Make Information Diffusion Explainable: LLM-based Causal Framework for Diffusion Prediction
Authors: Wenbo Shang
Zihan Feng
Yajun Yang
Xin Huang
Venue: NeurIPS 2025 poster ()
Keywords: data mining
social networks
information diffusion
large language model
Primary area: machine_learning_for_sciences

Abstract: Information diffusion prediction, which aims to forecast future infected users during the information spreading process on social platforms, is a challenging and critical task for public opinion analysis. With the development of social platforms, mass communication has become increasingly widespread. However, most existing methods based on GNNs and sequence models mainly focus on structural and temporal patterns in social networks, suffering from spurious diffusion connections and insufficient information for the diffusion analysis. We leverage strong reasoning capability of LLMs and develop a LL**M**-based causal framework for d**i**ffusion inf**l**uence **d**erivation (MILD). Comprehensively integrating four key factors of social diffusion, i.e., connections, active timelines, user profiles, and comments, MILD causally infers authentic diffusion links to construct a diffusion influence graph $G_I$. To validate the quality and reliability of our constructed graph $G_I$, we proposed a newly designed set of evaluation metrics w.r.t. diffusion prediction. We show MILD provides a reliable information diffusion structure that 12% absolutely better than the social network structure and achieves the state-of-the-art performance on diffusion prediction. MILD is expected to contribute to high-quality, more explainable, and more trustworthy public opinion analysis.

Make Information Diffusion Explainable: LLM-based Causal Framework for Diffusion Prediction
Wenbo Shang" Zihan Feng" Yajun Yang Xin Huang Hong Kong Baptist University, Tianjin University {cswbshang, xinhuang) hkbu, edu.hk hk, (zihanfeng, yjyang)etju.edu.
Abstract
Information diffusion prediction, which aims forecast the future infected during the information spreading process on social platforms, is a challenging and critical task for public opinion analysis. With the development of social platforms, mass communication has become increasingly widespread. However, most existing methods based on GNNs and sequence models mainly focus on structural and temporal patterns in social networks, suffering from spurious diffusion connections and insufficient information for diffusion analysis. We leverage the strong reasoning capabilities of LLMs and develop an LLM-based causal framework for diffusion influence derivation, named MILD. By comprehensively integrating four key factors of social diffusion i.e., connections, active timelines, user profiles, and comments-MILDD causally infers authentic diffusion links to construct a diffusion influence graph, Gr. To validate the quality and reliability of our constructed graph G,, we propose newly designed set of evaluation metrics for diffusion prediction. In experiments, MILD provides reliable information diffusion structure that achieves an absolute improvement of 12% over the social network structure and achieves sfte-of--he-att performance in diffusion prediction. MILD is expected to contribute to higher-quale qughlr-quality more explainable, and more trustworthy public opinion analysis. The code and data available https: htops://ge / tit........ Sonn/Shang-uii MILD-Off fiaffficall-iii aaaa-IImmmmeettiiiin ementation.
Introduction
Information diffusion on social platforms (c.g., TikTok and Instagram) is characterized by broad reach and intricate, multifaceted pathways, leading the formation of numerous diffusion cascades. Information diffusion prediction aims to forecast the future participants of cascades, which is crucial for tracing information flow dynamics and quantifying user influence, benefiting downstream appli- cations such as social recommendation systems [21, 8, 15] and public opinion analysis [12, 13, 20]. Therefore, is fundamentally important to achieve accurate information diffusion prediction, relying on effectively modeling complex user interactions and influences.
Several learning-based based approaches have emerged for predicting information diffusion. Initial efforts focus on modeling the sequential nature of diffusion events, primarily employing Recurrent Neural Networks (RNNs) or Transformer architectures capture temporal influence patterns within observed cascades [1 1, 31, 32, 33, 35J. More recently, Graph Neural Networks (GNNs) have proven highly effective for graph data, leading to hybrid frameworks that combine GNNs with sequential models to capture both global social network structure and local diffusion dynamics [5, 23, 28, 29, 37, 41]. For instance, methods like MS-HGAT [28] and DisenIDP [3] utilize hypergraph networks to capture user interactions and employ self-attention to model diffusion influence. However, this "Gunnnee
'Equal Contribution. t Cooresponning Author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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fi Social relation
Extract
fz Active time
Derive
fa User profile
f4 Comments
Online social media
Extracted diffusion influencing factors
Diffusion influence graph G5
Figure 1: Overview of diffusion influence derivation in the proposed MILD framework.
model" paradigm has limitations in explicitly identifying key influences, which makes it hard to answer a fundamental question: who influences one to participate in the information diffusion?
In this paper, we propose novel model of LLM-basee diffusion influence derivation (MILD), which aims at tackling the fundamentally key question of shhoiinfuunncs-whiie -hho using causal derivation. In particular, MILD contains two derivations: explicitly deriving who-influences- -eeeinffuencee-whom diffusion connections the form of digraph G, to represent the cascade, and utilizing the obtained diffusion influence graph Gy to enhance diffusion prediction. We lay the foundation with key observation: there is an imbalanced diffusion ability for different social actors within cascades. Some are hub influencers, who can activate many inactive actors. But, some are minor influencers, even influencees (i.e., influenced users). For instance, a new participant in diffusion process is likely to be influenced by close friends or opinion leaders, while unrelated influencees have infffusion-influenciin ability on her/him. However, existing models cannot explicitly capture aato-influenceswwiie whom connec- tions within cascade, which blindly takes all participants in cascade as potential influencers. Furthermore, we have conducted experimental studies to validate this observation in Section 4.3.
For diffusion influence deriving, the authentic diffusion process is unknown, unexpluinable, and non-transparent, it becomes challenging. Leveraging strong reasoning capabilities, MILD employs the LLM like sociology expert at high level to comprehensively analyze four key diffusion influencing factors to derive who-influences-wiie whom pairs, as shown Figure 1. MILD extracts four key factors of social relationships, active timestamps, user profiles, and comments. Integrating these key factors, MILD finally derives a diffusion influence graph Gy to represent the cascade diffusion. To discover effective pathways for G2 construction, relax the formulated NP-hard problem and develop fast heuristic strategies to find potential diffusion pathways in polynomial time.
Additionally, propose well-designed set of evaluation metrics to verify the reliability of diffusion influence graph Gr, which aims at capturing real key diffusion pathways. To reveal that social relationship significantly differs from the information diffusion, we conduct comparison analysis visually and quantitatively to show the differences between our Gj and social relationships in Section 3.3. We found that Gy is more reliable and effective, representing 12% more real-worle diffusion pathways and 28% more key interactions compared with the social network.
Finally, we integrate the diffusion influence graph G₃ to enhance the performance on the diffusion prediction task and empirically demonstrate the effectiveness of MILD on two real-world datasets with diffusion benchmarks. Extensive experiments validate the superiority of MILD against eight Haae-of-the-aae competitors [37, 28, 3, 23, 14, 5, 29, 41], by achieving ~7% improvement on average.
2 Preliminaries
The social network G E,, is a directed graph, where V is the set of users, E V V V is the set of directed social relations (e.g., follower-followee), and O {o; &. V} is the set of user profiles, with each o contains attributes such as follower count, bi-follower count, and status count, etc. An information diffusion cascade social network G is an ordered sequence C= ((1), f1, the absolute timestamps which users become active; b, denotes the behavior of user v (e.g., like, comment, share). CI denotes the cascade length and |C] denotes the total number of cascades. Note that throughout this paper, all mentioned paths are simple paths without loops.
(Uk, tg. by)), where v; E V and V/ A by for all i i j: f Σ ... S t4 are
Given cascade and the social network G. the objective of MILD is to derive the diffusion influence graph Gy to represent the diffusion process based on four extracted key factors { T, O B} to

