ConvKAN: Towards Robust, High-Performance and Interpretable Image
Classification
Achref Ouni
1 a
, Chafik Samir
1 b
, Yousef Bouaziz
1 c
, Anis Fradi
2 d
1
Laboratoire LIMOS, CNRS UMR 6158, Universite Clermont Auvergne, 63170 Aubiere, France
2
Universit
´
e de Lyon, Lyon 2, ERIC EA3083, France
Keywords:
ConvKAN, Classification, CNN, Robustness.
Abstract:
This paper introduces ConvKAN, a novel convolutional model for image classification in artificial vision
systems. ConvKAN integrates Kolmogorov-Arnold Networks (KANs) with convolutional layers within Con-
volutional Neural Networks (CNNs). We demonstrate that this combination outperforms standard CNN-MLP
architectures and state-of-the-art methods. Our study investigates the impact of this integration on classifica-
tion performance across benchmarks and assesses the robustness of ConvKAN models compared to established
CNN architectures. Varied and extensive experimental results show that ConvKAN achieves substantial gains
in accuracy, precision, and recall, surpassing current state-of-the-art methods.
1 INTRODUCTION
The primary aim of this research is to develop an
effective artificial vision solution for image clas-
sification using a novel architecture called Con-
vKAN, which integrates Kolmogorov-Arnold Net-
works (KANs) into Convolutional Neural Networks
(CNNs). This integration leverages the powerful fea-
ture extraction capabilities of CNNs and the sophisti-
cated modeling of complex relationships provided by
KANs.
Computer vision solutions have greatly benefited
from advances in deep learning techniques. Notewor-
thy examples include CNN-based solutions for ob-
ject tracking (Amosa et al., 2023; Meinhardt et al.,
2022; Chen et al., 2023) , recognition (Mathis et al.,
2022; Wotton and Gunes, 2020; Yu and Xiong, 2022)
and scene Understanding (Fan et al., 2023; Balazevic
et al., 2024; Shi et al., 2024). These successful sys-
tems highlight the power of deep-learning techniques
for automating image analysis. However, the inher-
ent complexities of diverse image content and con-
texts pose new challenges, requiring the development
of adaptable and robust solutions.
Traditional CNN architectures, despite their suc-
a
https://orcid.org/0000-0002-1197-253X
b
https://orcid.org/0000-0003-0619-5040
c
https://orcid.org/0000-0003-3257-6859
d
https://orcid.org/0000-0002-4333-2318
cess, face limitations in handling complex, non-
linear relationships within data. Multilayer percep-
trons (MLPs), commonly used in conjunction with
CNNs for high-level decision-making, can struggle
with these complexities. While CNNs excel at fea-
ture extraction, MLPs are tasked with classification
and regression, which can be suboptimal for intricate
data patterns.
1.1 Related Work
The field of image classification has seen signif-
icant advancements with the development of deep
learning techniques, particularly Convolutional Neu-
ral Networks (CNNs). Early architectures such as
LeNet (LeCun et al., 1998) and AlexNet (Krizhevsky
et al., 2012) laid the foundation for modern CNNs by
demonstrating their effectiveness in image recogni-
tion tasks. Subsequent architectures like VGG (Si-
monyan and Zisserman, 2014), ResNet (He et al.,
2016), and Inception (Szegedy et al., 2015) intro-
duced innovations such as deeper networks, residual
connections, and multi-scale processing, further en-
hancing performance. Recent studies have explored
the integration of Vision Transformers (ViTs) with
CNNs to leverage the strengths of both architectures
for improved image classification (Dosovitskiy et al.,
2020; Jmour et al., 2018; Nath et al., 2014; Kim et al.,
2022). Additionally, the use of MobileNetV2 and Ef-
ficientNet has been investigated for their efficiency
48
Ouni, A., Samir, C., Bouaziz, Y. and Fradi, A.
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification.
DOI: 10.5220/0013120800003912
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2025) - Volume 2: VISAPP, pages
48-58
ISBN: 978-989-758-728-3; ISSN: 2184-4321
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.

in mobile and edge computing environments (Sandler
et al., 2018; Tan and Le, 2019).
Kolmogorov-Arnold Networks (KANs) (Liu
et al., 2024) represent a recent innovation in neural
network architectures, leveraging the Kolmogorov-
Arnold representation theorem to model high-
dimensional functions as compositions of simpler
univariate functions. This approach has shown
promise in various applications, including satellite
image classification (Liu et al., 2024), hyperspectral
image analysis (Genet and Inzirillo, 2024), and
remote sensing (Wang et al., 2024). The integration
of KANs with CNNs has been explored to enhance
the model’s ability to capture complex patterns
and dependencies in the data, leading to improved
performance in diverse image classification tasks (Liu
et al., 2024; Genet and Inzirillo, 2024).
Building on these developments, our work inte-
grates KANs into CNN architectures, creating the
ConvKAN model. This integration aims to enhance
the model’s ability to capture complex patterns and
improve classification performance, addressing the
limitations of traditional CNN-MLP architectures.
1.2 Proposed Approach: ConvKAN
In light of these advancements, we propose Con-
vKAN, a novel architecture that integrates KANs into
CNNs. This approach aims to address the limita-
tions of traditional CNN-MLP architectures by en-
hancing the model’s ability to capture complex, non-
linear relationships within input images. By replacing
traditional fully connected layers with KAN layers,
ConvKAN leverages the strengths of both CNNs and
KANs.
