[Twitter; cf. AZ’s acquisition of knowledge, alternate rules] 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 4 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.

…Overall, the grandmasters appreciated the concepts, describing them as ‘clever’ (Figure 8), ‘very interesting’ (Figure 16), and ‘very nice’ (Figure 18). Further, they found that the ideas often contained novel elements, commenting that the moves were ‘something new’ and even ‘not natural’ (Figure 16 & 10). Often, the grandmasters found the positions were very complex—making remarks such as that it was “very complicated—not easy to understand what to do”. Even when seeing AZ’s solutions, they remarked that it was a ‘very nice idea which is hard to spot’ (Figure 22).

…The qualitative examples suggest that AZ has different priors over the relevance of concepts in a chess position than humans. Human chess players formulate and adopt heuristic chess principles to inform their analysis, predisposing them to biases that influence which concepts they deem relevant for specific chess positions. An example is the 3 ‘golden rules’ of the opening: control the centre, develop your pieces, and bring your king to safety (Hansen2021; Brunia & van Wijgerden2021; King2000). Consequentially, in opening, humans may focus on moves that align with these guidelines. Instead, AZ is self-taught and does not seem to have the same priors over chess concepts as humans. We believe this lack of prior allows AZ to be more flexible—it can apply concepts to various different chess positions and change plans quickly. In essence, AZ formulates its own priors over the relevance of chess concepts for a given chess position. Examples of this behavior are that AZ plays over the entire board, as opposed to focusing on a specific side (see, eg. Figure 16, 17, 12, and 19); places less importance on the material value of pieces, and prioritises space and piece activity (see, eg. Figure 9 or 14). This may result in the super-human application of concepts, and new concepts… AZ does not care about how quickly the game finishes. The training loss function does not have a penalty term to encourage winning as quickly as possible. As a result, it has a different treatment of time. This results in sometimes choosing slow strategic wins (as can be seen in the chess positions in Figure 21). While the lack of time constraint may lead to super-human concepts, it also may result in complex concepts that are difficult for humans to learn.

**Table 4**: *Improvements in grandmasters’ performance.* The percentage scores are the percentage of puzzles that the grandmaster solved correctly (according to AZ’s solution). `# Puzzles` is the number of puzzles shown to the grandmaster in total.
Grandmaster	Percentage: Phase 1	Phase 3	Improvement	# Puzzles
1	0	42	+42	36
2	33	58	+25	36
3	25	42	+16	36
4	38	44	+6	48

…Overall, we find that all study participants improve notably between Phases 1 & 3, as shown in Table 4, suggesting that the chess grandmasters were able to learn and apply their understanding of the represented AZ chess concepts. The magnitude of improvement does not correlate with the chess player’s strength (ie. Elo rating).