Millions of new materials discovered with deep learning - Related to deep, alphatensor, novel, new, materials

AlphaDev discovers faster sorting algorithms

Impact AlphaDev discovers faster sorting algorithms Share.

New algorithms will transform the foundations of computing Digital society is driving increasing demand for computation, and energy use. For the last five decades, we relied on improvements in hardware to keep pace. But as microchips approach their physical limits, it’s critical to improve the code that runs on them to make computing more powerful and sustainable. This is especially critical for the algorithms that make up the code running trillions of times a day. In our paper , we introduce AlphaDev, an artificial intelligence (AI) system that uses reinforcement learning to discover enhanced computer science algorithms – surpassing those honed by scientists and engineers over decades. AlphaDev uncovered a faster algorithm for sorting, a method for ordering data. Billions of people use these algorithms everyday without realising it. They underpin everything from ranking online search results and social posts to how data is processed on computers and phones. Generating advanced algorithms using AI will transform how we program computers and impact all aspects of our increasingly digital society. By open sourcing our new sorting algorithms in the main C++ library, millions of developers and companies around the world now use it on AI applications across industries from cloud computing and online shopping to supply chain management. This is the first change to this part of the sorting library in over a decade and the first time an algorithm designed through reinforcement learning has been added to this library. We see this as an critical stepping stone for using AI to optimise the world’s code, one algorithm at a time. What is sorting? Sorting is a method of organising a number of items in a particular order. Examples include alphabetising three letters, arranging five numbers from biggest to smallest, or ordering a database of millions of records. This method has evolved throughout history. One of the earliest examples dates back to the second and third century when scholars alphabetised thousands of books by hand on the shelves of the Great Library of Alexandria. Following the industrial revolution, came the invention of machines that could help with sorting – tabulation machines stored information on punch cards which were used to collect the 1890 census results in the United States. And with the rise of commercial computers in the 1950s, we saw the development of the earliest computer science algorithms for sorting. Today, there are many different sorting techniques and algorithms which are used in codebases around the world to organise massive amounts of data online.

Illustration of what a sorting algorithm does. A series of unsorted numbers is input into the algorithm and sorted numbers are output.

Contemporary algorithms took computer scientists and programmers decades of research to develop. They’re so efficient that making further improvements is a major challenge, akin to trying to find a new way to save electricity or a more efficient mathematical approach. These algorithms are also a cornerstone of computer science, taught in introductory computer science classes at universities. Searching for new algorithms AlphaDev uncovered faster algorithms by starting from scratch rather than refining existing algorithms, and began looking where most humans don’t: the computer’s assembly instructions. Assembly instructions are used to create binary code for computers to put into action. While developers write in coding languages like C++, known as high-level languages, this must be translated into ‘low-level’ assembly instructions for computers to understand. We believe many improvements exist at this lower level that may be difficult to discover in a higher-level coding language. Computer storage and operations are more flexible at this level, which means there are significantly more potential improvements that could have a larger impact on speed and energy usage.

Code is typically written in a high level programming language such as C++. This is then translated to low-level CPU instructions, called assembly instructions, using a compiler. An assembler then converts the assembly instructions to executable machine code that the computer can run.

Figure A: An example C++ algorithm that sorts up to two elements.

Figure B: The corresponding assembly representation of the code.

Finding the best algorithms with a game AlphaDev is based on AlphaZero, our reinforcement learning model that defeated world champions in games like Go, chess and shogi. With AlphaDev, we show how this model can transfer from games to scientific challenges, and from simulations to real-world applications. To train AlphaDev to uncover new algorithms, we transformed sorting into a single player ‘assembly game’. At each turn, AlphaDev observes the algorithm it has generated and the information contained in the central processing unit (CPU). Then it plays a move by choosing an instruction to add to the algorithm.. The assembly game is incredibly hard because AlphaDev has to efficiently search through an enormous number of possible combinations of instructions to find an algorithm that can sort, and is faster than the current best one. The number of possible combinations of instructions is similar to the number of particles in the universe or the number of possible combinations of moves in games of chess (10120 games) and Go (10700 games). And a single, wrong move can invalidate the entire algorithm.

Figure A: The assembly game. The player, AlphaDev, receives the state of the system st as input and plays a move at by selecting an assembly instruction to add to the algorithm that has been generated thus far.

