Markov Chain Text Generation: Language from Probability

simulator beginner ~8 min
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Order-2 Markov — grammar without rules

A second-order Markov chain considers the previous two words to predict the next one. This simple mechanism produces surprisingly readable text, demonstrating that much of language structure is captured by local statistical patterns.

Formula

P(w_t | w_{t-n}, ..., w_{t-1}) = count(w_{t-n}...w_t) / count(w_{t-n}...w_{t-1})
Temperature sampling: P_temp(w) = Math.pow(P(w), 1/T) / Z where Z = normalization
Perplexity = Math.pow(2, H) where H = -(1/N) * sum(log2(P(w_i | context)))

Language as a Probability Machine

In 1948, Claude Shannon demonstrated a remarkable fact: you can generate surprisingly readable English text by simply choosing each word based on the statistical patterns of the words before it. He called these 'approximations to English,' and they laid the foundation for all modern language models — from simple chatbots to GPT. This simulation lets you build and run your own Markov chain text generator.

The Order of Memory

A first-order Markov chain picks each word based only on the single previous word. The result is grammatical chaos: 'the cat the house was running quickly the.' But increase the order to 2 or 3, and something magical happens — sentences begin to flow, clauses nest properly, and the output becomes eerily readable. The chain has no knowledge of grammar; it has only memorized local word sequences.

Temperature and Creativity

The temperature parameter reveals a fundamental tension in language generation: coherence versus creativity. At low temperatures, the model always picks the most probable next word, producing repetitive but correct text. At high temperatures, rare words get a fighting chance, producing novel combinations — but at the cost of coherence. Every modern AI writing assistant navigates this same tradeoff.

From Markov to Transformers

Modern language models like GPT-4 are, at their core, massively scaled versions of this same principle: predict the next token from context. The key innovation is replacing fixed n-gram lookups with neural attention mechanisms that can capture dependencies across thousands of tokens. But the Markov chain remains the clearest illustration of the idea that launched the AI revolution.

FAQ

What is a Markov chain in text generation?

A Markov chain models text as a sequence where each word depends only on the previous n words (the 'order'). By tallying how often each word follows each n-gram in a training text, the model builds a probability table that can generate new text by randomly sampling from these distributions.

How does chain order affect text quality?

Higher orders produce more coherent text because they capture longer-range patterns. Order 1 produces grammatical gibberish, order 2 produces plausible phrases, and order 4–5 often reproduces near-exact passages from the training text. Modern language models like GPT use the same principle but with much longer effective contexts.

What is temperature in text generation?

Temperature controls randomness. At temperature 1.0, the model samples directly from the learned probabilities. Lower temperatures make the model favor high-probability words (more repetitive but coherent), while higher temperatures flatten the distribution (more creative but less coherent).

How do Markov chains relate to modern AI language models?

Markov chains are the conceptual ancestor of modern language models. GPT and similar models generalize the same idea — predicting the next token from context — but use neural networks to model much longer dependencies and learn semantic relationships that simple n-gram models cannot capture.

Sources

Embed

<iframe src="https://homo-deus.com/lab/linguistics/markov-text/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub