An Engineer’s Guide to GEMM

gemm_corrected

I’ve spent most of the last couple of years worrying about the GEMM function because it’s the heart of deep learning calculations. The trouble is, I’m not very good at matrix math! I struggled through the courses I took in high school and college, barely getting a passing grade, confident that I’d never need anything so esoteric ever again. Right out of college I started working on 3D graphics engines where matrices were everywhere, and they’ve been an essential tool in my work ever since.

I managed to develop decent intuitions for 3D transformations and their 4×4 matrix representations, but not having a solid grounding in the theory left me very prone to mistakes when I moved on to more general calculations. I screwed up the first version of all my diagrams in a previous blog post, and most recently had to make a breaking API change to the open-source gemmlowp library, all because I’d messed up the ordering of the matrix multiplies.

The best way I know to fix something in my own mind is to try to explain it to somebody else, so here are my notes on the areas I found most confusing about matrix math as an engineer. I hope they’ll be helpful, and I look forward to getting corrections on anything I screwed up!

Row versus Column Major

The root of a lot of my difficulties are the two competing ways you can store matrix values in RAM. Coming from an image-processing world, when I see a 2D array of values my in-grained assumption is that it’s stored like letters on a page, starting in the top-left corner, and moving from left to right and jumping down at the end of the row. For example, if you have a matrix that you’d draw like this:
| 0 | 1 | 2 |
| 3 | 4 | 5 |
| 6 | 7 | 8 |

You would store it in memory in this order:
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

This is known as ‘row major’, because each row is stored in adjacent locations in memory.
The alternative storage scheme is ‘column major’, and the same matrix would be laid out like this in memory:
| 0 | 3 | 6 | 1 | 4 | 7 | 2 | 5 | 8 |

What this means is that we’re walking down the columns to get adjacent memory locations instead.

It’s important to know that both of these are just ways of storing the same matrix in memory, they’re an implementation detail that should not affect the underlying math, or the way you diagram your equations. There’s also no widespread agreement on what the ‘correct’ or canonical storage order to use is, so you’ll need to pay attention to what convention the code you’re interacting with expects.

Transpose

One thing you may notice about row versus column ordering is that if you screw it up and pass a square row-major matrix into a library that expects column major, or vice-versa, it will be read as the transpose of the actual matrix. Visually, you transpose a matrix by flipping all the columns into rows, like this:

| 0 | 1 | 2 | 3 |
| 4 | 5 | 6 | 7 |
| 8 | 9 |10 |11 |

Original

| 0 | 4 | 8 |
| 1 | 5 | 9 |
| 2 | 6 |10 |
| 3 | 7 |11 |

Transpose

Another way of visualizing this is drawing a line through the top-left to bottom-right corners, and flipping everything around on that diagonal. You’ll often see the transpose of a matrix indicated by adding an apostrophe to the name, so that the transpose of a matrix A is A’.

Argument Ordering

If you multiply two numbers, A * B is always the same as B * A. This is not true for matrix multiplications! Indeed, you can only multiply two matrices together at all if the number of columns on the left-hand-side is equal to the number of rows in the right-hand argument. Even if they’re both the same square size, and so can potentially be swapped, the result will still depend on the order.

There is one mathematical identity that crops up a lot in practice with transposes. If you have the standard GEMM equation of C = A * B, then C’ = B’ * A’. In words, if you swap the order of the two input matrices and transpose both of them, then multiplying them will give the transpose of the result you’d get in the original untransposed order.

#Errors % 2 == 0

What really led me into danger is that all three of storage order, transposing, and input order have effects that can mimic and cancel each other out. It’s like Jim Blinn’s old quote about all correct graphics programs having an even number of sign errors, except that there are three different ways to screw things up instead of one!

For example, what I realized last week was that I was working in a new code base that assumes row-major order, but gemmlowp assumes column major. Because I had been in a hurry and couldn’t figure out why my unit tests weren’t working, so I ended up swapping the input argument order. Since C’ = B’ * A’, the storage order error was canceled out by the argument order error! It made for very confusing code, so thankfully a co-worker slapped me round the back of the head (very politely) when he ran across it and I revisited it and figured out my errors.

