One instruction-conditioned encoder, recursive search, and a global readout,
for single-hop and multi-hop retrieval.
Website & docs · Quickstart · Combinations · Reproduce the paper
RDR is a dense retriever that searches recursively. An instruction, the query and the documents observed so far form a state. The encoder maps each state to one query vector, which searches a fixed document index. Each retrieved document can be appended to the state and encoded again. Repeating this builds a retrieval tree. The global readout then scores every retained candidate with all states of the tree.
Because the instruction is part of the state, one encoder does both jobs. With the recovery instruction it refines a single-hop query. With the continuation instruction it follows a multi-hop evidence chain.
The package rdr implements this operator. Dense retrieval, pseudo-relevance feedback, refinement chains, beam
retrieval and document-as-query expansion are all instances of it:
Search and readout strategies under the same encoder (Figure 2 of the paper):
- (a) Pseudo-relevance feedback encodes observations jointly into one query vector.
- (b) As in DC-PRF, a refinement chain reads out its last state, interpolated with the root.
- (c) Beam retrievers return realized paths, each document scored by its own chain.
- (d) Promoting retrieved documents to queries fuses parallel lists by rank.
- (e) RDR scores every retained candidate with all learned states.
The numbers are the change over the root query in multi-hop Recall@5 and single-hop nDCG@10.
pip install . # in the downloaded repository
# benchmark loaders for reproduce/: pip install ".[eval]"- Requirements. Python ≥ 3.9, PyTorch ≥ 2.1, sentence-transformers 3.x–5.x and transformers ≥ 4.51.
- Model. RDR-8B (weights not included in this anonymized repository) is fine-tuned from Qwen3-Embedding-8B. It loads as a sentence-transformers model (last-token pooling, normalized, 4096 dimensions) and needs about 16 GB of GPU memory in bf16.
- Hardware. Everything also runs on CPU in fp32.
from rdr import RecursiveRetriever
retriever = RecursiveRetriever("RDR-8B") # multi-hop prompts, TreeSearch(4, 3), GlobalReadout()
index = retriever.build_index({
"d1": "The novel Harbor Lights was written by Mara Voss.",
"d2": "Mara Voss was born in Linz, Austria, in 1961.",
"d3": "Linz lies on the Danube, the second-longest river in Europe.",
})
hits = retriever.search("Which river flows through the birthplace of the author of Harbor Lights?", index, top_k=3)
# [{"corpus_id": ..., "score": ..., "index": ...}, ...] (semantic_search-style hits)Change the search, keep the readout. The global readout is the default for every search. Realized outputs, such as a beam's chains, must be requested explicitly:
from rdr import ChainSearch, BeamSearch, ProbabilityChain, recovery_fusion
retriever.search(queries, index, search=ChainSearch(depth=4)) # 4 states
retriever.search(queries, index, search=BeamSearch(width=5)) # beam, global readout
retriever.search(queries, index, search=BeamSearch(width=5), readout=ProbabilityChain()) # BeamDR's output
retriever.search(queries, index, readout=recovery_fusion()) # + recovery viewSingle-hop. Use the recovery instruction at every context level, and the benchmark's own root instruction:
from rdr import RecursiveRetriever, instructions
retriever = RecursiveRetriever("RDR-8B", prompts="single-hop")
hits = retriever.search(queries, index, instruction=instructions.root_for("nanobeir", "NanoSciFact"))Two GPUs. Keep the encoder and the exact fp16 index search on separate devices. Query batches overlap: while one batch is encoded, the next is searched.
