95.24=156
84, 84.58a07
06.94-122
85.07=124
82.87=185
87.9 87.96=061
86.26+1.7
MDS
83
84.8 27.8
90.10 20
91. 11.18
92. 1.06
84.9012.14
84.20 an
89.72
87.88
MDSEns
61.29-023
59.57
99.17=0.1
66.562008
52.47=011
60.43-022
73.90=037
69.41+0.0
RMDS
88. 16
90.76_mm7
93.22gm0
84.
92. 11
89. 80.80
92. g1
91.400...0
Gram
58.33=4.P
18.98
72.64=234
91.52:445
62,34 62.34:5.27
60,44:341
58.66=483
71.73=330
67.37=504
EBO
86. 16
88.80 88.80.0.
94.32
91 am
89.47 89.47.009
89.25
87.58.
91:21
90.00.122
OpenGAN
52.81=7.0
54.62=706
56.14=3408
$2.81=37.00
56.14-1825
53.3445.79
53.71=7
54.61
54.31=17.45
GradNorm
14.4
55.3 41
63.72
53,91
$2.07 1400
60.501
54.90.00
57.5
g
56.67
ReAct
85.93-n55
88.29
92.81
89. 12:3.19
89.38:1.49
90.35-0075
=7.1
90.42
89. 1
MI.S
86.3 -6
88.72g0.
94.15
91.69 91.69
1974
89. 14
87.52.007
91.10g00
89.90
KLM
77.89=075
80,49
85.00=204
84. =11
82.35=003
78.37
79.19=0am
81.52+1
VTM
87. 87.75_.m78
89 39.62.001
94. 76
94.50
95.15
89 79
88 28.68.1077
93 93
91.88.055
KNN
89.73-014
91.56=026
94. 94.26=035
92.67=030
91.77=033
90.64:020
92.96=014
92.19
DICE
77.01
29.67
90.37
90.02
81 11
74.672455
78. 78
84.23gr
82.27
RankFeat
77.98-224
80.94:20
75. 75.87=512
68. 15
73,46=6.4
85,99
79,46=252
75.87
77.07=4M0
ASH
74. 14
76.44.06
83. 16
73.46
77. 77.45.139
79.89.1.9
75.27
78.49
77. 77.42:117
SHE
80.31=0o>
82.76a043
90.43-476
86.38=1330
81.57=1221
81.544051
85.32=144
84.06=2116
GEN
87.21
89. 39.20
93.83
91.97anm
90. 14g006
89 89.461205
88. 88.20.00
91.35g0m
90.30.a: in
NAC
89,83-029
92.02=030
94.
0620.7
95.64=045
91.85-025
20.93=023
44.60=050
93.37=#044
KAN
90.06_.47
91
97.86.075
97.39.n um
95.85
91.64
90.99.0 90
95.69_00
12.n
CIFAR-100
Benchmark
OpenMax
74.38
18.4
76.01 1.3
82.07
80.56::00v
79.29
76.41:025
79.48 :44
78. 18.46.008
MSP
78.47=007
82.07
78.42=0.0
77.32=071
79.22+8.29
80.27=0.11
77.76=044
78.
TempScale
n9.02:mmm
82.79 1nm
77.27
79
78.11
79.80
80.90:om
78.74
79.46.002
ODIN
78.18=014
74.54
190
79.90=0.11
=9.28=011
20.7
MDS
55.87
61 10:5
67.47
70.68 16.00
76.26.:0e
63. n::40
58.69.0m
69.39
65. 82:2
MDSEus
43.85=031
48.78
98.21
69.75
66.00=a00
59.44=0.0
RMDS
77.75...19
82.55 in1e
79.74
84.8% 11:00
83.65 ::05)
83.40
80.15:001
82.92
82.00
Gram
$3.91
=5.55
70.79
1.23
51.66=0.77
66.12
EBO
79.05
82.76.nns
79. 18 1.39
82.03
78.35 2003
79.52
80,91
79.77
80.15 10:9
OpenGAN
63.23-244
68.74=229
18.24
68. 15:24::115
65.84=1.43
67.88
67.25
GradNorm
70.32::0.1
69.95 1n.19
65.35 1.12
76.95
64.58 2003
69. 19..99.. 1..17
70.13:0.47
69.14:11.
