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Angshul
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SparseGeometricRAG

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----
-license: fair-noncommercial-research-license
-language:
-- en
-pretty_name: SparseGeometricRAG
-tags:
-- information-retrieval
-- retrieval-augmented-generation
-- rag
-- sparse-retrieval
-- cpu
-- low-latency
-- low-resource
-- beir
-- msmarco
----
-# 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 designed for a very specific operating point:
-- **low-cost hardware**, especially ordinary multicore CPUs;
-- **small structured state**, rather than dense embeddings for every chunk;
-- **bounded local computation**, with only **16 residual coordinates** touched per routed membership;
-- **top-10 retrieval quality**, because that is what a practical RAG generator usually consumes.
-The point of the system is **not** that it dominates the strongest neural retrievers in pure effectiveness. It does not. The point is that it offers a **useful quality / cost / hardware tradeoff** when the design goal is to keep retrieval simple, cheap, and CPU-native.
----
-## 1. Executive summary
-1. SparseGeometricRAG replaces dense document representations by a **coarse sparse location + tiny local directional code**.
-2. Each chunk stores only **F = 4** fuzzy branch memberships, branch centers use **B = 64** sparse coordinates, and each chunk-branch membership keeps only **S = 16** signed residual coordinates.
-3. Query-time local scoring is therefore **bounded and cheap**: the local geometric score is `O(CS)` with **`S = 16` fixed**.
-4. More detailed chunk-level evidence is postponed until after routing and shortlist reduction.
-5. On large-route datasets, a **small shortlist** can improve **both** speed and top-10 quality. In the frozen large-route experiments, **`P = 100`** was the best practical operating point.
-6. The selling point is simple: **credible top-10 retrieval on low-cost CPU hardware without needing a retrieval-time transformer stack.**
----
-## 2. Why this repository matters
-Most modern retrieval systems spend substantial effort on one of two tasks:
-1. learning a strong representation, and/or
-2. engineering a fast search layer for that representation.
-SparseGeometricRAG asks a different question:
-> **Can we reduce the representation itself so aggressively that the retrieval layer becomes cheap enough to run well on ordinary CPU hardware?**
-That is the core design philosophy behind the repository.
----
-## 3. Positioning and hardware story
-![Figure 1. Positioning and low-cost hardware story](figures/fig01_positioning_low_cost.png)
-**Figure 1.** The repository is positioned around a low-cost hardware argument. The aim is not to beat the strongest dense retrievers at any cost. The aim is to **avoid the cost structure** that usually makes such retrievers operationally heavy in the first place.
-![Figure 6. Hardware story](figures/fig06_hardware_story.png)
-**Figure 2.** The retriever is designed so that an ordinary multicore CPU, local disk, and system RAM are enough for the retrieval layer. A GPU may still exist elsewhere in a full RAG system—for example, for the generator—but the retriever itself does not require one.
----
-## 4. Method overview
-### 4.1 Offline indexing
-![Figure 2. Offline indexing pipeline](figures/fig02_offline_index_pipeline.png)
-**Figure 3.** The offline stage builds a compact structured index rather than a dense embedding database. The key compression step is to store only a sparse coarse location and a tiny local directional code.
-### 4.2 Query-time retrieval
-![Figure 3. Query-time pipeline](figures/fig03_querytime_pipeline.png)
-**Figure 4.** The query remains real-valued and sparse. Routing is weakly expanded only to find nearby branches. The decisive local comparison touches only **16 residual coordinates** per routed membership. More detailed chunk-level evidence is extracted only after shortlist reduction.
----
-## 5. Structured storage and complexity
-### 5.1 Storage structure
-![Figure 4. Structured storage budget](figures/fig04_storage_budget.png)
-**Figure 5.** The geometric storage is controlled by small frozen structural handles. The chunk-level geometric layer is bounded by `F` and `S`; branch centers and term graphs are shared structures.
-In conceptual terms, the structured storage grows as
-```text
-O(N F S)
-+ O(M B)
-+ O(M (K_assoc + K_route))
-+ O(total binary term support)
-```
-where:
-- `N` = number of chunks,
-- `M` = vocabulary size,
-- `F = 4` fuzzy memberships,
-- `B = 64` branch-center coordinates,
-- `S = 16` residual coordinates retained per membership.
-This is not byte-accurate accounting, but it captures the repository’s main structural claim: **the geometric layer stays small because it is sparse and fixed-size.**
-### 5.2 Query complexity
-![Figure 5. Query complexity by stage](figures/fig05_query_complexity.png)
-**Figure 6.** The important algorithmic fact is that the local geometric score is bounded by `O(CS)` with **`S = 16` fixed**. The system deliberately postpones richer chunk-level work until after routing and shortlist reduction.
-A concise query-time summary is:
-| Stage | Complexity |
-|---|---|
-| Sparse query construction | `O(query tokens)` |
-| Weak routing expansion | `O(Q K_r)` |
-| Posting traversal | `O(C)` |
-| Local geometric score | `O(C S)` with `S = 16` |
-| Candidate aggregation | `O(C log C)` in the frozen Python reference path; `O(C)` in the preserved later stamp-aggregation branch |
-| Cheap lexical pre-score | proportional to routed or gated binary term supports |
-| Shortlist selection | approximately linear / partial-selection cost in the routed candidates |
-| Final chunk evidence extraction | performed only on the shortlist `P` |
-| Final top-10 construction | small overhead once shortlist features are available |
-The preserved post-benchmark optimization branch additionally introduced:
-- **stamp-based candidate aggregation**, replacing sort-heavy deduplication by an `O(C)` pass; and
-- a **small gate before whole-chunk lexical scanning**.
-Those optimizations are important and preserved in the repository, but they were developed **after** the frozen six-dataset benchmark and should therefore be presented separately rather than silently replacing the reported benchmark code.
----
-## 6. Why top-10 rather than deep recall
-![Figure 7. Shortlist sweep](figures/fig07_shortlist_sweep.png)
-**Figure 7.** The experiments show why `P` should be treated as a **RAG parameter**, not a sacred retrieval constant inherited from a deep-recall setting. On a large route such as TREC-COVID, a small shortlist acts as a denoiser and `P = 100` is the best top-10 operating point. On a tiny route such as SciFact, aggressive pruning is unnecessary and quality improves as that artificial cutoff disappears.
-The practical reason is straightforward:
-> A generator typically consumes only a small context window. Retrieval quality far beyond the first few chunks may have little or no downstream utility.
-This is why the repository emphasizes `nDCG@10`, `MRR@10`, `P@10`, `R@10`, `Hit@10`, and latency, rather than selecting the operating point from deep-recall curves alone.
----
-## 7. Frozen six-dataset results for OURS
-![Figure 8. Frozen six-dataset heatmap](figures/fig08_six_dataset_heatmap.png)
-**Figure 8.** The frozen `100→10` CPU runs across six datasets.
-### 7.1 OURS only: concise summary
-| Dataset | nDCG@10 | MRR@10 | P@10 | R@10 | Hit@10 | Median latency (ms) | p95 latency (ms) |
-|---|---:|---:|---:|---:|---:|---:|---:|
-| SciFact | 0.5685 | 0.5452 | 0.0737 | 0.6663 | 0.6833 | 0.947 | 1.031 |
-| TREC-COVID | 0.5990 | 0.8252 | 0.6520 | 0.0163 | 1.0000 | 1.051 | 1.193 |
-| Quora | 0.7366 | 0.7287 | 0.1124 | 0.8407 | 0.8904 | 120.301 | 175.494 |
-| MS MARCO / DL19 | 0.3400 | 0.5189 | 0.2674 | 0.0916 | 0.7209 | 65.195 | 142.647 |
-| HotpotQA | 0.4670 | 0.6255 | 0.0964 | 0.4820 | 0.7507 | 28.944 | 42.568 |
-| NQ | 0.2579 | 0.2262 | 0.0462 | 0.3983 | 0.4342 | 33.686 | 44.161 |
-Two observations matter.
-1. The repository is strongest when the goal is **cheap CPU retrieval** with credible top-10 quality, not absolute dominance over the strongest neural stacks.
-2. The speed advantage is especially visible on the small-route / CPU-native side of the design space.
----
-## 8. Quality / latency positioning on CPU
-![Figure 9. SciFact quality versus latency](figures/fig09_scifact_quality_latency.png)
-**Figure 9.** SparseGeometricRAG is best understood as occupying a **low-cost corner** of the quality / latency plane. The repository does not claim to beat the strongest neural retrievers in effectiveness; its claim is that it can remain operationally simple and CPU-first while still giving a practical top-10 retriever.
----
-## 9. Full benchmark tables
-The tables below are intentionally complete rather than selective. `NR` means a compatible value was not available in the current ledger.
-### 9.1 nDCG@10
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 0.5780 | 0.3738 | NR | NR | NR | NR |
-| BM25 | 0.6650 | 0.6560 | 0.7890 | 0.2280 | 0.6030 | 0.3290 |
-| MiniLM + FAISS Flat | 0.6451 | 0.4725 | 0.8756 | 0.3654 | 0.4651 | 0.4387 |
-| BGE-base + FAISS Flat | 0.7404 | 0.7807 | 0.8890 | 0.4135 | 0.7260 | 0.5415 |
-| BGE-base + FAISS HNSW | 0.7404 | 0.7807† | 0.8890† | 0.4135† | 0.7260† | 0.5415† |
-| BGE-base + FAISS IVF-Flat | 0.7255 | 0.7807† | 0.8890† | 0.4135† | 0.7260† | 0.5415† |
-| BGE-base + FAISS IVF-PQ | 0.6979 | 0.7807† | 0.8890† | 0.4135† | 0.7260† | 0.5415† |
-| BGE-base + hnswlib HNSW | 0.7404 | 0.7807† | 0.8890† | 0.4135† | 0.7260† | 0.5415† |
-| BGE-base + ScaNN | 0.6783 | 0.7807† | 0.8890† | 0.4135† | 0.7260† | 0.5415† |
-| Contriever-MS MARCO + FAISS | 0.6770 | 0.5960 | 0.8650 | 0.4070 | 0.6380 | 0.4980 |
-| SPLADE++ | 0.7040 | 0.7270 | 0.8340 | 0.4330 | 0.6870 | 0.5370 |
-| Modern ColBERT | 0.7645 | 0.8341 | 0.8754 | 0.4499 | 0.7667 | 0.6169 |
-| **OURS — CPU, 100→10** | **0.5685** | **0.5990** | **0.7366** | **0.3400** | **0.4670** | **0.2579** |
-### 9.2 MRR@10
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 0.5437 | 0.5915 | NR | NR | NR | NR |
-| BM25 | 0.6460 | 0.8530 | 0.7790 | 0.1800 | 0.8030 | 0.2630 |
-| MiniLM + FAISS Flat | 0.6110 | 0.7244 | NR | NR | 0.4446 | NR |
-| BGE-base + FAISS Flat | 0.7034 | 0.9180 | 0.8823 | 0.3502 | 0.8611 | 0.4924 |
-| BGE-base + FAISS HNSW | 0.7034 | 0.9180† | 0.8823† | 0.3502† | 0.8611† | 0.4924† |
-| BGE-base + FAISS IVF-Flat | 0.6879 | 0.9180† | 0.8823† | 0.3502† | 0.8611† | 0.4924† |
-| BGE-base + FAISS IVF-PQ | 0.6615 | 0.9180† | 0.8823† | 0.3502† | 0.8611† | 0.4924† |
-| BGE-base + hnswlib HNSW | 0.7034 | 0.9180† | 0.8823† | 0.3502† | 0.8611† | 0.4924† |
-| BGE-base + ScaNN | 0.6494 | 0.9180† | 0.8823† | 0.3502† | 0.8611† | 0.4924† |
-| Contriever-MS MARCO + FAISS | 0.6207 | NR | NR | NR | NR | NR |
-| SPLADE++ | 0.6699 | NR | NR | 0.3830 | NR | NR |
-| Modern ColBERT | 0.7390 | 0.9533 | 0.8671 | 0.3849 | 0.9188 | 0.5655 |
-| **OURS — CPU, 100→10** | **0.5452** | **0.8252** | **0.7287** | **0.5189** | **0.6255** | **0.2262** |
-### 9.3 Precision@10
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 0.0797 | 0.4020 | NR | NR | NR | NR |
-| BM25 | 0.0863 | 0.6360 | ~0.1200 | NR | NR | NR |
-| MiniLM + FAISS Flat | 0.0883 | 0.5040 | 0.1337 | 0.0591 | 0.0974 | 0.0770 |
-| BGE-base + FAISS Flat | 0.0987 | 0.8300 | 0.1346 | 0.0656 | 0.1515 | 0.0884 |
-| BGE-base + FAISS HNSW | 0.0987 | 0.8300† | 0.1346† | 0.0656† | 0.1515† | 0.0884† |
-| BGE-base + FAISS IVF-Flat | 0.0973 | 0.8300† | 0.1346† | 0.0656† | 0.1515† | 0.0884† |
-| BGE-base + FAISS IVF-PQ | 0.0950 | 0.8300† | 0.1346† | 0.0656† | 0.1515† | 0.0884† |
-| BGE-base + hnswlib HNSW | 0.0987 | 0.8300† | 0.1346† | 0.0656† | 0.1515† | 0.0884† |
-| BGE-base + ScaNN | 0.0887 | 0.8300† | 0.1346† | 0.0656† | 0.1515† | 0.0884† |
-| Contriever-MS MARCO + FAISS | 0.0883 | NR | NR | NR | NR | NR |