Because I know I’m so prone to these kind of errors, I’ve forced myself to slow down when I’m tackling this kind of problem, and start off by working through a couple of examples on pen and paper. I find working visually with the diagram at the top of this post in mind has helped me immensely. Once I’ve got those examples straight, I’ll turn them into unit tests, with the hand calculations in the comments. You can see an example in gemmlowp/test/test.cc:698:


My other key tool is keeping around a simple reference GEMM function that’s unoptimized, but that I can easily step through and add logging statements to. Since a lot of my work involves cutting corners with precision to increase speed, it’s important that I have an understandable implementation that I can play with, and compare against more complex versions. You can see my version for gemmlowp at test.cc:36:


This includes some eight-bit specific code, but the structure is common across all my reference versions, with three nested loops across the m, n, and k dimensions of the matrices. It also doesn’t include some of the standard arguments like alpha or beta. This particular code assumes column major by default, but if any of the transpose flags are set to true, then the matrix is treated as row major.

Leading Dimensions

The final pieces of the puzzle for me were the lda, ldb, and ldc arguments. These left me confused initially because I struggled to find a clear representation of that they meant. I finally realized that they were the number of values you moved forward in memory when you reached the end of a row (in row-major order) or column (in column major). They’re strides that give a lot of flexibility when you only want to work with smaller tiles inside a larger matrix, since they let you skip over values you want to ignore. If you’re not dealing with sub-tiles, then they’ll be the number of columns for a row-major matrix, and the number of rows for a column-major one.

Anyway, I hope these notes help any other lost souls who are struggling with matrices. I’m now feeling a lot more confident, and I wish I’d taken the time to study them more carefully before. They’re very powerful tools, and actually a lot of fun once I moved past some of my confusion!

One Weird Trick for Faster Android Multithreading

deckchair

Photo by Gary Perlmutter

It’s not often that doing nothing speeds things up, but that’s exactly how Benoit Jacob just optimized the gemmlowp project on Android. Gemmlowp is a specialized library for doing large matrix multiplications on eight-bit values, which is vital for neural networks (as I’ve talked about before). He had managed to write great ARM assembler routines and careful memory management code to get strong single-core performance on Android, but when we tried to thread the code across two or four cores, we only saw a very small improvement. It wasn’t scaling with the number of cores, despite being a very parallelizeable  algorithm where we could easily split the calculations into independent shards.

Looking at the behavior with tools like systrace, we could see that there were lots of long gaps where cores weren’t being used. Another clue was that changing the cpu governor to a more aggressive mode (something that’s only possible for developers) made performance dramatically better. Governors exist to make sure that applications are efficient in their use of battery power, mostly by lowering the frequencies or disabling cores that aren’t in use. That led us to believe that something was making the governor believe we didn’t need all the cores, even though we were trying to do short bursts of very intensive computation that would benefit from them.

The problem was that we were doing a lot of comparatively ‘small’ calculations, sometimes only a few million operations at a time, with sync points in between. We were using the standard pthread_cond_wait() function in the worker threads to look for new chunks of work to be available. The trouble is that the ‘granularity’ of the waits seemed to be of the magnitude of a millisecond or so, which meant that if there wasn’t immediately new work after one chunk was completed, the thread would go to sleep for quite a while. That seemed to cause a double penalty where not only did the work take longer because of those thread delays, but the governor saw sparse usage of the cores and so downgraded performance even more to save power!

All of these theories about the exact mechanism are just our speculation, but we ended up adding a short period of busy-waiting before we drop back to pthread_cond_wait(), and that improved our overall performance massively. We’re now spinning in a NOP loop for about 32 million cycles (which may sound like a lot but is only about 10 to 20 milliseconds, depending on the clock rate), so by doing nothing we actually end up going faster! We found we could get most of the benefit with even shorter busy-wait lengths, but the current number of NOPs was optimal for our use cases.

It sounds incredible, but you can try it for yourself by changing kMaxBusyWaitNOPs to zero on line 33 in internal/multi_thread_gemm.h, and running the benchmark with:

./scripts/test-android.sh test/benchmark.cc

There’s a series of benchmark results reflecting different use cases, but on my Nexus 5 (with four cores) I see over double the speed with the busy-waiting in place. As an aside, the labeling is a bit off since they’re not floating point operations, but seeing 45 giga-ops on a real-world use case on a years-old phone still blows my mind, we have an incredible amount of computing power in our pockets!

The big concern is obviously power usage, so we used the Monsoon power monitor to check and we actually end up using substantially less energy per operation, as well as completing more quickly (268 pico-joules per op versus 353 single-threaded).

Once the busy-waiting was in place, we were able to see one remaining problem. The original code spun up as many worker threads as there were cores, but this ignored the main thread, which was effectively contending for one core with a worker. By instead having (N-1) worker threads, and having one worker function run on the main thread, we saw a noticeable improvement.

