Artificial Intelligence (AI) systems have made remarkable progress, attaining super-human performance across various domains. This presents us with an opportunity to further human knowledge and improve human expert performance by leveraging the hidden knowledge encoded within these highly performant AI systems. Yet, this knowledge is often hard to extract, and may be hard to understand or learn from. Here, we show that this is possible by proposing a new method that allows us to extract new chess concepts in AlphaZero, an AI system that mastered the game of chess via self-play without human supervision. Our analysis indicates that AlphaZero may encode knowledge that extends beyond the existing human knowledge, but knowledge that is ultimately not beyond human grasp, and can be successfully learned from. In a human study, we show that these concepts are learnable by top human experts, as four top chess grandmasters show improvements in solving the presented concept prototype positions. This marks an important first milestone in advancing the frontier of human knowledge by leveraging AI; a development that could bear profound implications and help us shape how we interact with AI systems across many AI applications.
In recent years, Artificial Intelligence (AI) systems have surpassed human intelligence in a variety of computational tasks. However, AI systems, like humans, make mistakes, have blind spots, hallucinate, and struggle to generalize to new situations. This work explores whether AI can benefit from creative decision-making mechanisms when pushed to the limits of its computational rationality. In particular, we investigate whether a team of diverse AI systems can outperform a single AI in challenging tasks by generating more ideas as a group and then selecting the best ones. We study this question in the game of chess, the so-called drosophila of AI. We build on AlphaZero (AZ) and extend it to represent a league of agents via a latent-conditioned architecture, which we call AZ_db. We train AZ_db to generate a wider range of ideas using behavioral diversity techniques and select the most promising ones with sub-additive planning. Our experiments suggest that AZ_db plays chess in diverse ways, solves more puzzles as a group and outperforms a more homogeneous team. Notably, AZ_db solves twice as many challenging puzzles as AZ, including the challenging Penrose positions. When playing chess from different openings, we notice that players in AZ_db specialize in different openings, and that selecting a player for each opening using sub-additive planning results in a 50 Elo improvement over AZ. Our findings suggest that diversity bonuses emerge in teams of AI agents, just as they do in teams of humans and that diversity is a valuable asset in solving computationally hard problems.
We propose a neural network-based approach to calculate the value of a chess square-piece combination. Our model takes a triplet (Color, Piece, Square) as an input and calculates a value that measures the advantage/disadvantage of having this piece on this square. Our methods build on recent advances in chess AI, and can accurately assess the worth of positions in a game of chess. The conventional approach assigns fixed values to pieces $(\symking=\infty, \symqueen=9, \symrook=5, \symbishop=3, \symknight=3, \sympawn=1)$. We enhance this analysis by introducing marginal valuations. We use deep Q-learning to estimate the parameters of our model. We demonstrate our method by examining the positioning of Knights and Bishops, and also provide valuable insights into the valuation of pawns. Finally, we conclude by suggesting potential avenues for future research.
While transformers have gained recognition as a versatile tool for artificial intelligence (AI), an unexplored challenge arises in the context of chess - a classical AI benchmark. Here, incorporating Vision Transformers (ViTs) into AlphaZero is insufficient for chess mastery, mainly due to ViTs' computational limitations. The attempt to optimize their efficiency by combining MobileNet and NextViT outperformed AlphaZero by about 30 Elo. However, we propose a practical improvement that involves a simple change in the input representation and value loss functions. As a result, we achieve a significant performance boost of up to 180 Elo points beyond what is currently achievable with AlphaZero in chess. In addition to these improvements, our experimental results using the Integrated Gradient technique confirm the effectiveness of the newly introduced features.
In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game. This score quantifies the ex-post strategic ability of the players based on empirically observable information, such as the actions of the players, the game's outcome, strength of the players, and a reference oracle machine such as a chess-playing artificial intelligence system. Specifically, I introduce two main concepts: first, the Game Intelligence (GI) mechanism, which quantifies a player's intelligence in a game by considering not only the game's outcome but also the "mistakes" made during the game according to the reference machine's intelligence. Second, I define gamingproofness, a practical and computational concept of strategyproofness. To illustrate the GI mechanism, I apply it to an extensive dataset comprising over a billion chess moves, including over a million moves made by top 20 grandmasters in history. Notably, Magnus Carlsen emerges with the highest GI score among all world championship games included in the dataset. In machine-vs-machine games, the well-known chess engine Stockfish comes out on top.