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enhance performances on diffusson prediction, where v denotes potential diffusion paths derived from social networks, T denotes the temporal order of participants based on their active time, O denotes the influence and activity levels of users derived from profiles, and B denotes the comments.
Diffusion influence graph. The diffusion influence graph is digraph G₁ (Vi, Fr), where Vi S V is the set of cascade participants (Vvrl = |C] = k), and EJ represents potential influence relationships. We represent the (binary) influence matrix of G2 as A E {0, 13 where A!j = represent v; influences vy, i.c., (e, - 02) E E,, otherwise 0.
Problem formulation of diffusion prediction. Given an observed cascade C. with & E Zt existing
participants, and an influence matrix A the problem of diffusion prediction is to find y E Z users as the candidate participants Top,(V) in future. Specifically, Top,, (V) = (o V fo(u A 2 fo(u A ), Vu E V Top,, and [Top,, (V)l 7, where fo(-) learned scoring function over all users in the social network G and 0 denotes the parameter of the learning model.
3 Methodology
This section introduces causal framework to enhance accurate diffusion prediction. Section 3.1 introduces a causal view C-+ Z -Y emphasizing the necessity of explicit key influence representa- tion Z. Section 3.2 outlines the method for prompting LLMs to infer who-inffuences--wher converting each cascade C into a structured diffusion influence digraph Z. Scction 3.3 proposes three evaluation metrics and a comparison analysis to assess the reliability and consistency of the derived Z. Section 3.4 integrates the LLM--drivee diffusion influence Z into a downstream predictor Y, explicitly highlighting key influences enhance prediction in practice.
graph,
3.1 Causal View on Information Diffusion
To better understand the limitations of existing information diffusion prediction methods, we take causal view of P(Y|C) (C) and construct a structural causal model (SCM) [22] in Figure 2(a). describes the causalities among three variables, i.c. the information diffusion cascade C, spurious and incomplete diffusion pathways U. and the diffusion prediction label Y. Specifically:
(1) C Y describes that existing works predict the next participant Y by learning from the observed historical cascade C: (2) C' - U + Y shows the dependence between and Y induced by the spurious and incomplete diffusion process U. To formulate the true causal relationship between C and Y. we employ the back-door adjustment to estimate P(Y P(Y|do(C)) (C) as follows. The detailed analysis is in Appendix C.I.
Figure 2: SCM.
P(Y(do(C)) = P -c, =u)
(I)
NEU
where a denotes specific spurious diffusion process of U. In Eq. 1, we observe that P(Y (())) comprises spurious diffusion directions, which may lead to incorrect decisions.
In this paper, we add intermediate variable Z between C and Y, the representation of the diffusion influence shown in Figure 2(b), satisfying the Front-door Adjustment. In our SCM, C+ Z + Y shows that the diffusion influence Z is derived from the cascade C. Then, MILD employs Z as the explicit diffusion cascade representation to make an accurate diffusion prediction label Y. Based the detailed analysis in Appendix C.2, can formulate our model by chaining together the two partial effects and summing over all states = of Z as follows:
P(Y]do(C)) = (EEC)))=EPPPE P(YIZ.C))PC)P(II CEC
(2)
where C' contains all observed cascade sequences in the training data, and 2 denotes specific diffusion influence matrix in Z. In Eq. 2, we can observe that when MILD captures the diffusion influence as closely as possible to the real-world one, we can achieve accurate prediction results. Therefore, MILD contains two parts: deriving explicit diffusion influence from the cascade (C -> Z), and making diffusion prediction based on the derived diffusion influence (Z + Y).
3

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Key factor Potential diffusion pathways (social relationships) zp
Diffusion path search
O Cascade sequence
Projection
C
Cascade subgraph
Social network
Cascade subgraph
Potential diffusion pathways
Key factor 2: Temporal order T
Key factor 3: User profile 0
Key factor 4: Comments B
Influence level
Key sentence extraction
Activity level
Temporal order
User profile
+ Potential diffusion path
Potential diffusion path
Potential diffiusion path
Z
Prompt
Merge
Predict
LLM Reasoning
Cascade C
Y
G
Diffusion prediction
Influence subgraph {G
C
Z
-
Y
Diffusion influence graph
Figure 3: The proposed MILD framework. (I) Z: To capture Z, construct four essential diffusion influencing factors for the LLM to understand and infer the diffusion process, which are social relationships vi temporal order T, user profiles O, and shared comments B. LLM-derived diffusion influence subgraphs are merged by aligning shared nodes and edges to form the final diffusion influence graph Z. (2) / - Y: A crafted cascade module integrates the structured diffusion influence graph Gy into the predictor, which can explicitly highlight key influences.
3.2 Diffusion Influence Deriving: C
In this part, we introduce our MILD to explicitly identify and extract the diffusion process of cascade into a structured diffusion influence graph Gy as the intermediate variable Z, making the diffusion process transparent and explainable, shown in Figure 3.
Given the current limitations of LLMs in reasoning about and structurally comprehending di- graphs [26, 27, 10, 19, 30, 39], we propose constructing potential diffusion paths to represent social relationships, thereby enhancing the LLM's understanding of social diffusion patterns. Specifi- cally, for given cascade sequence C' and social network G, we first extract the induced subgraph consisting all participants C, forming the cascade graph Ge = (Vo, Ec). Here, Ve represents the set of cascade participants, and Eg represents their social links within G. Subsequently, transform the cascade graph Ge into set potential diffusion paths, denoted as We define this process as the Diffusion Path Search problem. Its objective is to obtain diverse and high-quality set of paths V suitable for LLM analysis.
Definition 1: [Diffusion path search problem] Given a cascade graph Ge (Vc, Ea) with one unique root v the problem returns a collection of path structures V C Ge by satisfying the following three constraints: (D1) all paths z/ V start from the unique root vi; (D2) Ve covers all nodes in Vo: and (D3) V contains all possible paths between 01 and v E (v.ldis((vi, v.) 2 l).
Theorem 1: The diffusion path search problem is NP-hard.
The detailed proof of Theorem is shown in Appendix C. Given the NP-hardness of this problem, we propose a heuristic alternative algorithm based on the combination of Breadth First Search (BFS) and Depth First Search (DFS). This algorithm balances diffisiion consistency (long, deep paths) against diffusion coverage (short, shallow paths). First, we conduct the single-source BFS algorithm with original participant ei as the single source in O(Vel + (E time. The algorithm returns the BFS tree THPS composed of shortest paths between i1 and v E Vc, satisfying (D1) and (D2). In Tbrs, longer shortest paths signify greater social distance between participants, typically involving more complex information diffusion routes. In contrast, shorter paths indicate closer social distance

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and simpler diffusion routes. Based on this analysis, for each long shortest path in TEFS, we select its source s and target т, and then search all simple paths between s and in Ge using the DFS algorithm. satisfying (D3). However, in the complete graph of order n, all simple paths can be found in O(n)) time. Considering efficiency, we design a strict constraint on the density of Ge (details in Appendix B.3). If the density is less than r, we search all simple paths between and in O(Vc (az)) time, where dmaz denotes the maximum out-degree in Gc. Otherwise, we search all shortest paths between and in O(IVallEe) time. We iterate this process for each long shortest path in TBFS. Meanwhile, we preserve short paths in T TEFS that exclude the target from long paths for (D2). Since O(Vic + |Ecl) S O([V [[IVe + |V<||Ecl }) the total time complexity is O(VVcl d aa + Vc Ec ) Therefore, the algorithm can effectively search diffusion paths that satisfy (D1), (D2), and (D3) in polynomial time O(VV d'mar + IVc [Ec)).
Building on the preceding analysis, we design four critical factors for analyzing diffusion influence. First, the potential diffusion pathway set Vi represents social relationships. Second, the temporal order T. which tracks the time of participant comments or shares, reflects the order of their involvement. Third, user influence and activity levels O which are estimated under the guidance of communication theories from user profiles [2. 7, 4J. The detailed calculation process can be found in Appendix B.2. We assign a specific level for each estimation, i.e., 0-20%: poor, 20%-40%: low, 40%-80%: moderate, 80%-95%: high, 95%-100% outstanding. Lastly, the comment contents shared by participants B. We perform key sentence extraction on B based on the TextRank algorithm [16] to mitigate the limitations of input length in language models and enhance key semantics in B.
Diffusion influence deriving. We design the prompt to instruct the LLM to analyze the diffusion influence between users within each cascade. The potential diffusion path 1 E V, temporal order T, descriptions of user influence and activity levels O, and comments B are integrated into the designed template ((-), forming prompts ((),, T, O, B) to provide sufficient information for analysis. To guarantee the reliability of the derivation, we add basic principles of information diffusion to the design of the instruction. For instance, later participants do not influence earlier participants. The detailed prompt can be found in Appendix Figure 14. Then, we feed instructions and prompts into the LLM to derive diffusion influence in the form of user user-pair lists denoted as Uyl....) where U; conveys the information to By and influences by to participate in this cascade.
Out-of-the-bee diffusion influence representation. For each potential diffusion path, the LLM infers critical diffusion influences within paths, namely [[t; m.),,..). which form a directed influence subgraph Gj. As each cascade contains multiple diffusion paths, single cascade corresponds to set of several influence subgraphs {Gr}. We then merge {Gr} into unified diffusion influence graph G by aligning shared nodes and edges across these subgraphs, as shown in Figure 3. In GG, each node represents one participant in the corresponding cascade, and each directed edge (ci, vy) signifies that user vj engages in the cascade under the influence of user e; Thus, G₁ represents the transparent and explainable diffusion process and functions as the intermediate variable Z.
3.3 Measurements of Difffusion Influence G₁
To evaluate the reliability and consistency of G, derived from MILD, we carefully design quantitative measures: (EI) Diffusion pathways evaluation assesses whether G, can accurately capture the real- world information diffusion routes. (E2) Key interaction evaluation examines whether G2 observes participant interactions within cascades. (E3) Robustness evaluation assesses whether MILD can distinguish real and fake diffusion pathways under the interference of misleading instructions, ensuring consistent and reliable responses. (E4) Comparison of G, and Ge analyzes the role of social relationships in the diffusion process. Our findings are as follows:
1. The social network fails to effectively capture the real-world diffusion process compared to our Gy. Although it can establish the necessary social relationships to represent partial diffusion connections, it can scarcely capture key and implicit diffusion connections. (EI&E2)
2. Multiple diverse diffusion pathways can enhance MILD's inference ability in diffusion influence derivation compared to shortest relationships, indicating that the diffusion process is complex and cannot solely depend on the closest social relationships. (EI&E2)
3. Temporal order is critical for analyzing the diffusion process. (EI&E2)
4. MILD can distinguish real and fake diffusion processes under the interference of misleading instructions and generate consistent results of diffusion influence analysis. (E3)
5