I don’t recommend trying this approach at home unless you’re very sure you need it after careful profiling, since I’d hate to spawn a new generation of apps that are needlessly wasting users’ batteries. If you are in the situation where you’re doing heavy numerical computation in comparatively small chunks and need to spread the work across multiple cores, it’s worth taking a look at the WaitForVariableChange() code. One direction I would also recommend looking at is pthread_spin_lock() , since that promises a similar low-latency busy-waiting approach to waiting in a more standard way (and we may be reinventing the wheel here) but we haven’t had a chance to experiment with that deeply yet.

Anyway, these are just notes from our own adventures, and I’d love to hear from anyone else who’s explored the mysteries of numerical computation on smartphones, it’s a fascinating area for me!

Smartphone Energy Consumption

energybook

I never used to worry about energy usage but over the last few years most of my code runs on smartphones, so it has become one of my top priorities. The trouble is I’ve never had any training or experience in the area, so I’ve had to learn how to do it from experience, other engineers, and the internet, most of which feels more like folklore than engineering. A few days ago I was trying to learn more about the shiny new Monsoon power monitor on my desk when I came across “Smartphone Energy Consumption” from Cambridge University Press.

I’ve now had a chance to read it, and it has helped fill in a lot of gaps in my education. I highly recommend picking up a copy if you’re facing any of the same problems, and to give you a taster here are some of the things I learned. Rest assured that any mistakes in here are my own, not the authors!

There are lots of different ways to measure battery capacity – joules, watt-hours, and milli-amp hours. If I’m getting my physics straight, 1 watt hour is 3,600 joules, and if you assume a rough voltage of 4V, 1 milli-amp hour is 0.001 * 4v * 60 * 60, or 14.4 joules. A typical phone battery might have 2,000 mAh, or about 29,000 joules.

Most phones can’t dissipate more than 3 watts of heat, so that’s a practical limit for sustained power usage. Wearables can have much lower limits.

There are two main ways power is used in mobile chips. Switching loss is the power used to change gate states in the silicon, and static loss is more like a steady leakage. Switching power decreases with the square of the voltage, so halving the voltage reduces its effect by 75%, whereas static power shrinks linearly. That leads to some interesting situations, where having two cores running at half the voltage and frequency (since lower clock frequencies allow lower voltages to be used) may take the same time to complete a task, but at half the power of a single higher-voltage core. Turning off parts of the chip entirely is the key to reducing static leakage.

There’s a great practical guide to wiring up Monsoons, exactly what I need right now! There’s also a great section on human-battery interaction, that I just skimmed, but which covers a lot of research. The key takeaway for me was that users get very annoyed if their battery starts draining more quickly than it used to, and will uninstall recent apps to fix the problem, so developer should be highly motivated to reduce their power consumption.

I found a lot of very useful estimates for components power usages scattered through the book. These are just rough guides, but they helped my mental modeling, so here are some I found notable:

  • An ARM A9 CPU can use between 500 and 2,000 mW.
  • A display might use 400 mW.
  • Active cell radio might use 800 mW.
  • Bluetooth might use 100 mW.
  • Accelerometer is 21 mW.
  • Gyroscope is 130 mW.
  • Microphone is 101 mW.
  • GPS is 176 mW.
  • Using the camera in ‘viewfinder’ mode, focusing and looking at a picture preview, might use 1,000 mW.
  • Actually recording video might take another 200 to 1,000 mW on top of that.

A key problem for wireless network communication is the ‘tail energy’ used to keep the radio active after the last communication, even when nothing’s being sent. This is vital for responsiveness, but it can be ten seconds for LTE, so apparently short communications can use a lot more energy than you’d expect. Sending a single byte can use a massive amount of power if it keeps the radio active for ten seconds after!

A Microsoft paper showed that over 50% of the power on several popular games is consumed by the ads they show!

There’s some interesting work on modeling the tradeoffs between computation offloading (moving work to the cloud from the phone) and communication offloading (doing more work on the device to reduce network costs). I’m a big believer that we should do more work on-device, so it was great to have a better foundation for modeling those tradeoffs. One example they give is using the Android SDK on a 1080p image to detect faces on-device, and taking 3.2 seconds and 9 joules, whereas sending the image to a nearby server was quicker, even with the extra power of network traffic.