retriever = RecursiveRetriever("RDR-8B", encode_device="cuda:0", index_device="cuda:1")| Search strategies (which states form) | TreeSearch (RDR(H, b), default H=4, b=3), ChainSearch, BreadthSearch (RDR(2, m)), BeamSearch (as in MDR/BeamDR), DocAsQuerySearch (as in COR), JointFeedback (as in ANCE-PRF), DenseSearch |
| Readouts (how scores become a ranking) | GlobalReadout (Eq. 2, default); realized: PathProduct, ProbabilityChain, SequenceSum, ChainOrder, TerminalState; fusion: RRF, PostOrderRRF, Borda, CombMNZ, MaxOverStates; model-based: RootInterpolation, Assembly, StateReadout; views: recovery_fusion, ZAgreement |
| Prompts | presets "multi-hop", "single-hop", "single-hop-continuation", "bright-pro"; instructions by key (rdr.instructions); fully custom PromptConfig |
| Execution | level-synchronous batching, separate encode and index devices, in-flight query batches, CPU fallback, exact reproduction mode |
| Evaluation | Recall@k over gold groups, nDCG@k, α-nDCG@k; loaders for BRIGHT, NanoBEIR, CoIR, ToolRet, TopiOCQA, MuSiQue, BrowseComp+, FanOutQA, FRAMES |
Every class and parameter is documented in the API reference.
Multi-hop retrieval, Recall@5 (Table 1 of the paper):
| Model / configuration | MuSiQue | BrowseComp+ | FanOutQA | FRAMES |
|---|---|---|---|---|
| Qwen3-Embedding-8B, q₀ | 63.16 | 14.70 | 26.79 | 67.80 |
| GRITHopper-7B, recursive | 78.55 | 12.98 | 31.96 | 74.08 |
| RDR(1, 0) (q₀) | 58.51 | 16.87 | 28.63 | 66.77 |
| RDR(4, 3) | 80.14 | 25.28 | 37.78 | 77.41 |
| + recovery (z-agreement) | 81.45 | 25.28 | 40.66 | 77.89 |
| + Assembly | 79.62 | 23.63 | 49.29 | 79.20 |
Single-hop retrieval, nDCG@10 (Table 2 of the paper; BRIGHT-Pro reports α-nDCG@10):
| Model / configuration | BRIGHT | NanoBEIR | ToolRet | CoIR | TopiOCQA | Avg. | BRIGHT-Pro |
|---|---|---|---|---|---|---|---|
| Qwen3-Embedding-8B | 23.17 | 71.74 | 44.72 | 79.93 | 59.40 | 55.79 | 43.76 |
| BGE-Reasoner-8B | 36.97 | 60.90 | 42.26 | 65.32 | 41.85 | 49.46 | 61.82 |
| RDR(1, 0) (q₀, no context) | 29.02 | 66.55 | 46.45 | 78.77 | 63.37 | 56.83 | 55.92 |
| RDR(4, 3) | 30.84 | 68.13 | 48.04 | 78.88 | 70.79 | 59.34 | 61.13 |
Search × readout under one encoder (Table 3). Multi-hop is mean Recall@5 over four suites; single-hop is mean nDCG@10 over five suites:
| Search / readout | Multi-hop | Single-hop |
|---|---|---|
| Root query | 42.70 | 56.78 |
| as in ANCE-PRF: joint feedback / single vector | 38.15 | 52.71 |
| as in DC-PRF: chain / last state, root-interpolated | 44.68 | 57.57 |
| as in BeamDR: beam (W=5) / probability chain | 46.30 | n/a |
| as in COR: document-as-query tree / rank fusion | 30.08 | n/a |
| chain / global readout | 53.91 | 57.95 |
| beam (W=13) / global readout | 53.88 | 59.60 |
| RDR: learned tree / global readout | 55.15 | 59.34 |
The configurator lists every measured combination per suite.
reproduce/ holds one configuration per table, a runner that reads each saved traversal with every
readout of that table, and an aggregator that compares the results with the paper. See
reproduce/README.md for data preparation and the exact batching mode.
This repository accompanies an anonymous submission under double-blind review. Citation information will be added after the review period.
Apache-2.0 (see LICENSE). RDR-8B is fine-tuned from Qwen3-Embedding-8B (Apache-2.0).