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I0T Social Network
CC H/ Shortee: Path
(22 H/b Tempural Order CS Ours
News Datasel
Weibo Datasel
1.0
10
Bisance rewened 9.5
Dirsance thrsheic Average dironce 342
0.7-
0.7
Cosine Distance
0.8
dearage ditanse 0.323
0.2
Accuracy
0.6
0.6
3.6
0.6
0.5
0.4
0.4
0.4
0.3
Welbo
0."0
100 150 Cascade Index
(a) Diffusion Pathways
(b) Key Interaction
Cascade Index
Figure 4: Reliability evaluation of Gr.
Figure 5: Comparison of G2 and Go.
5. The forming process of social relationships differs from the diffusion process, although social relationships are significant for MILD in analyzing the diffusion process. (E4)
(E1) Diffusion pathways evaluation. In real-world data, diffusion pathways often appear in reply chains, in the form of {A= [comment] @ [comment]@C) [comment]). where @ indicates the reply and share behavior during the diffusion process. Thus, we can extract these real-world diffusion pathways as the ground truth, such as C conveying the information to B, who then passed it on to A, formulated as [[C, B], [B, A]]. Then, we evaluate G, based on our extracted ground- Ggt- Considering the scarcity and absence of reply comments in the dataset, we design the following evaluation method: (1) for each cascade, we evaluate G2 and Ggt once; (2) calculate the number of intersecting directed edges between G5 and Ggt (3) calculate the proportion of the intersection set in Ggt and then average the overall results, which can be formulated as follows.
Accuracy = 19
1
Σ Gg |E(G
LE(G)) n E(Gg))
(3)
where F..) denotes the edge set of the given graph and 1ggz| denotes the number of Ggt in the total set Ggt- To verify the effectiveness of our method, compare it with three representations of diffusion influence: (I) the original social network, (2) our method with the shortest potential diffusion paths, and (3) our method without temporal order. As shown in Figure 5(a), the social network fails to accurately capture the real-world diffusion process. Furthermore, diverse potential diffusion pathways and temporal order are critical and can provide necessary information for MILD to analyze the diffusion process.
(E2) Key interaction evaluation. As the well- communication theory, the Strength of Weak Ties [7] posits that "the strength of any tie is a function of the frequency and duration of interaction," " assess whether Gy can observe the key interactions among participants. We regard figh-freeuency interactions as key interactions. To ensure faimess in evaluation and avoid information leakage, we split the dataset by the cascade initiation time in an 8:2 ratio. We assess whether our method can observe key interactions in the 20% of newly occurred cascades based on the interactions in the 80% of historical cascades. The evaluation metric and baselines are the same as in the diffusion pathways evaluation. As shown in Figure 5(b), compared to the other representations, we find that G1 more effectively captures strong ties and key interactions among participants in new cascades.
(E3) Robustness evaluation. To evaluate whether MILD can distinguish real and fake diffusion paths, construct pairs of such paths and intentionally mislead the LLM assume that all paths real to analyze the influence strength. Initially, for each cascade, we generate multiple fake diffusion paths by retaining the same source and target nodes as the real paths, but randomly replacing the intermediate nodes with unrelated participants. We then mix all paths and prompt MILD to analyze the pair-wise influence strength within these "real" diffusion paths as P( 14-1) [O, 1]. where 2 is the predecessor of U; in the path v. We calculate the path influence strength P(t) and the margin difference between real and fake diffusion paths. The path influence strength of the true path v is denoted as P Perue (15). Similarly, the influence strength of a fake path a/ is P)ake()5)
P( = II P( u. P(v)) = II P(c.)e--))P(1)).
(4)
2
km 2

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marging
Σ
Perue (xb)
Psake(15 (1b",
V real, fake S C, (5)
real
1 fake
WEW fake
Based on the calculation, we introduce the Correct Distinguishing Rate (CDR), which assesses instances where the margin difference exceeds specified threshold d.
Σ (marginc)
f (margine))
{
if marging > 8 if marging S
CDR
CEC
(6)
|C|
Detailed proof is provided in Appendix C.8. We adjust the thresh- old 5 of marging; from 2% to 14% to observe MILD's ability to distinguish, as depicted in Figure 6. Our findings indicate that MILD can effectively distinguish real and fake diffusion paths with margin, even under the interference of misleading instruc- tions, showing strong robustness. The results consistently show that real paths have greater diffusion influence strength than fake paths. Even with a ó value of 10%, the CDR remains around 0.8 across two datasets. The detailed prompt is in Figure 16.
1.0
0.6
0.4
0.2
News
Weibo
2%
4%
6% 8%
10% 12% 14%
(E4) Comparison of G₁ and Gc. We quantify the differences between our diffusion influence graph G2 and the social rela- tionship graph Gc, analyzing the role of social relationships in the diffusion process. For each cascade, we calculate the cosine distance the difference between G₁ and Gc. A/ R and AC R the adjacency matrices of G2 and Gc, respectively, where lt denotes the number of participants in the cascade. The detailed calculation process is below.
Threshold
Figure 6: Robustness evaluation.
VI = flatten(A (A') R
VC = flatten (aatten(A)) E Rx
(7)
dis ( (A =1
VI VC
(8)
||T|| ||vol|
We calculate the matrix distances of all cascades in Figure 5. The range of dis(A ( A is [0, 1].
The gray line separates close- and far-distance samples. The red line represents the average distance between 2₁ and Gc. The results indicate that G₁ and Ge are relevant, as more samples fall in the close area. However, most G2 structures differ from those Gc, with a 0.35 distance on average. Our findings suggest that although social relationships way these relationships are structured differs from the diffusion process itself.
key factor in the diffusion process, the
3.4 Diffusion Prediction: Z Y
To empirically verify the effectiveness, we further evaluate G2 via the downstream prediction task. Following common workflows [23, 28, 29, 41], we use two-phase paradigm. First, following [6], we employ the subgraph-centre encoder to learn the social network G. Second, crafted attention module captures the diffusion cascades. Specifically, we aim to harness an L.LM-derived diffusion influence graph G as explicit structured intermediate representation Z for each cascade C. A key design principle the controlled exclusion of raw contextual features (e.g., user profile attributes or full-text embeddings) from the downstream predictor. This ensures that any gains in prediction accuracy can be attributed solely to the structured diffussion influence information encoded within G,, rather than to auxiliary side information. Formally, we inject the adjacency matrix A' of G₁ directly into the self att-ntttnnton computation. Given participant embeddings Hg E kxd we calculate
Q H2 W Attn V)- softmax
K= H W
V= W.
QK
+ aA' V. Ja
(10)
where Wº, W WV E dddd are learnable projections, d' == d/B with B attention heads, and M E (0, -00 jack enforces causality by masking future positions. The scalar a a temperature factor that calibrates the influence graph's impact attention scores. Subsequently, the multi-head outputs are concatenated and processed by position-wis feed-forward network to yield the final cascade representation H., which is distilled solely from Gy for downstream prediction tasks.

