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On July 4, the day the United States of America celebrates its independence, let's take a look at the best chess players in American history.

The United States has long produced top chess talent, with some of the game's finest players, authors, and theoreticians calling the U.S. home.

In recent years, the U.S. has been a force on the international chess scene, and its "big three" grandmasters are staples at the world's top tournaments. The United States had a world-championship contender in 2018, with GMFabiano Caruana coming up just short against the world champion, GMMagnus Carlsen.

Caruana obviously makes the list of the best-ever U.S. players, but where does he rank? And who is ahead of him?

There are many ways to make a "best-of-all-time" list. Your selections will be different from mine. I am using peak playing strength as my primary metric, not overall career achievement because I am most interested in the best possible chess produced by each American on this list.

Peak rating: 2763

Gata Kamsky is a true chess prodigy. He became a strong grandmaster at age 16 and reached his peak in the 1990s. His career pinnacle was in the 1996 FIDE world championship bracket, where he made the finals but dropped the championship match against the reigning FIDE world champion, GMAnatoly Karpov.

Kamsky was born in the Soviet Union but moved to the United States early in his career. Kamsky won the U.S. chess championship five times (1991, 2010, 2011, 2013, and 2014), cementing his status as an American chess legend.

Here is a 22-year-old Kamsky beating the super-GM Nigel Short in 26 moves.

Peak rating: 2768

Even with much recent success, Leinier Dominguez Perez remains an underrated American chess talent.

Dominguez Perez officially became an American chess player less than two years ago, in December 2018, when he transferred federations to the United States. Before that, he was the five-time Cuban chess champion.

His career peak was likely his sole first place in the 2013 FIDE Grand Prix leg in Greece, finishing ahead of 11 other super-GMs, including three others on this list.

Dominguez Perez's attacking prowess was on full display in 2014 when he practically wiped future-compatriot GMWesley So's kingside off the board in this brutal miniature.

Peak rating: 2811 (estimated by Edo)

It's not a stretch to call Paul Morphy the father of American chess.

A true prodigy, Morphy was not just a chess force at an early age. His game was also about 100 years ahead of its time in terms of style and even tactical strength.

GM Bobby Fischer called Morphy "the most accurate player who ever lived," which should tell you something because many chess fans give that title instead to Fischer.

Morphy's game peaked quite early, and the apex was his European tour in 1858 at age 21. Morphy pretty much destroyed every strong player the European continent could throw at him, and by the time he returned to the United States, he was recognized as the unofficial world champion.

Morphy retired from competitive chess a year later to begin his law practice, never returning to the game before his death at age 47.

Morphy is the author of arguably the most famous chess game ever played, an exhibition against the Duke of Brunswick and Count Isouard at an opera house in Paris. If you're going to show a chess beginner one game, use this one.

Peak rating: 2816

Hikaru Nakamura, while quite a formidable traditional chess force, is truly a chess player of the modern age.

Nakamura has made his mark as unquestionably the best American blitz chess player ever, and also the best American online chess player ever. Since most chess games in 2020 are both played online and at fast time controls, these are fairly important arenas.

Nakamura has also established a tremendous following on the live-streaming site Twitch and was called "the grandmaster who got Twitch hooked on chess" by Wired magazine. On Chess.com, Nakamura has won the two most recent editions of the Speed Chess Championship (2018-2019).

Of course, Nakamura has enjoyed solid over-the-board success as well, winning the U.S. championship five times.

No game quite captures the modern, fun, and online-friendly nature of Nakamura's style like his thorough trolling of the computer engine Crafty back in 2007, when Crafty was one of the world's strongest engines and Nakamura was just 20 years old.

Peak rating: 2822

Wesley So transferred to the United States federation six years ago, and since then he has established himself as one of the world's best players.

So is 26 years old and it's reasonable to think that his chess peak is just getting started. So's style of play is precise and safe, rarely getting himself into trouble. This less-risky approach has been cited (mostly unfairly) as evidence that So is not an exciting chess player.

That argument went right out the window last November when So destroyed the classical world chess champion, Carlsen, in the finals of the first FIDE world Fischer random chess championship. So ran up the score, winning the match 13.5-2.5, putting to rest any doubts of his brilliance and creativity.

