# Codenames Solo

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Codenames is probably one of my favorite party games published in recent years. The core concept is extremely simple: Find a single-word hint which semantically links the words from your team, while being as unrelated as possible to the words on your opponent’s team. In this blog post, I will briefly discuss how we can leverage language modeling to build a simple Codenames bot using streamlit and the OpenAI API. The resulting app is hosted on Streamlit Cloud and embedded below:

## The rules

First, let’s look at the rules of Codenames a bit more in-depth from a representation learning perspective: Let’s denote by $P$ the words on your team which you want to relate, and $N$ the ones you want to steer away from. In reality, $N$ is composed of three subsets:

• $N_{ntr}$: The neutral words. Wrongly guessing one of those will end your team’s turn but does not directly benefit your opponent.
• $N_{opp}$: Your opponent’s words. Wrongly guessing any of those will bring your opponent closer to victory.
• $N_{kll}$: The assasin word. Wrongly guessing it will make your team’s lose the game hence should be avoided at all cost.

### Spymaster

Each team is composed of two roles: First, the (unique) spymaster has full knowledge of $P$ and $N$ and is tasked with giving hints. In other words, they want to find an embedding function $\phi$ and a hint word $h \notin W$ such that:

\begin{align} \exists k_h,\ \exists W^{\ast} = \{w_1, \dots w_{k_h}\} \subseteq P, \text{ such that } \forall w \in W^\ast,\ || \phi(h) - \phi(w) || < \epsilon \\ \forall w \in N,\ || \phi(h) - \phi(w) || > \tau \end{align}

Following (1), the spymaster gives a hint in the form “$h : k_h$”, i.e. they give the hint word $h$, which they believe relates to $k_h$ words in $P$ while being far away from any of the words in $N$. In contrast, (2) states that the hint $h$ does not relate to any word from $N$. Note that in practice, a good spymaster would have different values of $\tau$, one for each subset $N_{ntr}, N_{opp}, N_{kll}$, where $\tau_{kll} > \tau_{opp} > \tau_{ntr}$, capturing how a wrong guess in each of these subsets impacts the game differently.

Finally, an ideal hint would be such that $\epsilon\ «\ \tau$. Intuitively, we can see the quantity $\epsilon - \tau$ as the amount of risk the spymaster is willing to take, taking into account potential wrong guesses from their spies. (This also means that “knowledge of your teammates’s semantic associations” is an implicit parameter when building the embedding $\phi$, which is all the fun of the game)

### Spies

On the other hand, the spies only see the words $W = P \cup N$ but do not know how it decomposes between $P$ and $N$ ($\sim$ latent variables from the spies perspective). In each turn, they receive the hint from the spymaster and their goal is to reconstruct the embedding $\phi$ to improve their knowledge of $P$.

### A representation learning problem

In summary, both spymaster and spies aim to build a semantic embedding of the words on the board, only with different information. We will denote by $\tilde{P}$ (resp. $\tilde{N}$) the words which have been guessed (correctly or incorrectly): All players know which team these cards belong to and as the game progresses, the spies increase their knowledge of $P$ and $N$.

• The spymaster has full knowledge of the “value” of each word on the board. In each round $t$, they have to build a new embedding based on which words have already been guessed on the board $\Phi^{\text{spymaster}}: \left( \tilde{P}_{t-1}, \tilde{N}_{t-1}, P, N \right) \mapsto \phi_t$.
• The spies only have partial information of what is currently visible on the board and the hint given by the spymaster. In other words: $\Phi^{\text{spy}}: \left( \tilde{P}_{t-1}, \tilde{N}_{t-1}, h_{\leq t}, k_{h, \leq t} \right) \mapsto \phi_t$.

## Building word embeddings

### Word2Vec

Word2Vec was proposed in 2013 by Mikolov et al and received a test of time award recently at NeurIPS 2023. The core idea of the paper is to build continuous representations of words by solving a local word prediction task. Using such a method, we can easily build the embedding $\phi$; However, it is not clear how we can make this embedding conditioned on our sets of words $P$ and $N$ to give appropriate hints.

• One potential direction is the literature on topic modelling such as LDA2Vec. However, such methods typicall act on a set of entire documents, while we only want to build a global understanding of the rather small subsets of words $N$ and $P$.
• An other idea is to use the geometries of word embeddings: We could modify the embedding learned by Word2Vec to condition it on our knowledge of $P$ and $N$, for instance, using projections or some form of clustering. After giving this idea a try on some toy examples, I found the quality of the hints to vary greatly, especially when trying to link more than 2 words. Nevertheless, if you want to dig more in this derection, there are several examples of Codenames bots using Word2Vec or more advanced word embeddings, such as Playing Codenames with Language Graphs and Word Embeddings, Koyyalagunta et al, 2021 or this blog post by Jeremy Neiman.

### LLM

LLMs (Large Language Models) are slightly different from the previous two methods in that they do not explicitly encode words. Rather, they are usually transformer-based, generally use sub-word tokenization and are trained for sentence prediction/generation.

Despite this different structure, LLMs do learn implicity to encode words (or rather tokens). In addition, one very interesting property of LLMs is their zero-shot learning ability, or what we often refer to as In-Context Learning: By prepending a prompt to a query, we can modify the “function” of the LLM since any past tokens will impact future predictions through the attention layers. For strong enough LLMs, in practice this generally means that we can easily get the model to solve a specific task by feeding it a relevant prompt/instruction, even if it hasn’t been explicitly finetuned for said tasks. I

As a result, we can define the function $\Phi^{\text{spymaster}}$ (resp. $\Phi^{\text{spy}}$) as handcrafting a prompt that integrates all the knowledge of the spymaster (resp. spy), then use it to query the LLM and returns the hint (resp. guess) from the spymaster (resp. spy).

## Codenames Solo

Based on these insights, we can build a simple “Solo mode” for Codenames by prompting a LLM to act as the sypmaster. Interestingly, the model used here seems to already know about the rules of the game since even a very simple instruction such as the one below yields reasonable hints:

You are playing Codenames as a bold and creative spymaster giving hints. Your answers should be in the format WORD - NUMBER.

Of course this instruction still results in occasional errors or suboptimal moves such as:

• The hint given is not in the right format (e.g. wrong formatting, or $k_h < 0$)
• The spymaster ignores one of the rule that the hint given must not be one of the words visible of the board.
• The hints tend to be a bit repetitive. For instance words like “Adventure”, “Nature”, “Agent” or “Space” are often given as hints to link more than 3 words.
• The spymaster does not pay enough attention to the words to avoid, leading to wrong guesses from the spies.

Nevertheless, the resulting spymaster performs quite well in practice, especially when we consider the simplicity of the prompt/methodology. With in-context learning, we can even easily change the language of the game on-the-fly by adding a simple instruction such as You play the game in French and you give all your hints in French (though to be honest, switching to a language different than English tends to decrease the quality of the hints). Hopefully, a bit of prompt engineering work could go a long way in defining better and more diverse spymasters for a better game experience.