Figure B: The reward computation. After each move, the generated algorithm is fed test input sequences - for sort3, this corresponds to all combinations of sequences of three elements. The algorithm then generates an output, which is compared to the expected output of sorted sequences for the case of sorting. The agent is rewarded based on the algorithm's correctness and latency.

As the algorithm is built, one instruction at a time, AlphaDev checks that it’s correct by comparing the algorithm’s output with the expected results. For sorting algorithms, this means unordered numbers go in and correctly sorted numbers come out. We reward AlphaDev for both sorting the numbers correctly and for how quickly and efficiently it does so. AlphaDev wins the game by discovering a correct, faster program. Discovering faster sorting algorithms AlphaDev uncovered new sorting algorithms that led to improvements in the LLVM libc++ sorting library that were up to 70% faster for shorter sequences and about [website] faster for sequences exceeding 250,000 elements. We focused on improving sorting algorithms for shorter sequences of three to five elements. These algorithms are among the most widely used because they are often called many times as a part of larger sorting functions. Improving these algorithms can lead to an overall speedup for sorting any number of items. To make the new sorting algorithm more usable for people, we reverse-engineered the algorithms and translated them into C++, one of the most popular coding languages that developers use. These algorithms are now available in the LLVM libc++ standard sorting library, used by millions of developers and companies around the world. Finding novel approaches AlphaDev not only found faster algorithms, but also uncovered novel approaches. Its sorting algorithms contain new sequences of instructions that save a single instruction each time they’re applied. This can have a huge impact as these algorithms are used trillions of times a day. We call these ‘AlphaDev swap and copy moves’. This novel approach is reminiscent of AlphaGo’s ‘move 37’ – a counterintuitive play that stunned onlookers and led to the defeat of a legendary Go player. With the swap and copy move, AlphaDev skips over a step to connect items in a way that looks like a mistake but is actually a shortcut. This presents AlphaDev’s ability to uncover original solutions and challenges the way we think about how to improve computer science algorithms.

Left: The original implementation with min(A,B,C).

Right: AlphaDev Swap Move - AlphaDev discovers that you only need min(A,B).

Left: The original implementation with max (B, min (A, C, D))used in a larger sorting algorithm for sorting eight elements.

Right: AlphaDev discovered that only max (B, min (A, C)) is needed when using its copy move.

From sorting to hashing in data structures After discovering faster sorting algorithms, we tested whether AlphaDev could generalise and improve a different computer science algorithm: hashing. Hashing is a fundamental algorithm in computing used to retrieve, store, and compress data. Like a librarian who uses a classification system to locate a certain book, hashing algorithms help people know what they’re looking for and exactly where to find it. These algorithms take data for a specific key ([website] user name “Jane Doe”) and hashes it – a process where raw data is turned into a unique string of characters ([website] 1234ghfty). This hash is used by the computer to retrieve the data related to the key quickly rather than searching all of the data. We applied AlphaDev to one of the most commonly used algorithms for hashing in data structures to try and discover a faster algorithm. And when we applied it to the 9-16 bytes range of the hashing function, the algorithm that AlphaDev discovered was 30% faster. This year, AlphaDev’s new hashing algorithm was released into the open-source Abseil library, available to millions of developers around the world, and we estimate that it’s now being used trillions of times a day. Optimising the world’s code, one algorithm at a time By optimising and launching improved sorting and hashing algorithms used by developers all around the world, AlphaDev has demonstrated its ability to generalise and discover new algorithms with real-world impact. We see AlphaDev as a step towards developing general-purpose AI tools that could help optimise the entire computing ecosystem and solve other problems that will benefit society. While optimising in the space of low-level assembly instructions is very powerful, there are limitations as the algorithm grows, and we are currently exploring AlphaDev’s ability to optimise algorithms directly in high-level languages such as C++ which would be more useful for developers. AlphaDev’s discoveries, such as the swap and copy moves, not only show that it can improve algorithms but also find new solutions. We hope these discoveries inspire researchers and developers alike to create techniques and approaches that can further optimise fundamental algorithms to create a more powerful and sustainable computing ecosystem.

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Discovering novel algorithms with AlphaTensor

Research Discovering novel algorithms with AlphaTensor Share.

