The following is AI generated from my prompts today. Before reading on you may want to ask yourself, is this next question one worth answering?
Imagine you’re packing for a vacation and you’ve got a massive suitcase (512-dimensional embeddings) but only room for a carry-on (5 dimensions). How do you fit everything in without forgetting the essentials—like your toothbrush (semantic relationships)? That’s the conundrum we’re tackling with embedding compression.
Embeddings are those fancy, high-dimensional vectors AI uses to represent text, images, and other data. They’re the magic sauce behind everything from recommending your next binge-watch to making chatbots sound (almost) human. But here’s the catch: they’re huge, and storing or processing them at scale can feel like trying to fit an elephant into a phone booth.
So, we ask: Can we compress embeddings without losing their essence?
First up in our brainstorming session is the metalog distribution. These bad boys are flexible, math-y tools that summarize data distributions with just a handful of coefficients. The dream? Replace hundreds of numbers in an embedding with a neat little package of, say, 5 or 13 coefficients.
Sounds great, right? But here’s the kicker: embeddings aren’t just a collection of random numbers. Each dimension holds a secret handshake with the others. Compressing dimensions independently might mean losing these relationships—and turning your AI from a genius into someone guessing at trivia night.
Enter copulas, which sound like something you’d need in a grammar class but are actually all about relationships. They model the dependencies between dimensions, ensuring that if one dimension goes wild, the others stay in sync.
Even better, fancy types like vine copulas can handle non-linear, complicated relationships. Think of them as the dance choreographers of your embeddings—ensuring every dimension stays in step, no matter how crazy the music gets.
The big question: can we pair copulas with metalog distributions to shrink embeddings while preserving their semantic sparkle? Could this be the peanut butter and jelly of compression?
Let’s be real for a second—this isn’t all sunshine and perfect cosine similarities. Shrinking embeddings too much (like going from 512 to 5 dimensions) might turn your AI into that one friend who remembers the gist of your story but gets all the details wrong. For tasks like similarity search or clustering, preserving those fine-grained relationships is critical.
And don’t even get us started on the computational load. Training vine copulas on high-dimensional data can be as intensive as convincing your cat to take a bath.
While metalogs drastically reduce the size of marginals, the added overhead from the vine copula may offset these gains, particularly for high-dimensional data. Compression using this method is likely only smaller when:
The vine structure is sparse.
Dependencies are simple.
Embedding dimensions are reduced before applying the copula.
Experimentation is key to determining whether the compression is worth it for a specific use case like pushing AI on IoT devices.