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Table 2: Performance of information diffusion prediction (averaged from 5 runs). Higher scores better. Corresponding standard deviations (+) are provided in the Appendix A.3.
Datasets
News
Welho
Metrics
110 10
116:50
110100
M@11 10
MG:50
M@ 100
11@ 10
1100550
11@ 100
M@ 10
M@
M@ 100
DyHGGN [37]
18.94
24.50
27.31
10.50
10.76
10.80
10.51
15.39
18.30
6.01
6.23
6.27
MSHGAT [28]
20.10
25.82
28.85
11.68
11.95
11.99
11.41
18.34
21.77
6.16
6.48
6.53
DisenIDP
29.08
18.83
6.73
7.01
RoiDil [23]
20.95
27.02
29.80
12.52
12,80
12.84
12.99
20.46
24.70
7.76
8.12
8.18
MINDS [14]
20.04
28.70
6.24
MGCLI15) [5]
21.26
28.11
31.93
12.90
13.18
13.24
13.04
20.18
24.75
7,60
7.99
8,03
GODEN (29)
22.01
29.14
33.17
13.34
13.67
13.75
14.08
21.95
26.71
8.09
8.28
8.52
CARE [41]
22.47
32.01
13.35
7.65
MILD (Ours)
24.07
31,33
35.52
15.50
15.85
15.91
14.71
23.37
28.17
8,71
9.10
9.17
Improveeent (%)
47.12
+7.52
+7.08
+6.67
+5.19
+7.14
44.47
+5.47
+7.66
+9.89
+7.63
Experiments
Datasets, We mainly evaluate the performance on two real- world datasets, News and Weibo, including the social network structure, detailed user profiles, and information diffusion cascades. In particular, cascade contains participant IDs with specific participation behavior, timestamps, associated comments, and the original post. Following general settings, we split the cascades in an 8:1:1 ratio for training, validation, and testing the order of post time. Additionally, we further conduct empirical analysis to support our motivations on four widely used datasets: Twitter [9], Douban [40], Android [24], and Christianity [24]. Owing to the absence of textual data (participation behavior, user profiles, the original post, and comments) for I.M reasoning, we only use them for motivation analysis in Appendix A.2.
Table I: Statistics of the used datasets.
Datasets
News
Weibo
# Users
10,255
31,061
# Edges
83,959
294,577
# Cascades
1,291
1,910
Avg Len.
63.45
175.46
Competitors. We evaluate the proposed MILD against eight state-of-the-art models for information diffusion prediction: DyHGCN [37], MS-HGAT [28], DisenIDP [3], RotDiff [23], MINDS [14], MGCL [5], GODEN [29], and CARE [41]. Generally, these methods adopt a two-phase framework- "Graph Cascade"-thae employs GNNs learn various user relations, and then uses RNNs or Self-Attention to learn sequential cascades. Following standard settings [5, 29, 41], we use Hit rate @Hits@k K) and Mean Average Precision (MAP@ K) evaluate the performance of information diffusion prediction. For comprehensive evaluation, we report the results at K E {10, 50, 100). We provide more details of competitors and metrics in Appendix D.2 and D.3.
Implementation Details. In the diffusion path search algorithm, we impose the graph-density GPT-4o with the temperature set to
constraint 1.5 for efficiency. For LLM inference, and top_k set to 1 to ensure the reproducibility of G,, leaving all other parameters at their default values. For the diffusion predictor, model weights are optimized with AdamW at a learning rate of le-3. The number of GAT layers is 1, and the number of attention heads is 6. a defaults to Some hyperparameters are analyzed in Appendix A. We train with mini-batches of size 32, using 256-dimensional embeddings, for up to 50 epochs. All baselines are re-evaluated under their original published settings, with a uniform maximum cascade length of 200 for fair comparison. All experiments are conducted on 2 NVIDIA RTX 1000 (32 GB) GPUs.
4.1 Diffusion Prediction
Table 2 demonstrates that our MILD significantly outperforms eight state-of-the-arr baselines on two real-world information diffusion prediction datasets, achieving average improvements of 6.3% on Hits@ K and 7.4% on MAP@K. Unlike leading methods such as CARE and GODEN, which model social network structure and temporal sequences to implicitly capture patterns, MILD's core distinction is the explicit modeling and integration of a structured diffusion influence graph derived using LLMs. This directly represents the underlying dynamics driving user participation, factor often lacking explicit capture in prior work. These improvements underscore two key insights: (1) LLMS can discern causal influence patterns beyond surface-level statistics; and (2) integrating this influence structure enhances the cascade learner's power by focusing on critical transmission links. Crucially, these gains are achieved without using additional raw contextual data as direct input
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Table 3: Ablation studies information diffusion prediction.
Dutasets
News
Weibo
Metries
H6850
H@
M6:50
HG:50
H@ (0:100
M6
M@
w/o Path Selection
23.14
29.20
33.72
14.53
14.76
11.82
14.33
21.96
27.15
8.44
8.82
8.87
w/o Post Content
23.72
29.98
33.65
14.90
15.21
15.24
14.58
22.87
27.64
8.51
8.96
9.02
w/o Time Information
23.16
30.08
33,97
14.77
14.83
14.36
22.15
26.83
8.49
w/o User Profile
23.77
30.73
34.62
14,96
15.24
15.28
14.52
22.81
27.46
8.52
8.90
8.93
Social biss
22.92
27.64
31,35
14.90
14.33
22.12
26.64
8.45
w/o Inftaence bias
21.81
27.52
30.62
14.03
14.31
14.35
14.08
21.98
26.21
8.26
8.62
8.68
Fall Model
24,07
31.33
35.52
15.50
15.85
15:91
14.71
23.37
28.17
8.71
9.10
9.17
News Dataset
Weibo Dataset
20.25
Jen Wate Deggne
Grach Scale
Depres
Nidea
Sate
0.23
HaRL 18950
11550
Degrne
hodes
Hay 100
Hak
Genint
Laa
Gemie
LLMMA-
DecoSaet
00
40
Th
170
Number Nodes (Graph Scake
Aug. Node Degroz (Graph Density)
Figure 7: Stability across different LLMs.
Figure Runtime of our heuristic algorithm.
for the prediction task. This controlled setting rigorously validates that the predictive power stems directly from the structured diffusion influence representations extracted by our LLM. These findings highlight the value of explicit influence modeling in diffusion and the insights of LLMs.
4.2 Ablation Study
To investigate the contributions of MILD's s components, particularly LLM-basee influence identi- fication and its subsequent integration, we conduct comprehensive ablation studies in Table 3. (1) Ablation on Four Key Factors: We first ablate the four key factors used by the LLM to identify the diffusion influence graph. Removing any single factor-w/o Structure, w/o Post Content, w/o Time Information, or w/o User Prefile-consistently degrades performance, which verifies their necessity in the diffusion influence analysis. The largest performance drop, seen in w/o Structure, highlights the significance of our novel algorithm of potential diffusion pathways. (2) Ablation on Gy: We evaluate whether G1 effectively enhances diffusion prediction performance and more accurately represents the diffusion process than social networks. The w/o Influecce bias variant (removing influence graph integration) results in a significant performance drop, validating the necessity of explicit influence modeling Gy. The w Social bias variant (using simple social adjacency instead of our G1) shows only marginal improvement over w/o Influecce bias. This significant gap between w Social bias and MILD convincingly proves that G, can more accurately represent the diffusion process than social networks, and truly capture the nuanced influence relationships to enhance prediction performance.
MILD across Different LLMs. To evaluate the adaptability of MILD across a diverse range of LLMs, we measure performance six advanced models: Gemini 2.5, Claude 4, LLaMA 3, Qwen 3, Qwen-Tuete Turbo, and DeepSeek RI. As illustrated in Figure 7, MILD exhibits consistently strong performance across all variants, indicating stable behavior under changes in the underlying LLM.
Efficiency Evaluation of our Heuristic Algorithm. We evaluate the computational efficiency of our heuristic algorithm on a range of graphs with varying scales and densities. As shown in Figure 8, our heuristic solution demonstrates strong efficiency, achieving a time cost of 0.0334 seconds per cascade, even on large-scale, dense graphs comprising millions of nodes and an average degree of 120.
4.3 Empirical Analysis on Influence
Influence Intervention. To validate the existence of spurious influences in cascades, we conduct Influence Intervention experiments. Self-attention mechanisms are widely adopted to capture inter- node influence [28, 29, 37]. We randomly mask 1% of the self-attention weights (setting the masked Q_K values to -oo) and observe the results. Interestingly, Figure 9 shows that randomly masking some influences does not eritically impair performance- it even performs better than full attention when less than 15% are masked, indicating the presence of numerous spurious diffusion influences. Therefore, accurately identifying key influences is crucial for enhancing prediction performance. This observation is also evident on the widely used benchmark datasets (see Appendix A.2).

