Blasphemy was a severe crime which warranted an equally severe punishment. Many times, blasphemers would be punished wit

Lastly, we have treason. Treason was a very common crime that was administered by the king himself. The Middle Ages was a turbulent time that was marked by social change, wars, revolutions, rebellions, religious changes, and other unrest. Many times, at the end of one of these events, the losing side was charged with treason and sentenced to death. Sometimes this would be a single prominent leader and other times it would be scores of people. In nearly every case, being found guilty of treason meant death.

Furthermore, it was not just any death. Treason was often marked by the cruelest executions imaginable. The king’s grip on a territory was often only as strong as their military force and their internal deterrent force against rebellion. Horrific executions such as being drawn and quartered, being burned at the stake, or being slowly flayed alive were all administered to traitors. This was a bid to assert the monarch’s full control over the populace as well as serve as the ultimate deterrence.

AlphaGo Zero uses a deep neural network, f, with parameters θ. The neural network takes in as an input a representation of the raw board’s current position and history s. The neural network outputs (p, v) = f(s), where:

Other punishments included stoning, as according to the Old Testament, and hangings. In fact, the last hanging for blasphemy in England actually occurred in 1697 when a young man was hanged for denying the truth of Christ’s miracles and the integrity of the Old Testament.

The neural network can be thought of as “pruning” the Monte Carlo Search Tree. This concept may be familiar from pruning Decision Trees in supervised learning with the intent of lowering the chance of overfitting. In the Monte Carlo Search Tree, pruning simply means reducing the number of explored nodes that serve little value to the end result.

The deep neural network is built from two blocks — “convolution blocks” and “residual blocks.” The former applies convolutional, batch normalization, and ReLU layers sequentially. The latter is comprised of two convolutional layers with a skip connection before a ReLU layer.

The Monte Carlo Tree Search can be thought of as an “intelligent tree search,” given the goal of predicting which end nodes will be the most valuable without performing an exhaustive search. A pure Monte Carlo Tree Search would not be able to be as effective without its counterpart, the deep neural network that determines the worth of each move.

p is a vector of move probabilities, each representing the probability of selecting each possible move a (including passing a turn). Formally stated, this is p.a = Pr(a|s), where . denotes sub (p.a = p sub a). This corresponds to a policy network — determining what the best next move is.

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in mind the most obvious way one could improve their Data Science skills is by taking part in Data Science competitions. I’m aware many people complain about competitions and how much they differ from real-world applications of AI/ML. However, I agree with competitors that say “competitions are a great way to become better problem solvers”.

The position’s value, along with other counters like the visit count to each node, is determined by ‘backing up’ through visited nodes and arriving back at the top node for another exploration.

By combining the Monte Carlo Search Tree with a deep neural network, the model can foresee and follow the likeliest path to victory without using the expensive resources required to perform an exhaustive search. Instead, the model combines the neural intuition (neural network) of where to go next with an intelligent computer-based solution (search tree) to create the ultimate Go player.

Unfortunately, blasphemy was a common crime because it could occur in a moment via a minor slip of the tongue. In the wrong company or in the presence of someone with an agenda, an unkind word towards a local priest or bishop could be spun into heresy or blasphemy with dire consequences. It was often used against someone’s enemy as an easy way to cause them grief. It was difficult to try and prove or disprove what someone had actually said or not.

The model then chooses an action to play from the root state proportionate to its exponentiated visit count. In other words, the model considers both the objective value of a next move and how sure it is of its value (visit count, how many times it has visited that node).

v is a scalar value, estimating the probability given a current board s that the current player will win. This corresponds to a value network — determining how valuable a move is.

The model is able to perform two tasks in parallel. In one thread, it gathers all the data aggregated from previous games it has played against itself. In the second, it trains the neural network on the previous game (the game it has just played). The network parameters are updated at the conclusion of each game.