APTx Neuron

This repository offers a Python code for the PyTorch implementation of the APTx Neuron and experimentation on MNIST dataset, as introduced in the paper "APTx Neuron: A Unified Trainable Neuron Architecture Integrating Activation and Computation".

Paper Title: APTx Neuron: A Unified Trainable Neuron Architecture Integrating Activation and Computation

Author: Ravin Kumar

Sources:

• Arxiv.org
• Research Gate

Github Repositories:

• APTx Neuron (Pytorch + PyPI Package): APTx Neuron
• APTx Activation Function (Pytorch + PyPI Package): APTx Activation Function
• Experimentation Results with MNIST (APTx Neuron): MNIST Experimentation Code

Cite Paper as:

Kumar, Ravin. "APTx Neuron: A Unified Trainable Neuron Architecture Integrating Activation and Computation." arXiv preprint arXiv:2507.14270 (2025).

Or,

@article{kumar2025aptx,
  title={APTx Neuron: A Unified Trainable Neuron Architecture Integrating Activation and Computation},
  author={Kumar, Ravin},
  journal={arXiv preprint arXiv:2507.14270},
  year={2025}
}

---

APTx Neuron

Abstract: We propose the APTx Neuron, a novel, unified neural computation unit that integrates non-linear activation and linear transformation into a single trainable expression. The APTx Neuron is derived from the APTx activation function, thereby eliminating the need for separate activation layers and making the architecture both computationally efficient and elegant. The proposed neuron follows the functional form $y = \sum_{i=1}^{n} ((\alpha_i + \tanh(\beta_i x_i)) \cdot \gamma_i x_i) + \delta$, where all parameters $\alpha_i$, $\beta_i$, $\gamma_i$, and $\delta$ are trainable. We validate our APTx Neuron-based architecture on the MNIST dataset, achieving up to 96.69% test accuracy within 11 epochs using approximately 332K trainable parameters. The results highlight the superior expressiveness and computational efficiency of the APTx Neuron compared to traditional neurons, pointing toward a new paradigm in unified neuron design and the architectures built upon it.

The APTx Neuron is a novel computational unit that unifies linear transformation and non-linear activation into a single, expressive formulation. Inspired by the parametric APTx activation function, this neuron architecture removes the strict separation between computation and activation, allowing both to be learned as a cohesive entity. It is designed to enhance representational flexibility while reducing architectural redundancy.

Mathematical Formulation

Traditionally, a neuron computes the output as:

$y = \phi\left( \sum_{i=1}^{n} w_i x_i + b \right)$

where:

• $x_i$ are the inputs,
• $w_i$ are the weights,
• $b$ is the bias,
• and $\phi$ is an activation function such as ReLU, Swish, or Mish.

The APTx Neuron merges these components into a unified trainable expression as:

$y = \sum_{i=1}^{n} \left[ (\alpha_i + \tanh(\beta_i x_i)) \cdot \gamma_i x_i \right] + \delta$

where:

• $x_i$ is the $i$-th input feature,
• $\alpha_i$, $\beta_i$, and $\gamma_i$ are trainable parameters for each input,
• $\delta$ is a trainable scalar bias.

This equation allows the neuron to modulate each input through a learned, per-dimension non-linearity and scaling operation. The term $(\alpha_i + \tanh(\beta_i x_i))$ introduces adaptive gating, and $\gamma_i x_i$ provides multiplicative control.

---

📥 Installation

pip install aptx_neuron

or,

pip install git+https://github.com/mr-ravin/aptx_neuron.git

---

Usage

1. APTx Neuron-based Layer with all $\alpha_i$, $\beta_i$, $\gamma_i$, and $\delta$ as trainable:

The setting is_alpha_trainable = True keeps $\alpha_i$ trainable. Each APTx neuron will have $(3n + 1)$ trainable parameters, where $n$ is input dimension. Note: The default value of is_alpha_trainable is True.

import aptx_neuron
input_dim = 8  # assuming input vector to be of dimension 8.
output_dim = 1 # assuming output dimension equals 1.

aptx_neuron_layer = aptx_neuron.aptx_layer(input_dim=input_dim, output_dim=output_dim, is_alpha_trainable=True)

2. APTx Neuron-based Layer with $\alpha_i=1$ (not trainable); While $\beta_i$, $\gamma_i$, and $\delta$ as trainable:

The setting is_alpha_trainable = False makes $\alpha_i$ fixed (non-trainable). Each APTx neuron will then have $(2n + 1)$ trainable parameters, thus reducing memory and training time per epoch. Here, $n$ is input dimension.

import aptx_neuron
input_dim = 8  # assuming input vector to be of dimension 8.
output_dim = 1 # assuming output dimension equals 1.

aptx_neuron_layer = aptx_neuron.aptx_layer(input_dim=input_dim, output_dim=output_dim, is_alpha_trainable=False)  # α_i is fixed (not trainable)

---

Experimentation on MNIST dataset

Run the below command to train an APTx Neuron-based fully-connected neural network on the MNIST dataset. The model will automatically save training loss and accuracy values in the ./result/ directory.

