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Our generative prediction model will follow the same framework outlined in Graves’ paper where he demonstrated both generative text, and generative handwriting. Karpathy’s and char-rnn Show Shine Womens Cute Bows High Heel Platform Snow Boots Black ttkL0Y
has some fantastic examples on how this framework is used to generate data that is represented as text.

Generative Sequence Model Framework

In the text-generation example, assuming we have a model that has been pre-trained already, we feed in an initial random character into the model that with an initially empty state. The model will use the state’s information along with the current input, to generate a probability distribution for the next character. That distribution will be sampled randomly (possibly we distort the sampling process by applying temperature ), to obtain a prediction for the next character. The sampled character will be placed back as the next input, as well as the current internal state of the model.

A simple model that fits this framework is the basic N-GRAM character modelling method. In N-GRAM, all we do is keep a record of frequencies of the previous N characters and use the historical table of frequencies as the probability distribution we can draw to generate the next character.

This framework can also be represented by a recurrent neural network, where the states are the hidden states of recurrent LSTM nodes, and the output values of the network can be converted into a discrete probability distribution via applying softmax layer to the outputs. To train the weights of the neural network, we need a way to compare the predicted distribution, to the actual distribution of the training data. What is usually done is that cross-entropy loss function is usually applied, to compare the model’s predicted probabilities after the softmax layer, with the actual data of the entire sequence generated.

This has been done in Graves’ sequence generation paper and implemented as char-rnn by Karpathy. char-rnn has been used successfully to generate not only Shakespeare’s text, but also bizarre examples such as Linux source code, LaTeX documents, wikipedia formatted xml articles, and music scores.

I wanted to create a char-rnn like tool, but for learning to draw sketches, rather than learning to generate character sequences. SVG data is readily available on the web, although obviously not as easy to obtain as text data. In the end, I created a tool called sketch-rnn that would attempt to learn some structure from a large collection of related .svg files, and be able to generate and dream up new vectorised drawings that is similar to the training set. Just as how char-rnn can take Donald Trump quotes to generate hypothetical Donald Trump wisdom , I wanted to be able to feed in a large collection of .svg pictures of cats and have an algorithm come up with new vectorised pictures of cats. It was difficult to obtain .svg pictures of cats in sufficient quantities, while it was quite easy to obtain .svg files for Chinese characters, so in the end this turned into an experiment to generate fake Kanji.

In analyzing these embellishments, we will consider the predictive-, tension-, and outcome-related responses arising at each moment as the embellishment is approached and resolved. Due to the complexity involved, we will not consider imaginative responses. [7] In addition, we will need to analyze separate the what and the when dimensions of expectation.

By way of example, consider the anticipation illustrated in Figure 30. Here the anticipation occurs as part of an authentic V-I cadence with the final tonic pitch anticipated. The numbers identify three moments that we will analyze separately. The moments can be designated the (1) pre-anticipation, (2) anticipation, and (3) post-anticipation moments.

(1) Consider first the pre-anticipation moment.

Figure 30a

Outcome response : With an already established key context, the listener hears a dominant chord. The chord itself is the "outcome" of preceding expectations. As an outcome, we need to consider its response valence. Since the chord is a simple major sonority, it exhibits a low degree of sensory dissonance and so will tend to evoke a relatively positive valence.

Tension response : At the same time, musicians would note that the dominant function would normally be considered "dissonant" insofar as it needs resolution. This way of speaking can be re-interpreted in terms of the tension response . We would note that the V chord has a low probability of being followed by silence (i.e., it is unsuitable for closure). Experienced listeners will have a strong expectation that some further sounds will occur. Moreover, the V chord has a high probability of being followed by a I chord and the supertonic has a similarly high probability of leading to the tonic. In short, the listener has a relatively good idea of what to expect next; there is little of the stress that comes with uncertainty. Consequently, the tension response has only a very small negative valence.

There is one aspect to the tension response, however, in which there is relatively higher uncertainty. This has to do with when a tonic chord might appear. Since the dominant chord occurs on the downbeat, one possible moment of occurrence would be the downbeat of the next measure. Another possibility, might be the third beat of the current measure.

(2) Consider now the moment when the anticipation note appears (C eighth-note).

Figure 30b

Outcome response : The first thing to note is that the sonority is now more dissonant. That is, the outcome response has a comparatively negative valence.

Prediction response : Since the previous moment lead the listener to make a prediction, we can now consider the successfulness of this prediction. The pitch of the anticipation was indeed the optimum prediction arising from the previous moment, so there is a predictive "reward" associated with the "what". That is, the prediction response is positively valenced. However, the timing of the onset for this note is very low. Recall that the third beat or the downbeat of the next measure were more likely moments for "when" for this event might occur.

