How Language Models Actually Work: Parameters, Probabilities, and Interpretability

When you read that GPT-2 small has 82 million parameters or GPT-3 has 175 billion, it feels surreal.
M means million, B means billion.
Yes, these models really pass around that many numbers through their layers every time they generate a single sentence. Oh my gosh… 🤯

But what do all those parameters actually do?

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📦 What are Parameters?

Parameters are the weights inside the network’s giant matrices.

• GPT-2 small: ~82M
• GPT-2 medium: ~345M
• GPT-2 large: ~762M
• GPT-2 XL: ~1.5B
• GPT-3: up to 175B

Each parameter is just a floating-point number. Alone, meaningless. But collectively, they encode patterns learned during training: grammar, facts, styles of text.

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🧠 Encoding Knowledge

When people say a model “encodes knowledge”, they don’t mean it memorizes sentences like flashcards.
It’s more like this:

The weights are tuned so that, when you feed in “Paris is the capital of”, the internal math makes “France” pop out with the highest probability.

So knowledge is not literal sentences but probability biases baked into the weights.

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🎲 Probability Distributions

At each step, the model doesn’t output one word — it outputs a distribution: probabilities for every token in its vocabulary.

Example for the prompt “Paris is the capital of”:

• France → 0.40
• United States → 0.20
• Spain → 0.05
• … (rest spread over thousands of tokens)

That vector of numbers must sum to 1. It’s the model’s beliefs about what could come next.

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🌀 “Flat” vs “Sharp” Distributions

• Sharp distribution: one option dominates (France=0.9).
• Flat distribution: multiple plausible options (France=0.3, US=0.2, Spain=0.1).

Small models like DistilGPT2 tend to be flatter — they’re less confident. Larger models sharpen the distribution because they’ve captured more context and facts.

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🎲 Sampling and Randomness

When generating, you can:

• Always pick the most probable token (deterministic, “greedy”).
• Or sample: roll the dice according to probabilities. That gives variety — sometimes you’ll get “France,” sometimes “US.”

This is why, even with the same prompt, you can get very different continuations.

Temperature controls this randomness:

• Low temperature (<1) → sharper, more deterministic.
• High temperature (>1) → flatter, more chaotic.

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🧪 What about Ablations?

In interpretability research, people do ablations: zeroing out an attention head, a neuron, or a slice of embeddings to see how outputs change.
It’s like pulling out one guitar string mid-song — the melody shifts, and you learn what that string was doing.

For example, you might find one head in layer 3 that consistently looks up “X is the capital of Y” relations.

Normal inference doesn’t ablate anything; this is just a research tool to peek inside.

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🔑 Takeaway

• Giant parameter counts = giant matrices full of patterns.
• Knowledge is encoded as probabilities, not sentences.
• The model outputs a probability distribution for every next token.
• Sampling introduces randomness; temperature controls how “creative” it feels.
• Ablations help us understand what each piece is contributing.

So yes — it’s all about probabilities in AI models.
And once you see it this way, the mystery turns into math: billions of little numbers, shaping the likelihood of the next word you read.

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