69 69.47:.2m
78.65=0.0
82.8
83.01
80.15=045
80.52+0.70
MLS
79.21
82. :0
78.91 1.4
81. 1:
78.39
79.75
81 11.05:mmm
79.67
80.14 10.0
KLM
73.91=025
79
79.34
75.77=045
75.70=8.24
76.56=0
76.24=052
76.35=110
VIM
72.21
77.76
$1.89:1.0
83. 14.44
85.91 1:07
75.85 1.1T
74.9%
81.70-na2
19.46.11
KNN
77.02=025
84
79.43
80.18=0.15
82.40=a017
81.66:0577
DICE
78.04
80.72.0.30
19.86.119
84.22 :2:0
77.63::034
78.33
79.38
80.01 a..8
18
RankFeaa
58.04-216
65.72:0022
12.14
69.40=1.05
63.82++1.3
65.36=2.4
ASH
76.48..1.3
79.92..030
77.23::46
85.6011.4
80.72:000
78.76.0.66
78.20 18
80.58 :056
79.79 ::.m
SHE
78.15=005
79.74:0.66
76.76=1.97
80.97=3.
73.64
78.95=0.1
76.92=1.16
1..5
GEN
79.38 no0
83.25 10.13
78. 290229:206
$1.41:1.0
78. 78.74:081
80,28
81.31:00
79.68 a0os
80.23 23:2.....
72.02=000
79.86=0.2
93.26=1.34
89.36=0554
73.06::053
75.94=0.41
=7.07=030
83.36:0.44
KAN
72.97
81.37 10.22
92.29
87.161444
89.43:.00v
77.42..001
77.17.0017
86.57 -n.0
83.44:1.9
22

---

Published as a conference paper at ICLR 2025
Table 18: AUROC performance on ImageNet-200 FS and ImageNet-IK: FS benchmarks.
Method
OOD
Avg
Avg
Avg Overall
SSB-hard
NINCO
INaturalist
Textures
OpenImage-O
ImageNet-200
Benchmark
OpenMax
47.64=020
a4
72.44=0a7
69. 12.366
62.31
50.89
67. 07.96=039
61.13
MSP
50.94:025
57.76:046
65.11
62.80
24.35
66.11-037
61.41:04
TempScule
50.05
56.86:4477
70.18
65.65aa43
62.29
53.46=0.37
66.04=041
61.01an4
ODIN
44.31 a000
32.36
70.192092
67. 10
61 48
48.33
66.25_a0a
59 59.092um0
48.59.0048
56.65:004
68, 21.25
73.84
61.90
$2.62:090
61.85209
MDSSEs
34, 44.22..044
41 11
43 43.63.20.4
67.54
48, 10:36
37. 37.90
13.18
47.07
RMDS
26.24
60.95
41.71
64.61
63.52.0.5
58.59
66.62=1.11
63.41a1m
59.12
63.35
58.42-0075
75.86=0.10
61.51
61.23:.074
65. (5.26=033
63.65
EBO
47,56.9.29
53.45
65.91 1141
68, 68.03
59.83 10.1
50.51
64 19.59
58 26
OpenGAN
41.58a5.51
46.51
61.78
59,02
58.53
44.04:421
59.78=483
53.48
GradNorm
53.50
35.32
70.38
73.
63.52.1.35
54.41
69 =1.01
63.1721.9
ReAct
47.25
53.84:aa5
69 69.45:334
71.45:2004
+22302
50.55
67. 27.73-2226
60.86:227
MLS
48.18:+028
54.43
67. 1.20
67.12
60.66:0044
$1.30
24:
59.67=0m4
KLM
54.03-2071
60.524t113
25.37
62:106
66.20.1..0
57.28
68 08:56:033
64,05
VIM
45.34=072
$7.09
71.34:145
82.54
65,70
$1.22=008
73.19=110
64.40=1.s
44.05.:042
54.5
71.53
11,88
12.0799
49.28
71 84
62.82.a77
DICE
18.11
54.31
66.5312214
72.51
611.33.084
51.21
66.92-1.12
60.64g1.14
RankFcat
46.41
43.03=229
22.74=4550
20.60
40,74
44.72=107
28.03=396
34.70=330
ASH
58.51
77.9621.58
29.39:001
69.09.0.11
54.7420.4
75.48=095
67.18:006
SHE
52.82
56.64:00
72.20=245
74.27
64.95
54.73
70.47=139
64.18=141
GEN
48.33
24.85
68. 2443
66.58
60.87 20.28
$1.592m34
65 46.0.44
59.91 59,91ana
NAC
60.79.0.0
67.01-05)
60.05g0:4
KAN
58.37 29447
61. 10anss
84.13
83.30
70.40 10:26
59.74
79.28
71,46
Image/Ne-1K FS Benchmark
OpenMax
53.79
60.28
73.54
57.03