---

News Dataset
Weiho Datasee
Self-Afientood (Bofore) Arg Farrence: 9089
Influence-biar (Ours)
30.0
12.4 26.7
-8-MA1910
dog Varionce: 0.0234
12.2
Opecy
29.0
12.0
26.3
29.3
11.0
28.3
10
20
11.6
25.7
15
Ratlo Influsnco Intervention
Ratio Influence Intervention
Figure 9: Influence intervention.
Figure 10: Attention visualization.
Attention Visualization. To better understand the role of G7, we further visualize the Q_ K attention matrix for case from the Weibo dataset (Appendix A.2 provides more cases). As shown in Figure 10, the left shows self-attention, and the right shows our MILD with influence bias. Furthermore, we also compute the variance of attention weights to provide quantitative assessment. Both the visual patterns and the increased variance indicate that our proposed MILD effectively amplifies key diffusion influences, leading to the significant performance gains in diffusion prediction.
5 Related Work
Information diffusion on social media reflects how users influence one another and propagate opinions across network. Information Diffusion Prediction aims to identify which users will be "infected" by a piece of content, given observed diffusion cascades and the social graph [34, 8, 18, 13]. Recent approaches typically combine GNNs with sequence models capture, respectively, the social network structure and the temporal ordering within cascades [36, 37, 28, 23, 3, 5, 29, 41, 25J. Concretely, GNNs are often used learn homophilous reflecetlc that friends often share interests- while sequence models, such as RNNs or self-attention, encode the dependencies among users within specific cascade. For example, GODEN [29] employs an ODEEbased GNN to track dynamic user relations before applying self-attention to model the cascade sequence. CARE [41] uses a GAT to embed the social graph, and then applies a Transformer for cascade modeling enhanced by retrieved in-context historical cascades to enrich current predictions. However, despite their effectiveness in modeling structure and sequence, these methods often face significant challenges in explicitly distinguishing the nuanced influence mechanisms driving user participation in diffusion process. Furthermore, a common constraint across existing works is relying solely on network structure and basic cascade metadata (user IDs and timestamps). They largely overlook richer contextual signals, such as detailed user profiles, post content, and interaction metadata. In this work, we introduce two new datasets featuring such rich contextual information. Leveraging these datasets, propose MILD, a framework that explicitly exploits and understands the diverse diffusion influences, enabling more explainable prediction and significant performance improvements.
6 Conclusion and Future Work
We propose MILD, a novel diffusion influence inference framework that builds on four diffusion influencing factors and guides LLMs to comprehend and infer the authentic diffusion process, thereby improving diffusion prediction performance. We show that MILD provides a reliable diffusion process analysis that achieves 12% absolute improvement over the social network structures. We conduct extensive experiments on large-scale real-world datasets and verify the effectiveness of MILD. This diffusion influence analysis further contributes better and more explainable public opinion analysis.
Limitations. This work is limited by the availability of accessible real-world datasets composed of user profiles, social network structure, and diffusion dynamics. Due to privacy concerns and government regulations, accessing extensive social and public opinion data has become increasingly challenging. Recognizing the necessity of such datasets, we are dedicated to addressing this limitation by legally constructing novel benchmark datasets in the future.
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Acknowledgments and Disclosure of Funding
This work is supported by the Hong Kong RGC Projects (No. 12200424), the RMGS project (Artificial Intelligence and Big Data Analytics for Social Good), and the National Natural Science Foundation of China (No. 62472304 and No. 62436001). The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the funding agencies. We would like to express our gratitude to the anonymous reviewers for their valuable feedback.
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Question: Are the creators original owners of assets (e.g.. code, data, models), used in the paper. properly credited and are the license and terms of explicitly mentioned and properly respected?
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16. Declaration of LLM usage
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Please refer to our L.M policy http:///aarrae...c/ooooeeeeee//e for what should or should not he deseribed.
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35.5
28.7
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23000000
35.0
13.4
13.
M6 000
25.3
27.7
25
27-
1.0
34.3
16.5
27.3
8.4
1.8
(w) News Dataset
(b) Weibo Dataset
Figure 11: Hyperparameter analysis of information diffusion predictor two real-world datasets.
Twitter Dataset
Douban Dataset
Android Dataset
Christianity Dataset
59.0
59.5
63.0
63.5
2100
335
11.0-
MARC337
114
20.4
26.2
<Bn 303
73
78
36.5-
56.0
-Bn MAR0337
11.
58.5
112
57.5
08.0
23.0
47.5
11.
25.01
35.5
37.9
23.5
16.5
13.
35.5
20
15
20
6.8
$5.0
15
15.0
Rato Influaane Insovvntiiz
Ratoo Influrnce Insorvectinn
Batto Inflannee Intervestion (9)
Ratio Inflanace Intervention (S1
Figure 12: Influence intervention on four widely-used basic datasets.
A Additional Evaluation
A.1 Sensitivity Analysis
As illustrated in Figure 11. we conduct a comprehensive sensitivity analysis two key hyperparameters using both the News and Weibo datasets, which Temperature Factor and (2) Number of GNN Layers L. Each hyperparameter is varied independently while the others remain fixed. Performance trends are evaluated to inform robust settings. (/) Temperature Factor a: This parameter, introduced in Eq. 10, modulates the sharpness of attention weights based on the influence graph. A larger emphasizes the strongest influence connections by increasing the softmax contrast, potentially suppressing sccondary or implicit correlations such as shared preferences among users in the same cascade-thal may still contribute valuable contextual signals. While emphasizing dominant influence paths is beneficial to certain extent, excessive a values risk discarding useful structural information and thereby degrading performance. On the other hand, very small a leads to overly uniform attention, reducing the model's 'ss ability to distinguish key influencers. Empirical results indicate that setting
1 provides a balanced calibration, effectively preserving both focused attention and peripheral contextual relevance. (2) Number of GNN Layers We employ classical GAT encoder for social representation learning, and examine how the number of GNN layers affects performance. Deeper GNNs aggregate information from more distant neighbors, which can, in principle, capture higher-order structural signals and extend homophily-be where node embeddings become indistinguishable and less informative. In experiments. single GAT layer (L = 1) consistently yields the best results. This suggests that in diffusion- most relevant information is often localized within the closest neighborhood. which represents frequent co- participants in cascades, thus making deeper aggregation unnecessary and potentially harmful. We note that other hyperparameters (c.g., hidden dimensionality, learning rate) follow expected trends and exhibit limited sensitivity. Their configurations are reported in the implementation details.
reasoning. However, increasing J. introduces the risk of over-smoothing.
networks, the
A.2 Empirical Analysis on Influence
this paper, we use LLMs to analyze the key influences information diffussion. Widely-used benchmark datasets do not include any textual data for advanced LLMs, and only contain a social network structure and basic cascade metadata (participant IDs and timestamps). Therefore, we analyze these datasets here, as in Section 4.3, verify our observation that there is an imbalanced diffusion ability for different social actors within cascades. To empirically assess the necessity and robustness of the causal influences, we introduce controlled intervention experiment. Specifically, for a given cascade, we randomly select a fraction of patticipantto-parriiiaaa influence edges and set their corresponding attention scores to - Do, eliminating these links from contributing to the diffusion dynamics modeled by the attention mechanism. We then evaluate how this partial influence masking affects the performance of the downstream diffusion prediction task. As illustrated in Figure 12, we observe a counter-in counter-intuitive but insightful result: moderate levels influence masking, particularly at intervention ratios below 15 15%, do not degrade model performance. In fact, across all four benchmark datasets, slight performance improvements are consistently observed under such interventions. This phenomenon suggests that many influence relations in social cascades either spurious redundant. While some users play critical roles
19

