---
kind: concept
slug: multi-hop-reasoning
title: Multi-hop reasoning
summary: >-
  Multi-hop reasoning answers a question by chaining two or more facts. Benchmarks, prompting, interleaved retrieval, document-link pretraining and looped transformers approach it differently. Score the answer and the evidence chain together: one baseline reaches 5.41 joint F1 against 43.93 answer F1 (author-reported).
tags: [reasoning, question-answering, evaluation, dataset, prompting, recurrence, pretraining]
papers: ["2011.01060", "2101.02235", "2203.15827", "2205.09712", "2210.02406", "2212.10509", "2604.07822"]
related: [knowledge-graph-reasoning, dataset-curation, chain-of-thought-prompting, in-context-learning, llm-evaluation, adversarial-evaluation, retrieval-augmented-generation, task-decomposition, neural-symbolic-integration, looped-transformer, grokking, adaptive-halting, language-model-pretraining]
status: draft
updated_at: 2026-10-24
---

## Overview

A multi-hop question cannot be answered from one passage or one fact. The
system must find a first fact, use it to reach a second, and so on until it
has the answer. The shared problem is that a correct final answer does not
show that the chain was followed. The benchmark behind the first variant
addresses it by asking for three outputs at once: the answer, the supporting
sentences and the evidence triples that spell out the reasoning path
[arxiv:2011.01060 §2.1].

The seven papers on this page take different routes. One builds benchmarks
with gold chains, from templates or from crowd-written steps. One gets a
language model to write its own sub-questions with prompts only. One
interleaves reasoning sentences with retrieval, so each new sentence becomes
the next search query [arxiv:2212.10509 §3.1]. One loops a frozen model over
a given context, selecting facts and then deriving one new fact from them
[arxiv:2205.09712 §4]. One trains small models from scratch on synthetic
chains and studies whether recurrence helps them generalize. One changes
pretraining so that linked documents share a training input, and reports its
largest gains on multi-document QA [arxiv:2203.15827 §4.2]
[arxiv:2203.15827 §5.3]. Their settings differ, so their numbers are not
directly comparable [arxiv:2101.02235 §5.2] [arxiv:2210.02406 §4]
[arxiv:2212.10509 §4] [arxiv:2604.07822 app. A] [arxiv:2203.15827 §5.1]
[arxiv:2205.09712 §5].

## Variants

### Template-generated chains over Wikipedia and Wikidata

This is the construction of [2WikiMultiHopQA](/papers/2011.01060). Two Wikidata
triples are chained, and a question template is filled in from them.

- **Question types.** Four types: comparison, inference, compositional and
  bridge-comparison [arxiv:2011.01060 §2.2]. An inference question names one
  entity and one relation, and the answer is reached through a logical rule.
  A compositional question names the entity and both relations
  [arxiv:2011.01060 app. A.3] [arxiv:2011.01060 app. A.4].
- **Sources.** Summary paragraphs of English Wikipedia articles give the
  context. Wikidata triples give the evidence [arxiv:2011.01060 §3.1].
- **Templates and rules.** Templates were written by hand. Inference uses 28
  logical rules over single-valued relations, checked by hand
  [arxiv:2011.01060 §3.2] [arxiv:2011.01060 app. A.3].
- **Generation checks.** Each object of a triple must appear in the matching
  Wikipedia summary. Bridge questions also need paragraph checks
  [arxiv:2011.01060 §3.2] [arxiv:2011.01060 alg. 1] [arxiv:2011.01060 alg. 2].
- **Distractors and split.** A bigram tf-idf retriever adds distractor
  paragraphs, and a single-hop model splits the data into harder and easier
  parts [arxiv:2011.01060 §3.2] [arxiv:2011.01060 tab. 1].
- **Size.** 192,606 questions in total [arxiv:2011.01060 tab. 1].

### Joint scoring of answer, supporting facts and evidence

This is the metric defined for the benchmark. It can be applied to any system
that outputs an answer, sentences and triples in the same format.