75.24
67.96
MSP
56.66
64.93
76.35
69.33
71.28
60.79
72.32
67.71
TempScale
55.71
64.60
77.33
70.84
72.32
60.16
73.50
68.16
ODIN
54.22
60.59
77.43
73.40
57.41
75.62
MDS
39,22
52.83
54.06
86.26
60.75
46.02
67.02
58.62
MDSEms
37.13
47,80
$3.32
73.39
53.24
42.47
59.98
52.98
RMDS
67.50
72.13
Gram
$1.93
60.63
71.36
84.83
69.40
56.28
75.20
67.63
EBO
52.93
60.28
74.01
73,89
72.22
$6.61
73.37
66.67
GradNorm
61.33
64.06
85.99
76.85
62.70
83.49
75.17
ReAct
55.34
64,51
87.93
81.08
79.34
59.93
82.78
73.64
MI.S
53.56
61.43
75.61
73.42
72.66
$7.49
73.90
67.34
KLM
56.87
67.26
80.88
70.73
74.74
62.06
75.45
70.10
VIM
45.88
59.12
72.22
93.09
75.01
$2.50
80.10
69.06
43.78
59.86
67.79
90.29
69.98
51.82
76.02
66.34
DICE
54.01
60.29
82.52
83,89
76.42
57.15
80.94
71.43
RankFeat
50.30
40.37
34.34
66.29
44.98
45.34
48.54
47.26
54.66
66.38
89.53
81.77
60.52
86.75
76.25
SHE
58.15
64.27
84.71
87.48
76.92
61.21
83,04
74.31
GEN
$2.95
62.73
78.47
71.82
72.62
$7.84
74.31
67.72
NAC
76.28
KAN
55.88
69.55
91.55
93.45
82.15
62.71
89.05
78.52
23

---

Published as a conference paper at ICLR 2025
Table 19: Tab. Med. Caucasian Eth. as InD (AUROC metric).
Table 20: Tab. Med. > 70 y.o. as InD (AUROC metric).
Table 21: Tab. Med. Feature multiplication (AUROC metric).
Method
eICU- Eth.
Method
eICU- Age
Method
eCCU -Synthetic OOD
Avg Overall
MDS
58.5
MDS
50.8
F= 10
J = 100
J 1000
RMDS
51 6
RMDS
48.3
MDS
59.9-14
79.5
87 2200
13
55.8119
KNN
49.6:01
RMDS
51.5-13
57,8+14
64.0=13.
57.77=867
VIM
$7.3
VIM
48.8+0.1
KNN
57.3-14
75.4
86 86.5213
13.07 13:07:114
SHE
50.5117
SHE
50.4=07
VIM
17.9-1
77.6
88.3
74 11.60
KLM
$1.61211
KLM
$1,0
SHE
55.7.113
71.2.22
804411
69. 19.10.205
OpenMax
48.7
OpenMax
48.1
KLM
24.1.04
63.1211
22.1
63. 10:2:5
MSP
48.41:00
MSP
48.1
OpeaMax
51.0=6.
56.1+27
71.4+12
59.50=224
MLS
49.1+11
MLS
48.0=005
MSP
50.9:04
55.8
71.3
59.33:2240
TempScale
48.4+1.0
TemppScule
48.1
MI.S
50.9207
55.8131
20.8
59: 19.17
ODIN
48.4:10
ODIN
48.1
TampScall
50,9=66
59.33-244
EBO
49.1=111
EBO
48.0ga5
ODIN
EBO
50.9_07
50.9:04
55.9x27
55.5131
70.2.1
71 71.45.
59.40:240
58.87
GRAM
GradNorm
50.8=2.7
50.4#34
GradNorm
48.6188
48.7
GradNom
48.9.61
$2.0.04
10.
59.5179
73.6235
53.83=129
61.20
ReAct
48.1
ReAct
48.2.007
ReAct
50.9=03
55,7+34
69.9=122
58. 58.83=2273
DICE
49.9+28
DICE
48.1
DICE
$2.2=1a
62.8
75.6=14
63.53:1.57
ASH
52.6217
ASH
48.6113
ASH
50.1.14
54.6131
69.7
58. 13
KAN
61.4111
KAN
50,5
KAN
64,6=22
83.0226
89,8
79.13-522
Table 22: FPR @95 performance CIFAR- 10 and CIFAR-100 benchmarks.
Method
Near 0OD
Far OOD
Avg Near
Avg Far
Avg Overall
CIFAR
TIN
MNIST
SVHN
Textures
Places365
CIFAR-10
Benchmark
OpenMax
48,064125
19.18:11
23.33
31.50aam
38.52:2277
43.622 23.62_2.37
29.60
34.33
MSP
13.08
43.27
23.64 Lsni
16
34.96144
42.47
48. 19
31.72.1:44
37.21
TempScale
55.81
46.11
23.53-2706
26.97
38, 16
45.27
50.96-433
33.48:235
35031
ODIN
77.001134
75.38.1e.
