Angshul/SparseGeometricRAG
SparseGeometricRAG CPU-first sparse geometric retrieval for practical top-10 RAG No transformer inference at retrieval time. No retrieval GPU requirement. No dense document-vector dot products. No external API. SparseGeometricRAG is a retrieval system built around one systems objective: make the retrieval layer cheap enough to run on ordinary multicore CPU hardware without turning the corpus into a dense embedding database. It uses sparse TF-IDF geometry, fuzzy… See the full description on the dataset page: https://huggingface.co/datasets/Angshul/SparseGeometricRAG.
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1# Method2 3## Offline representation4 5For each chunk, construct a sparse normalized TF-IDF vector. Keep its top `F=4` coordinates as fuzzy branch memberships. For branch `j`, keep a sparse `B=64` membership-weighted center. For every chunk-branch membership, retain only `S=16` residual coordinates chosen from terms actually present in the chunk and store their **signs**, not document-specific residual amplitudes.6 7A zero-inclusive branch-local sign variance is shrunk toward the global term variance and converted to a mild inverse reliability weight, approximately `variance^-0.2`. The corpus also produces a sparse PPMI association graph and a second-order context graph for query routing.8 9## Query routing and local scoring10 11The query retains real TF-IDF amplitudes. Weak second-order expansion exposes nearby branches. A branch-local signed score evaluates only the 16 stored residual coordinates and is weighted by fuzzy membership, route strength, query-mass significance, and inverse local sign variance.12 13## Early rescue and chunk shortlist14 15The routed representations are cheaply ordered using geometric evidence plus whole-chunk **binary IDF^1** support. The best `P` representations are mapped to their corresponding chunks. No dense 384/768-dimensional embedding is required at this stage.16 17## Final chunk score18 19For each shortlisted chunk, the final lexical statistic is binary presence weighted by **IDF squared**:20 21```text22sum_{t in query ∩ chunk} IDF(t)^223```24 25It is combined with a weak length correction, query coordination, sparse semantic presence, and coverage of the three rarest query terms. The validated score components retain their per-query z-normalization.26 27## High-quality branches and soft diversity28 29Branch quality is query-specific. For branch `j`, define branch-specific evidence `E_dj` using the geometric membership contribution. The quality score is the mean of the top three evidences in that branch:30 31```text32H_j = mean(top3_d E_dj)33```34 35Only the ten branches with largest `H_j` are eligible for a diversity bonus. Rank 1 is pure relevance. For ranks 2–10, a candidate can receive a small bonus if one of its high-quality supporting branch centers deviates from the centroid of branches already represented. Repeated branches are allowed.36 37This is **not blind diversification** and it is **not one-document-per-branch**.38