- **Per-task scores.** Answer, supporting-fact and evidence scores are each
  computed as exact match and F1 [arxiv:2011.01060 §2.1].
- **Joint score.** Precision and recall are each the product of the three
  task values. Joint EM is 1 only when all three tasks match exactly
  [arxiv:2011.01060 §2.1] [arxiv:2011.01060 eq. 1].

### HotpotQA-style baseline with an evidence branch

The paper's baseline extends the HotpotQA baseline with one block that predicts
evidence. The question predicts the relations, and the context gives the
subject and object of each relation [arxiv:2011.01060 §5.2].

- **Result.** Test joint F1 of 5.41, with evidence F1 of 14.94 and answer F1 of
  43.93 [arxiv:2011.01060 tab. 5]. These are author-reported numbers.
- **Gap to humans.** On 100 test samples, the human average reaches 66.69 joint
  F1 and the model 9.79 [arxiv:2011.01060 tab. 7] [arxiv:2011.01060 §5.3].

### Implicit-step questions with decomposition and evidence (StrategyQA)

The questions in [StrategyQA](/papers/2101.02235) do not state their reasoning
steps, so a strategy has to be inferred before the facts can be looked up
[arxiv:2101.02235 §1]. The benchmark has yes/no questions only.

- **Data.** 2,780 questions. Each has a decomposition into steps, and each
  retrieval step has Wikipedia paragraphs that answer it
  [arxiv:2101.02235 §2.2] [arxiv:2101.02235 §4].
- **Collection.** Crowd workers write a question from a Wikipedia term. Questions
  that at least four of five pretrained solvers answer correctly are removed,
  and so are questions that all three fine-tuned solvers answer correctly
  [arxiv:2101.02235 §3.1]. The decomposition is written before evidence is
  matched, so the writer does not see the context [arxiv:2101.02235 §3.2].
- **Quality check.** In a 100-question sample checked by the authors, 82 were
  judged to have implicit steps [arxiv:2101.02235 tab. 5].
- **Cost.** About $4 per example, with three evidence matchers per decomposition
  [arxiv:2101.02235 §4].
- **Baselines.** Accuracy with no context is 63.6 ± 1.3. With gold paragraphs it
  is 70.7 ± 0.6, and with gold paragraphs plus the last step 72.0 ± 1.0. Experts
  reach 87% [arxiv:2101.02235 tab. 9] [arxiv:2101.02235 tab. 7]. These are
  author-reported test-set numbers.
- **Retrieval.** Recall@10 is 0.174 for question-based BM25 retrieval, 0.195
  with a predicted decomposition and 0.282 with a gold decomposition
  [arxiv:2101.02235 tab. 9]. Accuracy with predicted-decomposition retrieval is
  61.7 ± 2.2 [arxiv:2101.02235 tab. 9].
- **Licence.** The paper's own licence is CC0. The dataset's licence is not
  confirmed in the card, so do not copy the dataset into a derived work.

### Prompt-level decomposition into sub-questions (DecomP)

[Decomposed Prompting](/papers/2210.02406) uses prompts only. No model is
trained [arxiv:2210.02406 §2].

- **Mechanism.** A decomposer prompt writes a program of sub-tasks. Each sub-task
  goes to a few-shot prompt, a symbolic function, or a recursive call of the same
  procedure [arxiv:2210.02406 §3] [arxiv:2210.02406 §3.3]. A controller sends
  each answer back to the decomposer until it writes an end marker
  [arxiv:2210.02406 §3.2].
- **Letter concatenation.** The method outperforms chain-of-thought (CoT) and
  least-to-most prompting across the tested lengths [arxiv:2210.02406 §4.1]
  [arxiv:2210.02406 fig. 7].
- **List reversal.** The decomposed method generalizes to longer lists, where
  base CoT does not [arxiv:2210.02406 §4.2] [arxiv:2210.02406 fig. 8].
- **Open-domain QA.** Decomposed retrieval beats the no-context baseline in every
  setting reported. Results are answer F1 on 300 dev questions per dataset
  [arxiv:2210.02406 §4.4] [arxiv:2210.02406 fig. 12]. The corpora for the
  2WikiMultihopQA and MuSiQue settings pool paragraphs from the train, dev and
  test questions, so the numbers do not reflect a corpus built from evaluation
  questions alone [arxiv:2210.02406 app. A.1].
- **Math.** Adding a CoT answer-extraction sub-task raises the reported GSM8K
  score from 36 to 50.6 and MultiArith from 78 to 95 [arxiv:2210.02406 §4.5]
  [arxiv:2210.02406 app. B]. The metric is not stated, and the samples are 300
  and 200 examples. The gain comes from one change in answer extraction
  [arxiv:2210.02406 app. B].
- **Model size.** Only GPT-3-sized models reliably produced the structured
  output, so the decomposer cannot simply be a small model
  [arxiv:2210.02406 §4.4].

