DFAMS: Dynamic-flow guided Federated Alignment based Multi-prototype Search

TL;DR

DFAMS introduces a dynamic-flow guided federated retrieval framework that improves document relevance and knowledge alignment across heterogeneous sources, enhancing retrieval accuracy and downstream question answering performance.

Contribution

The paper presents a novel DFAMS framework that uses dynamic information flow and multi-prototype contrastive learning for improved federated retrieval across diverse knowledge sources.

Findings

DFAMS outperforms existing methods by up to 14.37% in knowledge classification accuracy.

DFAMS achieves up to 6.45% improvement in downstream QA accuracy.

Experimental results validate DFAMS's effectiveness across five benchmarks.

Abstract

Federated Retrieval (FR) routes queries across multiple external knowledge sources, to mitigate hallucinations of LLMs, when necessary external knowledge is distributed. However, existing methods struggle to retrieve high-quality and relevant documents for ambiguous queries, especially in cross-domain scenarios, which significantly limits their effectiveness in supporting downstream generation tasks. Inspired by Dynamic Information Flow (DIF), we propose DFAMS, a novel framework that leverages DIF to identify latent query intents and construct semantically aligned knowledge partitions for accurate retrieval across heterogeneous sources. Specifically, DFAMS probes the DIF in LLMs by leveraging gradient signals from a few annotated queries and employing Shapley value-based attribution to trace neuron activation paths associated with intent recognition and subdomain boundary detection. Then, DFAMS leverages DIF to train an alignment module via multi-prototype contrastive learning, enabling fine-grained intra-source modeling and inter-source semantic alignment across knowledge bases. Experimental results across five benchmarks show that DFAMS outperforms advanced FR methods by up to 14.37\% in knowledge classification accuracy, 5.38\% in retrieval recall, and 6.45\% in downstream QA accuracy, demonstrating its effectiveness in complex FR scenarios. Our code are anonymous available at https://anonymous.4open.science/r/DFAMS/

Tables

Table 1. Table 1: Performance comparison (%) on Wiki , Med , PEP , MMLU , and MIRAGE , where bold indicates the best result, and symbol slash "/" denotes inapplicable metrics .

Method	In-Domain								Out-of-Domain
	Wiki			Med			PEP		MMLU	MIRAGE
	Cls Acc ($\uparrow$)	Recall ($\uparrow$)	QA Acc ($\uparrow$)	Cls Acc ($\uparrow$)	Recall ($\uparrow$)	QA Acc ($\uparrow$)	Cls Acc ($\uparrow$)	QA Score ($\uparrow$)	QA Acc ($\uparrow$)	QA Acc ($\uparrow$)
Qwen2.5-7B
No RAG	/	/	59.30	/	/	75.20	/	7.56	79.05	68.05
Merged-RAG	/	48.49	77.20	/	33.89	79.60	/	8.33	77.74	65.78
Prompt	32.47	25.93	63.66	48.82	34.68	79.59	66.86	6.21	80.77	69.17
CoT Prompt	58.67	38.17	71.40	48.82	31.40	80.72	77.91	5.92	80.52	69.47
SFT	41.13	25.60	61.97	49.35	24.70	75.73	68.76	7.23	78.23	67.97
RopMura	62.83	48.92	77.47	53.09	41.59	82.01	75.92	7.18	80.38	69.97
RAGRoute	76.07	50.04	78.40	69.04	35.78	73.64	51.47	7.14	80.20	69.77
DFAMS	85.03	53.83	78.94	71.81	42.82	82.82	82.85	8.39	86.17	79.88
LLaMA3.1-8B
No RAG	/	/	60.40	/	/	68.27	/	5.35	59.31	61.90
Merged-RAG	/	48.49	76.48	/	33.89	74.17	/	5.38	56.30	62.68
Prompt	36.18	25.93	64.67	49.57	34.72	71.65	65.99	5.17	63.90	61.51
CoT Prompt	58.20	38.14	68.98	48.92	31.59	74.46	76.75	4.82	63.55	63.43
SFT	42.61	26.12	63.78	49.31	26.41	70.41	63.95	4.86	58.31	62.11
RopMura	62.83	48.92	76.78	53.09	41.59	75.37	75.92	4.46	64.06	61.82
RAGRoute	76.07	50.04	76.83	69.04	35.78	74.55	51.47	4.58	64.37	63.16
DFAMS	84.36	53.83	78.60	72.57	42.82	77.65	81.98	8.08	64.89	64.89

Table 2. Table 2: Adaptive retrieval accuracy comparison between different methods on Wiki and Med datasets.

\rowcolorgray!10 Method	Wiki Acc ($\uparrow$)	Med Acc ($\uparrow$)
Prompt	69.73	84.20
Probing RAG	99.98	92.80
DFAMS	99.95	93.67

Table 3. Table 3: Comparison of routing, retrieval, and total processing times for different methods on the Med dataset.

\rowcolorgray!10 Method	Routing (s)	Retrieval (s)	Total (s)
Prompt	14.25	1.35	15.59
Merged-RAG	0	3.89	3.89
RAGRoute	0.0023	1.64	1.64
DFAMS	0.13	1.34	1.48

Table 4. Table 4: Ablation analysis of Dynamic Information Flow modeling on Wiki and Med datasets

\rowcolorgray!10 Method	Wiki ($\uparrow$)	Med ($\uparrow$)
Frozen (no Align-MLP)
Random	53.19	42.90
Full	64.05	52.67
DFAMS	67.74	54.68
Trained (with Align-MLP)
Random	81.49	66.47
Full	82.42	68.36
DFAMS	85.03	71.81

Table 5. Table 5: Ablation Analysis of Multi-Prototype Alignment and Routing Components on Wiki dataset

\rowcolorgray!10 Variant	Accuracy ($\uparrow$)	Recall ($\uparrow$)
Full Method	85.03	53.83
w/o Inter-KB Alignment	75.89	52.09
w/o Intra-KB Alignment	83.28	50.68
w/o Adaptive Triggering	79.56	53.83
w/o Semantic Routing	80.67	48.67

Table 6. Table 6: Key Notations used in the DFAMS framework

Symbol	Description
$I$	Number of isolated knowledge bases (KBs)
$𝒦i={\left\{d_{i\ell }\right\}}_{\ell =1}^{M_i}$	The $i$-th KB containing $M_i$ documents $d_{i\ell }$
$x$	Input query for KBs selection and retrieval
$f_{\text{route}}$	Maps $x$ to document allocations over KBs
$𝐰=[w_1,\dots ,w_I]$	Document allocation vector; $w_j$ is the number retrieved from ${𝒦}_j$
$\Theta$	Parameterized knowledge in the LLM
$𝒟=\{{𝒦}_1,\dots ,{𝒦}_I\}$	KBs representing non-parameterized knowledge
$R$	Retrieved subset of KBs for answering query
$𝒫$	Task-specific prompt
$y$	Ground-truth answer to query $x$
${𝒟}_{\text{probe}}$	Dedicated probing dataset for neuron attribution and domain selection analysis
$h_t$	Output of attention sublayer in layer $t$
$W_{t1},b_{t1}$	FFN projection weights and biases at layer $t$
$\text{Act}(\cdot )$	Activation function
${\varphi }_j$	Shapley Shapley value for neuron $j$
$g_j^{\left(\gamma \right)}$	Gradient of supervised loss w.r.t. ${\theta }_j$
$H_{jk}^{\left(\gamma \right)}$	Hessian of loss capturing 2nd-order interactions
${\omega }_{jj}^{\left(j\right)}$	Weighting coefficient for self-contribution of neuron $j$ in Shapley approximation
${\omega }_{jk}^{\left(𝒮\right)}$	Weighting coefficient for pairwise contribution between neurons $j$ and $k$
$𝐳$	DIF embedding composed of high-attribution neuron activations
$\text{Concat}(\cdot )$	Concatenates input set into a single vector
$g_{\text{align}}$	Projection function mapping $𝐳$ to aligned query embedding $𝐫$ in the semantic space
${ℒ}_{\text{CL}}$	supervised contrastive loss
$B$	Batch size used for contrastive training
$P\left(i\right)$	Set of in-batch positive samples sharing the same KB label as sample $i$
$A\left(i\right)$	All other in-batch samples excluding $i$ (i.e., positive + negative candidates)
${\tau }_{cl}$	Temperature scaling factor in contrastive loss
${𝝁}_m$	Prototype vector in the contrastive-aligned space
${ℒ}_{\text{PCL}}$	Intra-KB prototype contrastive loss
$C\left(i\right)$	Closest prototype(s) to sample $i$
$AC\left(i\right)$	All prototypes excluding those in $C\left(i\right)$
${\tau }_{pcl}$	Temperature scaling factor in ${ℒ}_{\text{PCL}}$
$𝐪$	Embedded representation of an unseen query
$\text{sim}(\cdot ,\cdot )$	Cosine similarity between two embeddings
$s_i$	Similarity between $𝐪$ and prototype ${𝐩}_i$
$T$	Total retrieval slots to be allocated
$\tau$	Adaptive triggering threshold
$ℐ$	Top-$N$ nearest prototypes

