mlnomad/xor-single-nmn-neuron

Single YatNMN Neuron Model for the XOR Problem

This repository contains a PyTorch model with a single, non-linear YatNMN neuron that has been trained on the XOR dataset.

Model Description

This model demonstrates that the XOR problem can be solved by a single neuron, provided the neuron is sufficiently complex. Unlike a standard nn.Linear layer, which is a linear operator, this model uses a YatNMN neuron from the nmn library.

The YatNMN neuron is an inherently non-linear operator inspired by physical inverse-square laws, allowing it to learn the non-linear decision boundary required to solve XOR.

Training Results

• Final Loss: 0.3466
• Accuracy: 100.00%

With sufficient training using the Adam optimizer, the model achieves 100% accuracy, correctly learning the XOR function. This contrasts with a standard single neuron, which typically stalls at 50% or 75% accuracy.

How to Use

import torch
import torch.nn as nn
# Make sure to install the nmn library: pip install nmn
from nmn.torch.nmn import YatNMN

# Define the model architecture
class SingleNonLinearNeuron(nn.Module):
    def __init__(self, input_size, output_size):
        super(SingleNonLinearNeuron, self).__init__()
        self.non_linear = YatNMN(input_size, output_size, bias=False)
    def forward(self, x):
        return self.non_linear(x)

# Instantiate the model and load the weights from the hub
# Note: You'll need to have huggingface_hub installed
from huggingface_hub import hf_hub_download
model = SingleNonLinearNeuron(input_size=2, output_size=1)
model_path = hf_hub_download(repo_id="mlnomad/xor-single-nmn-neuron", filename="xor-single-nmn-neuron-model.pth")
model.load_state_dict(torch.load(model_path))
model.eval()

# Example prediction
input_data = torch.tensor([[1.0, 1.0]]) # Expected XOR output: 0
with torch.no_grad():
    logits = model(input_data)
    prob = torch.sigmoid(logits)
    prediction = (prob > 0.5).float().item()
    print(f"Input: [1.0, 1.0], Prediction: {prediction}") # Should correctly predict 0.0