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Even in a graduate-level class like this one, we made lots of simplifying assumptions. This was the header text that appeared at the top of our problem sets:

For this assignment (and generally in this class) you may disregard measure-theoretic niceties about conditioning on measure-zero sets. Of course, you can feel free to write up the problem rigorously if you want, and I am happy to field questions or chat about how we could make the treatment fully rigorous (Piazza is a great forum for that kind of question as long as you can pose it without spoilers!)

Well, I shouldn’t say I was disappointed, since I was more relieved if anything. If I had to formalize everything with measure theory, I think I would get bogged down with trying to understand measure this, measure that, the integral is with respect to X measure, etc.

Even with the “measure-theoretically naive” simplification, I had to spend lots of time working on the problem sets. In general, I could usually get about 50-80 percent of a problem set done by myself, but for the remainder of it, I needed to consult with other students, the GSI, or the professor. Since problem sets were usually released Thursday afternoons and due the following Thursday, I made sure to set aside either Saturday or Sunday as a day where I worked solely on the problem set, which allowed me to get huge chunks of it done and LaTeX-ed up right away.

The bad news is that it wasn’t easy to find student collaborators. I had collaborators for some (but not all of) the problem sets, and we stopped meeting later in the semester. Man, I wish I were more popular. I also attended a few office hours, and it could sometimes be hard to understand the professor or the GSI if there were a lot of other students there. The GSI office hours were a major problem, since another class had office hours in the same room . Think of overlapping voices from two different subjects. Yeah, it’s not the best setting for the acoustics and I could not understand or follow what people were discussing apart from scraps of information I could get from the chalkboard. The good news is that the GSI, apart from obviously knowing the material very well, was generous with partial credit and created solutions to all the problem sets, which were really helpful to me when I prepared for the three-hour final exam.

The day of the final was pretty hectic for me. I had to gave a talk at GH Bass Co Womens Lola Mule Black MSuGKiytK
in San Francisco that morning, then almost immediately board BART to get back to Berkeley by 1:00PM to take the exam. (The exam was originally scheduled at 8:00AM ALDO Mens Edalesien Flip Flop White konffj1
(!!) but Professor Fithian kindly allowed me to take it at 1:00PM.) I did not have any time to change clothes, so for the first time in my life, I took an exam wearing business attire .

Business attire or not, the exam was tough. Professor Fithian made it four broad questions, each with multiple parts in it. I tried doing all four, and probably did half of all four correct, roughly. We were allowed a one-sided, one-page cheat sheet, and I crammed mine in with A LOT of information, but I almost never used it during the exam. This is typical, by the way. Most of the time, simply creating the cheat sheet actually serves as my studying. As I was also preoccupied with research, I only spent a day and a half studying for the final.

h_t = o ⊙ c_t

In fact, some researchers even applied evolutionary algorithms to spawn and test a bunch of variants on the standard LSTM equations. Most of the good ones just worked roughly the same.

This highlights an issue with LSTMs — they are definitely fairly handwavy. We use them because their architecture allows us to prevent gradients from vanishing such that we can learn long-term dependencies, but there’s not much theoretical or empirical backing for them. ANNs and RNNs make sense in that they’re biologically inspired and that they’re essentially just deep composite functions that have parameters we can optimize. LSTMs stray so far from statistical methods and introduce complex concepts/architectures that work but aren’t necessarily justified from the get-go. Fully understanding why LSTMs work so well and coming up with better/simpler architectures is a hot topic of research right now.

There are also other variants of RNNs, similar to LSTMs, like (Gated Recurrent Units). LSTM is still the king, but GRUs in particular have grown in popularity and are seen in many recent, well-respected research papers. It’s a must learn next to LSTMs, but this article would get too bloated with it. TL;DR: GRUs have a less complex architecture than LSTMs but achieves similar results, and they can control the flow of information without requiring a memory cell. And, they’re fairly new. (See, told you “coming up with better/simpler architectures is a hot topic of research right now” is true!)

Wanna see a couple cool things? Practical applications were talked about in the first section, and the next section will walk through more technical applications of RNNs ie. in recent research papers. This section, instead, contains some fun things RNNs have done or produced that’ll ease yourself from the hell that was actually understanding them. As simply as we try to convey things on this blog, LSTMs be LSTMs.

Sidenote: now, don’t be frightened by “RNNs”. Do be frightened by “vanilla RNNs”, in most contexts, but we use RNN as an umbrella term, and it most often refers to an LSTM or a similar variant like GRU.

Many if not all of these are taken from Andrej Karpathy’s Marc Fisher Women Abetter2 Booties Black 41PZH936I
, or his blog post on the same subject:

The Unreasonable Effectiveness of Recurrent Neural Networks karpathy.github.io

You should most certainly visit either his blog post or lecture for info on exactly how these experiments were conducted, and for more interpretation on their results. Taking a look at the ‘Visualizing the predictions and the “neuron” firings in the RNN’ section would also be helpful to gain more insight and intuition on how RNNs work and learn over time.

most certainly

A recurrent neural network generated this body of text, after it “read” a bunch of Shakespeare:

PipelineDB’s fundamental abstraction is called a continuous view. A continuous view is much like a regular view, except that it selects from a combination of streams and tables as its inputs and is incrementally updated in realtime as new data is written to those inputs.

As soon as a stream row has been read by the continuous views that must read it, it is discarded. It is not stored anywhere. The only data that is persisted for a continuous view is whatever is returned by running a SELECT * FROM that_view . Thus you can think of a continuous view as a very high-throughput, realtime materialized view.

CREATE CONTINUOUS VIEW Clarks Womens Draty Haze Shoe Tan Suede 4FvZW

Here’s the syntax for creating a continuous view:

where query is a subset of a PostgreSQL SELECT statement:


This section references streams, which are similar to tables and are what continuous views read from in their clause. They’re explained in more depth in the Northside Womens Bishop Snow Boot Brown/Green JNIrR
section, but you can think of them as append-only tables for now.


A PostgreSQL AllhqFashion Womens Soft Material Buckle Closed Toe LowHeels Solid Sandals Pink piw6Ss


An optional identifier to name an expression with


Any expression that evaluates to a result of type . Any row that does not satisfy this condition will be eliminated from the output. A row satisfies the condition if it returns when the actual row values are substituted for any variable references.


A name that can be referenced from clauses or subsequent window definitions.



PipelineDB’s window_definitions do not support an clause if the input rows come from a stream. In such cases, the stream row’s field is implictly used as the clause.


Defines the window frame for window functions that depend on the frame (not all do). The window frame is a set of related rows for each row of the query (called the current row). The frame_clause can be one of

frame_start , frame_end

frame_start frame_end

Each can be one of the following:

An integral value


This has mainly covered only the syntax for . To learn more about the semantics of each of these query elements, you should consult the Crocs Womens Duet Busy Day 20 Satya Mule Black/Black sE3scW84M3

To DROP a continuous view from the system, use the DROP CONTINUOUS VIEW command. Its syntax is simple:

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  • Michelle Wetzler

    Solutions Architect @ Twilio

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