Reply to Kenichi (Programming ML - chapter 3 with nx)

chapter3.livemd

Chapter 3: Walking the Gradient

Mix.install([
  {:vega_lite, "~> 0.1.6"},
  {:kino, "~> 0.8.1"},
  {:kino_vega_lite, "~> 0.1.7"},
  {:explorer, "~> 0.5.6"},
  {:kino_explorer, "~> 0.1.4"},
  {:nx, "~> 0.5"}
])

Resolving Hex dependencies...
Dependency resolution completed:
New:
  castore 1.0.3
  complex 0.5.0
  explorer 0.5.7
  kino 0.8.1
  kino_explorer 0.1.5
  kino_vega_lite 0.1.9
  nx 0.5.3
  rustler_precompiled 0.6.2
  table 0.1.2
  table_rex 3.1.1
  telemetry 1.2.1
  vega_lite 0.1.7
* Getting vega_lite (Hex package)
* Getting kino (Hex package)
* Getting kino_vega_lite (Hex package)
* Getting explorer (Hex package)
* Getting kino_explorer (Hex package)
* Getting nx (Hex package)
* Getting complex (Hex package)
* Getting telemetry (Hex package)
* Getting rustler_precompiled (Hex package)
* Getting table (Hex package)
* Getting table_rex (Hex package)
* Getting castore (Hex package)
==> table
Compiling 5 files (.ex)
Generated table app
==> vega_lite
Compiling 5 files (.ex)
Generated vega_lite app
===> Analyzing applications...
===> Compiling telemetry
==> complex
Compiling 2 files (.ex)
Generated complex app
==> nx
Compiling 31 files (.ex)
Generated nx app
==> kino
Compiling 37 files (.ex)
Generated kino app
==> kino_vega_lite
Compiling 4 files (.ex)
Generated kino_vega_lite app
==> table_rex
Compiling 7 files (.ex)
Generated table_rex app
==> castore
Compiling 1 file (.ex)
Generated castore app
==> rustler_precompiled
Compiling 4 files (.ex)
Generated rustler_precompiled app
==> explorer
Compiling 19 files (.ex)

16:05:47.989 [debug] Copying NIF from cache and extracting to /Users/nicolo.gnudi/code/personal/Library/Caches/mix/installs/elixir-1.14.2-erts-13.0.4/cef305cfa5849d5cca8a9505684ac16a/_build/dev/lib/explorer/priv/native/libexplorer-v0.5.7-nif-2.16-x86_64-apple-darwin.so
Generated explorer app
==> kino_explorer
Compiling 4 files (.ex)
Generated kino_explorer app

:ok

Read the data

data =
  __DIR__
  |> Path.join("pizza.txt")
  |> Path.expand()
  |> File.read!()
  # convert any two or more spaces into a comma
  |> String.replace(~r/[[:blank:]]{2,}/, ",")
  |> Explorer.DataFrame.load_csv!()

Linear regression with bias

☝️ From chapter 2

defmodule C2.LinearRegressionWithBias do
  @doc """
  Returns a list of predictions.
  """
  def predict([item | rest], weight, bias) do
    [predict(item, weight, bias) | predict(rest, weight, bias)]
  end

  def predict([], _weight, _bias), do: []

  # The function predicts the pizzas from the reservations.
  # To be more precise, it takes the input variable, the weight
  # and the bias, and it uses them to calculate ŷ.
  def predict(x, weight, bias), do: x * weight + bias

  @doc """
  Returns the mean squared error.
  """
  def loss(x, y, weight, bias) when is_list(x) and is_list(y) do
    predictions = predict(x, weight, bias)
    errors = Enum.zip_with([predictions, y], fn [pr, y] -> pr - y end)
    squared_error = square(errors)
    avg(squared_error)
  end

  def train(x, y, iterations, lr) when is_list(x) and is_list(y) do
    Enum.reduce(0..(iterations - 1), %{weight: 0, bias: 0}, fn i, %{weight: w, bias: b} = acc ->
      current_loss = loss(x, y, w, b)