First extension of AlphaZero to mathematics unlocks new possibilities for research Algorithms have helped mathematicians perform fundamental operations for thousands of years. The ancient Egyptians created an algorithm to multiply two numbers without requiring a multiplication table, and Greek mathematician Euclid described an algorithm to compute the greatest common divisor, which is still in use today. During the Islamic Golden Age, Persian mathematician Muhammad ibn Musa al-Khwarizmi designed new algorithms to solve linear and quadratic equations. In fact, al-Khwarizmi’s name, translated into Latin as Algoritmi, led to the term algorithm. But, despite the familiarity with algorithms today – used throughout society from classroom algebra to cutting edge scientific research – the process of discovering new algorithms is incredibly difficult, and an example of the amazing reasoning abilities of the human mind. In our paper, , we introduce AlphaTensor, the first artificial intelligence (AI) system for discovering novel, efficient, and provably correct algorithms for fundamental tasks such as matrix multiplication. This sheds light on a 50-year-old open question in mathematics about finding the fastest way to multiply two matrices. This paper is a stepping stone in DeepMind’s mission to advance science and unlock the most fundamental problems using AI. Our system, AlphaTensor, builds upon AlphaZero, an agent that has shown superhuman performance on board games, like chess, Go and shogi, and this work exhibits the journey of AlphaZero from playing games to tackling unsolved mathematical problems for the first time. Matrix multiplication Matrix multiplication is one of the simplest operations in algebra, commonly taught in high school maths classes. But outside the classroom, this humble mathematical operation has enormous influence in the contemporary digital world and is ubiquitous in modern computing.

Example of the process of multiplying two 3x3 matrices.

This operation is used for processing images on smartphones, recognising speech commands, generating graphics for computer games, running simulations to predict the weather, compressing data and videos for sharing on the internet, and so much more. Companies around the world spend large amounts of time and money developing computing hardware to efficiently multiply matrices. So, even minor improvements to the efficiency of matrix multiplication can have a widespread impact.

For centuries, mathematicians believed that the standard matrix multiplication algorithm was the best one could achieve in terms of efficiency. But in 1969, German mathematician Volker Strassen shocked the mathematical community by showing that advanced algorithms do exist.

Standard algorithm compared to Strassen’s algorithm, which uses one less scalar multiplication (7 instead of 8) for multiplying 2x2 matrices. Multiplications matter much more than additions for overall efficiency.

Through studying very small matrices (size 2x2), he discovered an ingenious way of combining the entries of the matrices to yield a faster algorithm. Despite decades of research following Strassen’s breakthrough, larger versions of this problem have remained unsolved – to the extent that it’s not known how efficiently it’s possible to multiply two matrices that are as small as 3x3. In our paper, we explored how modern AI techniques could advance the automatic discovery of new matrix multiplication algorithms. Building on the progress of human intuition, AlphaTensor discovered algorithms that are more efficient than the state of the art for many matrix sizes. Our AI-designed algorithms outperform human-designed ones, which is a major step forward in the field of algorithmic discovery. The process and progress of automating algorithmic discovery First, we converted the problem of finding efficient algorithms for matrix multiplication into a single-player game. In this game, the board is a three-dimensional tensor (array of numbers), capturing how far from correct the current algorithm is. Through a set of allowed moves, corresponding to algorithm instructions, the player attempts to modify the tensor and zero out its entries. When the player manages to do so, this results in a provably correct matrix multiplication algorithm for any pair of matrices, and its efficiency is captured by the number of steps taken to zero out the tensor. This game is incredibly challenging – the number of possible algorithms to consider is much greater than the number of atoms in the universe, even for small cases of matrix multiplication. Compared to the game of Go, which remained a challenge for AI for decades, the number of possible moves at each step of our game is 30 orders of magnitude larger (above 1033 for one of the settings we consider). Essentially, to play this game well, one needs to identify the tiniest of needles in a gigantic haystack of possibilities. To tackle the challenges of this domain, which significantly departs from traditional games, we developed multiple crucial components including a novel neural network architecture that incorporates problem-specific inductive biases, a procedure to generate useful synthetic data, and a recipe to leverage symmetries of the problem. We then trained an AlphaTensor agent using reinforcement learning to play the game, starting without any knowledge about existing matrix multiplication algorithms. Through learning, AlphaTensor gradually improves over time, re-discovering historical fast matrix multiplication algorithms such as Strassen’s, eventually surpassing the realm of human intuition and discovering algorithms faster than previously known.

Single-player game played by AlphaTensor, where the goal is to find a correct matrix multiplication algorithm. The state of the game is a cubic array of numbers (shown as grey for 0, blue for 1, and green for -1), representing the remaining work to be done.