In this famous game against the top Chinese GM Ding Liren, So answers any lingering questions you might have about whether three pieces are better than a queen.

Peak rating: 2844

Fabiano Caruana is currently at the top of his career and sits just 28 rating points behind Carlsen on the live list. Caruana and Carlsen are the only players above 2800. The pair fought a close battle in the 2018 world chess championship, with Carlsen needing the tiebreaks to retain his title.

Caruana is still in contention for the next world championship whenever that process resumes, with the American one game off the lead of the 2020 candidates' tournament at the time of its postponement halfway through the schedule.

Caruana's chess highlight reel is too extensive to fully appreciate in this space. He won the U.S. chess championship on his first try in 2016, and he was the four-time Italian chess champion before transferring to the U.S. federation.

Why pick a draw for Caruana's showcase game, when all the other players get wins?

This game against Carlsen in the 2018 world chess championship represents the peak of chess on two levels. On the surface, you have the tremendous underdog Caruana outplaying and pressuring the world champion Carlsen, who was lucky to escape with the draw and maintain an even match.

On a deeper level, there is a beautiful and inscrutable endgame lurking in this game that astounded everyone who analyzed it. The chess super-computer "Sesse" found a forced checkmate for Caruana in 30 moves in real-time, as millions watched the game around the world. The legendary former world champion GMGarry Kasparov said no human could ever spot the win. Yet it was in there, on the board as surely the 64 squares themselves.

I still get goosebumps playing over this endgame.

Peak rating: 2785

Bobby Fischer stands as the most legendary U.S. chess player ever and is universally considered one of the three greatest world champions, along with Carlsen and Kasparov.

Fischer was responsible for a renaissance in American chess in the 1970s as he racked up ridiculous winning streaks on his way to the world title over GMBoris Spassky in 1972. Fischer elevated the game of chess to geopolitical philosophy, representing American individualism against the Soviet chess machine.

The most striking aspect of Fischer's chess was how far ahead he was of his competition. His peak rating of 2785, earned before the considerable rating inflation in the 50 years since would place him near the top of the chess world even today.

Computer studies have confirmed Fischer's strength and accuracy as other-worldly for his time. His style was universal, elegant and above all, accurate. His fierce competitive spirit is something the computer engines can't measure; Fischer had one of the strongest wills to win in chess history.

Fischer's career was cut short by disagreements with chess organizers along with mental and physical health problems. Nonetheless, in the short time he spent at the top of the game, he changed it forever with the millions of American players he inspired.

Almost as a side note, Fischer invented Fischer random chess (chess 960), which is considered one of the most creative chess variants. Fischer also held a patent for a chess clock with an increment, which is the preferred time control today of many players.

The below game, one of the most famous in chess history, shows the stunning chess clarity possessed by Fischer even as young as age 13 when he eviscerated a leading American chess master, Donald Byrne.

Peak rating: 3500+

I can already see the objections in the comment section. But the headline in this article said "chess players," not chess humans, and I am a big fan of non-human chess.

AlphaZero is an artificial intelligence project that plays chess. Given just the rules of the game, AlphaZero taught itself to play chess to superhuman levels in mere hours using machine-learning techniques.

It stormed onto the chess scene in late 2017 when its operators released the results of a 100-game match with Stockfish, the traditional champion chess engine.

AlphaZero plays chess differently from most computers, possessing an almost-intuitive understanding of the game and handling many positions in a beautiful, human-like manner. Of course, AlphaZero is stronger than any human, but if you played through its games you'd think it had a distinct personality. Maybe it does.

AlphaZero inspired a whole wave of neural-network chess engines, including the international open-source project Lc0, which currently sits second behind Stockfish on the computer ratings list. The machine-learning approach pioneered by AlphaZero transformed the scientific basis of computer chess, and it will be the neural-network engines that evolve the game to its next levels, wherever that may be.

Is AlphaZero American? AlphaZero runs on American TPUs. The project's inventor, the AI company DeepMind, is headquartered in the United Kingdom, but the company has been owned by an American corporation (Google/Alphabet) since before there was an AlphaZero.

If George Washington was born a British subject but can still be considered a founding father of the United States, we can extend that same leeway to AlphaZero, especially on the American day of independence from Great Britain.

