| # Retrieval literature through the speed lens |
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| Speed is not a secondary metric in this project. A retriever that produces an excellent rank at a cost incompatible with interactive RAG has solved a different problem. |
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| ## The computational boundary we measure |
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| A RAG request pays for **query representation + retrieval + shortlist scoring + top-10 selection**. For ANN baselines, the literature often reports ANN search after the dense query embedding has already been computed. We therefore keep two latency columns whenever possible: |
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| 1. **ANN/search-only latency** — useful for comparing indexes. |
| 2. **End-to-end query latency** — the number relevant to an actual RAG request. |
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| The two must never be silently mixed. |
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| | Family | Query-time representation | Search object | Speed implication | |
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| | BM25 | tokenization only | inverted postings | no neural query inference; strong classical latency reference | |
| | FAISS Flat / IVF / PQ | dense query embedding | dense vectors / quantized vectors | optimized vector search; encoder cost is normally outside ANN timing | |
| | HNSW | dense query embedding | graph over dense vectors | very fast ANN search, but memory-heavy graph and query encoder remain | |
| | ScaNN | dense query embedding | partitioned/quantized dense vectors | search is optimized around MIPS/quantization; encoder cost is separate | |
| | Contriever / BGE | neural dense encoder | ANN dense index | representation quality is strong, but query inference is part of deployed RAG cost | |
| | SPLADE | neural sparse encoder | sparse inverted index | sparse search, but query sparse vector is produced by a transformer | |
| | ColBERTv2 | neural token encoder | compressed multi-vector index + late interaction | excellent quality, but multiple query vectors and late interaction increase work | |
| | **Sparse Geometric RAG (this repo)** | **TF-IDF query vector; no neural inference** | **fuzzy sparse branches + 16-coordinate signed residuals** | **query formation is cheap; routing and local scoring touch tiny sparse structures; only a small shortlist reaches chunk-level scoring** | |
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| ## Primary references |
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| - Johnson, Douze, Jégou, *Billion-scale similarity search with GPUs* (FAISS): https://arxiv.org/abs/1702.08734 |
| - Douze et al., *The Faiss Library*: https://arxiv.org/abs/2401.08281 |
| - Malkov and Yashunin, *Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs*: https://arxiv.org/abs/1603.09320 |
| - Guo et al., *Accelerating Large-Scale Inference with Anisotropic Vector Quantization* (ScaNN): https://arxiv.org/abs/1908.10396 |
| - Izacard et al., *Unsupervised Dense Information Retrieval with Contrastive Learning* (Contriever): https://arxiv.org/abs/2112.09118 |
| - Formal et al., *SPLADE v2*: https://arxiv.org/abs/2109.10086 |
| - Santhanam et al., *ColBERTv2: Effective and Efficient Retrieval via Lightweight Late Interaction*: https://arxiv.org/abs/2112.01488 |
| - Xiao et al., *C-Pack: Packaged Resources To Advance General Chinese Embedding* (BGE family): https://arxiv.org/abs/2309.07597 |
| - Thakur et al., *BEIR: A Heterogeneous Benchmark for Zero-shot Evaluation of Information Retrieval Models*: https://arxiv.org/abs/2104.08663 |
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| ## Why this method is different computationally |
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| FAISS, HNSW, and ScaNN solve the problem “search a database of dense vectors quickly.” This project asks a prior question: **does the retrieval database need a dense vector per chunk at all?** The stored object is instead a coarse fuzzy location plus a very small signed departure from its local center. Query-time work follows that sparse geometry. |
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| The intended speed story is therefore not “we wrote a faster HNSW.” It is: **avoid most of the arithmetic and memory traffic that make ANN necessary in the first place.** |
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