Table 7. Table 7: Hyperparameter summary across different datasets and experimental scenarios.

Hyperparameter	Wiki	Med	PEP	MMLU	MIRAGE
Number of KBs	10	4	4	10	4
Learning Rate	2e-4	1e-4	1e-4	2e-4	1e-4
Epochs	13	20	6	13	20
CL Epochs	12	22	4	12	22
Batch Size	64	64	64	64	64
Threshold	0.85	0.95	0.80	0.85	0.95

Table 8. Table 8: Layer-wise attribution results on the PEP dataset.

\rowcolorgray!10 Layer	Act	Grad ($\times {10}^{-6}$)	Shapley	Cls Acc ($\uparrow$)
26	7.53	0.671	0.3765	72.70
27	-10.19	1.030	1.1895	72.51
4	3.13	0.662	0.1357	56.61
3	3.89	0.615	0.1339	46.17
15	4.36	0.635	0.0737	27.83

Table 9. Table 9: Performance of DFAMS with different backbone models on the Wiki dataset.

\rowcolorgray!10 Backbone	Cls Acc ($\uparrow$)	Recall ($\uparrow$)
Qwen2.5-0.5B	81.23	50.75
Qwen2.5-3B	83.91	51.39
Qwen2.5-7B	85.03	53.83

Table 10. Table 10: Cls Acc of different learning rates using DFAMS.

\rowcolorgray!10 Learning Rate	1e-3	5e-4	1e-4	5e-5	1e-5
Cls Acc ($\uparrow$)	81.51	83.56	85.03	83.22	54.25

Equations

$$f_{\text{route}}:x\mapsto \mathbf{w}=[w_1,w_2,\dots ,w_I],w_j\in {\mathbb{N}}_0,$$

$${\varphi }_j=-g_j^{(\gamma )}{\theta }_j-\frac{1}{2}{\omega }_{jj}^{(j)}{\theta }_j^2{H}_{jj}^{(\gamma )}-\frac{1}{2}{\theta }_j\sum _{k\ne j}{\omega }_{jk}^{(\mathcal{S})}{H}_{jk}^{(\gamma )}{\theta }_k,$$

$${\mathcal{L}}_{\text{CL}}=-\sum _i\frac{1}{|P(i)|}\sum _{p\in P(i)}\log \frac{\exp ({\mathbf{r}}_i^{\top }{\mathbf{r}}_p/{\tau }_{cl})}{{\sum }_{a\in A(i)}\exp ({\mathbf{r}}_i^{\top }{\mathbf{r}}_a/{\tau }_{cl})},$$

$${\mathcal{L}}_{\text{PCL}}=-\sum _i\frac{1}{|C(i)|}\sum _{m\in C(i)}\log \frac{\exp ({\mathbf{r}}_i^{\top }{\mathbf{\mu }}_m/{\tau }_{pcl})}{{\sum }_{j\in AC(i)}\exp ({\mathbf{r}}_i^{\top }{\mathbf{\mu }}_j/{\tau }_{pcl})},$$

$$f_{\text{route}}(\mathbf{q})=\{\begin{array}{ll}0,& {\max }_i{s}_i<\tau ,\\ [w_1,\dots ,w_K],& \text{otherwise}\end{array}$$

$$w_k=\lfloor \frac{{\sum }_{i\in \mathcal{I},k_i=k}{s}_i}{{\sum }_{k^{\prime }}{\sum }_{i\in \mathcal{I},k_i=k^{\prime }}{s}_i}\cdot T\rfloor$$

$$w_k\leftarrow \lfloor \frac{{\sum }_{i\in \mathcal{I},k_i=k}{s}_i}{{\sum }_{k^{\prime }}{\sum }_{i\in \mathcal{I},k_i=k^{\prime }}{s}_i}\cdot T\rfloor$$

Full text

DFAMS: Dynamic-flow guided Federated Alignment based Multi-prototype Search

**

Zhibang Yang1,2††thanks: Equal contribution., Xinke Jiang1,211footnotemark: 1, Rihong Qiu1,2,311footnotemark: 1, Ruiqing Li1,2, Yihang Zhang1, Yue Fang1,2,**

** Yongxin Xu1,3, Hongxin Ding1,2, Xu Chu1,3, Junfeng Zhao1,3††thanks: Corresponding authors., Yasha Wang1,2,4†**

1National Engineering Research Center for Software Engineering, Peking University, Beijing, China

2School of Computer Science, Peking University, Beijing, China

3Key Laboratory of High Confidence Software Technologies, Ministry of Education, Beijing, China

4Peking University Information Technology Institute (Tianjin Binhai), Tianjin, China

{yangzb, XinkeJiang, RihongQiu, YueFang}@pku.stu.edu.cn

1 Introduction

Retrieval-Augmented Generation (RAG) leverages external knowledge documents Edge et al. (2024); Asai et al. (2023) to effectively enhance the factuality and verifiability of outputs from Large Language Models (LLMs) OpenAI (2022, 2023); Vu et al. (2024), significantly mitigating issues such as hallucination and knowledge obsolescence Ji et al. (2023); Cao et al. (2020); Jiang et al. (2024b, a); Asai et al. (2024); Su et al. (2024); Jeong et al. (2024); Baek et al. (2025). However, mainstream RAG approaches typically rely on a single, centralized vector database for knowledge storage and retrieval Kukreja et al. (2024); Bhavnani and Wilson (2009). In reality, knowledge is inherently distributed across multiple heterogeneous data sources — for instance, in medical scenarios, retrieval may need to simultaneously access electronic health records (EHR) Yuan et al. (2023), textbooks, and the latest research papers Zhao et al. (2025).

Forcibly aggregating all documents into a unified index not only incurs high retrieval costs but also raises concerns around data sovereignty Jiang (2024); Shokouhi et al. (2011); Kairouz et al. (2021). To address this, Federated Retrieval (FR) has emerged as a solution, enabling efficient cross-knowledge-base routing decisions that directly and precisely direct queries to the most relevant sources of knowledge Schölkopf (2019); Guerraoui et al. (2025); Wang et al. (2024c); Ryan et al. (2025); Shojaee et al. (2025).