Of course, there are many other American chess engines, most of them far stronger than the human players on this list, but here they are collectively represented by the intrepid AlphaZero, which changed computer chess forever.

I'll never forget where I was when I saw this game by AlphaZero against the reigning top computer engine Stockfish, and if you care about the evolution of chess, you might not either.

Who do you think are the top chess players in American history? Let us know in the comments.

Read the original post:
Who Are The 8 Best U.S. Chess Players Ever? - Chess.com

Welcome to Part 2 ofBitmovins Video Tech Deep Dive series: Super-Resolution with Machine learning.Before you get started, I highly recommend that you readSuper Resolution: Whats the buzz and why does it matter?. But if you would rather prefer to directly jump into it, here is a quick summary:

The focus of this series of blog posts will be on machine learning-based super-resolution.

In this post, we will examine:

Super-resolution, Machine learning (ML), and Video Upscaling are a match made in heaven. The three factors coming together is the reason behind the current popularity inMachine-learning based super-resolutionapplications. In this section, we will see why.

The concept of super-resolution has existed since the 1980s. The basic idea behind super-resolution was (and continues to be) tointelligentlycombinenon-redundant informationfrom multiple related low-resolution images to generate a single high-resolution image.

Some classic early applications were finding license plate information from several low-resolution images.

Several low-resolution snapshots of a moving car provides non-redundant but related information. Super-Resolution uses this related non-redundancy to create higher-resolution images, which can be useful in finding information such as license plate information or driver identification [Source].

But the recent wave of interest in super-resolution has been primarily driven by ML.

So, why ML and what changed now?

ML, in essence, is about learning theintelligencefor awell-defined problem. With the right architecture and enough data, ML can be significantly moreintelligentthan a human-defined solution (at least in that narrow domain). We saw this demonstrated stunningly in the case ofAlphaZero(for chess) andAlphaGo(for the board gameGo).

Super-resolution is awell-defined problem, and one could reasonably argue that ML would be a natural fit to solve this problem. With that motivation, early theoretical solutions were already proposed in the literature.

But, the exorbitant computational power and fundamental unresolved complexities kept the practical applications of ML-based super-resolution at bay.

However, in the last few years, there were two major developments:

These developments have led to a resurgence and come back for ML-based super-resolution methods.

It should be mentioned that ML-based super-resolution is a versatile hammer that can be used to drive manynails. It has wide applications, ranging frommedical imaging, remote sensing, astronomical observations, among others. But as mentioned inPart 1of this series, we will focus on howthe ML super-resolutionhammer can nail the problem ofvideo upscaling.

The last missing puzzle piece in this arc of the story isVideo upscaling.

When you think about it, video upscaling is almost a perfect nail for the ML-based super-resolution hammer.

Video provides the core features needed for the ML-based Super-Resolution. Namely:

The convergence of these three factors is why we are witnessing ahuge uptick in theresearchin this area, and also thefirst practical applicationsin the field of ML Super-Resolution powered Video upscaling.

I provided a historical timeline and the factors that lead to ML Super-Resolution powered Video upscaling. But, it might still not be clear on why it is superior to other traditional methods (bilinear,bicubic,Lanczos, among others). In this section, I will provide a simplified explanation to provide an intuitive understanding.

The superior performance simply boils down to the fact that the algorithm understands the nature of the content it is upsampling. And how it tunes itself to upsample that content in the best way possible. This is in contrast to the traditional methods where there is no tuning. In traditional methods, the same formula is applied without any consideration of the nature of the content.

One could say that:

ML-based super-resolution is to upsampling, whatPer-Titleis to encoding.

InPer-Title, we use different encoding recipes for the different pieces of content. In a similar way, ML-based super-resolution uses different upsampling recipes for different pieces of content.

The recipes can adapt itself on both at the:

Hopefully, by now, you are already excited about the possibilities of this idea. In this section, I would like to provide some suggestions on how you can incorporate this idea into your own video workflows and the potential benefits you might expect from it.

Broadly speaking, a video processing workflow typically has three steps involved:

Typically, there is a heavy emphasis on the encoding block for visual quality optimizations (Per-Title,3-Pass,Codec-Configuration, among others).

