Similarly, for any matrix X, we have ∇X‖X‖F2=2X.

labels.csv contains the labels for the training images

valid_ds

it likely leads to larger values in the Gram matrix

the image printing function requires that each pixel has a floating point value from 0 to 1

In practice, we can remove predicted bounding boxes with lower confidence even before performing non-maximum suppression, thereby reducing computation in this algorithm. We may also post-process the output of non-maximum suppression, for example, by only keeping results with higher confidence in the final output.

add an dimension

The best way to do this is by first using tesseract to get OCR text in whatever languages you might feel are in there, using langdetect to find what languages are included in the OCR text and then run OCR again with the languages found.

For comparison, we define an identical model, but initialize all of its model parameters to random values.

As is observed in the above results, after an nn.Sequential instance is scripted using the torch.jit.script function, computing performance is improved through the use of symbolic programming.

In the context of computer vision this schedule can lead to improved results.

The photorealistic text-to-image examples in Fig. 11.9.5 suggest that the T5 encoder alone may effectively represent text even without fine-tuning.

advanced

Without need for manual labeling, large-scale text data from books and Wikipedia can be used for pretraining BERT.

Since we use the fixed positional encoding whose values are always between −1 and 1,

position

To compute multiple heads of multi-head attention in parallel, proper tensor manipulation is needed.

Note that h heads can be computed in parallel if we set the number of outputs of linear transformations for the query, key, and value to pqh=pkh=pvh=po.

In the case of a (scalar) regression with observations (xi,yi) for features and labels respectively, vi=yi are scalars, ki=xi are vectors, and the query q denotes the new location where f should be evaluated.

the conditional probability of each token at time step 3 has also changed in Fig. 10.8.2

Using word-level tokenization, the vocabulary size will be significantly larger than that using character-level tokenization, but the sequence lengths will be much shorter.

flavor

we can easily get a deep-gated RNN by replacing the hidden state computation in (10.3.1) with that from an LSTM or a GRU.

Reset gates help capture short-term dependencies in sequences. Update gates help capture long-term dependencies in sequences.

Note that only the hidden state is passed to the output layer.

For instance, if the first token is of great importance we will learn not to update the hidden state after the first observation.

neuron

multiplicative nodes

detaching the gradient

Using the chain rule yields

Whenever ξt=0 the recurrent computation terminates at that time step t.

While we can use the chain rule to compute ∂ht/∂wh recursively, this chain can get very long whenever t is large. Let’s discuss a number of strategies for dealing with this problem.

where computation of ht−1 also depends on wh

Input from the first step passes through over 1000 matrix products before arriving at the output, and another 1000 matrix products are required to compute the gradient.

side-effect of limiting the influence

At other times, training eventually converges but is unstable owing to massive spikes in the loss.

Having a small value for this upper bound might be viewed as good or bad. On the downside, we are limiting the speed at which we can reduce the value of the objective. On the bright side, this limits by just how much we can go wrong in any one gradient step.

exponentially

There will be many plausible three-word combinations that we likely will not see in our dataset.

formulae

After all, we will significantly overestimate the frequency of the tail, also known as the infrequent words.

frequency

Even today’s massive RNN- and Transformer-based language models seldom incorporate more than thousands of words of context.

probabilistic classifier

compare

part of speech tagging

motivating

the expressive power of the network

stable

thus batch normalization layers function differently in training mode (normalizing by minibatch statistics) than in prediction mode (normalizing by dataset statistics).

priors

scaling issue

cannot

recover this degree of freedom

.

reduce

They are no longer necessary

features

add fully connected layers earlier in the network to increase the degree of nonlinearity

and occasionally on the serendipitous discoveries by lucky graduate students

given the increase in computation and data

separately

Pixel utilization for convolutions of size 1×1, 2×2, and 3×3 respectively.

on

desiderata

recognize a pig were

Because these networks are invariant to the order of the features, we could get similar results regardless of whether we preserve an order corresponding to the spatial structure of the pixels or if we permute the columns of our design matrix before fitting the MLP’s parameters.

irrespective of the spatial relation between pixels

Note that in this case, only the first layer requires lazy initialization, but the framework initializes sequentially. Once all parameter shapes are known, the framework can finally initialize the parameters.

including parameter initialization and backpropagation

are thereafter constant. This weight is not a model parameter and thus it is never updated by backpropagation

it will properly initialize each module’s parameters

daisy-chain

convolutional neural networks

subclass

logits

Finally a module must possess a backpropagation method, for purposes of calculating gradients. Fortunately, due to some behind-the-scenes magic supplied by the auto differentiation (introduced in Section 2.5) when defining our own module, we only need to worry about parameters and the forward propagation method.

Note that some modules do not require any parameters at all.

repeating patterns

recursively

recognition and detection

tunable parameters

softmax regression,

these techniques

I/O constrained

ordering

translation

the number of occurrences

Describe the relationships between algorithms, data, and computation.

bring you up to