23.83
68.61 iose
67.701.1.6
70.36.1
76. k.0
$7.62.444
1318
MDS
52.81
46.99:4.3
27.30:3355
27.94:141
47.67::454
49.90=330
32.22:3.4
38.11
MDSFins
91.87
92.66....
1930
74.34
76.07
16..51
92.26 (mm
61.47.00s
11.731os1
RMDS
43.86:3.8
33.91+1.99
21.49:2.2
23.46:1.48
25.25
31.20:20:2
38.89-2.19
25.35
29.86
Gram
91.68.1244
90.06.11.
70.30
13.91
94.64 12
90.49 M5
90.87_
72.34
78.51
66.60:4448
56,08:1431
24.99:1290
35. 35.12:6.11
$1.82:1611
61.34:485
41.69
48.24:1.39
OpenGAN
94.84+2.3
94,11
79.54 19954
75.27+2633
83.95
95. :5:33::455
94.48-400
83.5 13.55
87. 17:121
GradNorm
94.54
94.89.
:414
91.65:242
08.09:10.0
92.46:2228
94.72-042
91.90):221
92.84:2.6
ReAct
67.40=7.44
59.71=731
33.77=:8000
50.23+1595
$1.42+1142
44,20=3335
63.56 63.566-7.3
44. 90
51.12-11.5
MLS
66.59:4.41
56.06:4422
25.06=12.57
35.09
51,73+613
54.84=651
61:322466
41.68:3327
48, 73
KLM
90.55
85.18
76. 76.22+1220
59, 59.47=700
81 95
95,58=211
87 86.63633
78.31#454
81.49
VTM
19.19
10
18. 1.43
19.29
21.14
41.43:217
44.84-231
25.05=0:2
31,65
KNN
37.64=031
30.37=005
20.05=1.36
22.60=136
24.06
30.38=0043
34.01=035
24.27=040
27. 23.52+0083
DICE
73.71=70
66.37=76
30.83+10544
36.61
62 62.42++79
77. 19:
70.04-7.64
51,76:444
57.85+1.5
RankFeat
65.3221.4
56.4411m
611 16267777777
59.71 64.4917
43.70.2.
60.88 4.
$7.44179
58.59 58.59114
ASH
87.31
16
70.00=10.56
43
14
77,89
76-78-1
79.03=422
81,61=500
SHE
81.0011.0
78, 1.
42.222170.9
62.74.-m
84.6015 t0
76.3611.7
79.65_x47
66.48.194
70.87.491
GEN
58.7543.7
48.59#134
23.00=775
28.14.29
41
47.05=3322
53.67=314
34.73=1.5
41,04=487
NAC
15.15
16.55
13.
14.3
17.05
26.73
30.85 n
18.31
22.49.1:77
KAN
40.81
34.17.133
11.63
14.13
21.30109
32.49
37.49
19.89
25.75
CIFAR-100
Benchmark
OpenMax
60.17+6.77
$2.99
$3.82 $3.824474
53.20=117
91
54.85=1442
56.58-073
54. 54.50=a04
55.19=233
MSP
$8.9
50.70a0.44
57.23:446
59.07
61.88 28
56.62=087
54.80
58. as
$7.400:2300
TempScale
58.72+6a
50.2640.16
56.05=461
$7.71=208
61.56+143
56.46=004
54,49=045
57.94=114
56.79=131
ODIN
60.6446.5
$5. 19
45.94 45.942329
67 23
62.37=22
59.71
57. n551
58, 86
58, 45
MDS
88.001e.v
19.05
71.72,a
67.21
70.49
79.61
72.26.1. 83.53_ns0
76.01
MDSEns
95.94a6.16
95. 12.8226.12
2.83-2065
82,57
84,94 24.94
96.61 =017
95 88
66.74 n4
16.45=
RMDS
61.37.6.M
49.56110
$2.055..5
51 11.6511168
53.99
53.57
55.46_041
12.81
13
Gram
92.71
91 85
53, 53
20.06:1..
19.5
94.67=0m
92. 22.28
64 (4:442237
73. 73.72=1335
FBO
59.21
$2.0316.9
52.62
53.62,114
62.3512.
57.75
S5.62_ns1
56.59
56.2613375
OpenGAN
78.83
74.21 a1
63.09
70.35
74.77:11.8
73.75 12:32
76.52..2.v
70.491934
72.50 m0.2
GradNorm
84,301..
