What fraction of a 7B transformer lives in its embedding table at vocab 128k? · Zenaique

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**Around 7-8% of a 7B model lives in the embedding table when vocab is 128k.** Do the math directly: - Embedding table shape: `vocab_size x d_model = 128000 x 4096` - Parameter count: `128000 * 4096 = 524,288,000` (~524M) - Fraction of 7B: `524M / 7000M = 7.5%` That's just the **input embedding**. If the output head (the LM head that projects the final hidden state to vocab logits) is NOT tied to the input embedding, it costs the same again: another 524M parameters, bringing the embedding pair to ~1.05B, or 15% of a 7B model. **Why the answer isn't 'about 1%'.** A 1% of model embedding would require vocab ~17k at `d_model = 4096`, which is smaller than any modern tokenizer. **Why the answer isn't 'about 25% or 50%'.** The transformer stack itself (32 layers of attention + FFN at d_model 4096) is roughly 6 billion parameters in a 7B model. The embedding can't dominate that unless vocab climbs into the millions. This is why modern LLMs care about tokenizer choice: a larger vocab gives better compression and fewer tokens per word, but each thousand tokens of vocab adds 4M parameters to the embedding.

**About 7.5%, call it 7-8%. The math is concrete and worth memorizing.** Llama 3.1 8B uses vocab 128256 and `d_model = 4096`. The input embedding matrix is `128256 x 4096 ≈ 525M parameters`. On an 8B model that's roughly 6.6% of the total. If the output head is untied (Llama 3.1 keeps them untied), another 525M lives in the LM head, bringing the embedding pair to ~1.05B or 13% of the model. **Why this matters in practice.** - **Tokenizer choice has architectural weight.** A 32k vocab (Llama 2 era) cost only 131M params for the input embedding: about a quarter as much. The choice to grow vocab from 32k to 128k added ~400M params to the embedding pair on its own. - **Embedding tying flips with scale.** At small scale (sub-1B), tying input and output embeddings is the default to save parameters. At frontier scale, untying gives a measurable quality bump and the extra ~7% parameter cost is negligible compared to the quality gain. - **Output head dominates inference latency for some workloads.** At each generation step, the output head matmul (`hidden_dim x vocab`) is one of the largest single ops. At vocab 128k that's a 4096x128000 matmul per step. **The MCQ distractors are calibrated.** A: 1% would only apply if vocab were ~16k. C: 25% would require vocab ~430k, larger than any production tokenizer. D: 50% would require vocab approaching 1M, which only experimental ByT5 style byte level models approach.

Quick reference

TL;DR

128k vocab times d_model 4096 is ~524M parameters in the input embedding alone, about 7.5% of a 7B model. Untying the output head doubles the cost to ~15%.

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Easy to grasp

Imagine a giant phone book where every word the model knows has its own page, and each page is filled with a long list of numbers that describe what the word means. The phone book is huge: 128,000 pages times 4,096 numbers per page comes out to about 524 million numbers. On a 7 billion number model, that phone book alone is 7.5% of the whole thing. Not a rounding error, but not a black hole either: most of the model is still the stack of thinking layers above it. If you also keep a second phone book at the back of the model for turning answers into word scores, the pair takes about 15% of the total. Sharing one phone book for both ends (called tying) saves that 7.5% at a tiny cost in quality.

Key concepts

Transformer architecture Tokenization Embeddings

Detailed answer & concept explanation

~6 min read

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Quick scan · 2–4 min

Everything important, quickly.

5 min: do the multiplication, contrast tied vs untied embeddings, explain why Llama 3 moved to 128k vocab, and discuss how the fraction scales with model size.

Side-by-side

Model	Vocab	d_model	Embedding params	% of total
Mistral 7B (tied)	32k	4096	131M	1.9%
Llama 2 7B (tied)	32k	4096	131M	1.9%
Llama 3.1 8B (untied)	128k	4096	1.05B	13%
Llama 3.1 70B (untied)	128k	8192	2.1B	3%
Gemma 4 (untied)	256k	2048	1.05B	varies

Real-world examples

Real products, models, and research that use this idea.

Llama 3.1 8B: vocab 128256, d_model 4096, embedding pair ~1.05B (13% of 8B).
Llama 3.1 70B: vocab 128256, d_model 8192, embedding pair ~2.1B (3% of 70B): fraction shrinks at scale.
Mistral 7B: vocab 32000, d_model 4096, embedding pair ~131M (tied, so 1.9% of 7B).
Gemma 4: vocab 256000, d_model 2048, embedding pair ~1.05B; vocab grew while d_model shrank.

Interviewer follow-ups

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QWhy doesn't the embedding fraction scale linearly with model size?

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QHow would you choose vocab size for a new LLM?

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QWhat does the embedding table actually learn?

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Don't say this

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Most common mistake

Treating embeddings as negligible because they are a lookup. They're not: at 128k vocab they're 7-8% of a 7B model, and at 256k plus vocab the cost climbs further.

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References

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