-| SPLADE++ | 0.0937 | NR | NR | NR | NR | NR |
-| Modern ColBERT | 0.0977 | 0.8820 | 0.1327 | 0.0701 | 0.1548 | 0.0979 |
-| **OURS — CPU, 100→10** | **0.0737** | **0.6520** | **0.1124** | **0.2674** | **0.0964** | **0.0462** |
-### 9.4 Recall@10
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 0.7135 | 0.0105 | NR | NR | NR | NR |
-| BM25 | 0.7809 | 0.0158 | 0.8854 | NR | 0.6531 | NR |
-| MiniLM + FAISS Flat | 0.7833 | 0.0128 | 0.9503 | 0.5676 | 0.4870 | 0.6471 |
-| BGE-base + FAISS Flat | 0.8742 | 0.0221 | 0.9574 | 0.6277 | 0.7574 | 0.7469 |
-| BGE-base + FAISS HNSW | 0.8742 | 0.0221† | 0.9574† | 0.6277† | 0.7574† | 0.7469† |
-| BGE-base + FAISS IVF-Flat | 0.8609 | 0.0221† | 0.9574† | 0.6277† | 0.7574† | 0.7469† |
-| BGE-base + FAISS IVF-PQ | 0.8441 | 0.0221† | 0.9574† | 0.6277† | 0.7574† | 0.7469† |
-| BGE-base + hnswlib HNSW | 0.8742 | 0.0221† | 0.9574† | 0.6277† | 0.7574† | 0.7469† |
-| BGE-base + ScaNN | 0.7814 | 0.0221† | 0.9574† | 0.6277† | 0.7574† | 0.7469† |
-| Contriever-MS MARCO + FAISS | 0.7868 | NR | NR | NR | NR | NR |
-| SPLADE++ | 0.8230 | NR | NR | NR | NR | NR |
-| Modern ColBERT | 0.8647 | 0.0230 | 0.9516 | 0.6710 | 0.7739 | 0.8239 |
-| **OURS — CPU, 100→10** | **0.6663** | **0.0163** | **0.8407** | **0.0916** | **0.4820** | **0.3983** |
-### 9.5 Hit@10
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 0.7333 | 0.8600 | NR | NR | NR | NR |
-| BM25 | 0.8033 | 1.0000 | 0.9286 | NR | NR | NR |
-| MiniLM + FAISS Flat | NR | NR | NR | NR | NR | NR |
-| BGE-base + FAISS Flat | 0.8833 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS HNSW | 0.8833 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-Flat | 0.8700 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-PQ | 0.8567 | NR | NR | NR | NR | NR |
-| BGE-base + hnswlib HNSW | 0.8833 | NR | NR | NR | NR | NR |
-| BGE-base + ScaNN | 0.7900 | NR | NR | NR | NR | NR |
-| Contriever-MS MARCO + FAISS | 0.7967 | NR | NR | NR | NR | NR |
-| SPLADE++ | 0.8333 | NR | NR | NR | NR | NR |
-| Modern ColBERT | 0.8100 | NR | NR | NR | NR | NR |
-| **OURS — CPU, 100→10** | **0.6833** | **1.0000** | **0.8904** | **0.7209** | **0.7507** | **0.4342** |
-### 9.6 Median query latency (ms)
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 6.197 | 50.185 | NR | NR | NR | NR |
-| BM25 | 0.561 | 4.912 | NR | NR | NR | NR |
-| MiniLM + FAISS Flat | NR | NR | NR | NR | NR | NR |
-| BGE-base + FAISS Flat | 10.013 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS HNSW | 10.369 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-Flat | 10.050 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-PQ | 13.910 | NR | NR | NR | NR | NR |
-| BGE-base + hnswlib HNSW | 10.594 | NR | NR | NR | NR | NR |
-| BGE-base + ScaNN | 9.947 | NR | NR | NR | NR | NR |
-| Contriever-MS MARCO + FAISS | 7.472 | NR | NR | NR | NR | NR |
-| SPLADE++ | 13.493 | NR | NR | NR | NR | NR |
-| Modern ColBERT | 62.671 | NR | NR | NR | NR | NR |
-| **OURS — CPU, 100→10** | **0.947** | **1.051** | **120.301** | **65.195** | **28.944** | **33.686** |
-### 9.7 p95 query latency (ms)
-| Method | SciFact | TREC-COVID | Quora | MS MARCO / DL19 | HotpotQA | NQ |
-|---|---:|---:|---:|---:|---:|---:|
