How Do Neurons Work?

 from functools import partial
 from pathlib import Path
 from typing import List

from graphviz import Digraph
import holoviews
import hvplot.pandas
import numpy
import pandas
import torch

from graeae import EmbedHoloviews

Embed = partial(
    EmbedHoloviews,
    folder_path=PATH)

holoviews.opts(width=1000, height=800)

Numbers = List[float]

 def one_neuron(toes: float, weight: float=0.1) -> float:
     """This is a model to predict whether a team will win

     Args:
      toes: Average number of toes on the team
      weight: how much to weight to give to the toes

     Returns:
      prediction: our guess as to the probability that they will win
     """
     return toes * weight

 average_toes = [8.5, 9, 9.5, 10]
 predictions = [one_neuron(toe) for toe in average_toes]
 print("| Toes | Probability of Winning (%)|")
 print("|-+-|")
 for index, toes in enumerate(average_toes):
     prediction = predictions[index] * 100
     print(f"| {toes} | {prediction:.0f} % |")

 data = pandas.DataFrame({"Average Toes": average_toes,
                          "Probability of Winning": predictions})
 plot = data.hvplot(x="Average Toes", y="Probability of Winning").opts(
     width=1000, height=800, title="Toe Model")
 Embed(plot=plot, file_name="toes_only_predictions")()

 def weighted_sum(inputs: Numbers, weights: Numbers) -> float:
     """calculates the sum of the products

     Args:
      inputs: list of input data
      weights: list of weights for the inputs

     Returns:
      sum: the sum of the product of the weights and inputs
     """
     assert len(inputs) == len(weights)
     return sum((inputs[item] * weights[item] for item in range(len(inputs))))

 def network(inputs: Numbers, weights:Numbers) -> float:
     """Makes a prediction based on the inputs and weights"""
     return weighted_sum(inputs, weights)

 toes = [8.5, 9.5, 9.9, 9.0]
 record = [0.65, 0.8, 0.8, 0.9]
 fans = [1.2, 1.3, 0.5, 1.0]

 weights = [0.1, 0.2, 0.0]

print("|Game|Prediction|")
print("|-+-|")

predictions = [
    network([toes[game], record[game], fans[game]], weights)
               for game in range(len(toes))]
assert abs(predictions[0] - 0.98) < 0.1**5

for game, prediction in enumerate(predictions):
    print(f"|{game + 1}|{prediction:.2f}")

 data = pandas.DataFrame({"toes": toes, "record": record,
                          "prediction": predictions})
 data = data.sort_values(by="toes")
 prediction_plot = data.hvplot(x="toes", y="prediction")
 other = data.hvplot(x="toes", y="record")
 plot = (prediction_plot * other).opts(
     title="Toes vs Record & Prediction",
     width=1000,
     height=800,
 )

 Embed(plot=plot, file_name="toes_vs_record")()

print("|Game|Prediction|")
print("|-+-|")

device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
inputs = torch.tensor([toes, record, fans], device=device)
weights_vector = torch.tensor(weights, device=device)
predictions = inputs.T.matmul(weights_vector).tolist()
for game, prediction in enumerate(predictions):
    print(f"|{game + 1}|{prediction:.2f}|")