But, the other two (often overlooked) blocks are as important when it comes to visual quality optimization. In this instance, upsampling is a preprocessing step. And by choosing the right upsampling methods, such as super-resolution, one can improve the visual quality of the entire workflow. Sometimes, significantly more than that could be provided from the other blocks.

In the Part-3 of this series, we will delve more deeply into this. We will quantify how much quality improvements one could expect from tuning the pre-processing block with super-resolution. And use some real-life examples.

(This specific section is primarily meant for advanced readers who understand whatPer-Title,VMAF,convex-hullmeans. Please feel free to skip this section).

Like explained earlier, there are broadly three blocks in a video workflow. Roughly speaking, they work independently. But if we are smart about the design, we can extract synergies and use that to improve the overall video pipelines, that otherwise would not have existed.

One illustrative example is how Per-Title can work in conjunction with the Super-Resolution. This idea is depicted in the following figure.

VMAFvs Bitrate Convex hulls of video content. Green => 360p, Red => 720p, Blue => 1080p. BC : Bicubic, SR : SuperResolution.

In the above figure, for the illustrated bitrate: When using the traditional method the choice is clear. We will pick the 720p rendition. But, when using Super-Resolution, the choice is not very clear. We could either pick

The choice is determined by the complexity (vs) quality tradeoff that we are willing to make.

The takeaway message is two blocks synergistically working together to give more options and flexibility for the Per-Title algorithm to work with. Overall, a higher number of options translate to better overall results.

This is just one illustrative example, but within your own video workflows, you could identify regions where super-resolution can work synergically and improve the overall performance.

If your entire video catalog is a specific kind of content (anime for example), and you want to do a targeted upsample of these contents, then without doubtML Super-Resolution is the way to go!

In fact, that is what many companies alreadydo.This specific trend will only accelerate in the future, especially considering the popularity of consumer 4K TVs.

Visual quality enhancements,Synergies, andTargeted upsamplingare some ideas on how you can incorporate Super-Resolution into your video workflows.

Super-Resolution applied for targeted content such as Anime [Source]

We continued the story fromPart 1. We learned that :

In the follow-up, Part 3 of this series, we will look at how to do practical deployments, tools to use, and some real-life results.

This article was originally published as a blog post on the Bitmovin website byAdithyan Ilangovanand is re-published here with kind permission.

Originally posted here:
Super-Resolution: Why is it good and how can you incorporate it? - Display Daily

By now you've heard about the new kid on the chess-engine block, AlphaZero, and its crushing match win vs Stockfish, the strongest open-source chess engine.

The reactions from the chess community to this match ranged from admiration to utter disbelief.

But how does AlphaZero actually work?

How is it different from other engines and why is it so much better? In this two-part article Ill try to explain a bit of what goes on under AlphaZeros hood.

First, lets reflect on what happened. AlphaZero was developed by DeepMind (a Google-owned company) to specialize in learning how to play two-player, alternate-move games. It was primed with the rules of chess, and nothing else.

It then started learning chess by playing games against itself. Game one would have involved totally random moves. At the end of this game, AlphaZero had learned that the losing side had done stuff that wasnt all that smart, and that the winning side had played better. AlphaZero had taught itself its first chess lesson. The quality of chess in game two was a just a tiny bit better than the first.

Nine hours and 44 million games of split-personality chess later, AlphaZero had (very possibly) taught itself enough to become the greatest chess player, silicon- or carbon-based, of all time.

How on earth did it do it?

Google headquarters in London from inside, with the DeepMind section on the eighth floor. | Photo: Maria Emelianova/Chess.com.

It didnt calculate more variations than Stockfish.

Quite the opposite in fact: Stockfish examined 70 million positions per second while AlphaZero contented itself with about 0.1 percent of that: 80,000 per second. This brings to mind a remark made by Jonathan Rowson after Michael Adams crushed him in a match in 1998: I was amazed at how little he saw.

Stronger players tend to calculate fewer variations than weaker ones. Instead their highly-honed intuition guides them to focus their calculation on the most relevant lines. This is exactly what AlphaZero did. It taught itself chess in quite a human-like way, developing an intuition like no other chess machine has ever done, and it combined this with an amount of cold calculation.