86.851cm
86.97.114
69.90_79
92
85.32.00
85
13.681119
ReAci
61.301c41
$1.47
56.04-516
50.41 1212
55.04.002
55.30.0.1
$6.39 16.39_1034
54,20
54.93:2550
MIS
59.11
51.831.m
52.95
53.90.1M
62.39
57.68
$5.47_n44
56.731131
56.31
KLM
84.77.2.
71.07.0.5
73.09 1n87
50.30:744
81,80150
81,40.1.44
1..92...31
71.65
73.741482
VIM
70,59:644
54,66:20.42
48.32=1.07
46.22s5.0
46 29
61.57=0.77
62.63=027
50,74:100
54,70=240
KNN
72.801c.4
49.65
48.58.448
51.75
53.56 12.52
60.70...m
61. 11.
13.65
56.17 12.3
DICE
60.98:1.10
54,9340.3
51.79:357
49,58+332
64.23#1
29
$7.95
56.25
56.82=225
RankFieal
82.78
78.401c.9
75.01
58.4912M1
66.87.1531
77.42 96
80.59 1.10
69.45..m
73.16.11.9
ASH
68.06-20.44
63.35+0000
66.582238
46.00=267
61.27+274
62.95=0.9
65.71=024
59,20=244
61.37=230
SHE
60.4144.51
57.7446.73
58. 58.78a250
59.15
73.29
65.24=0m
59.07-a25
64. 64.12+220
62.44+19)
GEN
58.87=4..
49.98
53.92=891
$5.45=270
61.23s1.4
56.25=1m
54,42-033
56.71#159
55.95=2.00
NAC
81.37+1.27
61.59+0.74
21.97
24.39
40.65
73.57=1.16
71.48-1.08
40.14=:36
50,59
KAN
82,288176
55.74
39.61
57.1381234
45.76:2287
65.33+06i
69.01=145
51,962331
57.64
24

---

Published as a conference paper at ICLR 2025
Table 23: FPR @95 performance on ImageNet-200 FS and ImageNet-IK FS benchmarks.
Method
Near OOD
Far OOD
Near
Avg Far
Arg Overall
SSB-hard
NINCO
INaturalist
Textures
OpenImage-O
ImageNet-200
Benchmark
OpenMax
91.55
a5.00
68.19:
76.72
a7.39
88.27
74.10=044
a9.77=a41
MSP
89.08
79.30:042
67.24
79.79
74.22:0.10
84,19:021
73.75=006
77.93
TempScale
89.33==004
79.51=0.7
66.61:04s
79.67
74_10=0.2
84.42=0.15
73:46:024
77 77.84:0.0
ODIN
91.71 =9:09
36
65.50
13
76.03
89.18su116
73,55-063
29,8
MDS
93.90.0.16
88.52:n
74.46
74, 1.
83.68-20.5
91.21
77.41 =074
82.93:002
MDSEEs
96. 26.18
95.8 15
91. 91.392202
84, 16
93.52.t013
96.062013
89 =0.1o
92.37
RMDS
19.44.0.17
79.23:004
65.62:1115
66
74.82.s0.00
84.33:0.31
T2.39
77.17:064
Gram
86.37 =0.25
17.59
86 20:4
82.76
87, 20.54
86.98
85,41=025
86.04
EBO
=0.15
83.61
70.53
79, 46
77. 14:44
87, 67.16
75.71 15.71
80. 20.
OpenCiAN
94.47:1.M
81
84.7621887
28.77
GradNorm
91.16:9941
91 11368
78 12:
82. 11:95
84.81 10.33
91.42.1032
81 86
85.69 19.9
ReAct
91.22:10.50
84.61=072
67.52.225
72.82:1156
74.81 20.18
87.91
71.72=1144
78.20
MLS
90.68-t0.17
83.27
69. 10
a9.39
76.55
86.98=022
05.15=075
a9.88
KLM
91.97
85.33
66 17
80. #::48
77. 10.44
88.65
74 74.97=054
80.44:008
VMM
91.61
82.35
68.15
58.50
+4.54
86.98=002
67.06=063
75.03
KNN
91.73:a015
81.23
69.10=074
69.
