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apecafn 0.1.3

APEC and MAPEC Activation Functions for Neural Networks

APEC and MAPEC Activation Functions for Neural Networks

Overview
Installation
Usage
Activation Functions
Mathematical Formulation

APEC (Asymmetric Parametric Exponential Curvature)
MAPEC (Multiplicative Asymmetric Parametric Exponential Curvature)

Evaluation
Results
Contributing
License

Overview
This repository introduces two novel activation functions, APEC (Asymmetric Parametric Exponential Curvature) and its variant MAPEC (Multiplicative APEC), designed for deep learning models to capture complex patterns with improved performance. Functions have been tested on the CIFAR-100 dataset (results included) and on some of my experimental models (results not included).
Installation
pip install apec-afn

Usage
import torch
from apec import MAPEC

x = torch.randn([8])
f = MAPEC()

print(f(x))

Activation Functions

APEC: Offers a balance between flexibility and performance, as demonstrated by the improvement over traditional functions on CIFAR-100.
MAPEC: An extension of APEC with an additional multiplicative term, allowing for an even richer model expressiveness and an observed faster convergence (up to 15%).

Mathematical Formulation
APEC (Asymmetric Parametric Exponential Curvature)

APEC is designed to introduce a non-linear response with an adjustable curvature, defined by:
f(x)=α+β−x(γ−exp⁡(−x))+ϵ

Initialization: Parameters a and b are initialized with a normal distribution of zero mean and a standard deviation of 0.35. Parameter g is initialized with a mean of -1.375 and a standard deviation of 0.35.
Constraints: The default constraints for a, b, and g are [-2.0, +2.0], [-2.5, +2.5], and [-2.5, -0.25], respectively.
Stability: A small constant eps (1.0e-5) is added to prevent division by zero.

MAPEC (Multiplicative Asymmetric Parametric Exponential Curvature)

MAPEC extends APEC by adding a multiplicative term, enhancing its flexibility:
f(x)=(α+β−x−abs(γ)−exp⁡(−x)−ϵ+(x⋅δ))⋅ζ

Initialization: Parameters initialization values are -3.333e-2, -0.1, -2.0, +0.1 and +1.0 for alpha, beta, gamma, delta and zeta respectively.
Constraints: There are no constraints on the parameters for MAPEC, allowing for a fully adaptive response.
Stability: A small constant eps (1.0e-3) is subtracted from denominator to prevent division by zero.

These functions aim to provide enhanced flexibility and adaptability for neural networks, particularly beneficial for complex pattern recognition tasks.
Evaluation
To evaluate a model with a specific activation function on CIFAR-100 and plot training loss*, use:
python scripts/eval_cifar100.py --activation APEC --plot-loss

* Plotting training loss requires self-projection package to be installed.
Results
Evaluation results on CIFAR-100:

Activation
Average Loss
Accuracy

MAPEC 16e*
2.2004
43%

APEC
2.2235
43%

MAPEC 20e*
2.2456
43%

Mish
2.2704
43%

SELU
2.2674
42%

PReLU
2.2759
42%

ReLU
2.3933
39%

* Results provided for training with MAPEC activation for 20 and 16 epochs respectively.
APEC leads to the best performance, closely followed by Mish and SELU.
MAPEC leads to the faster convergence with performance closely followed by APEC.
You could look at training loss plots here.
Contributing
Contributions and suggestions are welcome! Feel free to fork the repository, open issues, and submit pull requests.
License
APEC is released under the MIT License. See the LICENSE file for more details.