Most existing FR methods are primarily designed with an emphasis on routing efficiency, privacy preservation, and downstream task integration Chakraborty et al. (2025). However, in real-world scenarios with complex semantics Clarke et al. (2008), users are more concerned with whether the system can accurately retrieve highly relevant documents to effectively support downstream generation tasks Shokouhi et al. (2011); Huang and Huang (2024), which does not receive sufficient attention in existing research. And due to limitations in current modeling strategies Wang et al. (2024c), existing approaches exhibit notable shortcomings in addressing this issueGuerraoui et al. (2025). On one hand, user queries often suffer from semantic ambiguity or compression, leading to a gap between surface expressions and underlying intent Yuan et al. (2025). In different contexts, the same question may require different knowledge sources to answer (as illustrate in Figure 1). In such scenarios, user queries often fail to align with the structured and detailed content in the knowledge base, limiting the accuracy and coverage of semantic matching in traditional FR methods Huang et al. (2021). Although some approaches leverage LLMs for prompt-based query rewriting Gao et al. (2022) to reduce ambiguity, they often struggle to capture fine-grained semantics due to limited prompt expressiveness, leading to suboptimal performance in semantically complex scenarios. On the other hand, in real-world applications knowledge bases are typically partitioned by data sources, forming multiple structured yet interrelated knowledge subsystems Wu et al. (2025). The semantic boundaries between these subsystems are often flooded and overlapping. However, some existing methods overlooking underlying semantic connections, which struggle to support cross-source recall and dynamic integration. Wang et al. (2024c).

Recent research has shown that when LLMs process tasks of different fields, the contribution of each parameter in the LLM model varies Dhamdhere et al. (2018); Yu et al. (2018); LeCun et al. (1989). Building on this line of work, further investigations into the structural and functional mechanisms of LLMs have revealed that, during inference, LLMs naturally form a Dynamic Information Flow (DIF)—a latent path through which information propagates dynamically across transformer layers, activating neural substructures associated with semantics, knowledge, and reasoning Zheng et al. ; Yu and Ananiadou (2024); Wang et al. (2024d). These findings suggest that LLMs may already possess an implicit capability to recognize user intent and organize knowledge into latent subdomains when processing complex queries. Inspired by this, we raise a central research question: Can DIF within LLMs be explicitly modeled to (1) more accurately identify users’ latent query intents, and (2) structurally segment and dynamically organize overlapping or fuzzy-boundary knowledge subdomains to mitigate semantic misalignment and cross-source retrieval failures in FR settings? As shown in Figure 1, we hypothesize that, when presented with a complex query, the LLM first identifies the user’s intent. If the model determines that the user is likely a doctor with an intent to retrieve clinical studies and guidelines, it will activate the corresponding neurons, forming a reasoning pathway that generates perception signals related to the target knowledge. These signals may be used to retrieve and align content from heterogeneous sources such as PubMed and EHR, integrating cross-subdomain knowledge for downstream generation.

To validate the above hypothesis, we need to address two core challenges: (C1) how to accurately detect the relevant DIF within LLMs; (C2) how to leverage the DIF-based internal semantic organization to support fine-grained knowledge base modeling while preserving semantic associations across multiple sources. To tackle these challenges, we propose a novel framework named DFAMS (Dynamic-flow guided Federated Alignment based Multi-prototype Search). DFAMS explicitly models the internal DIF of LLMs and constructs knowledge base partitions aligned with the model’s activation patterns, thereby preserving rich semantic signals. For Challenge C1, we utilize gradient signals under a small number of annotated DIF-probing samples, and apply Shapley value-based attribution methods to identify neuron flow paths associated with query intent recognition and subdomain boundary detection. For Challenge C2, during training, we extract DIF flows induced by queries over each knowledge base. These flows are then used to train an alignment module via multi-prototype contrastive learning, achieving fine-grained intra-source modeling and inter-source alignment. The goal is to maintain semantic continuity across sources while enabling effective knowledge base classification. In summary, our contributions are as follows:

• •

We reveal a high-dimensional, information-rich DIF in LLMs that encodes both user intent and subdomain knowledge, enabling more faithful query understanding. To our knowledge, this is the first work to exploit DIF for intent-aware, domain-sensitive retrieval modeling.

• •

We propose the DFAMS framework. By modeling DIF, we construct knowledge partitions that preserve inter-source semantic associations. DFAMS integrates multi-prototype contrastive learning during training and employs Adaptive Prototype-Guided Routing at inference time, significantly improving the performance.

• •

We develop an enhanced FR benchmark to encompass realistic and diverse query types, ranging from knowledge-free queries, multi-fragment queries within a single source, to cross-source retrieval. The benchmark integrates structured taxonomy, associated documents, user queries, and ground-truth answers, offering a solid foundation for evaluating FR in complex settings.

2 Related Work

2.1 Federated Retrieval

Federated search Shokouhi et al. (2011), extended into RAG by combining privacy-preserving federated learning (FL) Zhang et al. (2021) with RAG Lewis et al. (2020), enables retrieval across decentralized sources without sharing raw dataChakraborty et al. (2025), which has seen widespread adoption in privacy-critical domains such as healthcare Jiang (2024); Jung et al. (2025); Xiong et al. (2024), finance, and legal services Addison et al. (2024). Prior work in federated search mainly targets three aspects: (i) privacy and security through secure retrieval and encryption Jeon et al. (2021); Peng et al. (2021), (ii) retrieval efficiency via query routing Wang et al. (2024c), and (iii) integration of FL and RAG tailored to domain-specific tasks Wang et al. (2024a); Zeng et al. (2024); Shojaee et al. (2025). These advances have proven effective Zhao (2024); Xu et al. (2022); Wang et al. (2024a); Zeng et al. (2024); Shojaee et al. (2025); however, retrieving high-quality results in complex semantic scenarios remains challenging Wang et al. (2024c). Existing FR methods, prompt-based and embedding-based, struggle in this setting because queries often misalign with knowledge structures, which reduces dense vector accuracy Huang et al. (2021), and LLM-based prompt rewriting lacks fine-grained semantic precision Gao et al. (2022).

2.2 Neural Information Flow

Recent studies have shown that LLMs, like the human cortex Arbib (2003); Hawrylycz et al. (2012); Zador (2019); Wang et al. (2024b), exhibit functional partitioning across their architecture Dhamdhere et al. (2018); Yu et al. (2018); LeCun et al. (1989). Such functional partitions may emerge in the form of attention heads Zheng et al. (2024); Yin and Steinhardt (2025); Wu et al. (2024), feed-forward networks Bandarkar et al. (2024); Wendler et al. (2024); Sun et al. (2025), or neurons Huo et al. (2024); Tang et al. (2024), which are shaped during training and contribute differently across tasks Dhamdhere et al. (2018); Yu et al. (2018). Building on this partitions, information dynamically flows among these functional modules, forming a Dynamic Information Flow (DIF) Stolfo et al. ; Yu and Ananiadou (2024) To leverage DIF for downstream tasks, researchers attempt to detect DIF by quantifying the attribution of parameters in the LLM with respect to input query. Quantitative attribution methods have been extensively explored using various techniques, including forward-based methods Liang et al. ; Todd et al. (2023); Jiang et al. (2025); Dai et al. (2021) and backward-based methods Feng et al. (2025, 2024) or their combinations Xu et al. (2024). Among these methods, Shapley value-based approaches Ghorbani and Zou (2020); Adamczewski et al. (2024) have gained wide adoption. Although there has been extensive research on DIFs in large models, leveraging their powerful capabilities for modeling user intent and knowledge bases remains largely unexplored.

3 Method

We introduce DFAMS, a framework designed to enable LLM to perform semantically grounded FR across distributed knowledge bases, as illustrated in Figure 2. DFAMS operates in three stages: (1) formalizing the FR setting (Section 3.1); (2) extracting query-specific internal representations through Dynamic Information Flow (DIF) modeling (Section 3.2); and (3) aligning these representations with structured knowledge prototypes for adaptive, multi-source routing (Section 3.3). All key notations are summarized in Appendix A.

3.1 Problem Definition

Federated Retrieval Formalization.