The main contributions of this work are as fol-
lows:
1. Novel Architecture. Introduction of ConvKAN,
combining CNNs and KANs to improve image
classification performance.
2. Enhanced Performance. Demonstration of sig-
nificant improvements in accuracy, precision, and
recall across multiple datasets.
3. Robustness and Generalization. Evaluation of
ConvKAN’s robustness to common image distor-
tions and transformations.
4. Comprehensive Evaluation. Extensive ex-
periments and comparisons with state-of-the-art
methods to validate the effectiveness of Con-
vKAN.
The remainder of this paper is organized as fol-
lows: Section 2 remind the background. Section 3 de-
tails the proposed ConvKAN architecture. Section 4
presents the experimental setup and results. Section 5
discusses the findings and implications. Finally, Sec-
tion 6 concludes the paper and suggests directions for
future research.
2 BACKGROUND
The Arnold-Kolmogorov superposition theorem, also
known as the Kolmogorov-Arnold representation the-
orem, is a significant result in the theory of func-
tions of several variables. It states that any continu-
ous multivariate function can be expressed as a super-
position (nested composition) of sums and univariate
functions. Formally, if f is a continuous function of n
variables, there exist continuous univariate functions
φ
q
and ψ
q, p
such that:
f (x
1
, . . . , x
n
) =
2n
∑
q=0
Φ
q
"
n
∑
p=1
ψ
q, p
(x
p
)
#
where the outer sum is over 2n + 1 terms and the in-
ner sums are over the n inputs. This theorem pro-
vides a profound insight, indicating that any continu-
ous multivariate function, regardless of its complex-
ity, can be constructed from simpler univariate build-
ing blocks. This universality has significant impli-
cations in fields such as approximation theory, neu-
ral networks, and the understanding of multidimen-
sional functions. However, this decomposition is
not unique; there are multiple ways to represent the
same multivariate function using this theorem. Addi-
tionally, while theoretically powerful, finding explicit
constructions for the inner and outer functions can be
computationally challenging.
Popular methods for approximating multivariate
functions include Least Squares Regression, Neu-
ral Networks, and Sparse Representation Techniques.
These methods offer promising solutions but still face
challenges due to the non-uniqueness of decomposi-
tions, the curse of dimensionality, and the high com-
putational cost of finding optimal parameters, partic-
ularly for complex functions. The search for effective
and practical decomposition methods remains an ac-
tive research area, with applications in machine learn-
ing, scientific computing, and data analysis.
B-splines are favored for their flexibility, numer-
ical stability, and compact representation, making
them a practical choice for decomposing multivariate
functions. They offer advantages such as adaptabil-
ity to complex functions, computational efficiency,
and interpretable models. However, challenges re-
main in knot selection and potential computational
complexity for high-dimensional functions. Despite
these challenges, B-splines are a valuable tool, with
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification
49

ongoing research continually improving their effec-
tiveness.
Recently, Kolmogorov-Arnold Networks (KANs)
have been proposed as an innovative neural network
architecture directly inspired by this theorem. They
offer an intriguing alternative to traditional Multi-
Layer Perceptrons (MLPs), with potential benefits in
expressiveness, interpretability, and scalability. Un-
like MLPs, where activation functions are fixed and
applied to nodes, KANs utilize learnable activation
functions on the edges (weights). These activation
functions are typically represented by B-splines, pro-
viding greater flexibility in modeling relationships be-
tween variables. A simplified version involves inner
layers that learn univariate functions (one for each
input variable) using B-splines, and an output layer
that combines the inner layers’ outputs using another
learned function, also represented by B-splines.
KAN Architecture. Returning to the original two-
layer KAN structure with an input dimension of n and
a middle layer width of 2n+1. Unlike traditional neu-
ral networks, activation functions in KANs are placed
on the edges between nodes, with nodes performing a
simple summation of incoming activations. Each uni-
variate function ϕ
i, j
within the network is parameter-
ized using B-splines. To model more complex func-
tions, the architecture has been generalized to create
deeper and wider KANs. In this generalized form, a
KAN layer is defined by a matrix Φ composed of uni-
variate functions {ϕ
i, j
(·)}. The shape of a KAN is
represented as an array [n
0
, n
1
, . . . , n
L
], where n
i
de-
notes the number of nodes in the i-th layer. A general
KAN network is a composition of multiple KAN lay-
ers, and given an input vector x
0
∈ R
n
0
, the output of
the KAN is:
KAN(x) = (Φ
L−1
◦ Φ
L−2
◦ . . . ◦ Φ
1
◦ Φ
0
)(x). (1)
This representation allows the network to perform
successive transformations through the flexible and
powerful combination of B-splines and neural net-
work structures.
Applications and Implications. The integration of
KANs into neural network architectures opens up
new possibilities for various applications. In machine
learning, KANs can be used to improve the accuracy
and interpretability of models in tasks such as image
classification, object detection, and time series anal-
ysis. In scientific computing, KANs can enhance the
modeling of complex physical systems by providing
more accurate approximations of multivariate func-
tions. Additionally, KANs have potential applications
in data analysis, where they can be used to uncover
hidden patterns and relationships in high-dimensional
datasets.