Lets see how it did that.

IM Danny Rensch explains the AlphaZero match in a series of videos on Twitch.

The Analysis Tree

Chess engines use a tree-like structure to calculate variations, and use an evaluation function to assign the position at the end of a variation a value like +1.5 (Whites advantage is worth a pawn and a half) or -9.0 (Blacks advantage is worth a queen). AlphaZeros approach to both calculating variations and evaluating positions is radically different to what other engines do.

All popular chess engines are based on the minimax algorithm, which is a fancy name that simply means you pick the move that gives you the biggest advantage regardless of what the opponent plays. Minimax is invariably enhanced with alpha-beta pruning, which is used to reduce the size of the tree of variations to be examined. Heres an extreme example of how this pruning works: Say an engine is considering a move and sees its opponent has 20 feasible replies. One of those replies leads to a forced checkmate. Then the engine can abandon (or cutoff) the move it was considering, no matter how well it would stand after any of the other 19 replies.

Another issue is that if an engine prunes away moves that only seem bad, e.g. those that lose material, it will fail to consider any kind of sacrifice, which is partly why early engines were so materialistic. In current engines like Stockfish, alpha-beta pruning is combined with a range of other chess-specific enhancements such the killer-move heuristic (a strong move in another similar variation is likely to be strong here), counter-move heuristic (some moves have natural responses regardless of position I bet youve often met axb5 with axb5, right?) and many others.

AlphaZero, in contrast, uses Monte Carlo Tree Search, or MCTS for short. Monte Carlo is famous for its casinos, so when you see this term in a computing context it means theres something random going on. An engine using pure MCTS would evaluate a position by generating a number of move sequences (called playouts) from that position randomly, and averaging the final scores (win/draw/loss) that they yield. This approach may seem altogether too simple, but if you think about it youll realize its actually quite a plausible way of evaluating a position.

The Monte Carlo Casino.

AlphaZero creates a number of playouts on each move (800 during its training). It also augments pure MCTS by preferring moves that it has not tried (much) already, that seem probable and that seem to lead to good positions, where good means that the evaluation function (more on this next article) gives them a high value. Its really creating semi-random playouts, lines that seem appropriate to its ever-improving evaluation function. Isnt this quite like how you calculate? By focussing on plausible lines of play?

Notice that so far theres absolutely nothing chess-specific in what AlphaZero is doing. In my next article, when we look at how AlphaZero learns to evaluate chess positions, well see theres absolutely nothing chess-specific there either!

Like a newborn baby, AlphaZero came into the world with little knowledge, but is massively geared to learn. One weakness of MCTS is that since its based on creating semi-random playouts, it can get it completely wrong in tense positions where there is one precise line of optimal play. If it doesnt randomly select this line, it is likely to blunder. This blindness was probably what caused AlphaZeros Go playing predecessor, AlphaGo, to lose a game to 18-time world Go champion Lee Sedol. It seems not to have been an issue in the match with Stockfish, however.

MCTS has been used previously for two-player gameplay, but was found to perform much worse than the well-established minimax plus alpha-beta approach. In AlphaZero, MCTS combines really well with the employed neural network-based evaluation function.

In my next article, Ill explain more about this neural network and especially the fascinating way it learns, on its own, how to evaluate chess positions. Ill also describe the hardware AlphaZero runs on, and make some predictions about how all this will impact chess as we know it.

What do you think about how AlphaZero plays chess? Let us know in the comments.

Corrections: AlphaZero creates a number of playouts on each move, not 800. That was during training.

More:
How Does AlphaZero Play Chess? - Chess.com

Elizabeth Spelke, a cognitive psychologist at Harvard, has spent her career testing the worlds most sophisticated learning systemthe mind of a baby.

Gurgling infants might seem like no match for artificial intelligence. They are terrible at labeling images, hopeless at mining text, and awful at videogames. Then again, babies can do things beyond the reach of any AI. By just a few months old, they've begun to grasp the foundations of language, such as grammar. They've started to understand how the physical world works, how to adapt to unfamiliar situations.

Yet even experts like Spelke don't understand precisely how babiesor adults, for that matterlearn. That gap points to a puzzle at the heart of modern artificial intelligence: We're not sure what to aim for.