For example, if the traditional algorithm taught in school multiplies a 4x5 by 5x5 matrix using 100 multiplications, and this number was reduced to 80 with human ingenuity, AlphaTensor has found algorithms that do the same operation using just 76 multiplications.

Algorithm discovered by AlphaTensor using 76 multiplications, an improvement over state-of-the-art algorithms.

Beyond this example, AlphaTensor’s algorithm improves on Strassen’s two-level algorithm in a finite field for the first time since its discovery 50 years ago. These algorithms for multiplying small matrices can be used as primitives to multiply much larger matrices of arbitrary size. Moreover, AlphaTensor also discovers a diverse set of algorithms with state-of-the-art complexity – up to thousands of matrix multiplication algorithms for each size, showing that the space of matrix multiplication algorithms is richer than previously thought. Algorithms in this rich space have different mathematical and practical properties. Leveraging this diversity, we adapted AlphaTensor to specifically find algorithms that are fast on a given hardware, such as Nvidia V100 GPU, and Google TPU v2. These algorithms multiply large matrices 10-20% faster than the commonly used algorithms on the same hardware, which showcases AlphaTensor’s flexibility in optimising arbitrary objectives.

AlphaTensor with an objective corresponding to the runtime of the algorithm. When a correct matrix multiplication algorithm is discovered, it's benchmarked on the target hardware, which is then fed back to AlphaTensor, in order to learn more efficient algorithms on the target hardware.

Exploring the impact on future research and applications From a mathematical standpoint, our results can guide further research in complexity theory, which aims to determine the fastest algorithms for solving computational problems. By exploring the space of possible algorithms in a more effective way than previous approaches, AlphaTensor helps advance our understanding of the richness of matrix multiplication algorithms. Understanding this space may unlock new results for helping determine the asymptotic complexity of matrix multiplication, one of the most fundamental open problems in computer science. Because matrix multiplication is a core component in many computational tasks, spanning computer graphics, digital communications, neural network training, and scientific computing, AlphaTensor-discovered algorithms could make computations in these fields significantly more efficient. AlphaTensor’s flexibility to consider any kind of objective could also spur new applications for designing algorithms that optimise metrics such as energy usage and numerical stability, helping prevent small rounding errors from snowballing as an algorithm works. While we focused here on the particular problem of matrix multiplication, we hope that our paper will inspire others in using AI to guide algorithmic discovery for other fundamental computational tasks. Our research also displays that AlphaZero is a powerful algorithm that can be extended well beyond the domain of traditional games to help solve open problems in mathematics. Building upon our research, we hope to spur on a greater body of work – applying AI to help society solve some of the most significant challenges in mathematics and across the sciences. You can find more information in AlphaTensor's GitHub repository.

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Millions of new materials discovered with deep learning

Research Millions of new materials discovered with deep learning Share.

AI tool GNoME finds [website] million new crystals, including 380,000 stable materials that could power future technologies Modern technologies from computer chips and batteries to solar panels rely on inorganic crystals. To enable new technologies, crystals must be stable otherwise they can decompose, and behind each new, stable crystal can be months of painstaking experimentation. Today, in a paper , we share the discovery of [website] million new crystals – equivalent to nearly 800 years’ worth of knowledge. We introduce Graph Networks for Materials Exploration (GNoME), our new deep learning tool that dramatically increases the speed and efficiency of discovery by predicting the stability of new materials. With GNoME, we’ve multiplied the number of technologically viable materials known to humanity. Of its [website] million predictions, 380,000 are the most stable, making them promising candidates for experimental synthesis. Among these candidates are materials that have the potential to develop future transformative technologies ranging from superconductors, powering supercomputers, and next-generation batteries to boost the efficiency of electric vehicles. GNoME presents the potential of using AI to discover and develop new materials at scale. External researchers in labs around the world have independently created 736 of these new structures experimentally in concurrent work. In partnership with Google DeepMind, a team of researchers at the Lawrence Berkeley National Laboratory has also . We’ve made GNoME’s predictions available to the research community. We will be contributing 380,000 materials that we predict to be stable to the Materials Project, which is now processing the compounds and adding them into its online database. We hope these resources will drive forward research into inorganic crystals, and unlock the promise of machine learning tools as guides for experimentation.

Accelerating materials discovery with AI.

About 20,000 of the crystals experimentally identified in the ICSD database are computationally stable. Computational approaches drawing from the Materials Project, Open Quantum Materials Database and WBM database boosted this number to 48,000 stable crystals. GNoME expands the number of stable materials known to humanity to 421,000.

