Can giving an AI's search a bigger 'memory space' help it link ideas that only connect through something in between?

This explores whether more embedding dimensions let a system connect things that are only indirectly related, or whether bridging those links needs a different tool. The corpus says dimensionality helps, but it sets a ceiling and it isn't the main lever. It has no study that measures indirect-association gains directly, so what follows is pieced together from adjacent results.

Dimensions do set a hard limit. Communication-complexity theory shows that for any embedding size d, only a limited number of top-k document combinations can ever be returned, and that limit grows only polynomially with d. Even embeddings optimized directly on the test data hit it, on retrieval tasks that look trivially simple (Do embedding dimensions fundamentally limit retrievable document combinations?). So a low-dimensional space can't represent every combination of documents a query might need. Adding dimensions raises the cap, but it doesn't remove it.

Too few dimensions also hurts the long tail. When user and item embeddings are too small, recommenders overfit toward popular items to maximize ranking quality, and niche items get squeezed out over time (Does embedding dimensionality secretly drive popularity bias in recommenders?). Indirect connections tend to run through less common items, so cramped spaces lose them first. A related geometric finding suggests why. The leading eigenvectors of an embedding space separate broad taxonomy branches first, then finer sub-branches, tracking WordNet level by level (Do embedding eigenvectors organize taxonomy from coarse to fine?). Read that way, extra dimensions buy finer resolution inside a category. They don't add new kinds of links between categories. That reading is my inference, not something the note tests.

The bigger obstacle is that embeddings measure association, not relevance, and the corpus treats that as an architectural failure to be replaced, not tuned away (Where do retrieval systems fail and why?). The approaches that do handle indirect links take steps instead of making one vector jump. Graph databases follow relationships deterministically through multi-hop traversal, and they win on relational queries where similarity search fails (When do graph databases outperform vector embeddings for retrieval?). Hierarchical systems separate query planning from answer synthesis, which improves multi-hop performance (Do hierarchical retrieval architectures outperform flat ones on complex queries?). A grep-issuing agent searching raw text beats dense embeddings on entity-constrained multi-hop questions, because embeddings blur distinct entities together (Can direct corpus search beat embedding-based retrieval?).

Even where the goal is transfer to new domains, the fix isn't a wider vector. VQ-Rec maps item text to discrete codes that index learned embeddings, which removes the bias toward whatever text happens to look similar (Can discretizing text embeddings improve recommendation transfer?). Overall, dimensionality works like a resolution setting. Too low, and popular items crowd out the tail. Past a point, the gains flatten, and bridging an indirect association takes a search procedure or a structure that encodes the link.