📝 Fix formula for receptive field in docs (#12918)

SpaCy's HashEmbedCNN layer performs convolutions over tokens to produce
contextualized embeddings using a `MaxoutWindowEncoder` layer. These
convolutions are implemented using Thinc's `expand_window` layer, which
concatenates `window_size` neighboring sequence items on either side of
the sequence item being processed. This is repeated across `depth`
convolutional layers.

For example, consider the sequence "ABCDE" and a `MaxoutWindowEncoder`
layer with a context window of 1 and a depth of 2. We'll focus on the
token "C". We can visually represent the contextual embedding produced
for "C" as:
```mermaid
flowchart LR
A0(A<sub>0</sub>)
B0(B<sub>0</sub>)
C0(C<sub>0</sub>)
D0(D<sub>0</sub>)
E0(E<sub>0</sub>)
B1(B<sub>1</sub>)
C1(C<sub>1</sub>)
D1(D<sub>1</sub>)
C2(C<sub>2</sub>)
A0 --> B1
B0 --> B1
C0 --> B1
B0 --> C1
C0 --> C1
D0 --> C1
C0 --> D1
D0 --> D1
E0 --> D1
B1 --> C2
C1 --> C2
D1 --> C2
```

Described in words, this graph shows that before the first layer of the
convolution, the "receptive field" centered at each token consists only
of that same token. That is to say, that we have a receptive field of 1.
The first layer of the convolution adds one neighboring token on either
side to the receptive field. Since this is done on both sides, the
receptive field increases by 2, giving the first layer a receptive field
of 3. The second layer of the convolutions adds an _additional_
neighboring token on either side to the receptive field, giving a final
receptive field of 5.

However, this doesn't match the formula currently given in the docs,
which read:
> The receptive field of the CNN will be
> `depth * (window_size * 2 + 1)`, so a 4-layer network with a window
> size of `2` will be sensitive to 20 words at a time.

Substituting in our depth of 2 and window size of 1, this formula gives
us a receptive field of:
```
depth * (window_size * 2 + 1)
= 2 * (1 * 2 + 1)
= 2 * (2 + 1)
= 2 * 3
= 6
```

This not only doesn't match our computations from above, it's also an
even number! This is suspicious, since the receptive field is supposed
to be centered on a token, and not between tokens. Generally, this
formula results in an even number for any even value of `depth`.

The error in this formula is that the adjustment for the center token
is multiplied by the depth, when it should occur only once. The
corrected formula, `depth * window_size * 2 + 1`, gives the correct
value for our small example from above:
```
depth * window_size * 2 + 1
= 2 * 1 * 2 + 1
= 4 + 1
= 5
```

These changes update the docs to correct the receptive field formula and
the example receptive field size.
This commit is contained in:
Connor Brinton 2023-08-21 04:52:32 -04:00 committed by GitHub
parent 76a9f9c6c6
commit 6dd56868de
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2 changed files with 3 additions and 3 deletions

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@ -67,8 +67,8 @@ def build_hash_embed_cnn_tok2vec(
are between 2 and 8.
window_size (int): The number of tokens on either side to concatenate during
the convolutions. The receptive field of the CNN will be
depth * (window_size * 2 + 1), so a 4-layer network with window_size of
2 will be sensitive to 20 words at a time. Recommended value is 1.
depth * window_size * 2 + 1, so a 4-layer network with window_size of
2 will be sensitive to 17 words at a time. Recommended value is 1.
embed_size (int): The number of rows in the hash embedding tables. This can
be surprisingly small, due to the use of the hash embeddings. Recommended
values are between 2000 and 10000.

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@ -83,7 +83,7 @@ consisting of a CNN and a layer-normalized maxout activation function.
| `width` | The width of the input and output. These are required to be the same, so that residual connections can be used. Recommended values are `96`, `128` or `300`. ~~int~~ |
| `depth` | The number of convolutional layers to use. Recommended values are between `2` and `8`. ~~int~~ |
| `embed_size` | The number of rows in the hash embedding tables. This can be surprisingly small, due to the use of the hash embeddings. Recommended values are between `2000` and `10000`. ~~int~~ |
| `window_size` | The number of tokens on either side to concatenate during the convolutions. The receptive field of the CNN will be `depth * (window_size * 2 + 1)`, so a 4-layer network with a window size of `2` will be sensitive to 20 words at a time. Recommended value is `1`. ~~int~~ |
| `window_size` | The number of tokens on either side to concatenate during the convolutions. The receptive field of the CNN will be `depth * window_size * 2 + 1`, so a 4-layer network with a window size of `2` will be sensitive to 17 words at a time. Recommended value is `1`. ~~int~~ |
| `maxout_pieces` | The number of pieces to use in the maxout non-linearity. If `1`, the [`Mish`](https://thinc.ai/docs/api-layers#mish) non-linearity is used instead. Recommended values are `1`-`3`. ~~int~~ |
| `subword_features` | Whether to also embed subword features, specifically the prefix, suffix and word shape. This is recommended for alphabetic languages like English, but not if single-character tokens are used for a language such as Chinese. ~~bool~~ |
| `pretrained_vectors` | Whether to also use static vectors. ~~bool~~ |