      IO.puts("Iteration #{i} => Loss: #{current_loss}")

      cond do
        loss(x, y, w + lr, b) < current_loss -> %{acc | weight: w + lr}
        loss(x, y, w - lr, b) < current_loss -> %{acc | weight: w - lr}
        loss(x, y, w, b + lr) < current_loss -> %{acc | bias: b + lr}
        loss(x, y, w, b - lr) < current_loss -> %{acc | bias: b - lr}
        true -> acc
      end
    end)
  end

  defp square(list) when is_list(list) do
    for i <- list, do: i * i
  end

  defp avg(list) when is_list(list) do
    Enum.sum(list) / length(list)
  end
end

{:module, C2.LinearRegressionWithBias, <<70, 79, 82, 49, 0, 0, 18, ...>>, {:avg, 1}}

Plot the loss curve

# Extract "Reservations" and "Pizzas" from the dataframe
x = Explorer.Series.to_list(data["Reservations"])
y = Explorer.Series.to_list(data["Pizzas"])

[33, 16, 32, 51, 27, 16, 34, 17, 29, 15, 15, 32, 22, 37, 13, 44, 16, 21, 37, 30, 26, 34, 23, 39, 27,
 37, 17, 18, 25, 23]

alias VegaLite, as: Vl

# Generate a sequence that will be used as `weight`
# From -1 to -4, step 0.01
weights = Enum.map(-100..400, &(&1 / 100))

# Compute the loss for each weight, with bias=0
losses = Enum.map(weights, &C2.LinearRegressionWithBias.loss(x, y, &1, 0))

# Get the min loss index
min_loss_index = Enum.find_index(losses, &(&1 == Enum.min(losses)))

Vl.new(width: 600, height: 400)
|> Vl.layers([
  Vl.new()
  |> Vl.data_from_values(weight: weights, loss: losses)
  |> Vl.mark(:line)
  |> Vl.encode_field(:x, "weight", type: :quantitative)
  |> Vl.encode_field(:y, "loss", type: :quantitative),
  Vl.new()
  |> Vl.data_from_values(
    weight: [Enum.at(weights, min_loss_index)],
    min_loss: [Enum.at(losses, min_loss_index)]
  )
  |> Vl.mark(:circle, tooltip: true, size: "100", color: "red")
  |> Vl.encode_field(:x, "weight", type: :quantitative)
  |> Vl.encode_field(:y, "min_loss", type: :quantitative, title: "loss")
])

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Gradient Descent

defmodule C3.LinearRegressionWithoutBias do
  def predict([item | rest], weight, bias) do
    [predict(item, weight, bias) | predict(rest, weight, bias)]
  end

  def predict([], _weight, _bias), do: []
  def predict(x, weight, bias), do: x * weight + bias

  @doc """
  Returns the mean squared error.
  """
  def loss(x, y, weight, bias) when is_list(x) and is_list(y) do
    predictions = predict(x, weight, bias)
    errors = Enum.zip_with([predictions, y], fn [pr, y] -> pr - y end)
    squared_error = square(errors)
    avg(squared_error)
  end

  @doc """
  Returns the derivative of the loss curve
  """
  def gradient(x, y, weight) do
    predictions = predict(x, weight, 0)
    errors = Enum.zip_with([predictions, y], fn [pr, y] -> pr - y end)
    2 * avg(Enum.zip_with([x, errors], fn [x_item, error] -> x_item * error end))
  end

  def train(x, y, iterations, lr) when is_list(x) and is_list(y) do
    Enum.reduce(0..(iterations - 1), 0, fn i, weight ->
      IO.puts("Iteration #{i} => Loss: #{loss(x, y, weight, 0)}")
      weight - gradient(x, y, weight) * lr
    end)
  end

  defp square(list) when is_list(list) do
    for i <- list, do: i * i
  end

  defp avg(list) when is_list(list) do
    Enum.sum(list) / length(list)
  end
end

{:module, C3.LinearRegressionWithoutBias, <<70, 79, 82, 49, 0, 0, 18, ...>>, {:avg, 1}}

Train the system

iterations = Kino.Input.number("iterations", default: 100)

lr = Kino.Input.number("lr (learning rate)", default: 0.001)

iterations = Kino.Input.read(iterations)
lr = Kino.Input.read(lr)

weight = C3.LinearRegressionWithoutBias.train(x, y, iterations = 100, lr = 0.001)