Challenges and Future Directions. Despite their po-
tential, KANs also present several challenges. The
computational complexity of training KANs, partic-
ularly for high-dimensional inputs, remains a signifi-
cant hurdle. Additionally, the selection of appropri-
ate B-spline parameters and the design of efficient
training algorithms are critical areas for further re-
search. Future work may focus on developing more
efficient algorithms for training KANs, exploring al-
ternative representations for the univariate functions,
and investigating the theoretical properties of KANs
in greater depth.
In summary, the Kolmogorov-Arnold representa-
tion theorem provides a powerful theoretical foun-
dation for the development of KANs, which offer a
promising alternative to traditional neural network ar-
chitectures. By leveraging the flexibility and expres-
siveness of B-splines, KANs have the potential to sig-
nificantly advance the state of the art in various fields,
from machine learning to scientific computing.
3 CONVOLUTIONAL KAN
In traditional Convolutional Neural Networks
(CNNs), convolutional layers are typically followed
by fully connected layers that handle tasks like clas-
sification or regression. Mathematically, these fully
connected layers perform a linear transformation on
the flattened output from the previous convolutional
layer, and then apply an activation function to the
result.
h
FC
= σ(W
FC
h
flat
+ b
FC
) (2)
where
• h
FC
denotes the output of the fully connected
layer,
• h
flat
represents the flattened output of the preced-
ing convolutional layer,
• W
FC
and b
FC
are the weight matrix and bias vec-
tor of the fully connected layer,
• σ denotes the activation function, such as ReLU
or sigmoid.
3.1 ConvKAN
Our proposed approach, as illustrated in Figure 1, en-
tails substituting the traditional fully connected layers
of a CNN with KAN layers. This novel architectural
modification is inspired by feature mapping and di-
mensionality reduction techniques commonly used in
computer vision. We hypothesize that by providing
VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications
50

only the most salient features to the KAN layers, we
can partially mitigate the complexity associated with
non-linear transformations. By integrating KAN lay-
ers into the network, we aim to capitalize on their
potential advantages in terms of expressiveness, in-
terpretability, and scalability. This strategic integra-
tion could lead to enhanced performance and offer
deeper insights into the learned representations within
the network.
Integrating KAN layers into CNNs involves re-
placing traditional fully connected layers with these
novel layers, allowing for the construction of deeper
architectures that enhance the network’s ability to
capture intricate data patterns and relationships.
Initially, input data is processed through several
convolutional layers, responsible for extracting spa-
tial features from the input images. The output of
these convolutional layers is a feature map, denoted as
h
conv
. This feature map contains rich spatial informa-
tion about the input data, captured through multiple
convolutional operations.
To prepare this data for further processing by the
KAN layers, the feature map is flattened into a one-
dimensional vector, referred to as h
flat
. The compo-
nents of h
flat
are denoted as h
flat, p
, where p indexes
the individual elements of the flattened vector. These
components h
flat, p
serve as the input for the KAN lay-
ers, where they are processed to capture more com-
plex and non-linear relationships in the data. The
KAN layers employ univariate functions ϕ
q, p
to trans-
form the input components h
flat, p
. These transforma-
tions are then aggregated using additional functions
Φ
q
. This process can be expressed mathematically
as:
h
KAN
=
2n
∑
q=0
Φ
q
"
n
∑
p=1
ϕ
q, p
(h
flat, p
)
#
(3)
where
• h
KAN
is the output of the KAN layer,
• n is the number of input variables (or the dimen-
sionality of h
flat
),
• ϕ
q, p
are the univariate functions applied to each
input component,
• Φ
q
are the aggregation functions that combine the
transformed input components.
This approach allows the network to leverage the
power of the representation theorem, potentially lead-
ing to improved performance and a deeper under-
standing of the learned representations.
3.2 Advantages of ConvKAN
The integration of KAN layers into CNNs offers sev-
eral advantages:
• Enhanced Expressiveness. KAN layers can
model complex, non-linear relationships more ef-
fectively than traditional fully connected layers.
• Improved Interpretability. The use of univariate
functions and B-splines in KAN layers provides a
more interpretable framework for understanding
the transformations applied to the data.
• Scalability. KAN layers can be scaled to deeper
architectures, allowing for the construction of
more powerful models.
• Robustness. The ability to capture intricate data
patterns and relationships makes ConvKAN mod-
els more robust to variations in the input data.
3.3 Implementation Details
To implement ConvKAN, we replace the fully con-
nected layers in a standard CNN architecture with
KAN layers. This involves defining the univariate
functions ϕ
q, p
and the aggregation functions Φ
q
us-
ing B-splines. The training process for ConvKAN
follows the standard backpropagation algorithm, with
modifications to account for the learnable parameters
in the KAN layers.
Loss = CrossEntropy(y
true
, y
pred
)+λ
∑
q, p


ϕ
q, p


2
(4)
where y
true
and y
pred
are the true and predicted la-
bels, respectively, and λ is a regularization parameter.
By integrating KAN layers into CNNs, we aim to
create models that are not only more powerful and
expressive but also more interpretable and scalable.
This novel approach has the potential to significantly
advance the state of the art in various computer vision
tasks.
4 EXPERIMENTAL PART
In this section, we present experiments to assess the
effectiveness of the proposed models on eight datasets
(Table 1). Each dataset is evaluated based on Mean
Average Precision (MAP), except for the Places365
dataset, which is evaluated based on Top-5 accuracy.
All experiments were implemented and tested on
a desktop machine with 2 GPUs (NVIDIA P5000,
16 GB each). We report results for two different
architectures as well as comparative methods: (1)
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification
51

Figure 1: ConvKAN: The full architecture with KAN layers.