74,43 1404
86.48
70.86:050
77.1 :9
DICE
90.94:10.0
84.24:
72.10
78884
77.79 29.4
87.5920.2
76. 0..24
80.78
RankFeat
95.78:00.10
96.98=a01
19..31
99.75
98.16
96.38
99.02=033
97.97
ASH
90.29:0042
84.21
63.1621221
65.99
71.69.0041
87.25
66.95-004
75.07
SHE
91.16=0.13
86.49=am2
71.48
78.98
79,50
88.8220.36
76.65=0as
81.52=1.39
89.59
$0.12
66.47.2044
40:30
73.96
84.85
73.24=00.0
77.89 27.89
NAC
92.75
88.83
72.57
69.08
79.55 20.92
90.79.0016
73.73=006
80.562081
KAN
94.67
87. a.4
24.8
68.75
78.84
91.01=1.35
70.83-0025
78.90
ImageNet-1K FS Benchmark
OpenMux
86.76
76.41
49.98
62.28
60.05
81.59
57.44
67.10
MSP
84.47
72.37
61.75
75.27
67.29
78.42
68.10
72.23
TempScale
84.23
71.55
58.16
72.87
64.35
77.89
65.13
70.23
ODIN
86.01
80.40
$7.10
67.34
65.45
83.21
63.29
71.26
MDS
95.41
86.89
83.38
55.95
82.16
91.15
73.83
80.76
MDSEnS
96.22
93.56
78.56
92.72
94.89
86.25
89.71
RMDS
87.09
70,28
55.68
67.83
61.30
78.69
61.61
68.44
Gram
90.87
86.24
72.69
64.65
79.05
88.55
72.13
78.70
EBO
68.82
GradNorm
84.44
85.45
45.63
55.84
76.76
84.95
59.41
69.62
ReAct
86.90
72.97
40.64
53.47
55,89
79.94
50.00
61.97
KLM
90.19
74.14
58.60
68.69
66.22
82.17
64.50
71.57
VIM
88.85
77.85
$5.59
33.64
57.23
83.35
48.82
62.63
KNN
90.50
74.77
42.59
65.03
82.64
$6.69
67.07
DICE
86.93
79.87
54.89
63.84
66.53
83.40
61.75
70.4]
RankFeat
93.17
96.21
96.43
83.49
93.59
94.69
91.17
92.58
ASH
84.49
70.74
36.82
38.34
$2.33
77.61
42.50
56.54
SHE
85.10
80.47
50.97
52.17
69.38
82.78
$7.50
67.62
GEN
85.72
72.38
50.61
66.40
57.67
79.05
58.23
66.56
NAC
89.54
76.53
36.88
29.19
58.48
83.03
41.52
58.12
KAN
89.64
74.57
42.67
37.79
67.66
82.11
49.37
62.47
Table 24: Tab. Med. Caucasian Eth. as InD (FPR @95 metric).
Table 25: Tab. Med. 70 y.o. Inl (FPR @95 metric).
Table 26: Tab. Med. Feature multiplication
(FPR@ @95 metric).
Method
eICU Eth.
Method
Age
Method
eICU Syuthetic
Avg Overall
MDS
89.7:43
MDS
94.3
10
F
100
F 1000
RMDS
93.1s16
RMDS
95.6sa.1
MDS
81.6=1a
48.1
28.0=45
52.57=335
KNN
91.8:20
KNN
94,7101
RMDS
91.9-13
78.
64.22:77
18.27
VIM
90.7+43
VIM
94,6100
KNN
83.6=1a
53.4:53
29.8:56
55.601-437
SHE
93.2+1
SHE
95.1
VIM
81.9.1
48.7111
26.6
$2.40
KL.M
92.8114
KL.M
95.2ga1
88.2235
630116
616444
OpenMax
93.8
OpenMax
95,21a.
