basic idea

import torch
import torch.nn as nn
import torch.optim as optim
# Define a custom layer for quasipolynomial synapses
class QuasiPolynomialSynapse(nn.Module):
    def __init__(self, input_size, output_size, degree=2):
        super(QuasiPolynomialSynapse, self).__init__()
        self.input_size = input_size
        self.output_size = output_size
        self.degree = degree
        self.weights = nn.Parameter(torch.randn(output_size, input_size, degree))
        self.bias = nn.Parameter(torch.randn(output_size))

    def forward(self, x):
        # Compute the quasipolynomial terms
        x_expanded = torch.stack([x ** (i + 1) for i in range(self.degree)], dim=-1)
        output = torch.einsum('bij,kij->bk', x_expanded, self.weights) + self.bias
        return output

# Define the neural network model
class QuasiPolynomialNet(nn.Module):
    def __init__(self, input_size, hidden_size, output_size):
        super(QuasiPolynomialNet, self).__init__()
        self.synapse1 = QuasiPolynomialSynapse(input_size, hidden_size)
        self.synapse2 = QuasiPolynomialSynapse(hidden_size, output_size)

    def forward(self, x):
        x = torch.relu(self.synapse1(x))
        x = self.synapse2(x)
        return x

# Sample data
x = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
y = torch.tensor([[1.0], [0.0]])

# Initialize the model, loss function and optimizer
model = QuasiPolynomialNet(input_size=3, hidden_size=5, output_size=1)
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

# Training loop
for epoch in range(10000):
    optimizer.zero_grad()
    outputs = model(x)
    loss = criterion(outputs, y)
    loss.backward()
    optimizer.step()
    if epoch % 1000 == 0:
        print(f'Epoch [{epoch}/10000], Loss: {loss.item():.4f}')

# Generating larger sample input for testing
large_test_input = torch.randn(10, 3)  # Generates a 10x3 tensor with random values

# Testing the model
with torch.no_grad():
    test_output = model(large_test_input)
    print("Large Test Input:\n", large_test_input)
    print("Test Output:\n", test_output)