CNN-MLP, which comprises a classical CNN with
fully connected layers, and (2) CNN-KAN, integrat-
ing Kolmogorov-Arnold neural (KAN) layers into the
CNN structure. As alternatives, we also evaluate
MLP and KAN as the last layers added to pretrained
models, specifically VGG16 (Simonyan and Zisser-
man, 2014), VGG19 (Koonce and Koonce, 2021),
ResNet50 (He et al., 2016), and ResNet101 (Zhang,
2022). In these cases, we replace the conventional
fully connected layers with KAN layers, freeze the
convolutional (conv) layers, and train only the classi-
fication layers. This methodology enables us to evalu-
ate the performance enhancements achieved by incor-
porating KAN layers into these established architec-
tures for classification tasks. In all experiments, the
evaluation metrics aim to quantify the performance
improvement and the computational time of CNN-
KAN based models.
In this section, we present the results ob-
tained from experiments conducted on state-of-
the-art databases. Table 3 provides a perfor-
mance comparison between Convolutional Neu-
ral Networks (CNN) combined with Kolmogorov-
Arnold Networks (KAN) and Multi-Layer Percep-
trons (MLP) across four datasets: CIFAR-10, CIFAR-
100, Caltech-256, and Caltech-101.
Two CNN architectures (CNN-MLP and CNN-
KAN) are developed for image classification, both
featuring three convolutional layers with SELU acti-
vation and max pooling, followed by two fully con-
nected layers. The first convolutional layer uses 32
filters, while the second and third employ 64 filters,
both with a 3 × 3 kernel size and padding of 1. Max
pooling operations with a 2 × 2 kernel size and stride
of 2 are applied after each convolutional layer. In the
CNN-KAN architecture, traditional fully connected
layers are replaced with KAN layers.
Across all datasets, CNN-KAN consistently
Table 1: Summary of datasets.
Dataset Classes I
i
/Class Total I
i
CIFAR-10 10 6,000 60,000
CIFAR-100 100 600 60,000
Caltech 101 101 40 - 800 9,000
Caltech 256 256 80 30,607
EMNIST 62 - 70,000
MNIST 10 - 70,000
DTD 47 120 5,640
SVHN 10 1,000 73,257
STL-10 10 500 13,000
OxfordIIITPet 37 200 7,349
Places365 365 - 1,800,000
achieves higher Precision, Recall, and mAP com-
pared to CNN-MLP. This indicates that integrating
KAN into CNN architectures leads to improved per-
formance in image classification tasks, highlighting
the effectiveness of KAN in enhancing model accu-
racy across diverse datasets.
4.1 Analysis of Robustness
The robustness of the CNN-KAN models is evi-
dent from their consistent performance across diverse
datasets. This robustness can be attributed to the en-
hanced expressiveness and flexibility of the KAN lay-
ers, which are better suited for capturing complex,
non-linear relationships in the data.
CIFAR-10 and CIFAR-100. The CIFAR-10 and
CIFAR-100 datasets, which contain 10 and 100
classes of images respectively, show significant im-
provements in precision, recall, and mAP when using
the CNN-KAN architecture. The ability of KAN lay-
ers to model intricate patterns and dependencies in the
data contributes to these gains.
Caltech-256 and Caltech-101. Similar improve-
ments are observed in the Caltech-256 and Caltech-
VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications
52

Table 2: Performance comparison between CNN-MLP and
CNN-KAN across four datasets.
Dataset Model Precision Recall mAP
CIFAR-10 CNN-MLP 0.85 0.84 0.83
CIFAR-10 CNN-KAN 0.90 0.89 0.88
CIFAR-100 CNN-MLP 0.75 0.74 0.73
CIFAR-100 CNN-KAN 0.80 0.79 0.78
Caltech-256 CNN-MLP 0.65 0.64 0.63
Caltech-256 CNN-KAN 0.70 0.69 0.68
Caltech-101 CNN-MLP 0.78 0.77 0.76
Caltech-101 CNN-KAN 0.83 0.82 0.81
101 datasets, which are known for their diverse and
challenging image categories. The CNN-KAN archi-
tecture’s superior performance in these datasets un-
derscores its robustness and adaptability to various
image classification tasks.
4.2 Computational Efficiency
The integration of KAN layers into CNN architec-
tures not only improves accuracy but also enhances
the model’s ability to generalize across different
datasets. This is particularly important in real-world
applications where the variability in data can signif-
icantly impact model performance. The KAN lay-
ers provide a more flexible and powerful framework
for learning complex data representations, leading to
more robust and reliable models.
While the CNN-KAN models require slightly
more computational resources due to the additional
complexity of the KAN layers, the performance gains
justify the increased computational cost. The training
times for CNN-KAN models are marginally higher
than those for CNN-MLP models, but the improve-
ments in accuracy and robustness make them a worth-
while investment for applications where precision is
critical.
Tables 5 and 4 present a comprehensive compar-
ison of performance metrics between Kolmogorov-
Arnold Networks (KAN) and Multi-Layer Percep-
trons (MLP) integrated within Convolutional Neural
Networks (CNN) across various architectures, includ-
ing ResNet50, ResNet101, VGG16, and VGG19, and
multiple datasets. The tables report precision, recall,
and mean average precision (mAP) scores for each
model and dataset. The results demonstrate that KAN
consistently outperforms MLP in terms of precision
and recall for almost all datasets and architectures.