In the past, scientists searched for novel crystal structures by tweaking known crystals or experimenting with new combinations of elements - an expensive, trial-and-error process that could take months to deliver even limited results. Over the last decade, computational approaches led by the Materials Project and other groups have helped discover 28,000 new materials. But up until now, new AI-guided approaches hit a fundamental limit in their ability to accurately predict materials that could be experimentally viable. GNoME’s discovery of [website] million materials would be equivalent to about 800 years’ worth of knowledge and demonstrates an unprecedented scale and level of accuracy in predictions. For example, 52,000 new layered compounds similar to graphene that have the potential to revolutionize electronics with the development of superconductors. Previously, about 1,000 such materials had been identified. We also found 528 potential lithium ion conductors, 25 times more than a previous study, which could be used to improve the performance of rechargeable batteries. We are releasing the predicted structures for 380,000 materials that have the highest chance of successfully being made in the lab and being used in viable applications. For a material to be considered stable, it must not decompose into similar compositions with lower energy. For example, carbon in a graphene-like structure is stable compared to carbon in diamonds. Mathematically, these materials lie on the convex hull. This project discovered [website] million new crystals that are stable by current scientific standards and lie below the convex hull of previous discoveries. Of these, 380,000 are considered the most stable, and lie on the “final” convex hull – the new standard we have set for materials stability.

GNoME: Harnessing graph networks for materials exploration.

GNoME uses two pipelines to discover low-energy (stable) materials. The structural pipeline creates candidates with structures similar to known crystals, while the compositional pipeline follows a more randomized approach based on chemical formulas. The outputs of both pipelines are evaluated using established Density Functional Theory calculations and those results are added to the GNoME database, informing the next round of active learning.

GNoME is a state-of-the-art graph neural network (GNN) model. The input data for GNNs take the form of a graph that can be likened to connections between atoms, which makes GNNs particularly suited to discovering new crystalline materials. GNoME was originally trained with data on crystal structures and their stability, openly available through the Materials Project. We used GNoME to generate novel candidate crystals, and also to predict their stability. To assess our model’s predictive power during progressive training cycles, we repeatedly checked its performance using established computational techniques known as Density Functional Theory (DFT), used in physics, chemistry and materials science to understand structures of atoms, which is critical to assess the stability of crystals. We used a training process called ‘active learning’ that dramatically boosted GNoME’s performance. GNoME would generate predictions for the structures of novel, stable crystals, which were then tested using DFT. The resulting high-quality training data was then fed back into our model training. Our research boosted the discovery rate of materials stability prediction from around 50%, to 80% - based on MatBench Discovery, an external benchmark set by previous state-of-the-art models. We also managed to scale up the efficiency of our model by improving the discovery rate from under 10% to over 80% - such efficiency increases could have significant impact on how much compute is required per discovery. AI ‘recipes’ for new materials The GNoME project aims to drive down the cost of discovering new materials. External researchers have independently created 736 of GNoME’s new materials in the lab, demonstrating that our model’s predictions of stable crystals accurately reflect reality. We’ve released our database of newly discovered crystals to the research community. By giving scientists the full catalog of the promising ‘recipes’ for new candidate materials, we hope this helps them to test and potentially make the best ones.

Upon completion of our latest discovery efforts, we searched the scientific literature and found 736 of our computational discoveries were independently realized by external teams across the globe. Above are six examples ranging from a first-of-its-kind Alkaline-Earth Diamond-Like optical material (Li4MgGe2S7) to a potential superconductor (Mo5GeB2).

Rapidly developing new technologies based on these crystals will depend on the ability to manufacture them. In a paper led by our collaborators at Berkeley Lab, researchers showed a robotic lab could rapidly make new materials with automated synthesis techniques. Using materials from the Materials Project and insights on stability from GNoME, the autonomous lab created new recipes for crystal structures and successfully synthesized more than 41 new materials, opening up new possibilities for AI-driven materials synthesis.

New materials for new technologies To build a more sustainable future, we need new materials. GNoME has discovered 380,000 stable crystals that hold the potential to develop greener technologies – from enhanced batteries for electric cars, to superconductors for more efficient computing. Our research – and that of collaborators at the Berkeley Lab, Google Research, and teams around the world — exhibits the potential to use AI to guide materials discovery, experimentation, and synthesis. We hope that GNoME together with other AI tools can help revolutionize materials discovery today and shape the future of the field.

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