What does the dimensionality of an embedding mean, and what are the tradeoffs of higher-dimensional embeddings?

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The dimensionality of an embedding is how many numbers each vector holds. The model fixes it, so you rarely choose it yourself. No single number means anything on its own. Meaning comes from all the numbers together.

More dimensions give the model room to record finer distinctions, so quality usually improves. The gains shrink fast, while the costs grow in a straight line. Doubling the dimensions doubles storage and index memory, and roughly doubles the work per distance comparison. Stored as float32, each dimension takes 4 bytes:

384 dimensions: 1,536 bytes, about 1.5 GB per million vectors
1,536 dimensions: 6,144 bytes, about 6.1 GB
3,072 dimensions: 12,288 bytes, about 12.3 GB

A small, well-trained model often beats a weaker model with more dimensions. Judge models on your own data, not on dimension count.

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Likely follow-ups

Some models let you cut vectors down to fewer dimensions. How does that work, and what does it cost you? Training packs the most useful information into the leading dimensions, so a prefix still works. Name the quality you give up for the smaller vectors.
You're on a 1,536-dimension model and memory is tight. How do you shrink the index without switching models? Name scalar, binary and product quantization, how much smaller each makes the vectors, the recall each costs, and rescoring with full vectors.
You have two candidate models, one with 384 dimensions and one with 3,072. How do you decide which to ship? Build a labeled query set from your own data and compare recall@k. Then weigh storage, latency and embedding cost per million vectors.
Your old and new models both output 1,536 dimensions. Can you mix their vectors in one index? Each model learns its own space, so equal length doesn't make vectors comparable. Say what happens to results and why you re-embed the whole corpus.
How does dimension count feed into the total memory of an HNSW index? Raw vectors scale with dimensions. The graph's neighbor links scale with M, not with dimensions. Estimate both and add overhead.

What you can say

Dimensionality is how many numbers each embedding vector holds, and since the model fixes it, you mostly pick it by picking a model.
No single number means anything on its own, only the full set of numbers together carries the meaning.
More dimensions give the model room for finer distinctions, so quality usually goes up, but the gains shrink fast.
The cost grows in a straight line, since each float32 dimension is 4 bytes, so a million 1,536-dimension vectors take about 6 GB and 3,072 dimensions double that.
Doubling the dimensions also roughly doubles the work in every distance comparison, so search gets slower too.
So I don't judge a model by its dimension count, because a small, well-trained model often beats a weaker one with more dimensions, and I test on my own data.

Weak answers to avoid

Says each dimension stores one feature Dimensions aren't labeled features like topic or sentiment. The meaning is spread across all of them, so say that and skip made-up examples.
Assumes more dimensions always means better The quality gains shrink fast while costs grow linearly. A small, well-trained model often wins, so say you would test models on your own data.
Gives no numbers for the cost Saying 'more memory' is vague. Show the math, 4 bytes per float32 dimension times vector count, so 1,536 dimensions is about 6 GB per million vectors.
Treats dimension as a free tuning knob Training fixes the dimension for most models, so you choose it by choosing a model. Models trained for truncation are the exception, so name them as that.

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