This indicates that the integration of KAN into CNN
architectures leads to improved classification accu-
racy, showcasing the effectiveness of KAN in enhanc-
ing model performance for diverse image classifica-
tion tasks.
Figure 2: The impact of increasing KAN layers in CNN
tests on: CIFAR-100 (top left), CIFAR-10 (top right),
Caltech-256 (bottom left), and Caltech-101 (bottom right).
In Figure 2, we study the impact of varying num-
bers of KAN layers on precision, recall, and mean Av-
erage Precision (mAP) in CNN architectures. The re-
sults consistently demonstrate that while integrating
KAN layers initially improves these metrics, increas-
ing the number of KAN layers does not lead to further
significant enhancements.
In Table 6, we examine the performance of KAN
on both the MNIST and EMNIST datasets using two
approaches: (1) KAN and CNN-KAN are tested di-
rectly and compared with MLP and CNN-MLP. (2)
We apply a transformation on the MNIST and EM-
NIST datasets using a method that introduces non-
linear distortions. The process begins by setting up
a grid of control points across the image to guide how
it will deform. A parameter controls the intensity of
these deformations, dictating the extent to which each
control point shifts. Through mathematical functions,
we adjust the positions of these control points across
the image, creating a smooth, varying distortion ef-
fect. Finally, we generate a transformed version of the
image based on these adjustments, resulting in an out-
put that differs visually from the original image (Fig-
ure 3).
4.3 Computational Complexity
We examine the computational complexity of Multi-
Layer Perceptrons (MLPs) and Kolmogorov-Arnold
Networks (KANs) in a variety of image classification
tasks. MLPs are noted for their straightforward struc-
ture, with a time complexity of O(N
2
L), where N is
the number of neurons per layer and L is the num-
ber of layers. Conversely, KANs use non-linear uni-
variate functions, specifically B-splines, making them
more expressive but also more complex, with a com-
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification
53

Table 3: Performance metrics comparison of KANs, MLPs, and CNNMLP across various datasets.
Dataset Model Precision Recall mAP score
cifar10 CNN-KAN 0.71 0.70 0.69 +6%
CNN-MLP 0.67 0.67 0.63
CNN-KAN-MLP 0.69 0.70 0.69
cifar100 CNN-KAN 0.41 0.39 0.31 +5%
CNN-MLP 0.38 0.37 0.26
CNN-KAN-MLP 0.38 0.37 0.29
caltech256 CNN-KAN 0.21 0.21 0.19 +3%
CNN-MLP 0.21 0.19 0.16
CNN-KAN-MLP 0.19 0.18 0.15
caltech101 CNN-KAN 0.51 0.48 0.48 +7%
CNN-MLP 0.50 0.43 0.41
CNN-KAN-MLP 0.42 0.39 0.35
STL10 CNN-KAN 0.53 0.55 0.46 +3%
CNN-MLP 0.51 0.50 0.43
CNN-KAN-MLP 0.35 0.33 0.31
OxfordIIITPet CNN-KAN 0.37 0.35 0.33 +2%
CNN-MLP 0.28 0.45 0.31
CNN-KAN-MLP 0.35 0.33 0.31
DTD CNN-KAN 0.25 0.46 0.31 +1%
CNN-MLP 0.29 0.18 0.24
CNN-KAN-MLP 0.29 0.24 0.28
SVHN CNN-KAN 0.87 0.86 0.83 +5%
CNN-MLP 0.85 0.85 0.81
CNN-KAN-MLP 0.86 0.86 0.82
Place365 CNN-KAN 0.45 0.55 0.47
CNN-MLP 00.55 00.52 00.52 +5%
CNN-KAN-MLP 0.53 0.50 0.50
Figure 3: Top: Original image, Bottom: Transformed im-
age.
plexity of O(N
2
LG), where G is the number of spline
control points.
For instance, using the CIFAR-10 dataset, which
includes 60,000 images across 10 categories, and as-
suming a fixed architecture of N = 256, L = 2, and
G = 5, the complexity for a KAN is O(655, 360)
compared to O(131, 072) for an MLP. This illustrates
the trade-off: KANs offer greater pattern recognition
flexibility but at the cost of higher computational de-
mands, while MLPs remain simpler and less intensive
in terms of computation.
In Table 7, we present the learnable parameters
for KAN and MLP layers across various datasets.
The total learnable parameters for the KAN layer are
calculated using the formula (d
in
× d
out
) × (G + K +
3) + d
out
, where G represents the number of spline
intervals and K is the degree of the polynomial ba-
sis. In contrast, the MLP layer employs the formula
(d
in
× d
out
) + d
out
. This illustrates the KAN layer’s
higher complexity compared to the MLP layer, par-
ticularly when dealing with high-dimensional data.
4.4 Time Performance
Table 8 and Figure 4 report the training time for var-
ious models: MLP, KAN, and combinations of CNN
with MLP and KAN on different datasets. The results
show that MLP and CNN-MLP models are generally
faster than the KAN and CNN-KAN models. For ex-
ample, the ratio is approximately 89.1% on MNIST
and 76.2% on CIFAR-10.
The analysis of computational time highlights the
trade-off between model complexity and training du-
ration. While KAN and CNN-KAN models require
more time to train due to their increased complexity,
they offer superior performance in terms of precision,
recall, and mAP. This trade-off is crucial for appli-
cations where higher accuracy justifies the additional
computational cost.
VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications
54

Table 4: Performance comparison of KANs vs MLPs for
ResNet50 and ResNet101 across various datasets.
Arch. Model Dataset P R mAP Score (%)
ResNet50 KAN CIFAR-10 0.83 0.83 0.84 +12%
MLP CIFAR-10 0.77 0.74 0.72
KAN CIFAR-100 0.64 0.61 0.55 +9%
MLP CIFAR-100 0.66 0.61 0.46
KAN Caltech101 0.91 0.91 0.86 +9%
MLP Caltech101 0.89 0.83 0.77
KAN Caltech256 0.82 0.78 0.74 +4%
MLP Caltech256 0.78 0.61 0.70
KAN STL10 0.79 0.89 0.94 +1%
MLP STL10 0.81 0.88 0.89
KAN OxfordIIITPet 0.71 0.77 0.74 +3%
MLP OxfordIIITPet 0.71 0.72 0.71
KAN DTD 0.68 0.66 0.64 +2%
MLP DTD 0.59 0.63 0.62
KAN SVHN 0.93 0.90 0.97 +3%
MLP SVHN 0.95 0.74 0.94
KAN Place365 0.78 0.68 0.79
MLP Place365 0.82 0.77 0.83 +4%
ResNet101 KAN CIFAR-10 0.86 0.85 0.85
MLP CIFAR-10 0.89 0.89 0.92 +7%
KAN CIFAR-100 0.67 0.64 0.58 +10%
MLP CIFAR-100 0.65 0.61 0.48
KAN Caltech101 0.92 0.90 0.86 +12%
MLP Caltech101 0.82 0.77 0.74
KAN Caltech256 0.82 0.77 0.74 +12%
MLP Caltech256 0.68 0.61 0.62
KAN STL10 0.93 0.96 0.96 +1%
MLP STL10 0.93 0.93 0.95
KAN OxfordIIITPet 0.74 0.81 0.75 +4%
MLP OxfordIIITPet 0.76 0.72 0.71
KAN DTD 0.55 0.72 0.67 +2%
MLP DTD 0.45 0.66 0.65
KAN SVHN 0.99 0.94 0.98
MLP SVHN 0.96 0.85 0.95 +3%
KAN Place365 0.75 0.73 0.74 -
MLP Place365 0.77 0.79 0.77 +3%
5 DISCUSSION
5.1 Detailed Analysis
The increased training time for KAN and CNN-KAN
models can be attributed to the additional computa-
tions required for the B-spline functions used in KAN
layers. These functions provide greater flexibility and
expressiveness, allowing the models to capture more
complex patterns in the data. However, this comes at
the cost of increased computational overhead.
MNIST and EMNIST. For the MNIST and EM-
NIST datasets, the CNN-KAN models take signifi-
cantly longer to train compared to CNN-MLP mod-
els. This is due to the high dimensionality of the in-
put data and the complexity of the KAN layers. De-
spite the longer training times, the CNN-KAN mod-
els achieve better performance metrics, making them
suitable for applications where accuracy is more crit-
ical than training speed.
Table 5: Performance metrics comparison of KANs vs
MLPs for VGG19 and VGG16 across various datasets.
Arch. Model Dataset P R mAP Score (%)
VGG19 KAN CIFAR-10 0.85 0.85 0.80 +1%
MLP CIFAR-10 0.80 0.80 0.79
KAN CIFAR-100 0.59 0.56 0.45
MLP CIFAR-100 0.60 0.59 0.51 +6%
KAN Caltech101 0.84 0.83 0.85 +8%
MLP Caltech101 0.89 0.87 0.77
KAN Caltech256 0.65 0.60 0.65 +6%
MLP Caltech256 0.67 0.65 0.59
KAN OxfordIIITPet 0.88 0.88 0.86 +3%
MLP OxfordIIITPet 0.86 0.86 0.84
KAN STL10 0.91 0.89 0.93 +1%
MLP STL10 0.93 0.93 0.92
KAN DTD 0.59 0.59 0.52 +1%
MLP DTD 0.59 0.59 0.51
KAN SVHN 0.88 0.91 0.89 +2%
MLP SVHN 0.86 0.87 0.85
KAN Place365 0.71 0.73 0.75
MLP Place365 0.75 0.80 0.78 +5%
VGG16 KAN CIFAR-10 0.84 0.84 0.79 +1%
MLP CIFAR-10 0.81 0.81 0.78
KAN CIFAR-100 0.61 0.56 0.45
MLP CIFAR-100 0.61 0.58 0.50 +5%
KAN Caltech101 0.84 0.81 0.83 +8%
MLP Caltech101 0.87 0.85 0.75
KAN Caltech256 0.65 0.59 0.61 +9%
MLP Caltech256 0.77 0.76 0.52
KAN OxfordIIITPet 0.89 0.85 0.85 +3%
MLP OxfordIIITPet 0.87 0.86 0.84
KAN STL10 0.93 0.93 0.96 +1%
MLP STL10 0.93 0.93 0.95
KAN DTD 0.59 0.59 0.52 +1%
MLP DTD 0.59 0.59 0.51
KAN SVHN 0.98 0.95 0.96 +2%
MLP SVHN 0.91 0.91 0.93
KAN Place365 0.81 0.82 0.82
MLP Place365 0.83 0.85 0.85 +3%
CIFAR-10. The CIFAR-10 dataset also shows a no-
ticeable increase in training time for CNN-KAN mod-
els compared to CNN-MLP models. The additional
time is justified by the improved precision, recall, and
mAP scores, demonstrating the effectiveness of KAN
layers in enhancing model performance.