Advanced R

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In non-standard evaluation , you learned the basics of accessing and evaluating the expressions underlying computation in R. In this chapter, you’ll learn how to manipulate these expressions with code. You’re going to learn how to metaprogram: how to create programs with other programs!

Structure of expressions begins with a deep dive into the structure of expressions. You’ll learn about the four components of an expression: constants, names, calls, and pairlists.

Names goes into further details about names.

Calls gives more details about calls.

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takes a minor detour to discuss some common uses of calls in base R.

Pairlists completes the discussion of the four major components of an expression, and shows how you can create functions from their component pieces.

Parsing and deparsing discusses how to convert back and forth between expressions and text.

Walking the call tree with recursive functions concludes the chapter, combining everything you’ve learned about writing functions that can compute on and modify arbitrary R code.

Throughout this chapter we’re going to use tools from the pryr package to help see what’s going on. If you don’t already have it, install it by running install.packages("pryr") .

To compute on the language, we first need to understand the structure of the language. That will require some new vocabulary, some new tools, and some new ways of thinking about R code. The first thing you’ll need to understand is the distinction between an operation and a result:

We want to distinguish the action of multiplying x by 10 and assigning that result to y from the actual result (40). As we’ve seen in the previous chapter, we can capture the action with quote() :

quote() returns an expression : an object that represents an action that can be performed by R. (Unfortunately expression() does not return an expression in this sense. Instead, it returns something more like a list of expressions. See parsing and deparsing for more details.)

expression

An expression is also called an abstract syntax tree (AST) because it represents the hierarchical tree structure of the code. We’ll use pryr::ast() to see this more clearly:

As an aside, one question that sometimes gets brought up at this point in the conversation is, well, didn’t they only have two bombs to use? So wouldn’t a demonstration have meant that they would have only had another bomb left, perhaps not enough? This is only an issue if you consider the timescale to be as it was played out— e.g., using both bombs as soon as possible, in early August. A third plutonium bomb would have been ready by August 17th or 18th (they originally thought the 24th, but it got pushed up), so one could imagine a situation in which things were delayed by a week or so and there would have been no real difference even if one bomb was expended on a demonstration. If they had been willing to wait a fewmore weeks, they could have turned the Little Boy bomb’s fuel into several “composite” core implosion bombs, as Oppenheimer had suggested to Groves after Trinity.I only bring the above up because people sometimes get confused about their weapon availability and the timing issue. They made choices on this that constrained their options. They had reasons for doing it, but it was not as if the way things happened was set in stone. (The invasion of Japan was not scheduled until November 1st.) 3

So, obviously,they didn’t choose to demonstrate the bomb first. But what if they had? I find this an interesting counterfactual to ponder. Would dropping the bomb in Tokyo Bayhave been militarily feasible? I suspect so. If they could drop the bombs on cities, they could probably drop them near cities. To put it another way: I have faith they could have figured out a way to do it operationally, because they were clever people. 4

But would it have caused the Japanese high command to surrender?Personally, I doubt it. Why? Because it’s not even clear that the actual atomic bombings were what caused the Japanese high command to surrender. There is a strong argument that it was the Soviet invasion of Manchuria that “shocked” them into their final capitulation. I don’t know if I completely buy that argument (this is thesubject of a future blog post), but I am convinced that the Soviet invasion was very important and disturbing to the Japanese with regards totheir long-termpolitical visions for the country. If an atomic bombdropped on an actual city was not, by itself, entirely enough, what good would seeing a bomb detonatedwithout destruction do? One cannot know,but I suspect it would not have done the trick.

The maximum size of the mushroom cloud of a 20 kiloton nuclear detonationin Tokyo Bay, as viewed from the roof of the Imperial Palace today, as visualized by NUKEMAP3D . Firebombed Tokyo of 1945 would have afforded a less skyscraper-cluttered view, obviously.

Of course, the Chicago scientists suspected that as well, but said it was necessary from a moral point of view. Sure, the Japanesemight not surrender, but then, at least, you can say you showed them what was coming first. As it was, we gave no real warning whatsoever before dropping itonHiroshima.But here’s the question I come to next: could you demonstrate it, and then drop it on a city? That is, could the United States reallysay:“ we have made this apocalyptic weapon, unleashed the atom, and many other peril/hope clichés — and we have chosen not to use it to take life… yet. But if you don’t give in to our demands, we will unleash it on your people.” How could that not look like pure blackmail, pure terrorism?Could they then turn around and start killing people by the tens of thousands, having announced their capability to do so? Somehow I suspect the public relations angle would be almost impossible.By demonstrating it first, they would be implying that they knew that it was perhaps not just another weapon, not just another way to wage war. And that acknowledgment would mean that they would definitely be seen as crossing a line if they then went on to use it.

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