We formulate FR as a distributed retrieval problem over $I$ isolated data sources, where each source $i\in\{1,\dots,I\}$ privately hosts a knowledge base $\mathcal{K}_{i}=\{d_{i\ell}\}_{\ell=1}^{M_{i}}$ with $M_{i}$ documents. Due to strict privacy constraints, sources cannot exchange raw documents or intermediate representations. Given a user query $x$, the system must determine a routing vector:

[TABLE]

where $w_{j}$ specifies how many documents to retrieve from $\mathcal{K}_{j}$. The challenge lies in selecting the most relevant sources adaptively while avoiding unnecessary retrieval.

RAG in FR.

Following RAGRoute Guerraoui et al. (2025), we combine two types of knowledge: (i) parameterized knowledge $\Theta$ stored in the model weights, and (ii) non-parameterized knowledge $\mathcal{D}=\{\mathcal{K}_{1},\dots,\mathcal{K}_{I}\}$, representing distributed, domain-specific corpora. Given a query $x$, the goal is to generate a reliable response: $\texttt{Response}\leftarrow\Theta(x,R\mid\mathcal{P})$, where $\mathcal{P}$ is a task-specific prompt, and $R$ is the subset of knowledge bases deemed relevant. To handle queries answerable without external retrieval, we include an Others category solved solely by $\Theta$ Su et al. (2024). During training, supervision is single-source: each $(x,\mathcal{K}_{i},y)$ is paired with a single knowledge base or labeled as Others. At inference, the model generalizes to no-source, single-source, or multi-source retrieval by predicting per-source relevance scores and selecting those above a dynamic threshold $\delta$.

3.2 Dynamic Information Flow Modeling

To accurately interpret user intent and uncover domain-relevant semantics for routing (C1), we detect DIF capturing which neurons contribute most to domain-sensitive behavior, producing a compact, semantically grounded representation.

The process consists of two steps: (1) constructing a controlled probing dataset to isolate domain-selection behaviors; (2) identifying key layers and neurons via gradient-based Shapley attribution, and aggregating their activations into a DIF embedding.

Probing Dataset Construction.

Using benchmark training or test sets for attribution often yields spurious signals, as they contain mixed user specific intents. To address this, we construct a dedicated probing dataset $\mathcal{D}_{\text{probe}}=\{(x_{i},\mathcal{K}_{i})\}_{i=1}^{n_{\text{probe}}}$, where each query $x_{i}$ is synthesized with fixed instruction-style prompts explicitly designed to elicit domain-selection (e.g., asking the model to identify the most relevant knowledge base). Each label $\mathcal{K}_{i}\in\{1,\dots,I\}$ specifies the correct knowledge base. This dataset is disjoint from $\mathcal{D}_{\text{train}}$ and $\mathcal{D}_{\text{test}}$ to ensure no leakage.

Neuron Attribution and DIF Embedding.

Using $\mathcal{D}_{\text{probe}}$, we estimate the importance of each neuron using Shapley-based attribution. For a transformer block at layer $t$, the feed-forward network (FFN) computes each neuron activation as: $\theta_{t,j}=\textsc{Act}([h_{t}W_{t1}+b_{t1}]_{j})$, where $h_{t}\in\mathbb{R}^{d}$ is the output of the attention sublayer, $W_{t1}\in\mathbb{R}^{d\times 4d}$ and $b_{t1}\in\mathbb{R}^{4d}$ are projection weights and biases, and $\textsc{Act}(\cdot)$ denotes the nonlinearity. For each parameter $\theta_{j}\in\Theta$, its Shapley value $\phi_{j}$ is:

[TABLE]

where $g_{j}^{(\gamma)}=\partial\mathcal{L}_{\text{SFT}}/\partial\theta_{j}$ is the supervised loss gradient, and $H_{jk}^{(\gamma)}$ the Hessian for second-order interactions. The coefficients $\omega_{jj}^{(j)}$ and $\omega_{jk}^{(\mathcal{S})}$ weight self and pairwise contributions, respectively.

We then: ❶. Select the top layers $\mathcal{L}_{\text{top}}$ based on aggregated Shapley scores. ❷. Within each selected layer $\ell\in\mathcal{L}_{\text{top}}$, identify the most informative neuron groups $\mathcal{G}_{\ell}$ (adjacent units with the highest $\phi_{j}$). ❸. For a query $x$, collect the activations of these groups and concatenate them to form the DIF representation: $\mathbf{z}(x)=\textsc{Concat}\Big(\big\{h_{\ell}^{(g)}(x)\;\big|\;g\in\mathcal{G}_{\ell}\big\}_{\ell\in\mathcal{L}_{\text{top}}}\Big)$ captures both semantic intent and domain cues, and serves as the input for both inter- and intra-knowledge-base modeling (Section 3.3).

3.3 Multi-Prototype Knowledge Alignment & Routing

To bridge internal DIF representations and external distributed knowledge structure (C2), we map $\mathbf{z}$ to a semantic space using a projection $g_{\text{align}}$, producing $\mathbf{r}=g_{\text{align}}(\mathbf{z})$. We train it with two contrastive stages and use it for prototype-guided routing.

Inter-KB Alignment.

We apply supervised contrastive learning to model the boundary between different knowledge bases:

[TABLE]

where $P(i)$ denotes all in-batch positive samples that share the same knowledge base as $i$, excluding $i$ itself, and $A(i)$ includes all other in-batch samples except $i$. $\tau\in\mathbb{R}^{+}$ is a scalar temperature parameter.

Intra-KB Alignment.

Besides inter-KB modeling, we perform intra-KB modeling to capture fine-grained variations. Specifically, we first cluster embeddings within each class into prototypes $\{\boldsymbol{\mu}_{m}\}_{m=1}^{M}$ using KMeans to obtain initial cluster centers, which are then used to initialize and optimize $\mathcal{L}_{\text{PCL}}$for more detailed fine-grained modeling:

[TABLE]

where $C(i)$ denotes the set of prototypes most similar to $\mathbf{r}_{i}$ based on cosine similarity (typically the nearest prototype), and $AC(i)$ represents all prototypes excluding those in $C(i)$. During inference, given a query embedding $\mathbf{q}$, we compute its similarity scores $s_{i}=\text{sim}(\mathbf{q},\boldsymbol{\mu}_{i})$ to all learned prototypes $\boldsymbol{\mu}_{i}$. The routing function then proceeds in two stages:

Adaptive Triggering.

If the maximum similarity falls below a threshold $\tau$, i.e., $\max_{i}s_{i}<\tau$, the system abstains from retrieval.

[TABLE]

Semantic Routing.

Otherwise, it identifies the top-$N$ most similar prototypes $\mathcal{I}$ and allocates a total of $T$ retrieval slots across knowledge bases. The number of documents assigned to each knowledge base $k$ is computed as:

[TABLE]

This two-step mechanism ensures retrieval occurs only when necessary, with resources allocated by prototype-level semantic relevance.

4 Experiments

We conduct extensive experiments across multiple datasets to evaluate the effectiveness of DFAMS in Federated Retrieval settings and answer the following key research questions:

• •

RQ1 (Section 4.2): Does DFAMS consistently outperform existing advanced methods?

• •

RQ2 (Section 4.3): How do the proposed component contribute to performance improvements?

• •

RQ3 (Section 4.4): How sensitive is DFAMS to variations in model configurations?

4.1 Experimental Setup

LLM Backbones.

We implement DFAMS on four open-weight LLMs with varying scales to evaluate scalability and generalization: Qwen2.5-0.5B, Qwen2.5-3B, Qwen2.5-7B Yang et al. (2024), and Llama3.1-8B Grattafiori et al. (2024).

Retrieval Configuration.

Following Wu et al. (2025) and Guerraoui et al. (2025), DFAMS utilizes FAISS Douze et al. (2024) for dense vector retrieval across three FR scenarios, each comprising multiple knowledge bases. For each query, top-$10$ chunks are retrieved from selected sources across all relevant knowledge bases within the same scenario. Further details are provided in Appendix C

Datasets.