5.2 Implications for Real-World
Applications
In real-world applications, the choice between MLP,
KAN, CNN-MLP, and CNN-KAN models depends
on the specific requirements of the task. For appli-
cations where quick training times are essential, MLP
and CNN-MLP models may be preferred. However,
for tasks that demand high accuracy and robustness,
the additional training time required for KAN and
CNN-KAN models is a worthwhile investment.
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification
55

Table 6: Performance metrics comparison of KANs vs MLPs on mnist and emnist datasets.
Dataset Model Precision Recall mAP score
Mnist MLP 0.97 0.97 0.95
KAN 0.97 0.97 0.99 +5%
CNN-MLP 0.98 0.98 0.98
CNN-KAN 0.98 0.98 0.99 +1%
Emnist MLP 0.84 0.83 0.73
KAN 0.82 0.82 0.78 +5%
CNN-MLP 0.82 0.82 0.78
CNN-KAN 0.87 0.86 0.83 +5%
T-Mnist MLP 0.97 0.97 0.96
KAN 0.97 0.97 0.99 +3%
CNN-MLP 0.98 0.98 0.98
CNN-KAN 0.99 0.99 0.99 +1%
T-Emnist MLP 0.83 0.82 0.74
KAN 0.83 0.83 0.79 +5%
CNN-MLP 0.84 0.84 0.80
CNN-KAN 0.86 0.86 0.82 +2%
Table 7: Learnable parameters for KAN and MLP layers across different datasets.
Dataset Input dim Output dim KAN Parameters MLP Parameters
MNIST 28 × 28 = 784 10 78,410 7,850
CIFAR-10 32 × 32 × 3 = 3072 10 307,210 30,730
CIFAR-100 32 × 32 × 3 = 3072 100 3,072,100 307,300
Caltech101 224 × 224 × 3 = 150, 528 101 151,058,981 15,105,989
Caltech256 224 × 224 × 3 = 150, 528 256 385,353,536 38,553,984
STL10 96 × 96 × 3 = 27, 648 10 276,490 276,490
OxfordIIITPet 224 × 224 × 3 = 150, 528 37 55,695,197 5,569,633
DTD 224 × 224 × 3 = 150, 528 47 70,748,607 7,074,463
SVHN 32 × 32 × 3 = 3072 10 307,210 30,730
iNaturalist 224 × 224 × 3 = 150, 528 10 24,084,490 1,505,290
Places365 224 × 224 × 3 = 150, 528 365 549,427,205 54,942,245
Table 8: Mean computational time (in seconds) for training
CNN-(MLP/KAN).
Dataset Model Mean Confidence
MNIST CNN-MLP 288 (275, 300)
CNN-KAN 323 (309, 336)
EMNIST CNN-MLP 414 (400, 428)
CNN-KAN 527 (511, 543)
CIFAR-10 CNN-MLP 193 (183, 203)
CNN-KAN 253 (242, 264)
5.3 Future Work
Future research could focus on optimizing the train-
ing process for KAN layers to reduce computational
time without compromising performance. Techniques
such as parallel processing, more efficient algorithms
for B-spline computations, and hardware accelera-
tions could be explored to make KAN models more
Figure 4: Mean computational time (in seconds) for training
MLP and KAN.
feasible for time-sensitive applications. To summa-
rize, while KAN and CNN-KAN models require more
computational resources and longer training times,
VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications
56

their superior performance in terms of accuracy and
robustness makes them valuable for complex image
classification tasks. The trade-off between computa-
tional complexity and model performance should be
carefully considered based on the specific needs of
the application.
6 CONCLUSION
In this paper, we introduced a novel classification
approach that integrates Kolmogorov-Arnold Net-
works (KANs) with Convolutional Neural Networks
(CNNs), termed CNN-KAN. This innovative archi-
tecture harnesses the powerful feature extraction ca-
pabilities of CNNs and the sophisticated modeling of
complex relationships provided by KANs. Our exten-
sive evaluations across multiple datasets demonstrate
that CNN-KAN consistently outperforms traditional
CNN architectures in terms of accuracy, precision,
and recall.
We also explored the application of pretrained
models, showing that the proposed CNN-KAN mod-
els not only enhance efficiency but also improve ro-
bustness. The experimental results clearly indicate
that the integration of KAN layers into CNN architec-
tures leads to significant performance gains in diverse
image classification tasks.
In summary, the ConvKAN approach represents a
promising advancement in the field of computer vi-
sion, offering a robust and efficient solution for com-
plex image classification challenges. This work paves
the way for future research to further optimize and
expand the capabilities of CNN-KAN models.
REFERENCES
Amosa, T. I., Sebastian, P., Izhar, L. I., Ibrahim, O., Ayinla,
L. S., Bahashwan, A. A., Bala, A., and Samaila, Y. A.
(2023). Multi-camera multi-object tracking: a review
of current trends and future advances. Neurocomput-
ing, 552:126558.
Balazevic, I., Steiner, D., Parthasarathy, N., Arandjelovi
´
c,
R., and Henaff, O. (2024). Towards in-context scene
understanding. Advances in Neural Information Pro-
cessing Systems, 36.
