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All 5 example character models below were trained with the I’m releasing on Github. The input in each case is a single file with some text, and we’re training an RNN to predict the next character in the sequence.

Lets first try a small dataset of English as a sanity check. My favorite fun dataset is the concatenation of Paul Graham’s essays . The basic idea is that there’s a lot of wisdom in these essays, but unfortunately Paul Graham is a relatively slow generator. Wouldn’t it be great if we could sample startup wisdom on demand? That’s where an RNN comes in.

Concatenating all pg essays over the last ~5 years we get approximately 1MB text file, or about 1 million characters (this is considered a very small dataset by the way). Technical: Lets train a 2-layer LSTM with 512 hidden nodes (approx. 3.5 million parameters), and with dropout of 0.5 after each layer. We’ll train with batches of 100 examples and truncated backpropagation through time of length 100 characters. With these settings one batch on a TITAN Z GPU takes about 0.46 seconds (this can be cut in half with 50 character BPTT at negligible cost in performance). Without further ado, lets see a sample from the RNN:

“The surprised in investors weren’t going to raise money. I’m not the company with the time there are all interesting quickly, don’t have to get off the same programmers. There’s a super-angel round fundraising, why do you can do. If you have a different physical investment are become in people who reduced in a startup with the way to argument the acquirer could see them just that you’re also the founders will part of users’ affords that and an alternation to the idea. [2] Don’t work at first member to see the way kids will seem in advance of a bad successful startup. And if you have to act the big company too.”

Okay, clearly the above is unfortunately not going to replace Paul Graham anytime soon, but remember that the RNN had to learn English completely from scratch and with a small dataset (including where you put commas, apostrophes and spaces). I also like that it learns to support its own arguments (e.g. [2], above). Sometimes it says something that offers a glimmer of insight, such as “a company is a meeting to think to investors” . Here’s a link to 50K character sample if you’d like to see more.

Temperature. We can also play with the temperature of the Softmax during sampling. Decreasing the temperature from 1 to some lower number (e.g. 0.5) makes the RNN more confident, but also more conservative in its samples. Conversely, higher temperatures will give more diversity but at cost of more mistakes (e.g. spelling mistakes, etc). In particular, setting temperature very near zero will give the most likely thing that Paul Graham might say:

Temperature.

“is that they were all the same thing that was a startup is that they were all the same thing that was a startup is that they were all the same thing that was a startup is that they were all the same”

Layers to construct recurrent networks. Recurrent layers can be used similarly to feed-forward layers except that the input shape is expected to be (batch_size, sequence_length, num_inputs) . The CustomRecurrentLayer can also support more than one “feature” dimension (e.g. using convolutional connections), but for all other layers, dimensions trailing the third dimension are flattened.

The following recurrent layers are implemented:

For recurrent layers with gates we use a helper class to set up the parameters in each gate:

Please refer to that class if you need to modify initial conditions of gates.

Recurrent layers and feed-forward layers can be combined in the same network by using a few reshape operations; please refer to the example below.

Examples Daya by Zendaya Womens Starke Gladiator Sandal Red PDViDcIEyq

The following example demonstrates how recurrent layers can be easily mixed with feed-forward layers using Cushe Womens Bonsai Suede Casual SlipOn Flat Walking Shoe Brown/Pink 9cd571pu
and how to build a network with variable batch size and number of time steps.

A layer which implements a recurrent connection.

This layer allows you to specify custom input-to-hidden and hidden-to-hidden connections by instantiating BCBGeneration Womens Genie Ankle Boot Black 05GGKuZ
instances and passing them on initialization. Note that these connections can consist of multiple layers chained together. The output shape for the provided input-to-hidden and hidden-to-hidden connections must be the same. If you are looking for a standard, densely-connected recurrent layer, please see RecurrentLayer . The output is computed by

References

Examples

The following example constructs a simple CustomRecurrentLayer which has dense input-to-hidden and hidden-to-hidden connections.

The CustomRecurrentLayer can also support “convolutional recurrence”, as is demonstrated below.

Compute this layer’s output function given a symbolic input variable.

Dense recurrent neural network (RNN) layer

A “vanilla” RNN layer, which has dense input-to-hidden and hidden-to-hidden connections. The output is computed as

A long short-term memory (LSTM) layer.

Includes optional “peephole connections” and a forget gate. Based on the definition in [1] , which is the current common definition. The output is computed by

Compute this layer’s output function given a symbolic input variable

Gated Recurrent Unit (GRU) Layer

Implements the recurrent step proposed in Charm Foot Womens Fashion Studded Low Heel Short Western Boots Wine Red TOBqVfe
, which computes the output by

An alternate update for the candidate hidden state is proposed in [2] :

Dowd’s argument that there was no obstruction and therefore no need for a Trump interview has two threads. The first, and the one that has drawn immediate outraged responses , is the by-now familiar claim by Trump’s acolytes that a president cannot commit obstruction of justice by firing or giving instructions to executive branch law enforcement officials. The argument takes the noncontroversial truth that a president has wide Article II powers to hire and fire executive branch subordinates and considerable discretionary authority to supervise their work and distorts it into an absurd absolute. This extreme application of the so-called unitary executive theory has been given thorough scholarly debunkings elsewhere .

But one scarcely needs to be a scholar to discern its absurdity. If a president can never commit a crime by ordering his subordinates not to investigate or prosecute, regardless of how self-serving or corrupt the president’s motive, then a president can effectively exempt both himself and anyone he favors from the constraints of law. Anglo-American jurisprudence abandoned that idea — what the English called the royal prerogative — four centuries ago during the reign of King Charles I. The Framers did not revive this relic of absolutist monarchies in the U.S. constitution.

The second prong of Dowd’s obstruction argument is less shockingly authoritarian, but ultimately no less wrong. Essentially, he goes through various incidents possibly indicative of obstruction — Trump’s alleged remark to James Comey about letting General Flynn go, the Comey firing, and others — and tries to show that no obstruction occurred and therefore there can be no need for Trump to testify about them. The argument has two gaping holes.

The first was noted in the original Times report: incredibly, Dowd based his entire exposition on the wrong obstruction statute.

There are a number of federal obstruction of justice statutes. The three most important are 18 U.S.C. Sections 1503, 1505, and 1512. The Dowd letter says, “The only statute that could even theoretically be implicated on the alleged facts is 18 U.S.C. § 1505….” This is not only wrong, but laughably wrong. Sections 1503 and 1512 between them cover proceedings before judges, grand juries, Congress, and executive agencies, while 1505 is directed primarily at obstruction of proceedings before federal regulatory agencies. No prosecutor faced with allegations of obstruction of a federal grand jury investigation would ever use section 1505.

Not only do sections 1503 and 1512 fit the facts of this case far better than 1505, but Section 1512 is phrased to eliminate the technical issues raised in the Dowd letter, such as whether there was a “pending proceeding” at the time of Trump’s allegedly obstructive behavior and, if so, whether he was aware of its pendency.Section 1512(f) specifically provides that in 1512 prosecutions “an official proceeding need not be pending or about to be instituted at the time of the offense.” In short, under Section 1512(c), all the government must prove is that the defendant corruptly attempted to obstruct, influence, or impede some official proceeding (a term that includes grand jury investigations) that is either under way or that might reasonably be anticipated.

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