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Self AelfAntttio
Influcnce biis
Self-Ananiin
Inflonce
Sell-Aitctiin
Infuesce bas
Self Attetion
Infleccce bas
Figure 13: Attention Visualization (Q K): Self-Attention vs. our MILD with influence bias.
Table Performance on information diffusion prediction. The higher scores are better.
Datasets
News
Weibo
Metries
IIGP 10
11@50
11@ 100
MG 10
M0
M6 100
I1@10
11@50
11@) 100
M6 10
M6:50
M6 100
DyHGGN [37]
24.50
27.31
10.76
6.23
Standard Deviation
1.12
1.89
+ 1.45
+ 0.33
+ 0.41
+ 0.36
0.56
+ 0.66
+ 0.74
0.42
+ 0.47
0.35
MSHGAT (28)
20.10
25.82
28.85
11.68
11.95
11.99
11.41
18:34
21.77
6.16
6,48
6.53
Standard Devistion
0.98
= 1.25
+ 1.03
+ 0:47
+ 0.43
0.39
0.72
+ 0.67
+ 0.75
0.34
# 0.42
0.39
DiscalDP [3]
20.47
26.33
29.08
12.03
12.29
12,36
12.04
18.83
22.61
6.73
7.01
7.06
Standard
+.50
+ 0.13
0.09
1.37
+
0.47
RodDiff [23]
20.95
27.02
29.80
12.52
12.80
12.84
12.99
20.46
24.70
7.76
8.12
8.18
Standard Dovistion
1.30
0.69
0.79
MINDS [14]
20.04
25.66
28.70
11:72
11.93
11.98
11.69
18:07
21.66
6.24
6,51
6.57
Standard Deviation
0.89
1.10
+ 1.06
+ 0.2.5
1: 0.30
0.28
1.25
4: 1.54
4: 1.67
0.61
+ 0.78
0.71
MGCL [S]
21.26
28.11
31.93
12.90
13.18
13.24
13.04
20.18
24.75
7.60
7.99
8.03
Standard Deviation
1.67
1.58
:: 1.72
4. 0.54
4: 0.48
+: 0.63
1.40
d: 1.92
4: 1.88
+: 0.31
4 0.37
0.35
GODEN (29)
29.14
33.17
14.08
26.71
Standard Deviation
1.15
= 1.29
=: 1.68
+: 0.86
1: 0.79
+: 0.90
=: 1.34
+: 1.53
+ 1.44
= 0.67
=: 0.66
= 0.61
CARE
22.47
28.71
32.01
14.53
14.81
14.85
13.35
21.96
26.62
7.65
8.05
Standard Deviation
1.16
= 1.38
:: 1.33
1 0.68
4. 0.74
0.76
1.58
1: 1.82
4: 1.79
0.37
1: 0.34
MILD (Ours)
24,07
31.33
35.52
15.50
15.85
15.91
14.71
23.37
28.17
8.71
9,10
9.17
Standard Deviation
1.10
0.61
1.23
+
0.53
propagating information, others are likely peripheral participants whose modeled connections may introduce noise rather than signal. These findings strongly support our core hypothesis: the effectiveness of modeling information diffusion can be substantially improved by identifying and prioritizing key influences while suppressing inconsequential ones. This experiment serves an empirical validation of our influence-centric design: fine-grained representation of selective influence, rather than dense or fully-connected modeling assumption, yields more faithful and efficient representation of real- world information diffusion dynamics.
A.3 Experiment statistical significance
The dataset is divided according to the chronological order of events and cannot be shuffled. In real applications, we only past information diffusion events predict future events and avoid label leakage. Therefore, randomly selected five seeds for statistical significance. We clearly calculate the standard deviation. shown Table the experimental results show that our MILD consistently and stably outperforms eight baselines.
B Algorithm Details
B.1 Potential diffusion path search
The detailed diffusion path search algorithm can found Algorithm 1. Lines 1-2 conduct single-souree BFS algorithm with the original participant i as the single source, which returns the BFS tree Tars. Tars is composed of shortest paths between and E Ve. satisfying (DI) and (D2). For each shortest path in Taes. the algorithm filter the long shortest path & with length greater than E (Lines 3-4). Considering the efficiency.
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Algorithm Potential Diffusion Path Search.
Require: A cascade graph Ge Ec), the graph density constraint r, the threshold of shortest
path L.
Ensure: v E \V satisfies the requirements (DI), (D2) and (D3). Select the original participant vi as the source node;
2: TEFS shortest paths between i and 2s Vo \ v1 by single-source BFS;
3: for v E TBFS do
4: if | 2 &thnn
5:
Calculate the graph density of Ge by d = |Vel/| (Details in Appendix B.3) 6: Select the source s and the target in et; if 2 r then
7:
8:
(1) simple + fu/lus + Vo,, Vy .. E Gc} from s by DFS;
9:
U {1b jaimpette
else
11:
(1) shortest +
select all shortest paths from 8 to by BFS;
12:
Jhorteeti
13:
else
if Vo; E & and o $ v then
15:
L
16:
return V;
Line 5 calculates the graph density of Ge based on analysis in Appendix B.3 to control the time complexity of searching all possible paths. Firstly, the algorithm selects the source and target r of the filtered th. Then, conduct the DFS algorithm to find all simple paths between and if 2 and add them into v (Lines 7-9). d S r, conduct the BFS algorithm to find all shortest paths between s and 7 d 2 and add them into (Lines 10-12). If & is short shortest path, add & into V if any nodes in v are excluded by v (Lines 13-15). Finally, line 16 returns the satisfied V.
B.2 User Influence and Activity Levels Estimation
The estimation process of user influence and activity levels can be divided into four steps: key user attributes selection from user profiles. min-max normalization of the selected attributes, influence and activity values estimation, and assigning specific levels based on the estimated values.
1st step: key user attributes selection from user profiles. Based on well-known communication theory, we select the key user attributes. The details are as follows.
Follower Number (æ:) directly reflects user's network centrality, aligning with the scale-free feature described in complex network theory (Barabási-Alue model))2). Users with high number followers act as hub nodes that can trigger cascaded propagation, and the influence range follows a power-law distribution.
Bi-followers Number (x2). Based on the theory of strong ties (Granovetter) [7], mutual relationships represent bidirectional trust links, and such connections have higher conversion rate in information diffusion.
Published Statuses Number (æ3), which is in accordance with the attention economy model [4]. High- frequency publishers occupy users' attention bandwidth through content streams, thereby establishing temporal advantage.
Verified as an influential user by online platform (r.)).
2nd step: Min-Max Normalization of the selected attributes. For each of the above selected attributes, normalize the value all users based on min-max normalization follows.
Tscoled
(11)
Zmax
Trii
3rd step: Influence and activity estimation. Based on the normalized attrihutes, we calculate the influence and activity values of cach user. For influence values, assign the normalized value of the follower number as the influence value. For activity value, we calculate follows.
f (x) W272 + W3333 + 204744
(12)
where are the hyperparameters designed based on the above communication theories, which are we 0,1, wa 0.8, = O.I, respectively.
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namely 4th step: Assigning specific levels based on the estimated values. We assign specific levels for each estimation, ie.. 0-20%: poor, 20%-40%: low, 40%-80%: moderate, 80%-95%: high, 95%-100%; outstanding.
B.3
Graph Density Calculation in Diffusion Path Search Algorithm
The graph density calculation in Algorithm follows E. Lawler (1976), Combinatorial Oprimization: Networks and Matroids [17]. The formulation is:
graph density
(13)
[V
where |E] is the number of edges) and [V] is the number of nodes. This calculation formulation is closely relevant the time complexity analysis Section 3.2.
C Theoretical Analysis
C.1 Back-door Adjustment of Existing Methods
According the SCM, the statistical distribution P(Y(C) has following mathematical expression.
P(YIC) = Σ P( EEPre))(CC)))))))
(14)
The key capture the causal relationship between and Y. From the perspective of causal inference, we can achieve this via modeling P(Y (d((C), where do(C) denotes the do-calculus operation and introduces an intervention on C. Specifically, do(C") removes links from U to C and blocks associative paths from C' to Y apart from the direct causal one C - Y. We employ the basic back-door adjustment to estimate P(Y do(()) below.
P(Y]do(C)) Σ P()) NEU
(15)
However, the above equation does satisfy the backdoor condition since the ussociations between both C <- U and + are unobserved. Thus, the variable U is unobserved and implicit. Hence, U cannot be used block the backdoor path from Y. There no way to estimate P(u) and P(Y|C, u). The causal effect of historical cascade on future participants is not identifiable in this model.
C.2 Front-Door Adjustment of Our Method
We add the transparent diffusion influence as the intermediate variable Z between C and Y as shown in Figure 2. satisfies following front-door criterion: (C1) Z intercepts all directed paths from Y. (C2) there is no unblocked back-door path from C' to Z. and (C3) all backdoor paths from Z to Y are blocked by C. The (CI) condition requires Z to represent the nature of the cascade that provides necessary and sufficient information for predicting the next participants Y, and the (C2) and (C3) conditions suggest that only the observed cascade sequence C can be used to estimate the causal relationship C Z, the backdoor path from + + + Y, can be blocked by conditioning on C.
Based on the above conditions, we can formulate our model by chaining together the two partial effects and summing over all states of as follows If the do-calculus is performed on Z, the probability of Y is P(Y)do( Then, if the do-calculus is performed on X, the probahility of conducting the do-calculus of Z is P(Z(do(z))-
P(Y]do(C)) = Σ P(Y(do(Z))P(((a((()) (CI)= Σ P(Y)do(2))P((II) (C2)
ZEZ
ZEZ
EΣ Σ PVIZZC"))(CC)(((II (C3),
(16)
zEZ GEC
where C' contains all observed cascade sequences in training data, denotes the specific diffusion influence matrix in Z.
C.3 MILD Under Causal Framework
MILD is strictly designed to satisfy three front-door criteria in the causal framework to make more accurate diffusion prediction. (C1) Z intercepts all directed paths from C' Y. When Z can represent the information
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difffusio itself, Z can intercept all directed paths from to Y. To achieve it, MILD captures almost all necessary and sufficient diffusion information to derive Z based communication theories to make sure that Z can represent the nature of the information cascade. (C2) there is no unblocked back-door path from to Z, and (C3) all backdoor paths from Z to Y are blocked by C. MILD extract observed information cascades from the real-world social platform as C' to block the backdoor path from Z to Y, which is Z + C + U Y. satisfying (C2) and (C3).
C.4 Do-operation analysis of MILD
P(Y contains two do-operations, which can be formulated as P(Y P(Y))((C) based on the front-door criterion (CI), In MILD, do(C) is to select
Σ P(Y ( #E2
several users who can form an observed information cascade, forcing = c. do(Z) operation is to derive diffusion influence representation & based on given interventions, which are designed potential diffusion paths t. temporal order T, user influence and activity levels O, and comments B from specific cascade c, forcing LLM to derive Z 2. In the Z space, given the observed cascade without interventions, Z contains all possible random diffusion processes. Thus, P(Z do)))) can be assumed as P(z]do(C)) . 2 E Z. With interventions of Z, P(Y]do(Z)) is the probability of Transformer prediction Y conditioned our derived diffusion influence graph = Gr.
C.5 NP-Complete Proof of Hamiltonian Path Problem
Problem Definition, A Hamiltonian Path in graph is a path that visits each vertex exactly once, Given graph G (V, E), the Hamiltonian Path Problem (HPP) asks whether there exists such a path in G. If the path starts and ends at the same vertex, it is called a Hamiltonian Cycle.
Proof. As with any NP-completeness proof, this one has two parts. First, we will go over why Hamiltonian Path is in the NP class. To be in NP means that, given a proposed solution (a certificate) to the problem, we can verify the solution in polynomial time. In this case, that means that given a directed graph C and path between 2 vertices, can check in polynomial time if the path is Hamiltonian Path.
Step 1: Proving Hamiltonian Path is in NP. To show that HPP in NP, we need prove that a given solution can verified in polynomial time. Suppose we are given a certificate (a sequence of vertices). Then, we need to check two constraints: (1) The sequence contains all vertices exactly once. (2) There exists an edge between each consecutive vertex in the sequence. For time complexity analysis, if we check edges in an adjacency matrix, the verification takes at most ( time. While, if we check edges in adjacency lists, the verification takes most O(VV) + [E)) Thus, we can know that the verification be processed in polynomial time. Since the verification is polynomial, HPP belongs to NP.
Step 2: Proving Na-Hards To prove HPP NP-Hard, we reduce a known NP-Complete problem to it. standard reduction is from the Hamiltonian Cycle Problem (HCP), which is already NP-complete. Thus, we give the following explanations of the reduction from Hamiltonian Cycle to Hamiltonian Path. Given graph G = (V, E), we need to check it for Hamiltonian Cycle. The goal of the reduction is the transformation of modifying G to construct a new graph G'. First, we pick an arbitrary vertex E V. Then, we remove v from G, resulting in graph G', After transforming G, we can claim as follows,
Claim: G has a Hamiltonian Cycle if and only if G' has a Hamiltonian Path.
Here, we prove this claim and analyze that this reduction can be done in polynomial time. If G has a Hamiltonian Cycle, removing e will break this Hamiltonian Cycle into a Hamiltonian Path. Conversely, if G" has a Hamiltonian Path, adding e back can reconstruct Hamiltonian Cycle. This transformation is done in polynomial time, proving that HPP at least as hard as HCP. Since HCP is NP-Complete, and we have reduced it HPP in polynomial time, it follows that HPP is NP-Hard.
We prove HPP is in the NP class and is harhard. Thus, HPP an NP-complete problem.
C.6 NP-hard Proof of All Simple Path Problem
Problem Definition. Given graph G = (V, E), simple path is path in G that does not repeat any vertex. Given two random vertices in G as the source and target r, find all possible simple paths between and in G.
Proof. To prove that All Simple Path Problem (ASPP) is an NP-hard problem, we reduce proved NP-complete problem to it. As proved Appendix C.5, the Hamiltonian Path an NP-complete problem. Thus, we give the following explanations of the reduction from the Hamiltonian Path to All Simple Paths. Given a graph G = (V, E),, we need to check it for a Hamiltonian Path.
Claim: If you could find all simple paths between two nodes, you could determine if there is a Hamiltonian path between them by checking if any of the paths visit all the vertices.
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We explain this claim as follows. First, we construct an arbitrary instance of HPP. We choose any two vertices and / in G. Then, determine if there is Hamiltonian path starting at and ending t. Second, list all simple paths from s to and check if any these paths visit vertices exactly once. If such path exists, a Hamiltonian path. The ability to find all simple paths allows us to solve the Hamiltonian Path problem by simply checking the length of cach path. Hence, solving the problem of finding all simple paths would solve the Hamiltonian Path problem. This reduction from HPP can be done in polynomial time, which proves that ASPP NP-hard, HPP proven NP-complete problem.
C.7 NP-hard Proof of Diffusion Path Search Problem
Problem definition. Given cascade graph Ge (Ve, Ec)) with unique root vi, the problem returns a collection of path structures v S Gc. There are three constraints. (DI): paths db E start from the unique root 01. (D2): Ve covers all nodes in Ve. (D3); v contains all possible path between i1 and v E {u, (iiisss(v1, v.) 2 f).
As all paths in this paper are non-loop paths with no repeated nodes, the Diffusion Path Search Problem (DPSP) similar to the All Simple Paths Problem (ASPP). The proof of NP-hardness of DPSP is also similar to the proof of ASPP, which is Appendix C.6.
Proof. To prove that DPSP is an NP-hard problem, we reduce the proved NP-complete problem it. As proved Appendix C.5. the Hamiltonian Path is an NP-complete problem. If we can prove that a polynomial-time reduction exists from the Hamiltonian Path Problem (HPP) to the Diffusion Path Search Problem (DPSP), we prove the DPSP is an NP iP-hard problem. Thus, we give the following explanations of the reduction from the Hamiltonian Path the Diffusion Path. Given a graph G (V, E). we need check for Hamiltonian Path.
Claim: If you could find diffusion path set y/ between Hamiltonian path between them by checking if any of the path in vi visit all the vertices.
nodes and T. you could determine if there is
We explain this claim follows. First, we construct an arbitrary instance of HPP. We choose the same graph Ge and two vertices and t Gc. Second, we use an algorithm for the diffusion path search problem to list all potential diffusion paths in Vi between s and t. Then, we check if any enumerated path in v has length (where n = VcD. If such path exists, Ge contains Hamiltonian path. Otherwise, it does not.
Based on the above steps, we can find that the reduction requires modification to C. so it runs in ((1) time. The reduction can be done by simply checking the length of each path. Thus, it a polynomial-time reduction. While enumerating all paths may take exponential time, the reduction assumes the existence of a polynomial diffusion influence path search problem oracle. If such an oracle existed, solving the Hamiltonian Path Problem would also take polynomial time (contradicting its NP-completeness). Thus, the diffusion influence path search problem must be NP- hard.
C.8 Diffusion Influence Degree Proof in Robustness Evaluation
Here, we give the proof of the path diffusion influence degree.
Proof. Based on the chain rule of conditional probability, given diffusion path s (un, 12, Nh) with nodes, can easily obtain the diffusion influence degree of the whole path eb. which can be formulated as
P(v)=
II P(es/re....... P(r)) IKi5a
(17)
An information diffusion path indicates the predecessor passing the information to the successor. For example, given diffusion path t2,, vz). vi passes the diffusion influence to ey solely through v2 within this path, which means and vs are conditionally independent uy. Generally, v and 6i+1 are conditionally independent on v, Thus, the Equation 17 can be simplified as
P(V) = II P(os/ox-1,..,.:)) P(vi) = II P(cs)))
(18)
1685
D Details of Experimental Setup
D.1 Datasets
We conduct our experiments on two real- wolld datasets harvested from Weibo [38, 1J. leading Chinese microblogging platform. We refer to these two corpora as News and Weibo, detined as follows:
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News. This dataset consists of all repost cascades initiated by the official Weibo account "Daily News". social network structures and profiles. Each cascade captures the reposting timeline, interactions, and comment threads triggered by a single news post.
Weibo. This dataset contains social network structures, user profiles, and numerous repost cascades published by five randomly chosen opinion leaders the Weibo platform, one from each domain: sports, entertainment, technology, society, lifestyle. These hub influencers exhibit heterogeneous diftusion patterns due their distinct audience profiles.
Here, detail the data preprocessing methods applied News and Weibo, focusing primarily on user profile features, social graph construction, and cascade formation.
User Profile Features For every involved in cascade, extract the following 13 profile attributes:
bi_followers_com count
Number of mutual followers
verified_statiee
Boolean, official verification flag
followers_come location, province, city frienda_count
Total follower count
Self-declared geographic metadata
Number of followees
name, gender
Display name and gender
created_time verified_typo Statuses_coume
Account creation timestamp
Verification category (e.g- personal, media)
Total number of posts published
description
welftwritten bio text
Social Graph Construction We model the "following" relations among users as a directed graph G = (V, where each node v V is user and each edge (u - v) E & indicates that u follows v. This graph underpins all diffusion processes analyze.
Cascade Formation Each original post is treated information unit. To assemble a diffusion cascade, we
record for every participant: (1) The type of behavior (repost, comment, like); (2) The timestamp of the behavior; (3) Any textual content of comments. These elements yield temporally ordered cascade C { t,, o.) 1=b where u, the user, f, the action time, and a, the action type.
Table 5: Statisties of the four widely-used datasets.
Twitter
Douban
Android
Christianity
Users
12,627 309,651
12,232
9,958 48,573
2,897
Links
396,580
35,624
Density (9)
24.52
30.21
4.87
12.30
Cascudes
589
Avg. Len.
32.60
21.76
33.30
22,90
Densiry (%)
6.18
4.66
addition our News and Weibo datasets, the supplemented empirical evaluation, we benchmark against four widely used public diffusion collections, including Twitter [9], Douban [40], Android [24], and Christianity [24]. Each dataset comprises an underlying social network and a set of basic cascades, where each cascade records only user IDs and their timestamps. Table 5 presents the descriptive statistics for these benchmarks.
D.2
Competitors
Most existing methods for diffusion prediction adopt a two-phase framework: GNNs sequence models. In this setting, graph neural networks learn structural representations from social or diffusion graphs, and sequential models (e.g., RNNs or transformers) model cascade dynamics over time. We summarize the representative baselines as follows:
DyHGCN [37] builds dynamic heterogencous graph by combining the social network with historical diffusion paths. A heterogencous GCN captures time sensitive node embeddings, followed by multi-head self-attention model cascade-level dependencies.
MS-HGAT [28] represents diffusion history using timestamped hypergraphs and learns user embeddings through hierarchical attention. It integrates static social links with dynamic cascades using gated memory modules.
DisenIDP [3] disentangles user intent by constructing dual hypergraph networks, Intent-specific embeddings are generated and aligned using self supervised losses, allowing inn-inaieed modeling of diffusion factors.
25