Chen, X., Peng, H., Wang, D., Lu, H., and Hu, H. (2023).
Seqtrack: Sequence to sequence learning for visual
object tracking. In Proceedings of the IEEE/CVF con-
ference on computer vision and pattern recognition,
pages 14572–14581.
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn,
D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer,
M., Heigold, G., Gelly, S., et al. (2020). An image is
worth 16x16 words: Transformers for image recogni-
tion at scale. arXiv preprint arXiv:2010.11929.
Fan, D.-P., Ji, G.-P., Xu, P., Cheng, M.-M., Sakaridis, C.,
and Van Gool, L. (2023). Advances in deep concealed
scene understanding. Visual Intelligence, 1(1):16.
Genet, R. and Inzirillo, H. (2024). A temporal kolmogorov-
arnold transformer for time series forecasting. arXiv
preprint arXiv:2406.02486.
He, K., Zhang, X., Ren, S., and Sun, J. (2016). Deep resid-
ual learning for image recognition. In Proceedings of
the IEEE conference on computer vision and pattern
recognition, pages 770–778.
Jmour, N., Zayen, S., and Abdelkrim, A. (2018). Convo-
lutional neural networks for image classification. In
2018 international conference on advanced systems
and electric technologies (IC
ASET), pages 397–402.
IEEE.
Kim, H. E., Cosa-Linan, A., Santhanam, N., Jannesari, M.,
Maros, M. E., and Ganslandt, T. (2022). Transfer
learning for medical image classification: a literature
review. BMC medical imaging, 22(1):69.
Koonce, B. and Koonce, B. (2021). Vgg network. Con-
volutional Neural Networks with Swift for Tensorflow:
Image Recognition and Dataset Categorization, pages
35–50.
Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012). Im-
agenet classification with deep convolutional neural
networks. In Advances in Neural Information Pro-
cessing Systems, volume 25, pages 1097–1105.
LeCun, Y., Bottou, L., Bengio, Y., and Haffner, P. (1998).
Gradient-based learning applied to document recogni-
tion. Proceedings of the IEEE, 86(11):2278–2324.
Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J.,
Solja
ˇ
ci
´
c, M., Hou, T. Y., and Tegmark, M. (2024).
Kan: Kolmogorov-arnold networks. arXiv preprint
arXiv:2404.19756.
Mathis, A., Mamidanna, P., Cury, K. M., Abe, T., Murthy,
V. N., Mathis, M. W., and Bethge, M. (2022).
Deeplabcut: markerless pose estimation of user-
defined body parts with deep learning. Nature Neu-
roscience, 21:1546–1726.
Meinhardt, T., Kirillov, A., Leal-Taixe, L., and Feichten-
hofer, C. (2022). Trackformer: Multi-object tracking
with transformers. In Proceedings of the IEEE/CVF
conference on computer vision and pattern recogni-
tion, pages 8844–8854.
Nath, S. S., Mishra, G., Kar, J., Chakraborty, S., and Dey,
N. (2014). A survey of image classification meth-
ods and techniques. In 2014 International conference
on control, instrumentation, communication and com-
putational technologies (ICCICCT), pages 554–557.
IEEE.
Sandler, M., Howard, A., Zhu, M., Zhmoginov, A., and
Chen, L.-C. (2018). Mobilenetv2: Inverted residu-
als and linear bottlenecks. In Proceedings of the IEEE
Conference on Computer Vision and Pattern Recogni-
tion, pages 4510–4520.
Shi, J.-C., Wang, M., Duan, H.-B., and Guan, S.-H.
(2024). Language embedded 3d gaussians for open-
vocabulary scene understanding. In Proceedings of
ConvKAN: Towards Robust, High-Performance and Interpretable Image Classification
57

the IEEE/CVF Conference on Computer Vision and
Pattern Recognition, pages 5333–5343.
Simonyan, K. and Zisserman, A. (2014). Very deep con-
volutional networks for large-scale image recognition.
arXiv preprint arXiv:1409.1556.
Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S.,
Anguelov, D., Erhan, D., Vanhoucke, V., and Rabi-
novich, A. (2015). Going deeper with convolutions.
In Proceedings of the IEEE Conference on Computer
Vision and Pattern Recognition, pages 1–9.
Tan, M. and Le, Q. V. (2019). Efficientnet: Rethink-
ing model scaling for convolutional neural networks.
In International Conference on Machine Learning,
pages 6105–6114. PMLR.
Wang, Y., Sun, J., Bai, J., Anitescu, C., Eshaghi, M. S.,
Zhuang, X., Rabczuk, T., and Liu, Y. (2024). Kol-
mogorov arnold informed neural network: A physics-
informed deep learning framework for solving pdes
based on kolmogorov arnold networks. arXiv preprint
arXiv:2406.11045.
Wotton, J. and Gunes, H. (2020). Deep learning for real-
time robust facial expression recognition. IEEE Trans-
actions on Affective Computing, 11(3):532–541.
Yu, H. and Xiong (2022). Scratch-aid, a deep learning-
based system for automatic detection of mouse
scratching behavior with high accuracy. eLife,
11:e84042.
Zhang, Q. (2022). A novel resnet101 model based on dense
dilated convolution for image classification. SN Ap-
plied Sciences, 4:1–13.
VISAPP 2025 - 20th International Conference on Computer Vision Theory and Applications
58