We construct three in-domain evaluation benchmarks, Wiki, Med, and PEP. To further evaluate out-of-domain generalization, we test models trained on Wiki and Med using a subset of MMLU Hendrycks et al. (2020) and a subset of MIRAGE Xiong et al. (2024), following the setup of  Guerraoui et al. (2025) . Further construction details are provided in Appendix D.

Baselines.

We compare DFAMS with several representative retrieval and routing strategies: No-RAG, Merged-RAG , and two prompt-based methods Prompt and CoT Prompt Wei et al. (2023). We further compare with a supervised fine-tuning baseline (SFT) Hu et al. (2021). In addition, we consider two recent multi-source retrieval approaches: RAGRoute Guerraoui et al. (2025), which employs a binary classifier for each knowledge base to select the Top-$k$ sources, and RopMura Wu et al. (2025), a prototype-based multi-agent routing method. Implementation details are provided in Appendix E.

Evaluation Metrics.

We report three complementary metrics: (1) Cls Acc, which measures whether the predicted knowledge base(s) match the ground truth, including correct Others predictions for no-retrieval cases; (2) Recall, computed over Top-10 retrieved documents for retrieval-triggering queries, measuring the proportion of gold documents successfully retrieved excluding no-retrieval cases; (3) QA, the end-to-end answer accuracy, using accuracy(QA ACC) for multiple-choice and LLM-based scoring (QA Score) Zheng et al. (2023) for open-ended questions. More metric details are available in Appendix F.

4.2 Main Result Analysis (RQ1)

To address RQ1, we train DFAMS on the Wiki, Med, and PEP datasets, and evaluate it on both in-domain (Wiki, Med, PEP) and out-of-domain (MMLU, MIRAGE) benchmarks using Qwen2.5-7B and LLaMA3.1-8B, comparing against baselines from retrieval, prompt-based, and multi-source routing methods.

Comparison with Baselines.

Table 1 summarizes the performance of DFAMS compared with a range of baseline methods across three key metrics: Cls Acc, Recall, and QA Acc/Score. DFAMS consistently outperforms all baselines on both in-domain and out-of-domain datasets.

Comparison of Advanced Multi-Source Retrieval and Naive Methods.

In most cases, multi-source retrieval methods (RopMura, RAGRoute) achieve higher Cls Acc and Recall than Prompt-based or Merged-RAG baselines in most cases. For example, on the Wiki dataset with Qwen2.5-7B, RAGRoute achieves a Cls Acc of 76.07% and recall of 50.04%, compared to just 32.47% and 25.93% from Prompt. Similarly, RopMura outperforms Merged-RAG on Med in Recall (41.59% vs. 33.89%). While multi-source retrieval methods (RopMura, RAGRoute) generally achieve higher recall through broader source coverage, these gains often come at the cost of increased cross-domain noise. For instance, although RAGRoute obtains higher recall on the Med dataset, its QA accuracy (73.64%) falls short of that of Merged-RAG (79.60%). In contrast, prompt-based methods adopt a more conservative source selection strategy, often retrieving from fewer knowledge bases, which helps reduce cross-domain noise. Merged methods, on the other hand, rely on dense semantic similarity across the entire corpus; while the retrieved chunks may not always be precisely grounded, they tend to be semantically coherent.

Comparison of DFAMS and Advanced Multi-Source Retrieval.

Compared with advanced multi-source retrieval methods, DFAMS consistently achieves higher Cls Acc and Recall across all datasets and backbones. For instance, on Wiki with Qwen2.5-7B, DFAMS outperforms RAGRoute by +8.96% in Cls Acc (85.03% vs. 76.07%) and +3.79% in Recall (53.83% vs. 50.04%). These improvements stem from DFAMS’s fine-grained modeling of DIF, enabling more accurate identification of query intent and relevant knowledge sources. This leads to better routing and more focused retrieval with less cross-domain noise. As a result, DFAMS consistently achieves the highest QA accuracy across all datasets. For example, on the Qwen2.5-7B backbone, it reaches 82.82% QA accuracy on Med and 78.94% on Wiki, outperforming both RopMura and RAGRoute.

Adaptive Retrieval Capability.

DFAMS learns to decide whether external retrieval is needed for a given query. We evaluate its adaptive retrieval capability by grouping all sources into a single Knowledge class and using an Others class for queries answerable via parametric knowledge. As shown in Table 2, DFAMS achieves high accuracy on Wiki (99.95%) and Med (93.67%), closely matching Probing RAG and significantly outperforming the Prompt-based approach. These results highlight DFAMS’s ability to avoid unnecessary retrieval while preserving high coverage when external information is required.

Inference Efficiency.

We assess DFAMS’s efficiency by measuring average routing, retrieval, and total latency per sample on the Med dataset (Table 3). Despite relying on LLMs, DFAMS achieves a low end-to-end latency of 1.48s—substantially faster than Prompt (15.59s) and Merged-RAG (3.89s). Compared to RAGRoute (1.64s), DFAMS is slightly faster due to retrieving from fewer sources. In RAGRoute, its pursuit of higher recall often triggers more knowledge bases, and slower sources can increase latency despite parallel execution. Overall, DFAMS offers faster inference with precise routing.

4.3 Ablation Study (RQ2)

To answer RQ2, we conduct ablation studies on the two core components of DFAMS: (1) Dynamic Information Flow Modeling and (2) Multi-Prototype Knowledge Alignment and Routing, aiming to investigate their individual contributions to the overall system performance.

Dynamic Information Flow Modeling. We conduct ablation studies to test our central hypothesis: that DIF signals not only exist but can be effectively detected and exploited to improve model performance. We design two experimental settings: (1) Frozen LLM w/o Align-MLP: We remove the trainable Align-MLP and directly utilize the extracted DIF. This setting investigates whether native LLM activations inherently encode subdomain-aware signals—i.e., whether meaningful associations between user queries and knowledge subdomains can be inferred without explicit alignment. (2) Full DFAMS (w/ Align-MLP): We enable the trainable Align-MLP to utilize DIF to assesse whether modeling the knowledge base on DIF leads to improved alignment and enhanced downstream performance.

We conduct experiments on both the Wiki and Med datasets. Table 4 shows that in setting (1), DFAMS (2000-dim) outperforms both random (2000-dim) and full-layer (3584-dim) baselines, achieving +14.6% accuracy gain on Wiki and +11.78% on Med over the random baseline. These results validate our hypothesis: DIF captures query-subdomain associations and can be directly leveraged, even without further training. Moreover, DFAMS also surpasses the Full baseline, yielding +3.69% and +2.01% accuracy improvements on the Wiki and Med datasets, respectively. In setting (2), with Align-MLP enabled, DFAMS achieves +3.54% and +2.61% higher accuracy than the random and full-layer baselines on Wiki, and +5.34% and +3.45% on Med. These results highlight the benefit of leveraging DIF for knowledge base modeling, resulting in better alignment and improved downstream performance. Additional results and analyses are provided in Appendix H.

Ablation on Multi-Prototype Knowledge Alignment and Routing We conduct targeted ablations to evaluate the impact of DFAMS’s core components. Results are shown in Table 5. Disabling inter-KB alignment, which separates semantic boundaries across knowledge bases, causes the Cls ACC drop (-9.14%), highlighting its key role in knowledge base selection and adaptive retrival. Removing intra-KB alignment, responsible for modeling knowledge bases’ subdomain structures via multi-prototype contrastive learning, leads to the biggest recall decline (-3.15%), showing its importance for accuracy and high quality retrieval. On the inference side, removing adaptive triggering reduces accuracy (-5.47%), as the model can no longer skip unnecessary retrieval. Disabling Semantic Routing, which confines retrieval to only one top source, further decreases recall (-5.16%), highlighting the value of semantic-aware resource allocation across multiple knowledge bases.