Consider one of the most impressive examples of AI, AlphaZero, a program that plays board games with superhuman skill. After playing thousands of games against itself at hyperspeed, and learning from winning positions, AlphaZero independently discovered several famous chess strategies and even invented new ones. It certainly seems like a machine eclipsing human cognitive abilities. But AlphaZero needs to play millions more games than a person during practice to learn a game. Most tellingly, it cannot take what it has learned from the game and apply it to another area.

To some members of the AI priesthood, that calls for a new approach. What makes human intelligence special is its adaptabilityits power to generalize to never-seen-before situations, says Franois Chollet, a well-known AI engineer and the creator of Keras, a widely used framework for deep learning. In a November research paper, he argued that it's misguided to measure machine intelligence solely according to its skills at specific tasks. Humans don't start out with skills; they start out with a broad ability to acquire new skills, he says. What a strong human chess player is demonstrating isn't the ability to play chess per se, but the potential to acquire any task of a similar difficulty. That's a very different capability.

Chollet posed a set of problems designed to test an AI program's ability to learn in a more generalized way. Each problem requires arranging colored squares on a grid based on just a few prior examples. It's not hard for a person. But modern machine-learning programstrained on huge amounts of datacannot learn from so few examples. As of late April, more than 650 teams had signed up to tackle the challenge; the best AI systems were getting about 12 percent correct.

A self-driving car cannot intuit from common sense what will happen if a truck spills its load.

It isn't yet clear how humans solve these problems, but Spelke's work offers a few clues. For one thing, it suggests that humans are born with an innate ability to quickly learn certain things, like what a smile means or what happens when you drop something. It also suggests we learn a lot from each other. One recent experiment showed that 3-month-olds appear puzzled when someone grabs a ball in an inefficient way, suggesting that they already appreciate that people cause changes in their environment. Even the most sophisticated and powerful AI systems on the market can't grasp such concepts. A self-driving car, for instance, cannot intuit from common sense what will happen if a truck spills its load.

Josh Tenenbaum, a professor in MIT's Center for Brains, Minds & Machines, works closely with Spelke and uses insights from cognitive science as inspiration for his programs. He says much of modern AI misses the bigger picture, likening it to a Victorian-era satire about a two-dimensional world inhabited by simple geometrical people. We're sort of exploring Flatlandonly some dimensions of basic intelligence, he says. Tenenbaum believes that, just as evolution has given the human brain certain capabilities, AI programs will need a basic understanding of physics and psychology in order to acquire and use knowledge as efficiently as a baby. And to apply this knowledge to new situations, he says, they'll need to learn in new waysfor example, by drawing causal inferences rather than simply finding patterns. At some pointyou know, if you're intelligentyou realize maybe there's something else out there, he says.

This article appears in the June issue. Subscribe now.

Let us know what you think about this article. Submit a letter to the editor at mail@wired.com.

Special Series: The Future of Thinking Machines

Original post:
It's Called Artificial Intelligencebut What Is Intelligence? - WIRED

Game-playing artificial intelligence

AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess, shogi and go. This algorithm uses an approach similar to AlphaGo Zero.

On December 5, 2017, the DeepMind team released a preprint introducing AlphaZero, which within 24 hours of training achieved a superhuman level of play in these three games by defeating world-champion programs Stockfish, elmo, and the 3-day version of AlphaGo Zero. In each case it made use of custom tensor processing units (TPUs) that the Google programs were optimized to use.[1] AlphaZero was trained solely via "self-play" using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks, all in parallel, with no access to opening books or endgame tables. After four hours of training, DeepMind estimated AlphaZero was playing at a higher Elo rating than Stockfish 8; after 9 hours of training, the algorithm defeated Stockfish 8 in a time-controlled 100-game tournament (28 wins, 0 losses, and 72 draws).[1][2][3] The trained algorithm played on a single machine with four TPUs.

