A flat BM25 index over one billion documents occupies about 400 GB. Holding it in memory requires DRAM proportional to corpus size. Serving it from disk takes 4-12 seconds per query. Exact top-k lexical retrieval at this scale is therefore impractical within an interactive latency budget. Hierarchical BM25 gives up exact ranking in exchange for fixed bounds on memory and latency. A resident coarse index selects which of ~1K topical, size-balanced document groups a query visits, using two signals: the total frequency of each query term within a group, and, for informative terms spread too thinly across groups for frequency totals to reflect, whether several of them appear together in one document. Selected groups are then searched exhaustively and scored against ~100 KB of global statistics. Every returned score therefore equals the flat index's score, and the approximation is confined to selection alone. The resident footprint is ~4.4 GB, independent of corpus size. Sixteen-term queries over one billion documents return in ~300 ms (4.7x to 5.6x the throughput of a flat multi-threaded index), and a warmed cache sustains ~32 queries per second versus under 3 for flat indexing. At a 500K-document configuration, visiting 5-10% of clusters recovers 0.83-0.92 of the exhaustive result score. Billion-scale recall and a direct comparison against document-reordered BlockMax-WAND remain open.
Retrieval-augmented generation (RAG) spans lexical and dense retrieval, graph-based indexing, and agentic search, but these paradigms are usually evaluated on different benchmarks at one corpus size, leaving their accuracy-cost scaling unclear. To bridge this gap, we present a controlled study that varies corpus size along 28 strictly nested tiers spanning roughly 450-fold, while holding questions and a fixed bedrock of relevant and adversarial documents unchanged. Under one reader model and one judging protocol, we measure official accuracy, construction and query tokens, and latency. The results reveal a scale-dependent crossover rather than an unconditional winner. File-System Agent leads at the smallest shared tiers, but its sequential exploration costs 39 times more query tokens at the bedrock and becomes less effective as the search space grows. Around 10 million corpus tokens, BM25 overtakes it and leads at every larger shared tier, with a margin approaching 20 points at full scale. BM25 also anchors the low-cost end of the Pareto frontier without LLM-based construction. Dense retrieval remains efficient but less accurate, whereas graph-based RAG encounters construction walls before deployment scale and its scalable variants remain below BM25 at shared tiers. Overall, corpus growth increasingly favors global candidate ranking: lexical retrieval is the strongest scalable default, while agentic reasoning works best after ranked discovery rather than in place of it.
We propose Latent Terms, a method revealing that models trained for dense retrieval, whether single- or multi-vector, learn representations that can trivially be decomposed into retrieval-ready sparse features. When trained on frozen retrievers, Sparse Autoencoders without any retrieval-specific adjustments extract a latent vocabulary with approximately Zipfian collection statistics, directly suitable for classical sparse retrieval scoring via BM25. This approach enables sparse retrieval while requiring no learned expansion objective or sparse retrieval supervision whatsoever, and can be readily applied to any dense retriever. Latent Terms is able to match or outperform single-vector scoring methods from its own base model as well as comparable SPLADE variants. In addition, it substantially outperforms its base model on LIMIT, a task specifically designed to highlight the failures of single-vector retrieval. Overall, our results highlight that neural retrievers contain more expressive and indexable structure than their default scoring functions expose, but that other methods can nonetheless be leveraged.
In retrieval-augmented coding, failures often begin when the relevant file is absent from the retrieved context. Under frozen generic tokenization, where a BM25 index has been built by a search system whose analyzer the practitioner does not control, this failure is routine: BM25's logarithmic RSJ-odds IDF under-separates the identifier tail that distinguishes one function from another. We replace the outer logarithm of the Robertson-Spärck-Jones odds with a q-logarithm. At q=1 the transform recovers BM25 exactly by L'Hôpital's rule, and for q<1 it is a Box-Cox transform of the RSJ odds with lambda = 1-q. On CoIR CodeSearchNet Go (182K documents), oracle-tuned NDCG@10 rises from 0.2575 to 0.4874 (absolute +0.2299; +89.3% relative; zero sign reversals in 10,000 paired-bootstrap resamples, reported as p <= 10^-4). The effect is graded across code languages and is near-zero on BEIR text. A one-parameter closed form estimates a corpus-level q from hapax density and stays near q=1 on corpora where BM25 is already optimal. The index-time cost is a single pass over the sparse score matrix and query latency is unchanged. A tokenizer ablation shows that identifier-aware tokenization largely removes the incremental gain from q-IDF.