The notions of dominating sets of graphs began almost 400 years ago with the game of chess, which sparked the analysis of dominating sets of graphs, at first relatively loosely until the beginnings of the 1960s, when the issue was given mathematical description. It's among the most important problems in graph theory, as well as an NP-Complete problem that can't be solved in polynomial time. As a result, we describe a new hybrid cuckoo search technique to tackle the MDS problem in this work. Cuckoo search is a well-known metaheuristic famed for its capacity for exploring a large area of the search space, making it useful for diversification. However, to enhance performance, we incorporated intensification techniques in addition to the genetic crossover operator in the suggested approach. The comparison of our method with the corresponding state-of-the-art techniques from the literature is presented in an exhaustive experimental test. The suggested algorithm outperforms the present state of the art, according to the obtained results.
What is learned by sophisticated neural network agents such as AlphaZero? This question is of both scientific and practical interest. If the representations of strong neural networks bear no resemblance to human concepts, our ability to understand faithful explanations of their decisions will be restricted, ultimately limiting what we can achieve with neural network interpretability. In this work we provide evidence that human knowledge is acquired by the AlphaZero neural network as it trains on the game of chess. By probing for a broad range of human chess concepts we show when and where these concepts are represented in the AlphaZero network. We also provide a behavioural analysis focusing on opening play, including qualitative analysis from chess Grandmaster Vladimir Kramnik. Finally, we carry out a preliminary investigation looking at the low-level details of AlphaZero's representations, and make the resulting behavioural and representational analyses available online.
When inferring the goals that others are trying to achieve, people intuitively understand that others might make mistakes along the way. This is crucial for activities such as teaching, offering assistance, and deciding between blame or forgiveness. However, Bayesian models of theory of mind have generally not accounted for these mistakes, instead modeling agents as mostly optimal in achieving their goals. As a result, they are unable to explain phenomena like locking oneself out of one's house, or losing a game of chess. Here, we extend the Bayesian Theory of Mind framework to model boundedly rational agents who may have mistaken goals, plans, and actions. We formalize this by modeling agents as probabilistic programs, where goals may be confused with semantically similar states, plans may be misguided due to resource-bounded planning, and actions may be unintended due to execution errors. We present experiments eliciting human goal inferences in two domains: (i) a gridworld puzzle with gems locked behind doors, and (ii) a block-stacking domain. Our model better explains human inferences than alternatives, while generalizing across domains. These findings indicate the importance of modeling others as bounded agents, in order to account for the full richness of human intuitive psychology.
Transformer language models have made tremendous strides in natural language understanding tasks. However, the complexity of natural language makes it challenging to ascertain how accurately these models are tracking the world state underlying the text. Motivated by this issue, we consider the task of language modeling for the game of chess. Unlike natural language, chess notations describe a simple, constrained, and deterministic domain. Moreover, we observe that the appropriate choice of chess notation allows for directly probing the world state, without requiring any additional probing-related machinery. We find that: (a) With enough training data, transformer language models can learn to track pieces and predict legal moves with high accuracy when trained solely on move sequences. (b) For small training sets providing access to board state information during training can yield significant improvements. (c) The success of transformer language models is dependent on access to the entire game history i.e. "full attention". Approximating this full attention results in a significant performance drop. We propose this testbed as a benchmark for future work on the development and analysis of transformer language models.
We have seen numerous machine learning methods tackle the game of chess over the years. However, one common element in these works is the necessity of a finely optimized look ahead algorithm. The particular interest of this research lies with creating a chess engine that is highly capable, but restricted in its look ahead depth. We train a deep neural network to serve as a static evaluation function, which is accompanied by a relatively simple look ahead algorithm. We show that our static evaluation function has encoded some semblance of look ahead knowledge, and is comparable to classical evaluation functions. The strength of our chess engine is assessed by comparing its proposed moves against those proposed by Stockfish. We show that, despite strict restrictions on look ahead depth, our engine recommends moves of equal strength in roughly $83\%$ of our sample positions.
Machine learning (ML) systems across many application areas are increasingly demonstrating performance that is beyond that of humans. In response to the proliferation of such models, the field of Explainable AI (XAI) has sought to develop techniques that enhance the transparency and interpretability of machine learning methods. In this work, we consider a question not previously explored within the XAI and ML communities: Given a computational system whose performance exceeds that of its human user, can explainable AI capabilities be leveraged to improve the performance of the human? We study this question in the context of the game of Chess, for which computational game engines that surpass the performance of the average player are widely available. We introduce the Rationale-Generating Algorithm, an automated technique for generating rationales for utility-based computational methods, which we evaluate with a multi-day user study against two baselines. The results show that our approach produces rationales that lead to statistically significant improvement in human task performance, demonstrating that rationales automatically generated from an AI's internal task model can be used not only to explain what the system is doing, but also to instruct the user and ultimately improve their task performance.
Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess and Go, where a perfect simulator is available. However, in real-world problems the dynamics governing the environment are often complex and unknown. In this work we present the MuZero algorithm which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. MuZero learns a model that, when applied iteratively, predicts the quantities most directly relevant to planning: the reward, the action-selection policy, and the value function. When evaluated on 57 different Atari games - the canonical video game environment for testing AI techniques, in which model-based planning approaches have historically struggled - our new algorithm achieved a new state of the art. When evaluated on Go, chess and shogi, without any knowledge of the game rules, MuZero matched the superhuman performance of the AlphaZero algorithm that was supplied with the game rules.
This report presents Giraffe, a chess engine that uses self-play to discover all its domain-specific knowledge, with minimal hand-crafted knowledge given by the programmer. Unlike previous attempts using machine learning only to perform parameter-tuning on hand-crafted evaluation functions, Giraffe's learning system also performs automatic feature extraction and pattern recognition. The trained evaluation function performs comparably to the evaluation functions of state-of-the-art chess engines - all of which containing thousands of lines of carefully hand-crafted pattern recognizers, tuned over many years by both computer chess experts and human chess masters. Giraffe is the most successful attempt thus far at using end-to-end machine learning to play chess.
Since the advent of computers, many tasks which required humans to spend a lot of time and energy have been trivialized by the computers' ability to perform repetitive tasks extremely quickly. Playing chess is one such task. It was one of the first games which was `solved' using AI. With the advent of deep learning, chess playing agents can surpass human ability with relative ease. However algorithms using deep learning must learn millions of parameters. This work looks at the game of chess through the lens of genetic algorithms. We train a genetic player from scratch using only a handful of learnable parameters. We use Multi-Niche Crowding to optimize positional Value Tables (PVTs) which are used extensively in chess engines to evaluate the goodness of a position. With a very simple setup and after only 1000 generations of evolution, the player reaches the level of an International Master.
We present an end-to-end learning method for chess, relying on deep neural networks. Without any a priori knowledge, in particular without any knowledge regarding the rules of chess, a deep neural network is trained using a combination of unsupervised pretraining and supervised training. The unsupervised training extracts high level features from a given position, and the supervised training learns to compare two chess positions and select the more favorable one. The training relies entirely on datasets of several million chess games, and no further domain specific knowledge is incorporated. The experiments show that the resulting neural network (referred to as DeepChess) is on a par with state-of-the-art chess playing programs, which have been developed through many years of manual feature selection and tuning. DeepChess is the first end-to-end machine learning-based method that results in a grandmaster-level chess playing performance.
The game of chess is the most widely-studied domain in the history of artificial intelligence. The strongest programs are based on a combination of sophisticated search techniques, domain-specific adaptations, and handcrafted evaluation functions that have been refined by human experts over several decades. In contrast, the AlphaGo Zero program recently achieved superhuman performance in the game of Go, by tabula rasa reinforcement learning from games of self-play. In this paper, we generalise this approach into a single AlphaZero algorithm that can achieve, tabula rasa, superhuman performance in many challenging domains. Starting from random play, and given no domain knowledge except the game rules, AlphaZero achieved within 24 hours a superhuman level of play in the games of chess and shogi (Japanese chess) as well as Go, and convincingly defeated a world-champion program in each case.
The area of computation called artificial intelligence (AI) is falsified by describing a previous 1972 falsification of AI by British mathematical physicist James Lighthill. How Lighthill's arguments continue to apply to current AI is explained. It is argued that AI should use the Popperian scientific method in which it is the duty of scientists to attempt to falsify theories and if theories are falsified to replace or modify them. The paper describes the Popperian method and discusses Paul Nurse's application of the method to cell biology that also involves questions of mechanism and behavior. It is shown how Lighthill's falsifying arguments especially combinatorial explosion continue to apply to modern AI. Various skeptical arguments against the assumptions of AI mostly by physicists especially against Hilbert's philosophical programme that defined knowledge and truth as provable formal sentences. John von Neumann's arguments from natural complexity against neural networks and evolutionary algorithms are discussed. Next the game of chess is discussed to show how modern chess experts have reacted to computer chess programs. It is shown that currently chess masters can defeat any chess program using Kasperov's arguments from his 1997 Deep Blue match and aftermath. The game of 'go' and climate models are discussed to show computer applications where combinatorial explosion may not apply. The paper concludes by advocating studying computation as Peter Naur's Dataology.