DeepMind's paper on AlphaZero was published in the journal Science on 7 December 2018.[4] In 2019 DeepMind published a new paper detailing MuZero, a new algorithm able to generalise on AlphaZero work playing both Atari and board games without knowledge of the rules or representations of the game.[5]

AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm, and is able to play shogi and chess as well as Go. Differences between AZ and AGZ include:[1]

Comparing Monte Carlo tree search searches, AlphaZero searches just 80,000 positions per second in chess and 40,000 in shogi, compared to 70 million for Stockfish and 35 million for elmo. AlphaZero compensates for the lower number of evaluations by using its deep neural network to focus much more selectively on the most promising variation.[1]

AlphaZero was trained solely via self-play, using 5,000 first-generation TPUs to generate the games and 64 second-generation TPUs to train the neural networks. In parallel, the in-training AlphaZero was periodically matched against its benchmark (Stockfish, elmo, or AlphaGo Zero) in brief one-second-per-move games to determine how well the training was progressing. DeepMind judged that AlphaZero's performance exceeded the benchmark after around four hours of training for Stockfish, two hours for elmo, and eight hours for AlphaGo Zero.[1]

In AlphaZero's chess tournament against Stockfish 8 (2016 TCEC world champion), each program was given one minute per move. Stockfish was allocated 64 threads and a hash size of 1 GB,[1] a setting that Stockfish's Tord Romstad later criticized as suboptimal.[6][note 1] AlphaZero was trained on chess for a total of nine hours before the tournament. During the tournament, AlphaZero ran on a single machine with four application-specific TPUs. In 100 games from the normal starting position, AlphaZero won 25 games as White, won 3 as Black, and drew the remaining 72.[8] In a series of twelve, 100-game matches (of unspecified time or resource constraints) against Stockfish starting from the 12 most popular human openings, AlphaZero won 290, drew 886 and lost 24.[1]

AlphaZero was trained on shogi for a total of two hours before the tournament. In 100 shogi games against elmo (World Computer Shogi Championship 27 summer 2017 tournament version with YaneuraOu 4.73 search), AlphaZero won 90 times, lost 8 times and drew twice.[8] As in the chess games, each program got one minute per move, and elmo was given 64 threads and a hash size of 1GB.[1]

After 34 hours of self-learning of Go and against AlphaGo Zero, AlphaZero won 60 games and lost 40.[1][8]

DeepMind stated in its preprint, "The game of chess represented the pinnacle of AI research over several decades. State-of-the-art programs are based on powerful engines that search many millions of positions, leveraging handcrafted domain expertise and sophisticated domain adaptations. AlphaZero is a generic reinforcement learning algorithm originally devised for the game of go that achieved superior results within a few hours, searching a thousand times fewer positions, given no domain knowledge except the rules."[1] DeepMind's Demis Hassabis, a chess player himself, called AlphaZero's play style "alien": It sometimes wins by offering counterintuitive sacrifices, like offering up a queen and bishop to exploit a positional advantage. "It's like chess from another dimension."[9]

Given the difficulty in chess of forcing a win against a strong opponent, the +28 0 =72 result is a significant margin of victory. However, some grandmasters, such as Hikaru Nakamura and Komodo developer Larry Kaufman, downplayed AlphaZero's victory, arguing that the match would have been closer if the programs had access to an opening database (since Stockfish was optimized for that scenario).[10] Romstad additionally pointed out that Stockfish is not optimized for rigidly fixed-time moves and the version used is a year old.[6][11]

Similarly, some shogi observers argued that the elmo hash size was too low, that the resignation settings and the "EnteringKingRule" settings (cf. shogi Entering King) may have been inappropriate, and that elmo is already obsolete compared with newer programs.[12][13]

Papers headlined that the chess training took only four hours: "It was managed in little more than the time between breakfast and lunch."[2][14] Wired hyped AlphaZero as "the first multi-skilled AI board-game champ".[15] AI expert Joanna Bryson noted that Google's "knack for good publicity" was putting it in a strong position against challengers. "It's not only about hiring the best programmers. It's also very political, as it helps make Google as strong as possible when negotiating with governments and regulators looking at the AI sector."[8]

Human chess grandmasters generally expressed excitement about AlphaZero. Danish grandmaster Peter Heine Nielsen likened AlphaZero's play to that of a superior alien species.[8] Norwegian grandmaster Jon Ludvig Hammer characterized AlphaZero's play as "insane attacking chess" with profound positional understanding.[2] Former champion Garry Kasparov said "It's a remarkable achievement, even if we should have expected it after AlphaGo."[10][16]

