Update autodiff notebook to TF 2.x
Aurélien Geron
parent
15b5ba5e10
commit
1451060165
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@ -192,12 +192,12 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The good news is that it is pretty easy to compute the Hessians. First let's create functions that compute the first order derivatives (also called Jacobians):"
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"The good news is that it is pretty easy to compute the Hessians. First let's create functions that compute the first order partial derivatives (also called Jacobians):"
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]
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"cell_type": "code",
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"metadata": {},
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"source": [
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"tf.reset_default_graph()\n",
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"x = tf.Variable(3.)\n",
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"y = tf.Variable(4.)\n",
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"\n",
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"x = tf.Variable(3., name=\"x\")\n",
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"y = tf.Variable(4., name=\"y\")\n",
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"with tf.GradientTape() as tape:\n",
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" f = x*x*y + y + 2\n",
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"\n",
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"jacobians = tf.gradients(f, [x, y])\n",
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"\n",
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"init = tf.global_variables_initializer()\n",
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"\n",
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"with tf.Session() as sess:\n",
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" init.run()\n",
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" f_val, jacobians_val = sess.run([f, jacobians])\n",
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"\n",
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"f_val, jacobians_val"
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"jacobians = tape.gradient(f, [x, y])\n",
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"jacobians"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Since everything is symbolic, we can compute second order derivatives, and beyond. However, when we compute the derivative of a tensor with regards to a variable that it does not depend on, instead of returning 0.0, the `gradients()` function returns None, which cannot be evaluated by `sess.run()`. So beware of `None` values. Here we just replace them with zero tensors."
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"Since everything is symbolic, we can compute second order derivatives, and beyond:"
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]
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},
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"cell_type": "code",
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"execution_count": 36,
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"execution_count": 35,
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"metadata": {},
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"outputs": [],
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"source": [
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"hessians_x = tf.gradients(jacobians[0], [x, y])\n",
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"hessians_y = tf.gradients(jacobians[1], [x, y])\n",
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"x = tf.Variable(3.)\n",
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"y = tf.Variable(4.)\n",
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"\n",
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"def replace_none_with_zero(tensors):\n",
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" return [tensor if tensor is not None else tf.constant(0.)\n",
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" for tensor in tensors]\n",
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"with tf.GradientTape(persistent=True) as tape:\n",
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" f = x*x*y + y + 2\n",
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" df_dx, df_dy = tape.gradient(f, [x, y])\n",
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"\n",
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"hessians_x = replace_none_with_zero(hessians_x)\n",
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"hessians_y = replace_none_with_zero(hessians_y)\n",
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"d2f_d2x, d2f_dydx = tape.gradient(df_dx, [x, y])\n",
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"d2f_dxdy, d2f_d2y = tape.gradient(df_dy, [x, y])\n",
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"del tape\n",
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"\n",
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"init = tf.global_variables_initializer()\n",
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"\n",
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"with tf.Session() as sess:\n",
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" init.run()\n",
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" hessians_x_val, hessians_y_val = sess.run([hessians_x, hessians_y])\n",
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"\n",
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"hessians_x_val, hessians_y_val"
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"hessians = [[d2f_d2x, d2f_dydx], [d2f_dxdy, d2f_d2y]]\n",
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"hessians"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Note that when we compute the derivative of a tensor with regards to a variable that it does not depend on, instead of returning 0.0, the `gradient()` function returns `None`."
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]
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},
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{
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"source": [
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"And that's all folks! Hope you enjoyed this notebook."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.2"
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"version": "3.7.6"
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},
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"nav_menu": {
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"height": "603px",
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