Add clarifying notes to polynomial tutorials about fit limitations

Addresses feedback that the 3rd-degree polynomial fit for sin(x) over [-π, π]
may be confusing for beginners. Added educational notes explaining that:
- The example demonstrates gradient descent mechanics, not perfect fitting
- 3rd-degree polynomials have mathematical limitations for this task
- Higher-order terms (5th, 7th degree) are needed for better accuracy
- The imperfect fit is expected and teaches model architecture selection

Author: patrocinio

beginner_source/examples_autograd/polynomial_custom_function.py

@@ -16,6 +16,16 @@
 
 In this implementation we implement our own custom autograd function to perform
 :math:`P_3'(x)`. By mathematics, :math:`P_3'(x)=\\frac{3}{2}\\left(5x^2-1\\right)`
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 import torch
 import math

beginner_source/examples_nn/polynomial_module.py

@@ -9,6 +9,16 @@
 This implementation defines the model as a custom Module subclass. Whenever you
 want a model more complex than a simple sequence of existing Modules you will
 need to define your model this way.
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 import torch
 import math

beginner_source/examples_nn/polynomial_nn.py

@@ -12,6 +12,16 @@
 this is where the nn package can help. The nn package defines a set of Modules,
 which you can think of as a neural network layer that produces output from
 input and may have some trainable weights.
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 import torch
 import math

beginner_source/examples_nn/polynomial_optim.py

@@ -12,6 +12,16 @@
 we use the optim package to define an Optimizer that will update the weights
 for us. The optim package defines many optimization algorithms that are commonly
 used for deep learning, including SGD+momentum, RMSProp, Adam, etc.
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 import torch
 import math

beginner_source/examples_tensor/polynomial_numpy.py

@@ -12,6 +12,16 @@
 A numpy array is a generic n-dimensional array; it does not know anything about
 deep learning or gradients or computational graphs, and is just a way to perform
 generic numeric computations.
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 import numpy as np
 import math

beginner_source/examples_tensor/polynomial_tensor.py

@@ -16,6 +16,16 @@
 The biggest difference between a numpy array and a PyTorch Tensor is that
 a PyTorch Tensor can run on either CPU or GPU. To run operations on the GPU,
 just cast the Tensor to a cuda datatype.
+
+.. note::
+    This example is designed to demonstrate the mechanics of gradient descent and
+    backpropagation, not to achieve a perfect fit. A third-degree polynomial has
+    fundamental limitations in approximating :math:`\sin(x)` over the range
+    :math:`[-\pi, \pi]`. The Taylor series for sine requires higher-order terms
+    (5th, 7th degree, etc.) for better accuracy. The resulting polynomial will
+    fit reasonably well near zero but will diverge from :math:`\sin(x)` as you
+    approach :math:`\pm\pi`. This is expected and illustrates the importance of
+    choosing an appropriate model architecture for your problem.
 """
 
 import torch