4.4 Sensitivity Analysis (RQ3)

To assess how sensitive DFAMS is to variations in key configurations, we conduct experiments on the Wiki dataset.

Effect of Prototype Number.

From the result in Figure 3 (left), the accuracy increases with prototype count, peaking at 3 (53.8%), then declines (e.g., 52.1% at 4), suggesting that too few prototypes underfit subdomain diversity, while too many cause over-fragmentation.

Effect of Semantic Routing Top-$T$.

As shown in Figure 3 (right), when top-$T$ is 3, it achieves the best balance (84.2% accuracy, 53.8% recall). Lower $T$ values miss relevant sources, while higher $T$ dilutes document allocation across knowledge bases, reducing key information retrieval.

5 Conclusion

We propose DFAMS, a novel FR framework that explicitly models the DIF within LLMs to enhance query understanding and cross-source knowledge alignment. By leveraging gradient-based neuron attribution and Shapley value estimation, DFAMS identifies latent neural activation paths that reflect user intent and subdomain relevance. The framework also introduces a Multi-Prototype Knowledge Alignment and Routing strategy, which enables fine-grained modeling of individual knowledge bases. Our experiments show that DFAMS consistently outperforms existing FR methods , confirming its effectiveness in resolving semantic ambiguities and improving cross-source routing in complex settings.

Limitations

While DFAMS achieves consistent improvements in federated retrieval, several limitations still remain. First of all, the framework relies on extracting Dynamic Information Flow (DIF) signals from large transformer-based LLMs; while we demonstrate scalability to smaller models, the applicability of DIF-based modeling to fundamentally different architectures has not been thoroughly examined. Second, our evaluation is conducted on curated benchmarks with static knowledge bases. In real-world applications, knowledge sources often evolve continuously; when significant updates occur, the framework may require retraining or integration with continual learning strategies, which has not yet been fully explored. Addressing these aspects could further enhance the robustness and applicability of DFAMS in broader federated retrieval scenarios.

Future efforts will focus on optimizing prototype selection and update strategies, integrating DFAMS with advanced RAG techniques for improved end-to-end reasoning, and exploring its applicability in other specialized domains such as legal, finance, and scientific research.

Ethical considerations

To evaluate the efficacy of our work, we conducted experiments using five datasets: Wiki, Med, PEP, MMLU, and MIRAGE. Except for PEP, all datasets are publicly available and used in accordance with their respective licenses and terms of use. PEP was obtained and used with proper authorization. The datasets do not contain personally identifiable information, and no human or animal subjects were directly involved in this research.

Appendix A Notations Table

This section presents a comprehensive list of key notations and symbols employed in the DFAMS framework.

Appendix B Algorithm

In this section, we detail the full DFAMS workflow, spanning its probing, training, and inference stages. Algorithm 1 identifies domain-sensitive neurons in pretrained LLMs, while Algorithm 2 describes the training procedure. Finally, Algorithm 3 presents the adaptive prototype-guided routing mechanism used during inference to dynamically allocate retrieval resources based on semantic relevance.

B.1 Neuron Probing for DIF Extraction

To identify domain-sensitive neurons within pretrained LLMs, Algorithm 1 introduces how to locate the subset most relevant for DIF. The process initiates by iterating over a probing dataset, capturing the model’s loss and computing per-neuron gradients for each data sample. To measure each neuron’s importance regarding domain sensitivity, Shapley values are approximated for all neurons across the LLM’s layers. This approach quantifies each neuron’s marginal contribution to the model’s ability to capture domain-specific information. The cumulative Shapley scores are averaged over all samples in the probing set, after which the algorithm selects the layers with the highest aggregate Shapley mass. Within these layers, the most influential neuron groups are further identified based on group-wise Shapley values. The final output is a compact set of domain-relevant neurons, $\mathcal{N}$, which serve as the basis for extracting DIF representations in subsequent stages.

B.2 Two-Stage Contrastive Alignment of DIF

Algorithm 2 delineates a two-stage contrastive training procedure designed to optimize DIF embeddings for robust alignment across disparate knowledge bases (KBs). In the first stage, DIF embeddings are extracted for each training instance by probing the pretrained LLM at the identified neurons, yielding a compact representation that encapsulates domain-specific traits. The initial phase, inter-KB alignment, leverages contrastive learning to encourage DIF embeddings from semantically similar content across different KBs to occupy proximate regions in the embedding space. This is achieved by repeatedly updating the alignment network $g_{align}$ to minimize the contrastive loss $\mathcal{L}_{cl}$, drawing together positive pairs and repelling negatives. The second stage, intra-KB alignment, further refines the DIF space by introducing prototype representations for subdomains or classes within each KB, initialized via unsupervised clustering. Here, a prototype-based contrastive loss $\mathcal{L}_{pcl}$ is incorporated alongside the global loss, jointly optimizing $g_{align}$ to produce discriminative representations that not only bridge domains but respect intra-domain structure. The training concludes with the computation of updated prototypes representative of key semantic clusters, returning both the optimized alignment network and the learned prototypes for later inference.

B.3 Adaptive Prototype-Guided Routing

Algorithm 3 proposes a dynamic routing strategy for inference, leveraging the previously learned prototypes to efficiently allocate retrieval resources based on the semantic relevance of incoming queries. Upon receiving a query, the system first computes its DIF embedding by probing the pretrained LLM at the selected neuron set, followed by transformation via the trained alignment encoder. The query embedding is then compared to all domain prototypes using a similarity metric, yielding a relevance score for each prototype. If the highest similarity score falls below a predefined threshold, the system abstains from retrieval, indicating insufficient semantic alignment. Otherwise, the algorithm selects the top-N most relevant prototypes and aggregates similarity scores by knowledge base, proportionally allocating retrieval slots according to their relative relevance. This prototype-guided mechanism enables adaptive, fine-grained routing decisions that efficiently direct retrieval attention to the most promising knowledge sources, facilitating both high precision and scalable inference in multi-domain settings.

Appendix C Retrieval Pipeline and Indexing Strategies

We adopt FAISS Douze et al. (2024) for dense vector indexing across all retrieval settings. For the Wikipedia (Wiki) knowledge base, we follow the clustering strategy in RopMura Wu et al. (2025), partitioning 1M English passages into 10 semantically coherent knowledge bases. Passages are first embedded using Qwen-embedding-v2 Bai et al. (2023) for clustering, and subsequently indexed with all-MiniLM-L6-v2 Wang et al. (2020). For the Medical (Med) knowledge base Zhao et al. (2025), we replicate the knowledge base construction from RAGRoute Guerraoui et al. (2025), creating four distinct sources: PubMed, StatPearls, medical textbooks, and medical Wikipedia, each indexed using all-ßMiniLM-L6-v2. For the Private Enterprise Policy (PEP) knowledge base, which contains internal Chinese-language company documents spanning four sub-knowledge bases, we utilize the GTE-base-zh encoder Li et al. (2023) fr indexing. For each query, DFAMS retrieves the top-10 documents from the dynamically selected source(s).

Appendix D Dataset Construction and Sampling Strategies

We conduct evaluations on three in-domain corpora and two out-of-domain (OOD) benchmarks.

Wiki Dataset Construction.

The training set consists of 23,240 queries: among them, 2,100 queries explicitly require no retrieval, while 21,140 queries require retrieval of a single document from a single knowledge base. We deliberately exclude queries involving cross-knowledge-base or cross-document multi-segment retrieval to reduce data construction complexity, which also aligns better with practical scenarios. The test set contains 8,879 queries: 900 queries do not trigger retrieval, 969 queries require cross-knowledge-base multi-document collaboration, and 790 queries require same-knowledge-base multi-document collaboration. This setup is designed to verify the robustness of our method in realistic multi-knowledge-base scenarios.

