This repository contains the code for training and evaluating a hybrid neural network (pretrained CNN backbone + KAN network) for the parametric reconstruction of complex 3D objects from single images, using regression. The initial goal was to assess whether KANs can be effectively used in this context, and subsequently to experimentally evaluate whether their symbolic regression-oriented nature provides efficiency and advantages compared to traditional networks, while aiming to maintain comparable conditions.

• Parametric Reconstruction
• Neural Network
• Results
• Installation
• Usage
• Acknowledgments

Parametric reconstruction of 3D models consists in representing the shape of an object using a finite set of parameters, which define its geometry. This approach requires only a small amount of data (.json files) and allows the user to locally modify individual values without having to manipulate the entire mesh.

The first step involved creating a dataset in Blender using a parametric formula, introducing shape and color variations to derive the 6 representative parameters. All detailed information about the dataset can be found in its readme.txt file, available in the dataset installation instructions section.

Since some tests conducted with CNN-KAN networks were not satisfactory (in line with the numerous results observable in the dedicated section of the repository awesome-kan), the adopted strategy was to take the best from current technologies, namely a pretrained backbone for extracting image features:

• EfficientNet-B0: used as a large and stable network to verify the actual effectiveness of using KANs as final fully connected layers for regression;
• SqueezeNet: used in the later comparison between KAN and MLP networks, as being very lightweight and having few parameters allowed for a more direct comparison in terms of generalization capability, requiring the network to "reconstruct" the underlying formula in order to correctly predict the parameters.

Among the various KAN libraries tested, the most effective for this purpose were:

• EfficientKan by Blealtan and Akaash Dash;
• FourierKan by Fan Yijia.

Model evaluation, in addition to training and validation loss curves, was conducted using metrics such as MAE, RMSE and R2, calculated through the calcola_metrichefunction. Visual comparisons were then performed using the methods visualizza_pred_reale, for direct comparisons between input image and real/predicted mesh, and visualizza_metriche_immagini for a more in-depth analysis such as overlaying the real and predicted mesh and, most importantly, visualizing the Hausdorff distance.

For example, the best prediction of the second-best model EFFNETB0_UNLOCK_DROP_EFFK_6 yielded the following results:

The comparison between the worst predictions of the two top-performing models instead revealed that the best one is EFFNETB0_UNLOCK_DROP_FOURIER_6:

Real Mesh	Fourier_6	EfficientKan_6

With the following predicted parameters:

Even more interesting is the final comparison between the best-performing model EFFNETB0_UNLOCK_DROP_FOURIER_6 and the two models used to evaluate the performance difference between KAN and MLP layers SQUEEZENET_DROP4_CLASSICA_DROP_256 and SQUEEZENET_DROP4_FOURIER_DROP_256, sover three randomly selected test set images. Only the networks equipped with KAN layers showed superior performance in approximation, in particular the last image poses an interesting question as to what to reward when working with neural networks, the pure observation of metrics (like the neural network EFFNETB0_UNLOCK_DROP_EFFK_6) or going beyond what has been learnt and generalising as best as possible, as the truncated cone-shaped point in the picture was never encountered during training and only EFFNETB0_UNLOCK_DROP_FOURIER_6 ha attempted, mistakenly, to approximate it.

Clone the repository and install the dependencies using pip:

git clone https://github.com/antoniogrs/kan_parametric_reconstruction.git
cd kan_parametric_reconstruction
pip install -r requirements.txt

The dataset must be downloaded separately from Zenodo at the following link. After extracting the .rar file, place the dataset folder directly in the root of the project directory.

• 📦 Dataset: Download from Zenodo

• Python 3.13.2
• PyTorch 2.8.0,
• Cuda 12.9
• Blender 4.4

The script main.py allows you to either train new networks or evaluate them both through metrics and visually. Before evaluating, the network must be trained by uncommenting the following block of code:

# 2) Results visualization
#It’s essential to run the render in Blender first to have the image name!
img_data = IMG_MAP.get(nome)

if img_data is None:
    print(f"❌ Nessuna immagine associata a {nome}, salto.")
    continue

and keeping this one active:

# 1) Training and metrics calculation
print(f"\n\n--- INIZIO TRAINING: {nome} ---\n\n")
esegui_training_con_modello(classe_modello)

print(f"\n\n--- INIZIO TESTING: {nome} ---\n\n")
esegui_test(classe_modello)

Only after training the model with the chosen hyperparameters and rendering the predicted object (best and worst) in Blender, it is possible to comment out the first block and uncomment the second one to visualize the results. Make sure to properly update the MODELLI_DA_TESTARE list and the IMG_MAP dictionary. The training progress can be monitored using tensorboardX , while the training curves of multiple models can be plotted by uncommenting the following block:

risultati_modificato_path =os.path.join(BASE_DIR, 'results', 'CilindroSpiralato')
percorso_log = [f"{risultati_modificato_path}/{MODELLI_DA_TESTARE[0]}_CilindroSpiralato/loss_log.json",
                f"{risultati_modificato_path}/{MODELLI_DA_TESTARE[1]}_CilindroSpiralato/loss_log.json",
                f"{risultati_modificato_path}/{MODELLI_DA_TESTARE[2]}_CilindroSpiralato/loss_log.json",
                f"{risultati_modificato_path}/{MODELLI_DA_TESTARE[3]}_CilindroSpiralato/loss_log.json"]
plot_modelli(MODELLI_DA_TESTARE, percorso_log)
sys.exit()

I would like to thank my advisor Prof. Ugo Erra and Dr. Gilda Manfredi for their support during the development of this project, all the authors mentioned above for creating and developing the libraries used and the contributors of awesome-kan for providing for providing inspiration and useful tools. Finally the author of KAN for initiating a new and exciting line of research in this field.