Iteration 0 => Loss: 812.8666666666667
Iteration 1 => Loss: 304.3630879786667
Iteration 2 => Loss: 143.52657910198326
Iteration 3 => Loss: 92.6549949641037
Iteration 4 => Loss: 76.56463033997743
Iteration 5 => Loss: 71.47534841324155
Iteration 6 => Loss: 69.86564029693419
Iteration 7 => Loss: 69.35649966432483
Iteration 8 => Loss: 69.19546165926808
Iteration 9 => Loss: 69.14452634314573
Iteration 10 => Loss: 69.12841582049259
Iteration 11 => Loss: 69.12332016270709
Iteration 12 => Loss: 69.12170843794642
Iteration 13 => Loss: 69.12119865946183
Iteration 14 => Loss: 69.12103741970814
Iteration 15 => Loss: 69.12098642058018
Iteration 16 => Loss: 69.12097028987425
Iteration 17 => Loss: 69.12096518783261
Iteration 18 => Loss: 69.12096357408869
Iteration 19 => Loss: 69.12096306367155
Iteration 20 => Loss: 69.1209629022298
Iteration 21 => Loss: 69.12096285116675
Iteration 22 => Loss: 69.12096283501587
Iteration 23 => Loss: 69.12096282990741
Iteration 24 => Loss: 69.12096282829165
Iteration 25 => Loss: 69.1209628277806
Iteration 26 => Loss: 69.12096282761895
Iteration 27 => Loss: 69.12096282756781
Iteration 28 => Loss: 69.12096282755168
Iteration 29 => Loss: 69.12096282754655
Iteration 30 => Loss: 69.12096282754493
Iteration 31 => Loss: 69.12096282754443
Iteration 32 => Loss: 69.12096282754425
Iteration 33 => Loss: 69.1209628275442
Iteration 34 => Loss: 69.12096282754416
Iteration 35 => Loss: 69.12096282754418
Iteration 36 => Loss: 69.1209628275442
Iteration 37 => Loss: 69.12096282754418
Iteration 38 => Loss: 69.12096282754419
Iteration 39 => Loss: 69.12096282754418
Iteration 40 => Loss: 69.12096282754416
Iteration 41 => Loss: 69.12096282754419
Iteration 42 => Loss: 69.12096282754418
Iteration 43 => Loss: 69.12096282754418
Iteration 44 => Loss: 69.12096282754419
Iteration 45 => Loss: 69.12096282754418
Iteration 46 => Loss: 69.12096282754418
Iteration 47 => Loss: 69.12096282754416
Iteration 48 => Loss: 69.12096282754419
Iteration 49 => Loss: 69.12096282754418
Iteration 50 => Loss: 69.12096282754419
Iteration 51 => Loss: 69.12096282754419
Iteration 52 => Loss: 69.1209628275442
Iteration 53 => Loss: 69.12096282754416
Iteration 54 => Loss: 69.12096282754416
Iteration 55 => Loss: 69.12096282754419
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Iteration 99 => Loss: 69.12096282754416

1.8436928702010968

Putting Gradient Descent to the Test

defmodule C3.LinearRegressionWithBias do
  def predict([item | rest], weight, bias) do
    [predict(item, weight, bias) | predict(rest, weight, bias)]
  end

  def predict([], _weight, _bias), do: []
  def predict(x, weight, bias), do: x * weight + bias

  @doc """
  Returns the mean squared error.
  """
  def loss(x, y, weight, bias) when is_list(x) and is_list(y) do
    predictions = predict(x, weight, bias)
    errors = Enum.zip_with([predictions, y], fn [pr, y] -> pr - y end)
    squared_error = square(errors)
    avg(squared_error)
  end

  @doc """
  Returns the derivative of the loss curve
  """
  def gradient(x, y, weight, bias) do
    predictions = predict(x, weight, bias)
    errors = Enum.zip_with([predictions, y], fn [pr, y] -> pr - y end)

    w_gradient = 2 * avg(Enum.zip_with([x, errors], fn [x_item, error] -> x_item * error end))
    b_gradient = 2 * avg(errors)

    {w_gradient, b_gradient}
  end

  def train(x, y, iterations, lr) when is_list(x) and is_list(y) do
    Enum.reduce(0..(iterations - 1), %{weight: 0, bias: 0}, fn i, %{weight: weight, bias: bias} ->
      IO.puts("Iteration #{i} => Loss: #{loss(x, y, weight, bias)}")