Med Dataset Construction.

Following a similar processing pipeline as Wiki, we construct the training and test sets for the medical domain. The training set includes only “no retrieval” or “single-knowledge-base single-segment” queries to reduce annotation costs. The test set additionally incorporates “cross-knowledge-base multi-segment” and “same-knowledge-base multi-segment” queries to evaluate the system’s generalization ability in realistic multi-knowledge-base collaboration scenarios. The test set contains 2975samples, with 438 requiring cross-knowledge-base multi-document collaboration and 823 requiring same-knowledge-base multi-document collaboration, to assess robustness in real multi-knowledge-base environments.

PEP Dataset Construction.

We evaluate FR capabilities on a private enterprise policy dataset: the training set contains 2,088 samples, all querying single company policy documents from one knowledge base. The test set contains 344 samples, where queries are either categorized as “other” (requiring no retrieval) or require retrieval from a single knowledge base. Since PEP doesn’t have corresponding golden-label documents, recall statistics are not reported.

OOD Dataset Construction.

Following the evaluation paradigm of RAGRoute Guerraoui et al. (2025), we construct lightweight OOD test sets by extracting sub-questions from MMLU Hendrycks et al. (2020) and MIRAGE Xiong et al. (2024) that are most relevant to the topics covered by the existing four knowledge bases. For MMLU, we retain 1,222 questions that are potentially related to the WIKI knowledge base; for MIRAGE, we filter 1,546 open-domain QA samples with the highest entity co-occurrence with the four knowledge bases. Both subsets lack corresponding golden-label documents and are used solely to evaluate the model’s robustness and knowledge generalization under domain shift and non-retrieval conditions.

Appendix E Baseline Implementation Details

We evaluate six representative methods under the DFAMS benchmark. The implementation details of these baseline methods are as follows:

No-RAG.

As a non-retrieval baseline, we directly apply the original LLM without any external knowledge.

Merged-RAG.

There is no separation between individual knowledge bases — all content is integrated into a single, unified knowledge base and indexed together for retrieval.

Prompt.

A knowledge bases selection baseline where a powerful 70B teacher model is used to classify which knowledge bases should be retrieved. This is necessary because smaller models (e.g., 7B) exhibit poor performance on explicit knowledge bases routing tasks. The 70B model performs knowledge bases classification via prompt-based reasoning. Based on the selected corpora, relevant documents are retrieved and then passed to a 7B LLM for final answer generation.

CoT Prompt.

A knowledge bases selection where a 70B teacher model is used to perform corpus routing, but with chain-of-thought (CoT) prompting Wei et al. (2022). Compared to Prompt, this variant enhances reasoning by explicitly incorporating intermediate steps during knowledge bases classification and downstream answer generation.

SFT.

A supervised fine-tuning baseline trained on the $D_{train}$ dataset using a cross-entropy loss. We fine-tuned two base models, Qwen2.5-7B and LLaMA3.1-8B, to predict the correct knowledge base for each query. The training specifically targets improving knowledge base selection accuracy.

RopMura.

A recent joint retrieval and routing method Wu et al. (2025). As our focus is on knowledge bases selection, we isolate and evaluate only the knowledge bases selection module. Multi-turn dialog components are disabled for fair comparison.

RAGRoute.

For each knowledge bases, we train an MLP-based router whose architecture and training settings exactly match those of our Align-MLP, ensuring a fair comparison Guerraoui et al. (2025). All methods share the same encoder and retriever: we use all-MiniLM-L6-v2 for Wiki and Med, and gte-base-zh for PEP.

Appendix F Metric Definitions and Evaluation Configuration

We evaluate DFAMS using three complementary metrics:

Cls Acc.

This metric measures whether the method correctly identifies the relevant knowledge base(s). A prediction is considered correct if it matches the ground-truth KB in single-source cases, outputs Others when no retrieval is required, or fully covers all gold KBs in multi-source cases.

Recall.

This metric follows standard RAG evaluation and is computed over the Top-10 retrieved documents. It is calculated only for retrieval-triggering queries, and measures the proportion of gold documents that appear within the Top-10 retrieved results. Formally, it is defined as the number of retrieved gold documents divided by the total number of gold documents for a given query. Queries that do not require retrieval are excluded to better isolate and evaluate the retrieval component.

QA.

This metric evaluates the final response quality. For multiple-choice questions, we extract the predicted option(s) (e.g., A/B/C/D) from the model output and compare them against the ground-truth answer. For open-ended queries, responses are scored by an LLM-based judge Zheng et al. (2023) that assesses factual correctness and fluency. The score ranges from 0 to 10.

Appendix G Implementation Details

To train the Multi-Prototype Knowledge Alignment module of DFAMS, we adopt a two-stage process. In the first stage, each private knowledge base independently extracts its own DIF representations from its local training data $\mathcal{D}_{\text{train}}$, where the activations of the selected neuron groups across designated layers are concatenated and pooled across tokens (e.g., using AverageToken) to form the final DIF representations. These DIFs capture the semantic characteristics of the local knowledge bases without exposing the underlying textual content, and are securely stored and transferred to the aligner for training. In the second stage, the DIF representations from all participating knowledge bases are aggregated and fed into the Align-MLP for joint optimization. The aligner is trained with an inter-KB supervised contrastive loss and an intra-KB multi-prototype contrastive loss (PCL), with prototypes initialized via KMeans clustering. This two-stage design effectively reduces redundant computations, improves overall training efficiency, and satisfies the data-locality and privacy-preservation requirements inherent to federated retrieval scenarios.

We train the Align$-$MLP aligner using the AdamW optimizer with a learning rate of $2\times 10^{-4}$ and a cosine decay schedule. Unless otherwise specified, the batch size is set to 64, the temperature parameter to 0.07, and the number of contrastive learning (CL) epochs to four, during which only the CL objective is optimized. All models are trained for six epochs in total, with the final one to two epochs jointly optimizing both the CL and PCL. The DIF representations are extracted from the mlp.up$\_$proj components of the 26th and 27th transformer layers, where attribution-based analysis identifies neuron groups that are most relevant to the retrieval objective. Specifically, neurons are grouped in sets of 20, and the top 50 groups (corresponding to 1,000 neurons per layer) with the highest attribution scores are selected for DIF construction. The Align-MLP shares the same architecture as the probing network used in Probing-RAG, consisting of three fully connected layers with intermediate SiLU activations, layer normalization, and dropout regularization. The hidden dimension of the MLP is set to 512, and its input and output dimensions match those of the DIF representations to ensure alignment consistency.

We train the Align$-$MLP aligner using the AdamW optimizer with a learning rate of $2\times 10^{-4}$ and a cosine decay schedule. Unless otherwise specified, the batch size is set to 64, the temperature parameter to 0.07, and the number of contrastive learning (CL) epochs to four, during which only the CL objective is optimized. All models are trained for six epochs in total, with the final one to two epochs jointly optimizing both the CL and PCL objectives. The DIF representations are extracted from the mlp.up$\_$proj components of the 26th and 27th transformer layers, where attribution-based analysis identifies neuron groups most relevant to the retrieval objective. Specifically, neurons are grouped in sets of 20, and the top 50 groups (corresponding to 1,000 neurons per layer) with the highest attribution scores are selected for DIF construction. The Align-MLP follows the same architecture as the probing network used in Probing-RAG, consisting of three fully connected layers with intermediate SiLU activations, layer normalization, and dropout regularization. The hidden dimension of the MLP is set to 512, and both its input and output dimensions are aligned with the 2,000-dimensional DIF feature space. Across all experiments, the loss weighting parameter is fixed to $\alpha=0.95$, meaning that the PCL term contributes 0.05 of the total loss. Other hyperparameter configurations are summarized in Table 7.

