1. Curate a large representative subsample of tweets.
2. Feed all of them to an LLM in a single call with the prompt along the lines of "generate N unique labels and their descriptions for the tweets provided". This bounds the problem space.
3. For each tweet, feed them to a LLM along with the prompt "Here are labels and their corresponding descriptions: classify this tweet with up to X of those labels". This creates a synthetic dataset for training.
4. Encode each tweet as a vector as normal.
5. Then train a bespoke small model (e.g. a MLP) using tweet embeddings as input to create a multilabel classification model, where the model predicts the probability for each label that it is the correct one.
The small MLP will be super fast and cost effectively nothing above what it takes to create the embedding. It saves time/cost from performing a vector search or even maintaining a live vector database.