-| Exact TF-IDF | 14.605 | 56.716 | NR | NR | NR | NR |
-| BM25 | 5.645 | 7.336 | NR | NR | NR | NR |
-| MiniLM + FAISS Flat | NR | NR | NR | NR | NR | NR |
-| BGE-base + FAISS Flat | 15.398 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS HNSW | 12.925 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-Flat | 16.303 | NR | NR | NR | NR | NR |
-| BGE-base + FAISS IVF-PQ | 18.496 | NR | NR | NR | NR | NR |
-| BGE-base + hnswlib HNSW | 13.293 | NR | NR | NR | NR | NR |
-| BGE-base + ScaNN | 11.858 | NR | NR | NR | NR | NR |
-| Contriever-MS MARCO + FAISS | 9.628 | NR | NR | NR | NR | NR |
-| SPLADE++ | 19.156 | NR | NR | NR | NR | NR |
-| Modern ColBERT | 70.994 | NR | NR | NR | NR | NR |
-| **OURS — CPU, 100→10** | **1.031** | **1.193** | **175.494** | **142.647** | **42.568** | **44.161** |
-**Notes.** `NR` means “not reported under a compatible metric / protocol in the current ledger.” `†` indicates that, outside SciFact, the BGE ANN-backend rows mirror the BGE-base representation-level effectiveness reference rather than a separately rerun backend-specific effectiveness experiment.
----
-## 10. Reproducibility and repository structure
-![Figure 10. Repository map](figures/fig10_repository_map.png)
-**Figure 10.** The repository is organized so that the reusable retriever, the BEIR experiments, the full-scale MS MARCO campaign, the result artifacts, and the documentation remain clearly separated.
-A concise map is:
-```text
-geomretrieval/                 reusable sparse geometric retriever
-experiments/beir/             clean BEIR runners
-experiments/msmarco_scale/    full MS MARCO scale campaign
-results/                      frozen result JSONs
-configs/                      reproduction handles
-scripts/                      one-command runners
-docs/                         method, protocol, speed, baseline notes
-tests/                        smoke tests
-```
----
-## 11. What the repository does and does not claim
-### It does claim:
-- a **CPU-first** retriever with small structured state;
-- bounded local computation driven by **16-coordinate residual codes**;
-- a practical **top-10** evaluation philosophy;
-- a meaningful **low-cost hardware** story;
-- full reproducibility artifacts, experiment history, and result tables.
-### It does not claim:
-- that it dominates the strongest neural retrievers in pure accuracy;
-- that all latency figures across all baselines are strictly apples-to-apples end-to-end systems timings;
-- that top-10 quality and deep-recall quality should always share the same shortlist setting.
-This is precisely why the repository is interesting: it highlights a different design point in the retrieval landscape.
----
-## 12. Bottom line
-The central selling point is simple:
-> **SparseGeometricRAG is a retriever designed so that expensive retrieval hardware is optional rather than mandatory.**
-If the goal is to deploy a practical RAG retriever on low-cost CPU hardware, keep the retrieval layer simple, avoid retrieval-time transformer inference, and still obtain usable top-10 quality, then this repository offers a concrete and reproducible answer.