Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks (1907.06732v3)

Abstract: The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Pad\'e Activation Units (PAUs) can both approximate common activation functions and also learn new ones while providing compact representations. Our empirical evidence shows that end-to-end learning deep networks with PAUs can increase the predictive performance. Moreover, PAUs pave the way to approximations with provable robustness. https://github.com/ml-research/pau

• The paper introduces Padé Activation Units (PAUs) that enable deep networks to learn flexible, adaptive activation functions.
• It leverages rational Padé approximants for better approximation and convergence compared to traditional static activations.
• Empirical results on MNIST, CIFAR-10, and ImageNet show PAUs improve performance with minimal increases in computational overhead.

Overview of Padé Activation Units: End-to-end Learning of Flexible Activation Functions

The paper "Padé Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks" by Alejandro Molina, Patrick Schramowski, and Kristian Kersting investigates the integration of Padé approximants into deep learning frameworks as adaptive activation functions. Historically, the choice of activation functions, such as ReLU, Sigmoid, or Tanh, has had significant consequences for the efficacy of neural networks. Typically, these functions are chosen based on existing literature and fixed during network training. Recognizing the limitations posed by such predetermined selections, this paper proposes a paradigm shift towards more adaptable models using Padé Activation Units (PAUs).

Key Concepts

The ingenuity of this paper lies in leveraging Padé approximants—rational functions with adjustable coefficients—to replace static activation functions. This enables deep learning models to autonomously learn and optimize activation functions during training, thus facilitating improvements in predictive performance and network flexibility. Padé approximants have shown advantages over polynomial representations typically used in activation functions due to their superior convergence properties and ability to better approximate functions outside of polynomial behavior.

Empirical Conclusions

Through rigorous empirical evaluation across standard datasets like MNIST, CIFAR-10, and ImageNet, the paper demonstrates that networks utilizing PAUs can consistently outperform those relying on static activations. Notably, PAUs preserved or improved the predictive performance across various architectures, including VGG, ResNet, and MobileNetV2, with marginal increases in network parameter counts. This highlights the PAUs' capability to seamlessly integrate into existing frameworks without substantial computational overhead.

In controlled experiments on MNIST and Fashion-MNIST using architectures such as LeNet and VGG, PAUs not only matched the best performance of competing activation functions but also frequently surpassed them, offering improved stability and convergence behavior. The CIFAR-10 results further emphasized the advantages of adaptive learning for activation functions, particularly for architectures like MobileNetV2, where flexibility in activation could drive considerable gains due to the architecture's inherent compactness and depth.

Extended Benefits and Future Directions

One theoretical contribution of the work is the proof that Padé networks with PAU activation functions retain universality in function approximation, akin to networks with traditional non-polynomial activations. This implies that PAUs, despite their adaptability, do not sacrifice the theoretical expressiveness necessary for comprehensive function modeling.

The paper raises significant implications for future AI development, particularly in automated model selection and hyperparameter tuning. With PAUs, practitioners can delegate the task of selecting optimal activation functions to the network itself, maximizing performance while minimizing manual experimentation. Additionally, the potential to employ PAUs in sparsity-driven research, such as neural network pruning (e.g., lottery ticket hypothesis), opens avenues for creating efficient, robust models with minimized computational costs. This could leverage global optimal training strategies or enhance robustness by exploiting the fine-tuned properties of PAUs.

In conclusion, Padé Activation Units represent a promising step towards flexible and efficient learning paradigms in AI. By adopting rational approximations, they offer an adaptable, scalable mechanism that broadens the horizons for deep learning applicability and innovation.