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RotDiff [23] maps users into hyperbolic space, where Lorentzian rotations encode asymmetric influence patterns. Rotated self-attention captures hierarchical dependencies for cascade prediction.
MINDS [14] introduces multi-scale hypergraph learning jointly capture micro- and macro-level cascade patterns, An adversarial alignment module ensures cross-scale consistency.
MGCL [5] applics contrastive learning to suppress noise from low-quality graphs. Multiple structural views are generated, and agreement is enforced via contrastive objectives to enhance embedding quality.
GODEN [29] formulates diffusion continuous- process using neural ODEs. Two coupled ODEs evolve node and edge states, which are fused with timestamp-aware attention for temporal prediction.
CARE [41] enhances prediction by retrieving semantically similar historical cascades. These retrieved instances are encoded via a transformer to support sirteval-augmenter diffusion modeling.
D.3 Evaluation Metrics
To assess the accuracy of predicting the next participant in diffusion cascade, adopt two widely- used ranking metries of the diffusion prediction task: Hitx@K K and Mean Average Precision@ K (MAP@K), Hits measures the recall a fixed cutoff, i.e. the fraction cascades for which the true participant appears among the top K predictions. While MAP@ K further penalizes late placements by weighting each hit by the inverse of its rank, thus evaluating the quality of the ordering within the top- K list.
Formally, let N be the number of test cascades, and for each cascade let u, denote the ground-truth next participant and
U: = [ ai. KG
be the ordered list of top-K predictions. Define the rank function
if ühr for some S K, 00, otherwise,
rank(u:) =
and the indicator [|]. Then:
Hits@K
(rank(us) s K].
(19)
N
1=1
1
[rank(u (w,) < K
MAP@К
(20)
N
rank(u) (w.
By combining these two metrics, we capture both the ability to include the true user within limited prediction budget and the precision with which it is ranked among the top candidates.
E Prompt Design
Prompt design in MILD. We design the prompt to instruct the LLM to analyze the diffussin influence between users within each cascade. The potential diffusion path & E V, temporal order 7', descriptions of user influence and activity levels O, and comments B are integrated into the designed template Φ(-). forming prompts (1b, T, O, B3 provide sufficient information for analysis. To guarantce the reliability of the derivation, add common sense information diffusion to design the instruction. For instance, the latter participants do not influence the earlier participants. The detailed prompt can be found in Appendix Figure 14.
Prompt design in measurements of Gr. In Rohustness Evaluation, we construct real and fake diffusion paths within cascades, and design the misleading instructions to lead the LLM into believing that all paths are real to analyze the influence degree. For each cascade, we create multiple real and fake diffusion paths. We randomly select one user out the real path to replace one user in the real path to create the fake diffusion path iterate it several times. We then mix all paths as real diffusion paths. Then we instruct the LLM to analyze the diffusion degrees of cach edge in each path. The detailed prompt can be found in Appendix Figure 15.
Prompt design in ablation studies. We conduct ablation studies to evaluate the necessity of the four key diffusion influencing factors. For each ablation study, remove the relevant factor from the prompt. For instance, if evaluate the necessity of temporal order, change the original prompt ( T, B) (16, O, B) as the prompt for the ablation study the temporal order. The detailed prompt can be found in Appendix Figure 16. The prompts without user profiles and shared comments are similar to the prompt without temporal order. Particularly, for the ablation study without our potential diffusion pathways, we use all shortest paths in Tars replace the potential diffusion paths in the original as ((v T, O, B). where e denotes the shortest path. The detailed algorithm can be found Section 3.2 and Algorithm
26

