better example model for Chain

docs/concepts/chain.md

@@ -9,35 +9,54 @@ When we say models are implemented in a declarative way in Refiners, what this m
 
 ## A first example
 
-To give you an idea of how it looks, let us take an example similar to the one from the PyTorch paper[^1]:
+To give you an idea of how it looks, let us take a simple convolution network to classify MNIST as an example. First, let us define a few variables.
+
+```py
+img_res = 28
+channels = 128
+kernel_size = 3
+hidden_layer_in = (((img_res - kernel_size + 1) // 2) ** 2) * channels
+hidden_layer_out = 200
+output_size = 10
+```
+
+Now, here is the model in PyTorch:
+
 
 ```py
 class BasicModel(nn.Module):
     def __init__(self):
         super().__init__()
-        self.conv = nn.Conv2d(1, 128, 3)
-        self.linear_1 = nn.Linear(128, 40)
-        self.linear_2 = nn.Linear(40, 10)
+        self.conv = nn.Conv2d(1, channels, kernel_size)
+        self.linear_1 = nn.Linear(hidden_layer_in, hidden_layer_out)
+        self.maxpool = nn.MaxPool2d(2)
+        self.linear_2 = nn.Linear(hidden_layer_out, output_size)
 
     def forward(self, x):
-        t1 = self.conv(x)
-        t2 = nn.functional.relu(t1)
-        t3 = self.linear_1(t2)
-        t4 = self.linear_2(t3)
-        return nn.functional.softmax(t4)
+        x = self.conv(x)
+        x = nn.functional.relu(x)
+        x = self.maxpool(x)
+        x = x.flatten(start_dim=1)
+        x = self.linear_1(x)
+        x = nn.functional.relu(x)
+        x = self.linear_2(x)
+        return nn.functional.softmax(x, dim=0)
 ```
 
-Here is how we could implement the same model in Refiners:
+And here is how we could implement the same model in Refiners:
 
 ```py
 class BasicModel(fl.Chain):
     def __init__(self):
         super().__init__(
-            fl.Conv2d(1, 128, 3),
+            fl.Conv2d(1, channels, kernel_size),
             fl.ReLU(),
-            fl.Linear(128, 40),
-            fl.Linear(40, 10),
-            fl.Lambda(torch.nn.functional.softmax),
+            fl.MaxPool2d(2),
+            fl.Flatten(start_dim=1),
+            fl.Linear(hidden_layer_in, hidden_layer_out),
+            fl.ReLU(),
+            fl.Linear(hidden_layer_out, output_size),
+            fl.Lambda(lambda x: torch.nn.functional.softmax(x, dim=0)),
         )
 ```
 
@@ -49,7 +68,7 @@ As of writing, Refiners does not include a `Softmax` layer by default, but as yo
 ```py
 class Softmax(fl.Module):
     def forward(self, x: torch.Tensor) -> torch.Tensor:
-        return torch.nn.functional.softmax(x)
+        return torch.nn.functional.softmax(x, dim=0)
 ```
 
 !!! note
@@ -64,9 +83,12 @@ Let us instantiate the `BasicModel` we just defined and inspect its representati
 >>> m
 (CHAIN) BasicModel()
     ├── Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
-    ├── ReLU()
-    ├── Linear(in_features=128, out_features=40, device=cpu, dtype=float32) #1
-    ├── Linear(in_features=40, out_features=10, device=cpu, dtype=float32) #2
+    ├── ReLU() #1
+    ├── MaxPool2d(kernel_size=2, stride=2)
+    ├── Flatten(start_dim=1)
+    ├── Linear(in_features=21632, out_features=200, device=cpu, dtype=float32) #1
+    ├── ReLU() #2
+    ├── Linear(in_features=200, out_features=10, device=cpu, dtype=float32) #2
     └── Softmax()
 ```
 
@@ -78,17 +100,28 @@ The children of a `Chain` are stored in a dictionary and can be accessed by name
 Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
 >>> m.Conv2d
 Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
->>> m[3]
-Linear(in_features=40, out_features=10, device=cpu, dtype=float32)
+>>> m[6]
+Linear(in_features=200, out_features=10, device=cpu, dtype=float32)
 >>> m.Linear_2
-Linear(in_features=40, out_features=10, device=cpu, dtype=float32)
+Linear(in_features=200, out_features=10, device=cpu, dtype=float32)
 ```
 
-The Chain class includes several helpers to manipulate the tree. For instance, imagine I want to wrap the two `Linear`s in a subchain. Here is how I could do it:
+The Chain class includes several helpers to manipulate the tree. For instance, imagine I want to organize my model by wrapping each layer of the convnet in a subchain. Here is how I could do it:
 
 
 ```py
-m.insert_after_type(fl.ReLU, fl.Chain(m.pop(2), m.pop(2)))
+class ConvLayer(fl.Chain):
+    pass
+
+class HiddenLayer(fl.Chain):
+    pass
+
+class OutputLayer(fl.Chain):
+    pass
+
+m.insert(0, ConvLayer(m.pop(0), m.pop(0), m.pop(0)))
+m.insert_after_type(ConvLayer, HiddenLayer(m.pop(1), m.pop(1), m.pop(1)))
+m.append(OutputLayer(m.pop(2), m.pop(2)))
 ```
 
 Did it work? Let's see:
@@ -96,14 +129,22 @@ Did it work? Let's see:
 ```
 >>> m
 (CHAIN) BasicModel()
-    ├── Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
-    ├── ReLU()
-    ├── (CHAIN)
-    │   ├── Linear(in_features=128, out_features=40, device=cpu, dtype=float32) #1
-    │   └── Linear(in_features=40, out_features=10, device=cpu, dtype=float32) #2
+    ├── (CHAIN) ConvLayer()
+    │   ├── Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
+    │   ├── ReLU()
+    │   └── MaxPool2d(kernel_size=2, stride=2)
+    ├── (CHAIN) HiddenLayer()
+    │   ├── Flatten(start_dim=1)
+    │   ├── Linear(in_features=21632, out_features=200, device=cpu, dtype=float32)
+    │   └── ReLU()
+    └── (CHAIN) OutputLayer()
+        ├── Linear(in_features=200, out_features=10, device=cpu, dtype=float32)
         └── Softmax()
 ```
 
+!!! note
+    Organizing models like this is actually a good idea, it makes them easier to understand and adapt.
+
 ## Accessing and iterating
 
 There are also many ways to access or iterate nodes even if they are deep in the tree. Most of them are implemented using a powerful iterator named [`walk`][refiners.fluxion.layers.Chain.walk]. However, most of the time, you can use simpler helpers. For instance, to iterate all the modules in the tree that hold weights (the `Conv2d` and the `Linear`s), we can just do:
@@ -117,8 +158,6 @@ It prints:
 
 ```
 Conv2d(in_channels=1, out_channels=128, kernel_size=(3, 3), device=cpu, dtype=float32)
-Linear(in_features=128, out_features=40, device=cpu, dtype=float32)
-Linear(in_features=40, out_features=10, device=cpu, dtype=float32
+Linear(in_features=21632, out_features=200, device=cpu, dtype=float32)
+Linear(in_features=200, out_features=10, device=cpu, dtype=float32)
 ```
-
-[^1]: Paszke et al., 2019. PyTorch: An Imperative Style, High-Performance Deep Learning Library.