Note: For this MNIST experimentation, we have hardcoded is_alpha_trainable=True inside run.py. If you wish to explore the full flexibility and modularity of APTx Neuron (including toggling α trainability), we recommend using the official PyPI package:

pip install aptx-neuron

Or, install directly from GitHub:

pip install git+https://github.com/mr-ravin/aptx_neuron.git

1. Model Training

To train the model from scratch (using Python 3.12.11 on cpu):

python3 run.py --total_epoch 20

This command will:

• Train the model on MNIST
• Save training and validation loss/accuracy in the ./result/ directory
• Use the default device: cpu

2. Model Inference

To perform inference on the test set using the trained model (reproducibility mode):

python3 run.py --mode infer --device cpu

---

Reproducibility on MNIST dataset

1. Inference on Pre-trained model

• ✅ Test Accuracy: 96.69%

• 📁 Model Weights File: ./weights/aptx_neural_network_11.pt

• 💻 Environment: Python 3.12.11, Pytorch >=1.8.0, and Device: cpu

• Command: python3 run.py --mode infer --device cpu --load_model_weights_path ./weights/aptx_neural_network_11.pt

⚠️ Important: The codebase was refactored after training. Use this command to reproduce the test accuracy correctly under the same configuration. 🚀 Note: This result was obtained using default hyperparameters on CPU. 🔧 Further optimization (e.g., learning rate scheduling, weight initialization, architecture tuning, or training on GPU etc.) has the potential to improve accuracy even further.

2. Visualise Model Performance

2.1 Visual analysis of train and test loss values

2.2 Visual analysis of train and test accuracy values

2.3 Training & Evaluation Metrics (APTx Neuron on MNIST)

Epoch	Train Loss	Test Loss	Train Accuracy (%)	Test Accuracy (%)
1	85.58	36.73	84.16	89.12
2	33.27	17.82	90.16	90.76
3	19.97	28.16	91.80	90.82
4	9.98	27.00	92.55	90.66
5	15.28	24.45	93.59	93.03
6	13.88	9.13	97.11	96.33
7	9.35	8.84	97.47	95.53
8	0.00	7.73	97.38	95.51
9	1.10	9.19	97.51	94.47
10	6.41	8.69	97.56	95.59
11	0.00	6.81	98.75	96.69
12	0.00	6.57	99.11	96.53
13	0.00	6.67	99.19	96.57
14	0.00	7.29	99.21	96.40
15	0.00	6.90	99.23	96.46
16	0.00	6.25	99.60	96.63
17	0.00	6.21	99.77	96.58
18	0.00	6.02	99.79	96.65
19	0.00	5.95	99.78	96.68
20	0.00	6.13	99.81	96.56

✅ Best Test Accuracy: 96.69% at Epoch 11
📌 Indicates potential for further improvement with better optimization or deeper architecture.

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Conclusion

This work introduced the APTx Neuron, a unified, fully trainable neural unit that integrates linear transformation and non-linear activation into a single expression, extending the APTx activation function. By learning per-input parameters $\alpha_i$, $\beta_i$, and $\gamma_i$ for each input $x_i$, and a shared bias term $\delta$ within a neuron, the APTx Neuron removes the need for separate activation layers and enables fine-grained input transformation. The APTx Neuron generalizes traditional neurons and activations, offering greater representational power. Our experiments show that a fully connected APTx Neuron-based feedforward neural network achieves 96.69% test accuracy on the MNIST dataset within 11 epochs using approximately 332K trainable parameters, demonstrating rapid convergence and high efficiency. This design lays the groundwork for extending APTx Neurons to CNNs and transformers, paving the way for more compact and adaptive deep learning architectures.

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📜 Copyright License

Copyright (c) 2025 Ravin Kumar
Website: https://mr-ravin.github.io

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