Give me Monsters! (Part 4)

In our previous episode, we took at stab at modeling Hit Points, which lead us to exploring the representation of dice rolls as expressions. Today, we’ll relax a bit, and finish up the missing parts of the top section of the Monster description:

Goblin Stat Block

What are we missing at that point? The creature type (“small humanoid”), Alignment (“neutral evil”), the Armor Class, and Speed. Let’s add that in, and improve our Markdown renderer in the process.

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Give me Monsters! (Part 3)

Now that we have a reasonably working Abilities block, let’s take a stab at a slightly more challenging section of the Stat Block, the Hit Points.

Goblin Stat Block

Hit Points represent the “life force” of a creature, so to speak. Mechanically, this is how much damage a creature can take until it dies, and is expressed in dice rolls (2d6 for a Goblin), and a default average number, if one doesn’t want to roll the dice (7 for a Goblin). What this means is that, when creating a Goblin, you could either give him 7 hit points, or roll and add 2 6-sided dice, which would result in hit points between 2 and 12.

Things can get a tad more complicated - for instance, Constitution influences hit points. A creature with high CON will get a bonus (more on this later), resulting in expressions likes 4d10+8, which translates to roll 4 10-sided dice, sum them, and add 8 to the result.

Beyond Hit Points, dice rolls play a central role in D&D, and show up everywhere (see for instance the Hit description for the Goblin’s Scimitar and Shortbow, under Actions). We need a reasonably general way to model them.

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Give me Monsters! (Part 2)

Time to start creating monsters! We will begin with the Abilities section of the Stat Block.

Goblin Stat Block

First, what are Abilities? Every creature is described by 6 Ability Scores, which describe by a number from 1 to 20 (or possibly more) how able the creature is, across 6 dimensions:

  • STR (Strength)
  • DEX (Dexterity)
  • CON (Constitution)
  • INT (Intelligence)
  • WIS (Wisdom)
  • CHA (Charisma)

Ability scores have a dual usage: as raw scores, and as Ability Modifiers, which indicate a bonus or malus for that ability (see the rules for details). As an example, the Goblin has an INT score of 10, which is perfectly average and gives a modifier of 0; his DEX is 14, giving him a +2 bonus, and a CHA of 8, with a malus of -1.

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Give me Monsters! (Part 1)

I have been going through a bit of coding demotivation lately. Nothing dramatic, I simply did not feel like writing code, and most of my creative energy has gone into other activities, most notably Dungeons & Dragons (D&D in short).

And then, unexpectedly, I got excited again. Long story short, I take my new Dungeon Master duties seriously, and have been spending quite a bit of time preparing the campaign for my Adventurers. For those of you not familiar with D&D, the game works along these lines: a group of Adventures (the players) are immersed in a fictional universe (think Lord of the Rings), where they can decide to do whatever they please. One person plays the role of the Dungeon Master (or DM), responsible for the universe around them, constructing an (hopefully) engaging storyline, narrating events, reacting to the Adventurers’ choices and resolving their outcomes based on a fairly dense rule set.

So what does this have to do with programming?

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CNTK: études in F# (sequential models)

In my previous post, I introduced CNTK and how to use it from F#, with some comments on how the .Net API design makes it unpleasant to work with. In this post, I’ll present one direction I have been exploring to address these, to build models by stacking up layers into sequential models.

Let’s start by taking a step back, and briefly explaining what a sequential model is. In our previous post, we stated that the purpose of CNTK was to learn parameters of a Function, to minimize the error observed between known input and output data. That Function is a model, which transforms an input (what we observe) into a output (what we want to predict). The example we used was a simple linear combination, but CNTK supports arbitrarily complex models, created by combining together multiple functions into a single one.

Sequential models are one specific way of combining functions into a model, and are particularly interesting in machine learning. Imagine that you are trying to recognize some pattern in an image, say, a cat. You will probably end up with a pipeline of transformations of filters, along the lines of:

Original Image: pixels -> Gray Scale -> Normalize -> Filter -> … -> 0 or 1: is it a Cat?

As an F# developer, this probably looks eerily familiar, reminescent of pipelining with the |> operator:

[ 1; 2; 3; 4; 5 ] 
|> List.map grayScale 
|> List.map normalize 
|> List.map someOtherOperation
...

Can we achieve something similar with CNTK, to make the creation of models by stacking transformation layers on top of each other? Let’s give it a try.

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