KLM
91.0=1a
79.5644
60.9-97
17.13
MSP
93.5
MSP
95.3ga3
OpenMax
91.2:14
80.7
60.6
77 67:50
MLS
93.4=16
ML.S
95,3+01
91.0.14
79.2134
18.8
16.37234
TempScale
93.5
TempScale
95.3ga1
MLS
91,2-10
80.4ea7
61 11000
77 77.53:447
ODIN
93,5
ODIN
95,3403
TempScale
91.0-14
79.2.135
88.8113
766.3223.4
EBO
93.3
EBO
95.2ga1
ODIN
EBO
91.6:01
90.9=1A
79.0+24
82.01a1
63. 63.7
58 58.4a5.1
79. 10:10::39
76. 16-10:335
GRAM
93,6.12
GRAM
95.0sa3
GRAM
94.1_06
89.8111
87.93.0
GradNorm
92.0:322
GradNorm
95.3
GradNomn
91,3=1A
78. 78.61445
58.346.7
76.07=4.7
ReAct
94,5.13
ReAct
95.2403
ReAct
91.8=07
82.9sa9
65 65.5
80.07=440
DICE
93,0=22
DICE
94.9:0J1
DICE
88.3.111
66.9123
45.1
66.77.314
ASH
92.6=2.1
ASH
95.3
ASH
91.6-207
$1.01445
61
77.8724.77
KAN
91.6=3A
KAN
97.3+09
KAN
77.2=40
49.3:35
33.7452
53:42=404
25


Reviews:
[{"review_id": "qFbBDRcPVZ", "reviewer": "Reviewer_Asxo", "summary": "The paper introduces a new out-of-distribution (OOD) detection method leveraging Kolmogorov-Arnold Networks (KANs), which utilize “local neuroplasticity” to differentiate in-distribution (InD) data from OOD data via comparing the activation patterns of a trained KAN against an untrained counterpart. KANs stand out due to their spline-based architecture, which preserve specific network regions during training, aiding in the OOD detection.", "questions": "Questions and suggestions:\n\nMajor: \nTesting of approach on other large-scale datasets would be beneficial, consider other leaderboards from openOOD like ImageNet-200, 1K.\nThe choice of the K-means clustering approach looks quite arbitrary for initial data splitting. Why not use other clustering approaches like DBScan, Spectral, Agglomerative or even Gausian mixture? I believe, K-means choice should be justified here.\n\nOne can assume a dataset with a lot of natural clusters (like ImageNet-1K) will require a lot of time for training KANs. Show that the approach is actually scalable, robust, and not computationally burdensome in case of a large number of clusters.\n\nThe robustness of clustering approach is not evident for the case of regression task due to the poor internal separability of data clusters. I suggest adding one example of OOD detection where the training dataset is directly related to the regression task. \n\nThe method looks strongly backbone dependent and may be poorly working for the plethora of practical tasks where the good backbone feature extractor is not known. Is it possible to exemplify the method robustness for the case of the absence of backbone preprocessor? \nProbably, some classic ML tabular datasets (e.g. from sklearn) could be useful here.\n\n“Importantly, our experiments show that the previous methods suffer from a non-optimal InD dataset size” - this statement requires more experimental support. Currently, the method superiority was shown only for the CIFAR-10 dataset. \n\nMinor:\nLine 183 (figure caption): “- “(e) InD score S(x)∀x ∈ [−1,1] “ - why the InD score can take negative values? The original formula (5) contains absolute value operation brackets. Is this the typo? \n\nLine 187: “A simple, yet effective approach is to split the dataset based on class labels.”  - It is not obvious how to train KANs in case of such splitting. One can imagine a situation where positive class is OOD for a KAN trained on samples of negative class, and the maximization scoring procedure identifies positive class as an OOD. This point should be clarified or rephrased.\n\nI’m interested if the method will be robust for the case of NaN-enriched data samples? It is not a request for an additional analysis but rather an interesting point for the discussion of method limitations.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The described method is clearly defined and is easy to reproduce.\n\nThe method is validated across image and tabular medical data benchmarks, demonstrating improved performance and robustness compared to other state-of-the-art OOD detectors. \n\nThe findings highlight KANs' potential in enhancing model reliability across diverse environments by maintaining high detection accuracy, even with a relatively small training dataset.\n\nThe results (although not on all datasets) look promising in terms of different OOD detection accuracy especially for the case of low number of training samples.", "weaknesses": "Despite the clarity, some steps of the approach implementation look like ad-hoc tricks for improving the method’s performance without developing a deep intuition why a particular step is better than alternatives (please, see questions below for details).\n\nThe fact that not all datasets (leaderboards) from the OpenOOD were used for testing the approach, along with the obtained not perfect results on CIFAR-100, suggest that the datasets were selected manually. The authors need to prove absence of any selection bias. \n\nI am strongly concerned about the scalability of the proposed method, which requires splitting the training dataset into a number of subsets and fitting a model per a subset (see comments below).\n\nThe method resembles feature-preprocessor (backbone-dependent), being not applicable to the case where a good feature extractor is not known.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "exJIUB3P1X", "reviewer": "Reviewer_oW4J", "summary": "This paper introduces a novel OOD detection method that leverages the unique local neuroplasticity of Kolmogorov-Arnold Networks (KANs). By comparing the activation patterns of a trained KAN against its untrained counterpart, the method identifies OOD samples across diverse benchmarks, including computer vision and tabular medical data. Experimental results demonstrate that the KAN-based approach outperforms existing methods and shows resilience to variations in in-distribution dataset sizes. This robust, adaptable approach makes KANs a promising tool for enhancing the reliability of ML systems.", "questions": "Please answer the points raised in the questions.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. It introduces an innovative approach to OOD detection, offering fresh ideas and a unique viewpoint that advances the current understanding of OOD detection techniques.