      {w_gradient, b_gradient} = gradient(x, y, weight, bias)
      %{weight: weight - w_gradient * lr, bias: bias - b_gradient * lr}
    end)
  end

  defp square(list) when is_list(list) do
    for i <- list, do: i * i
  end

  defp avg(list) when is_list(list) do
    Enum.sum(list) / length(list)
  end
end

{:module, C3.LinearRegressionWithBias, <<70, 79, 82, 49, 0, 0, 20, ...>>, {:avg, 1}}

Train the system

iterations = Kino.Input.number("iterations", default: 20_000)

lr = Kino.Input.number("lr (learning rate)", default: 0.001)

iterations = Kino.Input.read(iterations)
lr = Kino.Input.read(lr)

%{weight: weight, bias: bias} =
  C3.LinearRegressionWithBias.train(x, y, iterations = iterations, lr = lr)

...
Iteration 19001 => Loss: 22.842736811406905
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%{bias: 13.172267656369339, weight: 1.0811301699901938}

Predict the number of pizzas

n_reservations = Kino.Input.number("number of reservations", default: 20)

n = Kino.Input.read(n_reservations)

C3.LinearRegressionWithBias.predict(n, weight, bias)

34.79487105617322

# https://gist.github.com/kenichi/d941ab3965d6a49e612f1664eccab337
defmodule C3Test do
  import Nx.Defn

  defn predict(x, w, b) do
    x
    |> Nx.multiply(w)
    |> Nx.add(b)
  end

  defn loss(x, y, w, b) do
    x
    |> predict(w, b)
    |> Nx.subtract(y)
    |> Nx.pow(2)
    |> Nx.mean()
  end

  defn weight_gradient(x, y, w, b) do
    x
    |> predict(w, b)
    |> Nx.subtract(y)
    |> Nx.multiply(x)
    |> Nx.mean()
    |> Nx.multiply(2)
  end

  defn bias_gradient(x, y, w, b) do
    x
    |> predict(w, b)
    |> Nx.subtract(y)
    |> Nx.mean()
    |> Nx.multiply(2)
  end

  def gradients(%Nx.Tensor{} = tx, %Nx.Tensor{} = ty, w, b \\ 0) do
    {
      weight_gradient(tx, ty, w, b),
      bias_gradient(tx, ty, w, b)
    }
  end

  def train(%Nx.Tensor{} = tx, %Nx.Tensor{} = ty, i, lr) do
    Enum.reduce(1..i, {0, 0}, fn iteration, {weight, bias} ->
      current_loss = loss(tx, ty, weight, bias)
      IO.puts("Iteration #{iteration} => Loss: #{Nx.to_number(current_loss)}")

      {wg, bg} = gradients(tx, ty, weight, bias)

      {
        adjust(weight, wg, lr),
        adjust(bias, bg, lr)
      }
    end)
  end

  defn adjust(value, gradient, lr) do
    gradient
    |> Nx.multiply(lr)
    |> then(&Nx.subtract(value, &1))
  end
end

{:module, C3Test, <<70, 79, 82, 49, 0, 0, 27, ...>>, true}

{weight_t, bias_t} = C3Test.train(Nx.tensor(x), Nx.tensor(y), iterations, lr)

...
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Iteration 19756 => Loss: 22.842737197875977
Iteration 19757 => Loss: 22.842737197875977
Iteration 19758 => Loss: 22.842737197875977
Iteration 19759 => Loss: 22.842737197875977
Iteration 19760 => Loss: 22.842737197875977
Iteration 19761 => Loss: 22.842737197875977
Iteration 19762 => Loss: 22.842737197875977
Iteration 19763 => Loss: 22.842737197875977
Iteration 19764 => Loss: 22.842737197875977
Iteration 19765 => Loss: 22.842737197875977
Iteration 19766 => Loss: 22.842737197875977
Iteration 19767 => Loss: 22.842737197875977
Iteration 19768 => Loss: 22.842737197875977
Iteration 19769 => Loss: 22.842737197875977
Iteration 19770 => Loss: 22.842737197875977
Iteration 19771 => Loss: 22.842737197875977
Iteration 19772 => Loss: 22.842737197875977
Iteration 19773 => Loss: 22.842737197875977
Iteration 19774 => Loss: 22.842737197875977
Iteration 19775 => Loss: 22.842737197875977
Iteration 19776 => Loss: 22.842737197875977
Iteration 19777 => Loss: 22.842737197875977
Iteration 19778 => Loss: 22.842737197875977
Iteration 19779 => Loss: 22.842737197875977
Iteration 19780 => Loss: 22.842737197875977
Iteration 19781 => Loss: 22.842737197875977
Iteration 19782 => Loss: 22.842737197875977
Iteration 19783 => Loss: 22.842737197875977
Iteration 19784 => Loss: 22.842737197875977
Iteration 19785 => Loss: 22.842737197875977
Iteration 19786 => Loss: 22.842737197875977
Iteration 19787 => Loss: 22.842737197875977
Iteration 19788 => Loss: 22.842737197875977
Iteration 19789 => Loss: 22.842737197875977
Iteration 19790 => Loss: 22.842737197875977
Iteration 19791 => Loss: 22.842737197875977
Iteration 19792 => Loss: 22.842737197875977
Iteration 19793 => Loss: 22.842737197875977
Iteration 19794 => Loss: 22.842737197875977
Iteration 19795 => Loss: 22.842737197875977
Iteration 19796 => Loss: 22.842737197875977
Iteration 19797 => Loss: 22.842737197875977
Iteration 19798 => Loss: 22.842737197875977
Iteration 19799 => Loss: 22.842737197875977
Iteration 19800 => Loss: 22.842737197875977
Iteration 19801 => Loss: 22.842737197875977
Iteration 19802 => Loss: 22.842737197875977
Iteration 19803 => Loss: 22.842737197875977
Iteration 19804 => Loss: 22.842737197875977
Iteration 19805 => Loss: 22.842737197875977
Iteration 19806 => Loss: 22.842737197875977
Iteration 19807 => Loss: 22.842737197875977
Iteration 19808 => Loss: 22.842737197875977
Iteration 19809 => Loss: 22.842737197875977
Iteration 19810 => Loss: 22.842737197875977
Iteration 19811 => Loss: 22.842737197875977
Iteration 19812 => Loss: 22.842737197875977
Iteration 19813 => Loss: 22.842737197875977
Iteration 19814 => Loss: 22.842737197875977
Iteration 19815 => Loss: 22.842737197875977
Iteration 19816 => Loss: 22.842737197875977
Iteration 19817 => Loss: 22.842737197875977
Iteration 19818 => Loss: 22.842737197875977
Iteration 19819 => Loss: 22.842737197875977
Iteration 19820 => Loss: 22.842737197875977
Iteration 19821 => Loss: 22.842737197875977
Iteration 19822 => Loss: 22.842737197875977
Iteration 19823 => Loss: 22.842737197875977
Iteration 19824 => Loss: 22.842737197875977
Iteration 19825 => Loss: 22.842737197875977
Iteration 19826 => Loss: 22.842737197875977
Iteration 19827 => Loss: 22.842737197875977
Iteration 19828 => Loss: 22.842737197875977
Iteration 19829 => Loss: 22.842737197875977
Iteration 19830 => Loss: 22.842737197875977
Iteration 19831 => Loss: 22.842737197875977
Iteration 19832 => Loss: 22.842737197875977
Iteration 19833 => Loss: 22.842737197875977
Iteration 19834 => Loss: 22.842737197875977
Iteration 19835 => Loss: 22.842737197875977
Iteration 19836 => Loss: 22.842737197875977
Iteration 19837 => Loss: 22.842737197875977
