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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. |
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| .. | ||
| models | ||
| __init__.py | ||
| _character_embed.py | ||
| _precomputable_affine.py | ||
| callbacks.py | ||
| extract_ngrams.py | ||
| extract_spans.py | ||
| featureextractor.py | ||
| parser_model.pxd | ||
| parser_model.pyx | ||
| staticvectors.py | ||
| tb_framework.py | ||