Anyway, it’s a great piece of work so if this sort of information is useful, go pick up a copy yourself, there’s a lot more than I can cover here!

Semantic Sensors

peoplecounter

Video from Springboard

The other day I was catching up with neighborhood news, and saw this article about “people counters” in San Francisco’s tourist district. These are cameras watching the sidewalks and totaling up how many pedestrians are walking past. The results weren’t earth-shattering, but I was fascinated because I’d never heard of the technology before. Digging in deeper, I discovered there’s a whole industry of competing vendors offering similar devices.

Why am I so interested in these? Traditionally we’ve always thought about cameras as devices to capture pictures for humans to watch. People counters only use images as an intermediate stage in their data pipeline, their real output is just the coordinates of nearby pedestrians. Right now this is a very niche application, because the systems cost $2,100 each. What happens when something similar costs $2, or even 20 cents? And how about combining that price point with rapidly-improving computer vision, allowing far more information to be derived from images?

Those trends are why I think we’re going to see a lot of “Semantic Sensors” emerging. These will be tiny, cheap, all-in-one modules that capture raw noisy data from the real world, have built-in AI for analysis, and only output a few high-level signals. Imagine a small optical sensor that is wired like a switch, but turns on when it sees someone wave up, and off when they wave down. Here are some other concrete examples of what I think they might enable:

  •  Meeting room lights that stay on when there’s a person sitting there, even if the conference call has paralyzed them into immobility.
  •  Gestural interfaces on anything with a switch.
  •  Parking meters that can tell if there’s a car in their spot, and automatically charge based on the license plate.
  •  Cat-flaps that only let in cats, not raccoons!
  •  Farm gates that spot sick or injured animals.
  •  Streetlights that dim themselves when nobody’s around, and even report car crashes or house fires.
  •  Stop lights that vary their timing cycle depending on whether there are any vehicles or pedestrians approaching from each direction, and will prioritize emergency vehicles.
  •  Drug cabinet doors that keep track of the medicines you have inside, help you find them, and re-order when you’re out.
  •  Shop window display items that spring to life when passers-by are looking at them, using eye tracking.
  •  Canary sensors scattered through crops that spot and report any pests or weeds they see, to minimize the use of chemicals.
  •  IFTTT-style hardware mashups, with quirky niche applications like tea-kettles that turn themselves on if you stare longingly at them, art installations that let you paint on them with hand gestures, or lawn sprinklers that know if it’s been raining, and only water the parts that are starting to go brown.

For all of these applications, the images involved are just an implementation detail, they can be immediately discarded. From a systems view, they’re just black boxes that output data about the local environment. Engineers with no background in vision will be able to integrate them, and get useful signals to drive their applications. There are already a few specialist devices like Omron’s Human Vision Components, but imagine when these become common components, standardized so they can be easily plugged into existing designs and cheap enough to be used on everyday items.

I don’t have a crystal ball, and all of these are purely my own personal musings, but it seems obvious to me that machine vision is becoming a commodity. Once the technology’s truly democratized, I believe it will give computers a window into the real world they’ve never had before, and enable interfaces and responses to the environment we’ve never even dreamed of. I think a big part of that will be the emergence of these “semantic sensors” that output human-meaningful data about what’s happening around them.

OpenHeatMap and DataScienceToolkit under new management

I’ve been running OpenHeatMap and the Data Science Toolkit for quite a few years now, but a few months ago I realized I wasn’t able to keep maintaining them. I know a lot of people out there are still using them, so I looked around for a partner I could transfer the ownership to. After some discussions, I arranged a deal with the myheatmap.com team to transfer the sites to them, for no charge, in return for their agreement to keep supporting the existing community. For the last few weeks they’ve been handling the servers, support, and maintenance, and I’m very glad they were able to step in. The goal is to keep the existing free services supported, but give them the ability to expand in a more commercial direction too, so that the site becomes more self-sustaining. All OpenHeatMap support requests should now go to help@openheatmap.com, which they administer.

The code behind DataScienceToolkit.org is all open-source on github, so that will continue to be available, but the DSTK site itself has an uncertain future. I’ve always tried to keep it open to anyone who wants to experiment with the APIs, but over the last year its come under denial-of-service level usage levels from a wide range of IP addresses. I spent some time learning firewall rules and attempting to block the problematic calls, but I wasn’t able to keep the levels low enough to keep the site consistently up. Since OpenHeatMap relies on the site as its geocoder, that meant the uploading there was also often unreliable. I came to the sad conclusion I didn’t have enough time to do the overhauling I’d need to deal with the problems, which is why I handed everything over to a team who can put in more time. The most common use of the DSTK was for geocoding US address, and with the Census Bureau now providing their own free API, that side of it became less essential too. The hosting of the large VMs unfortunately got lost when I shut down the jetpac.com site, so I’m afraid I don’t have those available any more.