Iteration 19838 => Loss: 22.842737197875977
Iteration 19839 => Loss: 22.842737197875977
Iteration 19840 => Loss: 22.842737197875977
Iteration 19841 => Loss: 22.842737197875977
Iteration 19842 => Loss: 22.842737197875977
Iteration 19843 => Loss: 22.842737197875977
Iteration 19844 => Loss: 22.842737197875977
Iteration 19845 => Loss: 22.842737197875977
Iteration 19846 => Loss: 22.842737197875977
Iteration 19847 => Loss: 22.842737197875977
Iteration 19848 => Loss: 22.842737197875977
Iteration 19849 => Loss: 22.842737197875977
Iteration 19850 => Loss: 22.842737197875977
Iteration 19851 => Loss: 22.842737197875977
Iteration 19852 => Loss: 22.842737197875977
Iteration 19853 => Loss: 22.842737197875977
Iteration 19854 => Loss: 22.842737197875977
Iteration 19855 => Loss: 22.842737197875977
Iteration 19856 => Loss: 22.842737197875977
Iteration 19857 => Loss: 22.842737197875977
Iteration 19858 => Loss: 22.842737197875977
Iteration 19859 => Loss: 22.842737197875977
Iteration 19860 => Loss: 22.842737197875977
Iteration 19861 => Loss: 22.842737197875977
Iteration 19862 => Loss: 22.842737197875977
Iteration 19863 => Loss: 22.842737197875977
Iteration 19864 => Loss: 22.842737197875977
Iteration 19865 => Loss: 22.842737197875977
Iteration 19866 => Loss: 22.842737197875977
Iteration 19867 => Loss: 22.842737197875977
Iteration 19868 => Loss: 22.842737197875977
Iteration 19869 => Loss: 22.842737197875977
Iteration 19870 => Loss: 22.842737197875977
Iteration 19871 => Loss: 22.842737197875977
Iteration 19872 => Loss: 22.842737197875977
Iteration 19873 => Loss: 22.842737197875977
Iteration 19874 => Loss: 22.842737197875977
Iteration 19875 => Loss: 22.842737197875977
Iteration 19876 => Loss: 22.842737197875977
Iteration 19877 => Loss: 22.842737197875977
Iteration 19878 => Loss: 22.842737197875977
Iteration 19879 => Loss: 22.842737197875977
Iteration 19880 => Loss: 22.842737197875977
Iteration 19881 => Loss: 22.842737197875977
Iteration 19882 => Loss: 22.842737197875977
Iteration 19883 => Loss: 22.842737197875977
Iteration 19884 => Loss: 22.842737197875977
Iteration 19885 => Loss: 22.842737197875977
Iteration 19886 => Loss: 22.842737197875977
Iteration 19887 => Loss: 22.842737197875977
Iteration 19888 => Loss: 22.842737197875977
Iteration 19889 => Loss: 22.842737197875977
Iteration 19890 => Loss: 22.842737197875977
Iteration 19891 => Loss: 22.842737197875977
Iteration 19892 => Loss: 22.842737197875977
Iteration 19893 => Loss: 22.842737197875977
Iteration 19894 => Loss: 22.842737197875977
Iteration 19895 => Loss: 22.842737197875977
Iteration 19896 => Loss: 22.842737197875977
Iteration 19897 => Loss: 22.842737197875977
Iteration 19898 => Loss: 22.842737197875977
Iteration 19899 => Loss: 22.842737197875977
Iteration 19900 => Loss: 22.842737197875977
Iteration 19901 => Loss: 22.842737197875977
Iteration 19902 => Loss: 22.842737197875977
Iteration 19903 => Loss: 22.842737197875977
Iteration 19904 => Loss: 22.842737197875977
Iteration 19905 => Loss: 22.842737197875977
Iteration 19906 => Loss: 22.842737197875977
Iteration 19907 => Loss: 22.842737197875977
Iteration 19908 => Loss: 22.842737197875977
Iteration 19909 => Loss: 22.842737197875977
Iteration 19910 => Loss: 22.842737197875977
Iteration 19911 => Loss: 22.842737197875977
Iteration 19912 => Loss: 22.842737197875977
Iteration 19913 => Loss: 22.842737197875977
Iteration 19914 => Loss: 22.842737197875977
Iteration 19915 => Loss: 22.842737197875977
Iteration 19916 => Loss: 22.842737197875977
Iteration 19917 => Loss: 22.842737197875977
Iteration 19918 => Loss: 22.842737197875977
Iteration 19919 => Loss: 22.842737197875977
Iteration 19920 => Loss: 22.842737197875977
