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Top AI Repos tracks AI repositories on GitHub and answers two different questions about each one: is it moving right now, and would you bet a product on it.
Top AI Repos tracks AI repositories on GitHub and answers two different questions about each one: is it moving right now, and would you bet a product on it.
This project extends the idea of the innovative architecture of Kolmogorov-Arnold Networks (KAN) to the Convolutional Layers, changing the classic linear transformation of the convolution to learnable non linear activations in each pixel.
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# Convolutional Kolmogorov-Arnold Network (CKAN) ## Paper All the mathematical explanation and experiments are explained in the [Academic Paper](https://arxiv.org/abs/2406.13155) ### Introducing Convolutional KAN Networks! This project extends the idea of the innovative architecture of Kolmogorov-Arnold Networks (KAN) to the Convolutional Layers, changing the classic linear transformation of the convolution to learnable non linear activations in each pixel. ## Authors This repository was made by: - Alexander Bodner | [email protected] | [Twitter](https://twitter.com/AlexBodner_) | [LinkedIn](https://www.linkedin.com/in/alexanderbodner/) - Antonio Tepsich | [email protected] | [Twitter](https://twitter.com/antotepsich) | [LinkedIn](https://www.linkedin.com/in/antonio-tepsich/) - Jack Spolski | [email protected] | [LinkedIn](https://www.linkedin.com/in/jack-spolski-9882a3196/) - Santiago Pourteau | [email protected] | [Twitter](https://twitter.com/SantiPourteau) | [LinkedIn](https://www.linkedin.com/in/santiago-pourteau-1bba8619a/) ### Credits This repository uses an efficient implementation of KAN which is available [here](https://github.com/Blealtan/efficient-kan). The original implementation of KAN is available [here](https://github.com/KindXiaoming/pykan). The original paper of the KAN is available [here](https://arxiv.org/pdf/2404.19756). ### What is a KAN? KANs are promising alternatives of Multi-Layer Perceptrons (MLPs). KANs have strong mathematical foundations just like MLPs: MLPs are based on the universal approximation theorem, while KANs are based on Kolmogorov-Arnold representation theorem. KANs and MLPs are dual: KANs have activation functions on edges, while MLPs have activation functions on nodes. KAN seems to be more parameter efficient than MLPs, but each KAN Layer has more parameters than a MLP layer. <img width="1163" alt="mlp_kan_compare" src="https://github.com/KindXiaoming/pykan/assets/23551623/695adc2d-0d0b-4e4b-bcff-db2c8070f841"> For more information about this novel architecture please visit: - The official Pytorch implementation of the architecture: https://github.com/KindXiaoming/pykan - The research paper: https://arxiv.org/abs/2404.19756 ### What is a KAN Convolution? KAN Convolutions are very similar to convolutions, but instead of applying the dot product between the kernel and the corresponding pixels in the image, we apply a **Learnable Non Linear activation function** to each element, and then add them up. The kernel of the KAN Convolution is equivalent to a KAN Linear Layer of 4 inputs and 1 output neuron. For each input i, we apply a ϕ_i learnable function, and the resulting pixel of that convolution step is the sum of ϕ_i(x_i). This can be visualized in the following figure.  ### Parameters in a KAN Convolution Suppose that we have a KxK kernel. In this case, for each element of this matrix we have a ϕ, which its parameter count is: gridsize + 1. For implementation issues, efficient kan defines:  This gives more expressability to the activation function b. So the parameter count for a linear layer is gridsize + 2. So in total we have K²(gridsize + 2) parameters for KAN Convolution, vs only K² for a common convolution. Consider that gridsize is typically (in our experiments) between k and k², but k tends to be a small value, between 2 and 16. ## Results The different architectures we have tested are: - KAN Convolutional Layers connected to Kan Linear Layers (KKAN) - Kan Convolutional Layers connected to a MLP (KANC MLP) - CKAN with Batch Normalization between convolutions (CKAN_BN) - CNN (Classic Convolutions connected to a MLP) - Normal Conv & KAN (Classic Convolutions and KANs after the flatten. They can be seen in the following Figures: **CNN architectures**  **KAN architectures**  The experiments were run using the script: "hiperparam_t
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Would you bet a product on this? Bounded 0–100 and slow moving.
matched fp:77e477256493d68d, topic:deep-learning
matched fp:77e477256493d68d, topic:computer-vision