Grandmaster Hikaru Nakamura was less impressed, and stated "I don't necessarily put a lot of credibility in the results simply because my understanding is that AlphaZero is basically using the Google supercomputer and Stockfish doesn't run on that hardware; Stockfish was basically running on what would be my laptop. If you wanna have a match that's comparable you have to have Stockfish running on a supercomputer as well."[7]

Top US correspondence chess player Wolff Morrow was also unimpressed, claiming that AlphaZero would probably not make the semifinals of a fair competition such as TCEC where all engines play on equal hardware. Morrow further stated that although he might not be able to beat AlphaZero if AlphaZero played drawish openings such as the Petroff Defence, AlphaZero would not be able to beat him in a correspondence chess game either.[17]

Motohiro Isozaki, the author of YaneuraOu, noted that although AlphaZero did comprehensively beat elmo, the rating of AlphaZero in shogi stopped growing at a point which is at most 100~200 higher than elmo. This gap is not that high, and elmo and other shogi software should be able to catch up in 12 years.[18]

DeepMind addressed many of the criticisms in their final version of the paper, published in December 2018 in Science.[4] They further clarified that AlphaZero was not running on a supercomputer; it was trained using 5,000 tensor processing units (TPUs), but only ran on four TPUs and a 44-core CPU in its matches.[19]

In the final results, Stockfish version 8 ran under the same conditions as in the TCEC superfinal: 44 CPU cores, Syzygy endgame tablebases, and a 32GB hash size. Instead of a fixed time control of one move per minute, both engines were given 3 hours plus 15 seconds per move to finish the game. In a 1000-game match, AlphaZero won with a score of 155 wins to 6 losses, with the rest drawn. DeepMind also played a series of games using the TCEC opening positions; AlphaZero also won convincingly.

Similar to Stockfish, Elmo ran under the same conditions as in the 2017 CSA championship. The version of Elmo used was WCSC27 in combination with YaneuraOu 2017 Early KPPT 4.79 64AVX2 TOURNAMENT. Elmo operated on the same hardware as Stockfish: 44 CPU cores and a 32GB hash size. AlphaZero won 98.2% of games when playing black (which plays first in shogi) and 91.2% overall.

Human grandmasters were generally impressed with AlphaZero's games against Stockfish.[20] Former world champion Garry Kasparov said it was a pleasure to watch AlphaZero play, especially since its style was open and dynamic like his own.[21][22]

In the chess community, Komodo developer Mark Lefler called it a "pretty amazing achievement", but also pointed out that the data was old, since Stockfish had gained a lot of strength since January 2018 (when Stockfish 8 was released). Fellow developer Larry Kaufman said AlphaZero would probably lose a match against the latest version of Stockfish, Stockfish 10, under Top Chess Engine Championship (TCEC) conditions. Kaufman argued that the only advantage of neural networkbased engines was that they used a GPU, so if there was no regard for power consumption (e.g. in an equal-hardware contest where both engines had access to the same CPU and GPU) then anything the GPU achieved was "free". Based on this, he stated that the strongest engine was likely to be a hybrid with neural networks and standard alphabeta search.[23]

AlphaZero inspired the computer chess community to develop Leela Chess Zero, using the same techniques as AlphaZero. Leela contested several championships against Stockfish, where it showed similar strength.[24]

In 2019 DeepMind published MuZero, a unified system that played excellent chess, shogi, and go, as well as games in the Atari Learning Environment, without being pre-programmed with their rules.[25][26]

The match results by themselves are not particularly meaningful because of the rather strange choice of time controls and Stockfish parameter settings: The games were played at a fixed time of 1 minute/move, which means that Stockfish has no use of its time management heuristics (lot of effort has been put into making Stockfish identify critical points in the game and decide when to spend some extra time on a move; at a fixed time per move, the strength will suffer significantly). The version of Stockfish used is one year old, was playing with far more search threads than has ever received any significant amount of testing, and had way too small hash tables for the number of threads. I believe the percentage of draws would have been much higher in a match with more normal conditions.[7]

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AlphaZero - Wikipedia