Iteration 19921 => Loss: 22.842737197875977
Iteration 19922 => Loss: 22.842737197875977
Iteration 19923 => Loss: 22.842737197875977
Iteration 19924 => Loss: 22.842737197875977
Iteration 19925 => Loss: 22.842737197875977
Iteration 19926 => Loss: 22.842737197875977
Iteration 19927 => Loss: 22.842737197875977
Iteration 19928 => Loss: 22.842737197875977
Iteration 19929 => Loss: 22.842737197875977
Iteration 19930 => Loss: 22.842737197875977
Iteration 19931 => Loss: 22.842737197875977
Iteration 19932 => Loss: 22.842737197875977
Iteration 19933 => Loss: 22.842737197875977
Iteration 19934 => Loss: 22.842737197875977
Iteration 19935 => Loss: 22.842737197875977
Iteration 19936 => Loss: 22.842737197875977
Iteration 19937 => Loss: 22.842737197875977
Iteration 19938 => Loss: 22.842737197875977
Iteration 19939 => Loss: 22.842737197875977
Iteration 19940 => Loss: 22.842737197875977
Iteration 19941 => Loss: 22.842737197875977
Iteration 19942 => Loss: 22.842737197875977
Iteration 19943 => Loss: 22.842737197875977
Iteration 19944 => Loss: 22.842737197875977
Iteration 19945 => Loss: 22.842737197875977
Iteration 19946 => Loss: 22.842737197875977
Iteration 19947 => Loss: 22.842737197875977
Iteration 19948 => Loss: 22.842737197875977
Iteration 19949 => Loss: 22.842737197875977
Iteration 19950 => Loss: 22.842737197875977
Iteration 19951 => Loss: 22.842737197875977
Iteration 19952 => Loss: 22.842737197875977
Iteration 19953 => Loss: 22.842737197875977
Iteration 19954 => Loss: 22.842737197875977
Iteration 19955 => Loss: 22.842737197875977
Iteration 19956 => Loss: 22.842737197875977
Iteration 19957 => Loss: 22.842737197875977
Iteration 19958 => Loss: 22.842737197875977
Iteration 19959 => Loss: 22.842737197875977
Iteration 19960 => Loss: 22.842737197875977
Iteration 19961 => Loss: 22.842737197875977
Iteration 19962 => Loss: 22.842737197875977
Iteration 19963 => Loss: 22.842737197875977
Iteration 19964 => Loss: 22.842737197875977
Iteration 19965 => Loss: 22.842737197875977
Iteration 19966 => Loss: 22.842737197875977
Iteration 19967 => Loss: 22.842737197875977
Iteration 19968 => Loss: 22.842737197875977
Iteration 19969 => Loss: 22.842737197875977
Iteration 19970 => Loss: 22.842737197875977
Iteration 19971 => Loss: 22.842737197875977
Iteration 19972 => Loss: 22.842737197875977
Iteration 19973 => Loss: 22.842737197875977
Iteration 19974 => Loss: 22.842737197875977
Iteration 19975 => Loss: 22.842737197875977
Iteration 19976 => Loss: 22.842737197875977
Iteration 19977 => Loss: 22.842737197875977
Iteration 19978 => Loss: 22.842737197875977
Iteration 19979 => Loss: 22.842737197875977
Iteration 19980 => Loss: 22.842737197875977
Iteration 19981 => Loss: 22.842737197875977
Iteration 19982 => Loss: 22.842737197875977
Iteration 19983 => Loss: 22.842737197875977
Iteration 19984 => Loss: 22.842737197875977
Iteration 19985 => Loss: 22.842737197875977
Iteration 19986 => Loss: 22.842737197875977
Iteration 19987 => Loss: 22.842737197875977
Iteration 19988 => Loss: 22.842737197875977
Iteration 19989 => Loss: 22.842737197875977
Iteration 19990 => Loss: 22.842737197875977
Iteration 19991 => Loss: 22.842737197875977
Iteration 19992 => Loss: 22.842737197875977
Iteration 19993 => Loss: 22.842737197875977
Iteration 19994 => Loss: 22.842737197875977
Iteration 19995 => Loss: 22.842737197875977
Iteration 19996 => Loss: 22.842737197875977
Iteration 19997 => Loss: 22.842737197875977
Iteration 19998 => Loss: 22.842737197875977
Iteration 19999 => Loss: 22.842737197875977
Iteration 20000 => Loss: 22.842737197875977

{#Nx.Tensor<
   f32
   1.081164002418518
 >,
 #Nx.Tensor<
   f32
   13.171684265136719
 >}

C3Test.predict(n, weight_t, bias_t)

#Nx.Tensor<
  f32
  34.79496383666992
>