\n2. The paper effectively harness the neuroplasticity characteristic of KANs, ensuring that learning new tasks only affects the network regions activated by the training data, effective motivation for OOD detection.\n3. The paper includes thorough experiments on standard benchmarks.", "weaknesses": "1. While the core idea is clear, the method appears loosely structured. Specifically, the role of multiplying location-specific information with regions activated by InD samples to achieve the delta function (used in the score function) is unclear (e.g., Eqn 5). Additionally, no study is provided to analyze these aspects, leaving parts of the methodology unexplored.\n2. The paper does not present or discuss the generalization performance of models when KANs are incorporated into the training scheme. \n3. Results on CIFAR-100 indicate minimal advantage over existing methods, as the improvements in detection performance appear statistically insignificant.\n4. Including a discussion on the computational cost of the proposed method would strengthen the paper. Given that the approach involves dividing the dataset into different groups, insights into computational efficiency would enhance understanding of the method’s practicality.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FLHuzSjZQd", "reviewer": "Reviewer_cRaW", "summary": "Authors utilize Kolmogorov Arnold Networks (KAN) for out of\ndistribution detection. The main idea is to leverage the fact that KAN\nuses BSplines as non-linear functions. Feature values that appear\nwithin InD, if they are concentrated in certain part of the feature\nspace - which is $\\mathbb{R}$ in this case, will only modify certain\nBSpline coefficients. In this scenario when a feature value that is\ndifferent than the InD comes, the BSpline coefficients at those\nlocations will not have been modified during training. Hence, the\ndifference in activation between trained and untrained network will be\nlow. Experiments with benchmark datasets and comparisons with large\nset of alternatives are presented.", "questions": "- It is not clear how different KAN$_i$'s are trained. It would be\n  good to explain this a bit more in depth.\n- Authors state that the method can be seamlessly integrated with any\n  pre-trained model. I do not really understand this. Doesn't one need\n  to use KAN model for this?\n- How are the pre-trained backbones used for KAN? Does one use the\n  features extracted from these networks and build classifiers and\n  regressors with KAN architecture?\n- Authors state that hyperparameters are tuned using a validation\n  set. How much do the trained hyperparameters generalize to OOD types\n  unseen in the validation set?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "+ The topic is very relevant.\n+ The idea is novel and quite intuitive.\n+ The results are motivating. Even though this is not the best\n  performing all around, it is one of the top algorithms.\n+ Authors do a great job explaining the method as well as motivating\n  the approach.\n+ Large set of experiments.", "weaknesses": "- The model - due to KANs - is heavily univariate. While authors do\n  dataset partitioning to alleviate the problem, I do not see how they\n  can actually do so. Unsupervised combinations of features are\n  mentioned, however, their applicability also raises questions.\n- Partitioning the dataset requires having multiple trained models,\n  which limits the applicability of the approach for large scale\n  problems.\n- KANs are interesting but most recent work do not use these\n  networks. This naturally limits the applicability of the approach.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WhBIkzfSHP", "reviewer": "Reviewer_WMKe", "summary": "The authors propose to use Kolmogorov-Arnold Networks (KAN) for out-of-distribution detection. The key advantage of KANs is their plasticity which results in avoiding catastrophic forgetting. The authors show that this property can be leveraged to detect OOD samples. \n\nThe method demonstrates good performance on small datasets, but the proposed method does not properly address the shortcomings of the KAN architecture, and the method was not validated in terms of scalability to realistic problems. Overall I rate weak reject.", "questions": "Line 43 has wrong citation \n\nYou mention that the hyperpareter search can be quite challenging. How did you decide for the parameter space especially regarding number of epochs, learning rate, partitionings?", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Originality: Given that KANs are a novel type of architecture the research is a very current  \n- The method is evaluated on image and tabular data, demonstrating feasibility across different domains. \n- Performance: The performance on the benchmarks is convincing and demonstrates superiority over a vast set of previous methods \n- Exhaustive experimentation on toy datasets including multiple important ablations that erase questions (such as stochasticity)", "weaknesses": "Major: \n- Scalability: No experiments demonstrate the method's scalability to larger images or real-world problems. \n- Insufficient capturing of joint distribution: I believe the partitioning problem of KANs is very severe. While the problem is mentioned I believe it is not properly addressed. Essentially, by partitioning the dataset you are just scaling the problem down to subclasses. What if the l-shaped differences, that you mention in Table 2, appear on an intra-class level instead of a class level? While this may work for toy data if the data is sufficiently separable using k-means or class labels directly, I doubt it will work for more difficult problems such as MVTech. \n- The influence of Model capacity is unclear: KANs are known for their improvements in lack of catastrophic forgetting. How does the model size influence this. Additionally, if KANs treat features individually, the difficulty of the problem and the necessary capacity of the method scales drastically with the image size.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)