### Interleaved retrieval and reasoning (IRCoT)

[IRCoT](/papers/2212.10509) retrieves in the middle of a chain of thought. The
model writes one sentence, and that sentence becomes the next search query.
The paragraphs found are added to the prompt before the next sentence is
written [arxiv:2212.10509 §3.1] [fig. 2]. No weights are trained: the method
is few-shot prompting over a base retriever [arxiv:2212.10509 abstract].

- **Loop.** The first retrieval uses the question. The loop ends when a
  sentence contains "answer is" or the step limit is reached. The paper sets
  the limit to 8 and caps collected paragraphs at 15 [arxiv:2212.10509 §3.1].
- **Demonstrations.** The authors annotated 20 questions per dataset and
  sampled three demonstration sets of 15 [arxiv:2212.10509 §4.1]
  [arxiv:2212.10509 app. G].
- **Readers.** GPT-3 uses chain-of-thought prompting for the answer; Flan-T5
  uses direct prompting [arxiv:2212.10509 §3.2] [arxiv:2212.10509 §4.1].
- **Results.** Author-reported answer F1 with GPT-3 (`code-davinci-002`),
  IRCoT against one-step retrieval: 60.7 against 53.6 on HotpotQA, 68.0 against
  54.8 on 2WikiMultiHopQA, 36.5 against 29.4 on MuSiQue, and 49.9 against 49.8
  on IIRC [arxiv:2212.10509 tab. 4]. With Flan-T5-XXL (11B), IRCoT is above
  one-step retrieval on all four sets, from 42.5 against 40.0 on IIRC to 66.5
  against 51.2 on 2WikiMultiHopQA [arxiv:2212.10509 tab. 4].
- **Factual errors.** In a manual check of 40 questions per dataset, the authors
  count 50% fewer reasoning chains with a false fact than one-step retrieval on
  HotpotQA, and 40% fewer on 2WikiMultiHopQA [arxiv:2212.10509 §5]
  [fig. 7].
- **Cost.** Each retrieval step needs its own reasoning call, and the prompt
  shows every paragraph gathered so far, so it grows with each step
  [arxiv:2212.10509 limitations] [arxiv:2212.10509 §3.1].

### Selection-inference loop over a given context (SI)

[Selection-Inference](/papers/2205.09712) wraps a frozen LLM in a loop over a
fixed context. Each step has two few-shot prompts on the same model. A
selection step picks a few facts from the context, and an inference step
derives one new fact from those facts alone, without the question. The new
fact is appended to the context [arxiv:2205.09712 §4] [arxiv:2205.09712 alg. 1].

- **Causal trace.** Selection scores each candidate context item instead of
  generating free text. The authors found free generation often invented facts,
  which breaks the link between the trace and the answer [arxiv:2205.09712 §4.1].
- **Step budget.** The number of steps is fixed per task, not learned. For
  bAbI tasks 1, 2, 3 and 15 the paper uses one step, and for bAbI 16 two
  [arxiv:2205.09712 app. D]. A halting rule is left to future work
  [arxiv:2205.09712 §7].
- **Results.** Author-reported 5-shot generative accuracy, averaged over the
  tasks, for Gopher 7B: 58.75% with SI, against 2.94% for vanilla prompting and
  41.32% for chain-of-thought (CoT) prompting on the same model
  [arxiv:2205.09712 §5] [arxiv:2205.09712 fig. 4a].
- **Fine-tuned variant.** The selection and inference steps are trained
  separately, on single steps only. The paper reports 78.95% for this variant
  [arxiv:2205.09712 §6] [arxiv:2205.09712 fig. 4b]. Prompt-only SI is reported
  in §6 as 57.93%; see Contradictions.
- **Limits.** Retrieval is out of scope, so the context must already hold the
  facts [arxiv:2205.09712 §4]. The authors name the selection module as the
  main failure point [arxiv:2205.09712 app. G].

### Recurrent-depth transformers on synthetic knowledge-graph chains

[Loop, Think, & Generalize](/papers/2604.07822) trains small models from
scratch on synthetic two-hop and longer queries over a knowledge graph. The
model gets a start entity and a relation sequence, and must output the end
entity in one forward pass [arxiv:2604.07822 §3.1] [arxiv:2604.07822 §4].

- **Recurrence.** A stack of 4 layers is applied R times. R = 1 is the vanilla
  model [arxiv:2604.07822 §4] [arxiv:2604.07822 §5.1].
- **Systematic generalization.** The vanilla 4-layer model fails on combinations
  of facts never seen together. With R = 4 the model generalizes, after three
  grokking stages. Convergence takes about 2k epochs at R = 4 and about 7k at R
  = 2 [arxiv:2604.07822 §5.2] [arxiv:2604.07822 fig. 3].
- **Depth extrapolation.** Raising recurrence at inference extends the reachable
  chain length. In the main curriculum setup, R = 8 reaches 24 hops and R = 6
  reaches 17 [arxiv:2604.07822 §6.2] [arxiv:2604.07822 fig. 5]. In the matched
  data setup, R = 8 reaches 19 hops, the same as the dynamic model
  [arxiv:2604.07822 §6.2] [arxiv:2604.07822 fig. 7].
- **Overthinking.** For the dynamic model, out-of-distribution accuracy stops
  improving after about 15 iterations [arxiv:2604.07822 §6.2]
  [arxiv:2604.07822 fig. 8]. The authors say adaptive halting does not fix this
  [arxiv:2604.07822 §6.2].
- **Adaptive halting.** Each example stops once successive predictions differ by
  less than a KL threshold and the entropy is below a threshold. The paper gives
  0.01 and 3.00 [arxiv:2604.07822 §6.2] [arxiv:2604.07822 app. C].
- **Limits.** The tokens and vocabulary are synthetic, and the authors do not
  claim the results carry over to LLMs trained at scale [arxiv:2604.07822 app. A].
  Without a permutation constraint on the graph, a model can reach high accuracy
  by reading a short suffix of the relations [arxiv:2604.07822 app. K]. Grokking
  to 4 hops took over 1.3M training steps [arxiv:2604.07822 §6.2].

### Document-link pretraining (LinkBERT)

[LinkBERT](/papers/2203.15827) changes what a pretraining input contains
rather than how questions are answered. An anchor segment is paired with a
second segment that is contiguous, random or from a linked document, and a
three-way relation loss is added to masked language modeling
[arxiv:2203.15827 §4.2] [eq. 1]. The linked document is chosen with probability
inversely proportional to its in-degree [arxiv:2203.15827 §4.3].

- **Results.** Author-reported MRQA F1 for LinkBERT against BERT at the same
  scale: HotpotQA 54.6 against 49.8 (tiny), 78.2 against 76.0 (base) and 80.8
  against 78.1 (large) [arxiv:2203.15827 tab. 1]. The authors report the average
  gain as +4.1, +2.6 and +2.5 [arxiv:2203.15827 abstract].
- **Link source matters.** For LinkBERT-tiny, random links match BERT-tiny on
  HotpotQA (49.8). Replacing hyperlinks with TF-IDF neighbours gives 50.0, and
  hyperlinks give 54.6 [arxiv:2203.15827 tab. 5] [arxiv:2203.15827 §5.5].
- **Few labels.** With 10% of the fine-tuning data, LinkBERT-base reaches 70.5
  on HotpotQA against 64.8 for BERT-base [arxiv:2203.15827 tab. 4].
- **Cost.** Continued pretraining of base takes 4 days on four A100 GPUs, and
  tiny takes 1 day on two 2080 Ti GPUs [arxiv:2203.15827 §5.1]. The cost of
  building the link graph is not stated.
- **Limits.** The paper's pretraining code is not in its repository, so the
  link sampling and the relation head cannot be checked against code
  [arxiv:2203.15827 §4] [code: README.md#L24]. The MRQA split is not the
  official one, so its numbers are not comparable to leaderboard results
  [arxiv:2203.15827 §5.2].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Need questions with a gold reasoning chain and no human labelling | Template generation over Wikidata triples, as in [2WikiMultiHopQA](/papers/2011.01060) | The triples give the evidence for free. Templates and rules were checked by hand, and the paper reports that some mismatches remain [arxiv:2011.01060 §3.2] [arxiv:2011.01060 §5.4] |
| Need questions whose steps are implicit, and budget for crowd work | Crowd-written questions with decomposition, as in [StrategyQA](/papers/2101.02235) | Each example cost about $4 with three evidence matchers [arxiv:2101.02235 §4]. Check the dataset licence before reuse |
| Need to know whether a system found the chain, not only the answer | Joint scoring with evidence triples [arxiv:2011.01060 eq. 1] | Answer scores alone can hide a missing chain. In the baseline, evidence F1 is 14.94 against an answer F1 of 43.93 [arxiv:2011.01060 tab. 5] |
| Have a large frozen LLM, no training budget, and need structured multi-step prompts | Decomposed prompting, as in [DecomP](/papers/2210.02406) | No training is needed. The decomposer needs a GPT-3-sized model, and each step resends the prompt and history [arxiv:2210.02406 §4.4] [arxiv:2210.02406 §3.2] |
| Need retrieval whose next query depends on reasoning already done, with a frozen LLM and no training budget | Interleaved retrieval, as in [IRCoT](/papers/2212.10509) | No training is needed. It beats one-step retrieval on all four sets with Flan-T5-XXL and on three with GPT-3; the GPT-3 IIRC result is flat [arxiv:2212.10509 tab. 4]. Each step needs its own reasoning call [arxiv:2212.10509 §3.1] |
| Need traceable deduction over facts already in the context, with a frozen LLM and several model calls per step affordable | Selection-inference, as in [Selection-Inference](/papers/2205.09712) | No training is needed. Each new fact is derived from selected facts only, so the trace is causal by construction. The paper's 7B result is 58.75% against 41.32% for CoT, both generative [arxiv:2205.09712 §5] [arxiv:2205.09712 fig. 4a]. Retrieval is not covered [arxiv:2205.09712 §4] |
| Need to study whether a model composes facts it never saw composed | Recurrent-depth model on synthetic chains, as in [Loop, Think, & Generalize](/papers/2604.07822) | The vanilla model fails on these combinations, and the recurrent model generalizes. The evidence is synthetic only [arxiv:2604.07822 §5.2] [arxiv:2604.07822 app. A] |
| Need a BERT-style encoder for multi-document QA, and can afford pretraining or continued pretraining with a link graph | Document-link pretraining, as in [LinkBERT](/papers/2203.15827) | Gains over BERT at each scale on MRQA. At tiny scale, random links remove the gain, so the link graph is what matters. Base continued pretraining took 4 days on four A100 GPUs [arxiv:2203.15827 tab. 1] [arxiv:2203.15827 tab. 5] [arxiv:2203.15827 §5.1] |
| Need answers deeper than training, at inference time | Raise recurrence at inference, with adaptive halting | Gains stop around 15 iterations for the dynamic model [arxiv:2604.07822 §6.2] |
| Need to train or run the paper's baseline | Check hardware and library versions first | Not verified here: the released code pins an old PyTorch release and was not run for this page |

Joint scores are much lower than single-task scores. Report all three task
scores with the joint score, so a reader can see where a system fails.

## Implementation sketch

Joint score from per-task precision and recall [arxiv:2011.01060 eq. 1]. The
paper's evaluation script follows this form; the zero check is an extra guard
that the paper does not discuss.

```pseudocode
# Joint F1 from the three tasks  [arxiv:2011.01060 §2.1] [eq. 1]
# Inputs: precision and recall per task, as floats in [0, 1]

def joint_f1(answer, support, evidence):
    # Joint precision is the product of the three task precisions
    p_joint = answer.p * support.p * evidence.p
    # Joint recall is the product of the three task recalls
    r_joint = answer.r * support.r * evidence.r
    if p_joint + r_joint == 0:
        return 0.0
    # Harmonic mean of the joint precision and recall
    return 2 * p_joint * r_joint / (p_joint + r_joint)
```

## Contradictions

- **StrategyQA retrieval.** The paper's text says predicted decompositions do not
  yet beat question-based retrieval [arxiv:2101.02235 §5.2]. Its table reports
  Recall@10 of 0.195 for predicted decompositions and 0.174 for question-based
  retrieval [arxiv:2101.02235 tab. 9]. Both are given here as reported; the
  difference is not resolved.
- **2WikiMultiHopQA tables.** The paper's tables may differ from its latest
  release: the repository says tables 5, 6 and 7 were recomputed later, and the
  updated numbers are not transcribed here [arxiv:2011.01060 tab. 5]
  [arxiv:2011.01060 §5.2].

- **Selection-Inference numbers.** Section 5 gives 2.94% for vanilla 7B, 41.32%
  for CoT 7B and 58.75% for prompt-only SI on the generative setting
  [arxiv:2205.09712 §5]. Section 6 gives 0.34% and 15.73% for vanilla and CoT
  7B, and 57.93% for prompt-only SI, on a task subset the paper does not state
  [arxiv:2205.09712 §6]. The introduction's ratios differ again from §5
  [arxiv:2205.09712 §1]. Both sets are given here as reported.
- **DecomP on 2WikiMultiHopQA.** IRCoT's main comparison lists DecomP at 59.3
  F1 on 2WikiMultiHopQA, below IRCoT's 68.0 [arxiv:2212.10509 tab. 1]. Its
  appendix gives an updated table where a newer DecomP beats IRCoT there by 2.8
  points [arxiv:2212.10509 app. C] [tab. 3]. Both are given here as reported.
  The comparison is leaderboard-style and not head-to-head.

Other numbers on this page come from different settings and metrics, so they
are not contradictions.

## Papers

- [2WikiMultiHopQA paper, arXiv:2011.01060](/papers/2011.01060): builds 2WikiMultiHopQA from Wikipedia and Wikidata, defines the joint metric and reports a baseline with evidence scores.
- [Did Aristotle Use a Laptop?, arXiv:2101.02235](/papers/2101.02235): StrategyQA, a crowd-built yes/no benchmark with implicit steps, decompositions and per-step evidence.
- [Selection-Inference, arXiv:2205.09712](/papers/2205.09712): frozen-LLM loop that selects facts from a given context and derives one new fact per step, with a fine-tuned variant.
- [Decomposed Prompting, arXiv:2210.02406](/papers/2210.02406): prompt-only decomposition into sub-questions, with sub-tasks that can be prompts, functions or recursive calls.
- [Interleaving Retrieval with Chain-of-Thought Reasoning, arXiv:2212.10509](/papers/2212.10509): IRCoT, alternating reasoning sentences with BM25 retrieval, using the newest sentence as the query.
- [Loop, Think, & Generalize, arXiv:2604.07822](/papers/2604.07822): recurrent-depth transformers on synthetic knowledge-graph chains, with grokking, depth extrapolation and overthinking.
- [LinkBERT, arXiv:2203.15827](/papers/2203.15827): pretrains BERT-style encoders on linked documents in one input, with a three-way relation loss; reports MRQA gains over BERT.