Both of the sites were failed startup ideas that took on a life of their own, even though I was never able to make them commercial ventures. I’m hopeful that a fresh team with new ideas will be able to provide a better service to everyone who uses them. I’m grateful to everyone who’s been in touch over the years, I kept supporting the site for so long because I saw the amazing projects you were all using them for. My deep thanks go to the community that formed around the sites.

How to Talk to Journalists

newspapers

Photo by Jon S

Now I’m at Google I don’t get to talk to reporters, which is a shame because they’re a lot of fun. When I was doing startups I learned a lot from hanging out with them, because they’re generally very smart, curious people who have a lot wider perspective on what’s happening than anyone else. I even dabbled in writing articles myself at the old ReadWriteWeb site many years ago.

I was talking to a startup founder recently, and realized she didn’t actually understand the basics of what a journalist’s job is like. Knowing the day-to-day routines and constraints on reporters is essential if you’re going to do a good job helping them cover what you’re doing.  Here’s my advice, based on my personal experiences over the last few years. I’d love to hear more from other people too, since I think this is far from the final word on the subject!

Connect Early and Selectively

Most founders want to wait until they hit a milestone they consider significant, and then mail-blast every high profile journalist they can find an email for. Every reporter’s inbox is piled up with so many of these every day that they’re almost never even read. Every writer has their own areas of interest, and their own long-term storylines about the tech world, and you first need to identify a handful of people who might truly care about what you’re doing, long before you’re looking for a story. Connect with them on Twitter or story comments, chat to them at conferences, and communicate your own enthusiasm about the things they care about. Don’t be a stalker, just be human. They’re in their jobs because they are interested in this new world we’re building so connect with them on that level.

Be Responsive

If you do start to build a relationship, one of the most helpful things you can do is provide quotes or off-the-record background for their stories. The key here is that they usually are up against a very tight deadline, they might need to submit in a matter of minutes, so drop everything and get back to them immediately. Make sure you know if what you’re saying will be quoted, or if it’s “on background”, before you say it! You can’t take back an ill-considered quote just because you regret it later.

Having quotes is essential for almost any story, since they’re the evidence to back up the writer’s version of events. Make sure you listen carefully to the reporter’s questions too, they’ll often give you an idea of what angle they’re interested in, so you can focus your response to fit. Be honest – having a quote that disagrees with someone else or the conventional wisdom can sometimes make an even better story than a confirmation.

Let the Story Emerge

A friend of mine used to curse about all the ’round number’ pitches that endlessly filled her inbox – “FooBar.com has reached 100,000 users!”. They’re boring for everyone outside that company. Only slightly better are fund-raising announcements, or new product features. What journalists care about are stories that readers will actually be interested in, and those need to be entertaining. Drama, surprise, tragedy, hope, and humor are all vital parts of the stories that engage people, so you have to let the journalists into the lives of your startup and let them decide what the real story is. It might be something you’re embarrassed by, like being turned down by every VC but finding alternative ways of staying afloat, or that you expanded too early, went through painful layoffs, but are now turning the corner. It might be something you don’t think about because you take it for granted, like that you have a great working environment for disabled people, or take interns from the local community.

Good reporters love getting to know people and teasing out the stories their readers will want to hear, so let them do their job and don’t bombard them with your own ideas, because you lack their perspective on what’s interesting. If you really are the next Facebook the stories about how you’re crushing it will come, don’t worry, but in the early days you need all the coverage you can get.

Blog

Everyone knows blogging’s been dead for years, but there’s no substitute for writing short-form articles in your own voice and publishing them yourself, and it actually helps journalists you’ll deal with in a lot of ways too. When you speak to them about a topic you’ve already blogged about, you’ll be far more articulate and quotable because you’ll have already worked through the ideas on paper once already. You’re also giving them something to link to in their articles as evidence to back up their own arguments. If you develop even a small audience on your blog, it’s actually useful for journalists to know you’re likely to link back to their own coverage, and so drive more readers in their direction. Any graphics or data you’ve produced can be very useful to quickly illustrate their stories too, especially about trends. Journalists tend to be voracious readers, so writing regular interesting posts is a great way to build a relationship as well, and it’s even better if you reference their work and engage their arguments. Your posts may end up sparking ideas for stories too, and if one’s got a lot of shares on social media that’s strong evidence people find the underlying topic interesting.