Appendix H Additional Results on Dynamic Information Flow

To verify our hypothesis regarding the presence of DIF, we analyzed the Shapley value heatmaps across four model sizes, as shown in Figure 4. The results reveal a consistent trend: the Shapley values increase in the early-to-middle layers (e.g., around layers 1–6 in Qwen2.5-7B), decrease in the intermediate layers, and rise again in the deeper layers (e.g., layers 26–27). This pattern suggests that shallow layers primarily capture intent-related signals, while deeper layers activate and integrate domain-specific knowledge. This observation supports our decision to extract DIF representations from the latter layers.

We also conduct a layer-wise attribution analysis on the PEP dataset, as reported in Table 8. Overall, the results show a generally positive correlation between Shapley magnitude and downstream performance—layers with higher Shapley values tend to achieve better classification accuracy. An exception is Layer 26, which attains slightly higher accuracy (72.70$\%$) despite a lower Shapley score (0.3765). In contrast, layers with small Shapley values, such as Layer 15 (0.0737), exhibit substantially lower accuracy (27.83$\%$). These observations confirm that Shapley-based analysis effectively highlights semantically informative layers contributing to domain-specific reasoning.

Finally, we compare three metrics—Shapley values, forward activations (Act) Xu et al. (2024), and gradients (Grad) Zhang et al. (2023)—with gradient values scaled by $10^{-6}$ for readability. Among them, Shapley values most closely track model performance, whereas Act and Grad show weaker alignment. For instance, Layer 15 exhibits relatively high Act (4.36) and Grad (0.635) but performs poorly (27.83$\%$). These results underscore the superior reliability of Shapley-based attribution in identifying influential layers.

Appendix I Effect of Backbone Model Size.

We evaluate DFAMS with Qwen2.5 models of 0.5B, 3B, and 7B parameters. As shown in Table 9, the 0.5B and 3B models achieve accuracy of 81.23% and 83.56%, and retrieval recall of 50.75% and 52.12%, respectively. Compared with the 7B model, the performance gap is relatively small, demonstrating that our framework can deliver strong performance even with smaller model sizes.

Appendix J Effect of Learning Rate

Table 10 shows the classification accuracy of DFAMS under varying learning rates. The model achieves the best performance at a learning rate of 1e-4, reaching 85.03% accuracy. Both larger (1e-3: 81.51%) and smaller (1e-5: 54.25%) learning rates lead to performance drops.

Appendix K Computational Resources and Software Environment

Experiments were conducted on a server equipped with dual Intel Xeon E5-2680 v4 CPUs (56 cores, 112 threads), 8 NVIDIA RTX 3090 GPUs (24GB each), and 377 GB of main memory, running Ubuntu 18.04.6 LTS. Python 3.11.10 was used with PyTorch 2.4.0, and packages were managed via Conda 23.5.2. Model training took approximately 1 minute per epoch on average, depending on the experimental setting. Data preprocessing, including extraction of around 1,000 DIF samples ( 4 MB), required about 10 minutes to obtain the DIF representations. During inference, generating QA accuracy results for 1,000 samples required approximately 5 hours on the same hardware configuration. All models and software packages, including HuggingFace Transformers 4.44.0, SpaCy 3.7.0, NLTK 3.8.1, and related dependencies, were used with default or explicitly stated parameter settings.

Appendix L The Use of Large Language Models

In this work, Large Language Models (LLMs) were used for language polishing and coding assistance. Specifically, LLMs supported refining the clarity and grammar of the manuscript, improving stylistic quality, and suggesting code snippets or troubleshooting strategies. All content generated by LLMs was carefully reviewed and verified by the authors before inclusion. The research design, critical analyses, and all final decisions were independently conducted by the authors. LLMs were not involved in generating new research ideas or conclusions.

Appendix M Prompt

In this section, we provide a detailed introduction to the prompts used in our framework:

Dataset Construction Prompt

You are a knowledge expert tasked with creating a high-quality multiple-choice question based on the following text excerpt.

Requirements:

•

Question should be clear, concise.

•

Provide four answer options A, B, C, and D.

•

Only one correct answer; the other three must be plausible but incorrect.

•

Answer must be directly supported by chunk.

•

Output the result strictly in JSON format.

Output Format:

{ "question": "Question content", "options": { "A": "Option A", "B": "Option B", "C": "Option C", "D": "Option D" }, "answer": "Correct letter (A-D)" }

Text excerpt:

text excerpt here (truncated to MAX_TEXT_LENGTH if needed)

Multi-Chunk Dataset Construction Prompt

You are an expert tasked with generating high-quality multiple-choice questions that integrates and synthesizes information across multiple chunks.

Requirements:

•

The question must require synthesis of information from all chunk_num text excerpts. Avoid disjointed or unrelated pairings.

•

The stem should naturally integrate ideas, characters, events, or facts from the various excerpts into a cohesive question.

•

Do not generate a question that simply juxtaposes unrelated content from different texts — such questions are considered invalid.

•

Ensure only one correct answer exists, and all distractors are plausible based on full context.

•

If the question cannot reasonably be formed without being disjointed, return false.

•

Return the result in strict JSON format.

Output Format:

{ "question": "Question content", "options": { "A": "Option A", "B": "Option B", "C": "Option C", "D": "Option D" }, "answer": "Correct letter (A-D)" }

Below are the chunk_num related text excerpts. You must combine their information meaningfully in your question:

text excerpt here (truncated to MAX_TEXT_LENGTH if needed)

DIF Probing Prompt

You are a domain-specific large language model connected to the following knowledge bases:

Knowledge Bases List: {database_list}

Given the query:

"{query}"

Please analyze and determine which knowledge base the query most likely belongs to. If it does not match any of the listed knowledge bases, respond with others.

Response Format:

Selected Knowledge Base: [name of the knowledge base or others]

Prompt for Short Answer QA

You are a professional QA assistant. Please answer the question based solely on the provided context. Follow the format below without omission:

Prompt Format:

<|im_start|>system

You are a professional QA assistant. Answer the question based on the given context.

<|im_end|>

<|im_start|>user

Context: {context}

Question: {question}

<|im_end|>

<|im_start|>assistant

Your answer here

<|im_end|>

Prompt for Multiple-Choice QA

You are a professional multiple-choice QA assistant. Based on the provided context, answer the question by selecting the most appropriate option from A/B/C/D. Output only the option letter (A, B, C, or D) as the final answer; you may optionally add an explanation afterward.

Prompt Format:

<|im_start|>system

You are a professional multiple-choice QA assistant. Please answer the question based on the given context by selecting one option (A, B, C, or D). Output only the option letter as the final answer, optionally followed by an explanation.

<|im_end|>

<|im_start|>user

Context: {context}

Question: {question}

Options:

A. {options.A}

B. {options.B}

C. {options.C}

D. {options.D}

Please select the best option based on the above information. Output only the option letter, for example: "B"

<|im_end|>

<|im_start|>assistant

Your answer here

<|im_end|>

Prompt for LLM Judgment of Open-Ended Answers

You are a professional evaluator. Given the question, reference answer, and scoring criteria, please score the model-generated answer strictly from 0 to 10 (integer only). Return only the integer score without any extra text.

Input:

Question: {question}

Reference Answer: {standard_answer}

Model Answer: {model_answer}

Scoring Criteria:

1. Relevance: Does the answer directly address the question? (up to 4 points)

2. Accuracy: Is the content consistent with the reference answer? (up to 4 points)

3. Completeness: Does the answer cover key points in the reference? (up to 2 points)

4. Penalties:

• Contains obvious errors: deduct 1–2 points

• Completely unrelated or no answer: 0 points

Examples:

• Perfect and complete: 10 points

• Mostly correct but missing some details: 8–9 points

• Partially correct: score proportionally (e.g., 3/5 key points = 6 points)

• Irrelevant but no errors: no deduction

• Completely wrong or no answer: 0 points

Please strictly follow the criteria and return only an integer score: