Graph-Guided Retrieval (G-Retrieval)

• Graph-Guided Retrieval is a method that employs passage graphs and Graph Attention Networks to capture relational signals in multi-turn queries.
• It leverages multi-round dynamic history modeling to iteratively update query embeddings based on both historical and current conversation context.
• Empirical evaluations demonstrate significant gains in recall and F1 scores, highlighting the method’s practical impact on open-domain question answering.

Graph-guided retrieval (G-Retrieval) refers to a set of computational techniques that leverage a graph structure—explicitly encoding entities, passages, or documents as nodes and their relations as edges—to guide the retrieval of relevant information for downstream tasks such as open-domain question answering, dialogue, and knowledge-intensive reasoning. G-Retrieval departs from traditional passage-level retrieval by capturing the interplay between context, historical signals, and structural connections, allowing for the identification of paths or subgraphs most relevant to a given query.

1. Construction and Expansion of Passage Graphs

G-Retrieval frameworks typically begin by constructing a passage graph $G = \langle \mathcal{P}_m, \mathcal{E}_m \rangle$, where each node represents a passage, and edges correspond to explicit hyperlinks or other relational cues between passages. The initial passage set $\mathcal{P}_0$ is composed of:

• Passages containing historical answers from prior conversation turns (either predicted or gold).
• Passages retrieved by dense retrievers (e.g., using ALBERT, BERT, or other encoders) for the current round.
• Optionally, passages selected using shallow retrieval techniques such as TF-IDF.

Graph expansion is achieved by iteratively including all passages $\mathcal{P}_e$ that are linked via hyperlinks (edge expansion), formalized as:

$$\mathcal{P}_m = \mathcal{P}_{m-1} \cup \mathcal{P}_e \tag{6}$$

Through this, the model activates passages historically related to the conversation and uncovers new passages structurally proximal to known answer sources, yielding an expanded graph with richer candidate space.

2. Graph Neural Network-Based Utilization

Upon construction, the passage graph is processed via a Graph Attention Network (GAT). For each node (passage), its initial embedding $v_p$—typically produced by an ALBERT encoder—is refined via GAT layers:

$v_p^* = \mathrm{GAT}(v_p, G_m) \tag{7}$

Subsequent retrieval is performed by evaluating the semantic similarity between a refined question vector $v_q$ and each updated passage representation:

$$S_{a_i} = \frac{\exp(v_{p_i}^* \cdot v_q^\top)}{\sum_{j=1}^n \exp(v_{p_j}^* \cdot v_q^\top)} \tag{8}$$

Passages with the highest $S_{a_i}$ scores are prioritized for answer extraction via downstream ranker and reader components. The inter-passage relations—and especially the overlap of historical answer nodes with novel, linked passages—are thus leveraged for greater retrieval recall and answer coverage.

3. Multi-Round Relevance Feedback and Dynamic History Modeling

A core facet of G-Retrieval is its multi-round, dynamically conditioned retrieval, known as Dynamic History Modeling (DHM). Instead of a single retrieval pass, the system iteratively updates the question embedding using information from previously retrieved passages and history:

1. The concatenation of historical and current questions $$q_k^* = [\mathrm{CLS}]\, q_1 \,[\mathrm{SEP}]\, ...\, q_{k-1}\,[\mathrm{SEP}]\, q_k\,[\mathrm{SEP}]$$ is projected into vector form via

$v_q = W_q \cdot F_q(q_k^*) \tag{1}$

1. In subsequent rounds, the model generates triplets comprised of the current and one historical question together with the feedback from top-retrieved passages; each triplet is encoded and then combined through attention:

$$\alpha_i = \frac{\exp(W_a \cdot v_{q_i}^t)}{\sum_j \exp(W_a \cdot v_{q_j}^t)} \tag{4}$$

$v_q^{\text{(refined)}} = \sum_i \alpha_i v_{q_i}^t$

This mechanism places greater emphasis on aspects of history most relevant (as evidenced by retrieval feedback), refining the context-conditioned query representation and driving the next retrieval round. The procedure helps bridge coreference and entity disambiguation across conversation turns.

4. Empirical Evaluation and Performance

G-Retrieval methods as instantiated in "A Graph-guided Multi-round Retrieval Method for Conversational Open-domain Question Answering" (Li et al., 2021) are empirically validated on expanded QuAC-like datasets comprising over 11 million Wikipedia passages. Performance metrics include word-level F1, Mean Reciprocal Rank (MRR), Recall, and Human Equivalence Score (HEQ).

Key results:

• With predicted history answers, G-Retrieval yields ~5% absolute F1 improvement over baselines.
• With gold history answers, the improvement rises to ~11% absolute F1.
• The approach achieves gains in recall and ranking, showing that modeling relationships among historical answers and candidate passages directly translates to better answer retrieval, particularly in multi-turn settings.

The final scoring for an answer span aggregates scores from Explorer ($S_a$), Ranker ($S_b$), and Reader components ($S_s$, $S_e$):

$S = S_a + S_b + S_s + S_e \tag{15}$

5. Comparative Analysis with Prior Retrieval Methods

Contrasted with baseline systems such as DrQA or BERTserini—which treat retrieval as single-hop and lack explicit modeling of passage interactions—the G-Retrieval paradigm provides:

• Structural Efficiency: Precomputed embeddings and Maximum Inner Product Search (MIPS) are complemented by local GAT-based refinement, so large-scale reprocessing is avoided.
• Effectiveness via Relational Reasoning: Activation of historical answer passages and traversal of hyperlink-derived connections efficiently surface otherwise hard-to-find gold passages.

When compared with ORConvQA (a state-of-the-art conversational retriever at the time), the inclusion of both answer-based passage activation and multi-round feedback leads to clear, measurable gains in recall, MRR, and F1.

6. Broader Implications and Deployment Considerations

The graph-guided, multi-round retrieval approach underpins a range of practical implications for conversational and open-domain information-seeking systems:

• Robustness to conversational paraphrase, answer coreference, and context drift.
• Scalable retrieval in large passage collections, with efficient passage re-activation paths via hyperlink structure.
• Improved recall of passages supporting multi-hop reasoning, essential for complex or multi-turn queries.

Deployment considerations include the need for efficient graph expansion algorithms, scalable GAT embedding propagation, and caching mechanisms for repeated retrieval operations on popular historical passage subgraphs. Limitations may emerge if hyperlink structure is sparse or uninformative, necessitating generalizations to other relational cues beyond hyperlinks.

7. Mathematical Summary

To consolidate, the main mathematical components of G-Retrieval are:

Step	Equation / Operation	Description
Passage graph expansion	$$\mathcal{P}_m = \mathcal{P}_{m-1} \cup \mathcal{P}_e$$ (Eqn. 6)	Node set expanded with hyperlinks
GAT embedding	$v_p^* = \mathrm{GAT}(v_p, G_m)$ (Eqn. 7)	Node representation update
Similarity computation	$$S_{a_i} = \frac{\exp(v_{p_i}^* \cdot v_q^\top)}{\sum_{j=1}^n \exp(v_{p_j}^* \cdot v_q^\top)}$$ (Eqn. 8)	Query-passage affinity
Multi-round feedback	$\alpha_i$, $v_q^{(\mathrm{refined})}$ as above (Eqn. 4)	Attention-based history/context fusion
Final prediction	$S = S_a + S_b + S_s + S_e$ (Eqn. 15)	Joint scoring cascade for answer selection

By hybridizing relational graph modeling, neural embedding propagation, and step-wise context refinement, G-Retrieval delivers a robust, context-aware solution for large-scale conversational question answering.