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 this includes a layer that performs a dot product of the convolution kernel with the layer's input matrix. This product is usually the Frobenius inner product, and its activation function is commonly ReLU. As the convolution kernel slides along the input matrix for the layer, the convolution operation generates a feature map, which in turn contributes to the input of the next layer. This is followed by other layers such as pooling layers, fully connected layers, and normalization layers.

The theory of syntax that we’re working within this class is called X-bar theory. X-bar theory makes the claim that every single phrase in every single sentence in the mental grammar of every single human language, has the same core organization. Here’s a tree diagram that shows us that basic organization. Let’s look at it more closely. According to x-bar theory, every phrase has a head.

\((A \times B)_{ij} = \sum_{k = 1}^{m} A_{ik}B_{kj}\)

Generation is hard

Steep learning curve

Not applicable

Not powerful enough

Nonintuitive

fig, axs = plt.subplots(1, 2, figsize=(5, 2.7), layout='constrained')
xdata = np.arange(len(data1))  # make an ordinal for this
data = 10**data1
axs[0].plot(xdata, data)

axs[1].set_yscale('log')
axs[1].plot(xdata, data);
ax.annotate('local max', xy=(2, 1), xytext=(3, 1.5),
            arrowprops=dict(facecolor='black', shrink=0.05))
data = {'a': np.arange(50),
        'c': np.random.randint(0, 50, 50),
        'd': np.random.randn(50)}
data['b'] = data['a'] + 10 * np.random.randn(50)
data['d'] = np.abs(data['d']) * 100

fig, ax = plt.subplots(figsize=(5, 2.7), layout='constrained')
ax.scatter('a', 'b', c='c', s='d', data=data)
ax.set_xlabel('entry a')
ax.set_ylabel('entry b');

Not powerful enough

Plain unsuitable

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def doThis():
  doThat()
  yield thing

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