Speak Directly

I have never found PR firms helpful*. When I was on the other end of their pitches, I saw how much of a negative reaction their formulaic emails got from other reporters. I see them as middle managers inserting themselves between journalists and the founders they actually want to speak to, and I’ve run across too many who make their money by pandering to founder’s egos without helping the business. It’s possible it all makes sense in the corporate world, but as a founder you need to build your own direct relationships, and if you do have to cold-email somebody, at least make it a personal note in your own voice.

Think of it like dealing with investors, it’s not something you can delegate when you’re starting out. Reporters want to get heartfelt quotes from un-coached entrepreneurs, not rehearsed soundbites from someone sitting with a handler, and just the hassle of arranging interviews through a third-party can put them off. It does feel risky, but as an early-stage startup the reward of good coverage is so valuable, you need to take the plunge.

Focus on Your Work

Success in other areas makes good PR possible, and good coverage is a force multiplier, but PR shouldn’t take up more than a small percentage of your time as a founder. You can charm reporters all you want, but if you’re not doing anything fundamentally interesting, you won’t get a good story. Even if you do get coverage, if your product or business model don’t work it won’t help your traction. Journalists know you have a job to do, and would much rather you come back to them less frequently with amazing things to show, than spend all your time on little stories at the expense of everything else.

(*) The only situation I’d recommend getting help is if you find yourself in the center of a scandal, like Alasdair Allan and I did with the iPhone locationgate problem. There having the wonderful Maureen Jennings from O’Reilly performing traffic control for all the people who suddenly wanted to interview us was a life-saver. She was able to communicate effectively with everyone involved, we’ll forever be grateful to her for all her help!

Five Deep Links

deepdogs

Picture by Kevin Dooley

I’m coming up to a year at Google now, and I’ve been continuing to have an amazing time with the deep learning team here. Deep networks are not a silver bullet for all AI problems, but they do mean we are moving from a cottage industry of bespoke machine learning specialists hand-carving algorithms for each new problem, to mass production where general software engineers can get good results by applying the same off-the-shelf approaches to a lot of different areas. If you have a good object recognition network architecture, you can get damn fine results on scene recognition, location estimation, and a whole host of other tasks using the same model, just by varying the training data, or even just retraining the top layer.

The tools aren’t particularly easy to use right now which makes deep learning seem very intimidating, but work like Andrej Karpathy’s ConvNetJS shows that the code can be expressed in much more understandable ways. As the libraries and documentation mature, we’ll see tools that let any software engineer create their own deep learning solution by just creating a training set that expresses their problem and feed it into an automated system. I imagine there will be separate approaches for the big areas of images, speech, and natural language, but we’re at the point where we can produce semantically meaningful intermediate representations from all those kinds of real-world data, and then straightforwardly train against those. Anyway, enough of my excited ramblings, I mostly wanted to share some interesting deep learning articles I’ve seen recently.

How Google Translate Squeezes Deep Learning onto a Phone – I’ve been lucky enough to work with the former WordLens team to get their amazing augmented reality visual translator using deep neural networks for the character recognition, directly on the device. It was nice to see the technology from the WordLens and Jetpac acquisitions come together with all of the experience and smarts of the wider Google teams to make something this fun.

Composing Music with Recurrent Neural Networks – Mozart’s job is still safe for a while based on the final results, but it’s a great demonstration of how it’s getting easier for non-specialists to start working with neural networks. It also has the best explanation of LSTMs that I’ve seen!

gemmlowp – Benoit Jacob, of Eigen fame, has been doing a fantastic job of optimizing the kind of eight-bit matrix multiply routines that I find essential for running networks on device. Even better, because Google’s very supportive of open source, we’ve been able to release it publicly on Github. It’s been a great project to collaborate on, and I’m happy that we’ve been able to share the results.

Visualizing GoogLeNet Classes – I love that we’re still at the stage where we don’t really know how these networks work under the hood, and investigations like these are great ways of exploring what these strange mechanisms we’ve created are actually doing.

How a Driverless Car Sees the World – Yes, I have drunk the Google Kool-aid, but I’ve long thought this is one of the coolest projects happening right now. This is a great rundown of some of the engineering challenges it’s facing, including wheelchairs doing donuts in the road.