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Figure 14: Example Prompt for Diffusion Influence Deriving
SYSTEM
[English Version] Please identify all possible pairs of users that may have influence, considering the chronological order of replies, potential influence pathways, user influence activity, and user reply content. Note: 1. Users who reply earlier in the chronological order will not be influenced by later respondents; 2. Only the influence between the given user IDs will be analyzed. Use standard list format, and do not provide any text. Respond with pairs of user IDs in the following format: I..].
[Chinese Version| in 1i de P FET (F) A f & lnl & BiJ [a] NU Y mijj f.t. H M JJ HI ER
H lal
H A YE 1. H: B BE Sel PI AR i2 t
MH F ME 2. 2. uuser idZ Mi P It. 1E
user
id FX + La Pu
[[..1......
USER
English Version]
Reply timeline based on user IDs: '[4459',, '28931', '6603'].
Potential influence path: '['4659', '6603', '28931']".
User influence and activity levels:
User 4659; outstanding influence, outstanding activity level.
User 6603: high influence, high activity level.
User 28931: high influence, moderate activity level.
Comments published by each user: 4659: "Yi Siling wins the first gold medal at the London Olympics."
6603: "Watching this made my heart race! [Touched by the victory] [Thumbs up] [Thumbs up]." 'Especially that moment of overtaking."
28931:
[Chinese Version]
f id B 1= 4659", '28931', '6603') TE A fe: 4659', '6603', '28931"]
H uuñ 1
46 75 6603
28931 +F
# و #
46591 (e
6603 15 C CA
|1
28931 15 #1
ASSISTANT
[[4659, 6603), [4659, 28931], [28931, 6603]]
27

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Figure 15: Example Prompt without Temporal Order
SYSTEM
Please identify possible pairs users that may have influence, considering potential influence pathways, user influence and activity, and user reply content. Note: Only the influence between the given user IDs will be analyzed. Use standard list format, and do not provide any text. Respond with pairs of user IDs in the following format: II.........
USER
Potential influence path: ''4659", '6603', '28931']".
User influence and activity levels:
User 4659; outstanding influence, outstanding activity level.
User 6603: high influence, high activity level.
User 28931: high influence, moderate activity level.
Comments published by each 4659: "Yi Siling wins the first gold medal at the London Olympics."
6603: "Watching this made my heart race! [Touched by the victory] [Thumbs up] [Thumbs up]."
28931: "Especially that moment of overtaking."
ASSISTANT
[4659, 6603), [6603, 28931]]
Figure 16: Example Prompt and Fake Diffusion Paths
SYSTEM
Please analyze diffusion influence degree for each edge the diffusion path, with value range of [0.1]. The difference in propagation influence degrees within the same propagation path should not exceed 0.2. Carefully examine whether the content published by intermediate users discusses the same topic, there may he false propagation paths. Respond in standard JSON format, without any additional text, follows: [fddee [...,...]: influence_vale palueeeeevelueeee ...)...]
USER
Potential influence path: '''459'', '17264', '11799'].
Comments published by each user:
4659: "Lin Dan staged dramatic comeback against Lee Chong Wei to claim China's 26th gold medal." 17264: "Woooahhh (tarss] Such an emotional victory! This was so hard haud-fought!"
11799: "[Thumbs ullmmpp gold mevel][Moved by the win]."
ASSISTANT
[[edge [4659, 17264], influence_vall value 0.8), edge [17264, 11799), influence_ value 0.9)]
28


Reviews:
[{"review_id": "moHDFL88DX", "reviewer": "Reviewer_FSjJ", "summary": "This paper addresses the problem of information diffusion prediction. Noting the limitations of prior work based on graph neural networks and sequence models—particularly their lack of interpretability—the authors propose a Large Language Model (LLM)-based causal framework for diffusion influence derivation (MILD). The framework integrates four key factors underlying social diffusion dynamics. Experimental results demonstrate that the proposed approach outperforms traditional methods in both predictive performance and interpretability.", "questions": "About LLMs: Can the proposed method be adapted to use other open-source LLMs? Additionally, does the prompt design require few-shot examples to achieve good performance?\n\nAbout the causal mechanism: Beyond inspiring the use of LLMs to derive the diffusion influence graph, does the causal framework serve any additional role in the model? How is the do-operator concretely instantiated within the model architecture or inference process?\n\nOn Equation 10: Why do the authors choose to inject the diffusion influence using a +\\alpha A formulation instead of a masked A formulation? What are the advantages or motivations behind this design choice?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.\tThe motivation of the paper is sound. Building on the observation that traditional models lack interpretability, the authors propose a causal inference framework enhanced by large language models (LLMs), which is a well-founded approach.\n2.\tThe paper is well-written and easy to follow.\n3.\tThe authors conduct extensive experimental analysis, including comparisons with a wide range of baselines, ablation studies, and empirical evaluations, making the results relatively solid.\n4.\tThe proposed MILD model demonstrates clear improvements over many baseline methods.\n\nWeaknesses:\n1.\tThe core idea of the paper is essentially to leverage LLMs to capture a diffusion influence graph, which is then used for downstream prediction. However, I remain unconvinced about the effectiveness or necessity of the causal inference aspect as claimed. (See Questions)\n2.\tThe discussion around the use of LLMs is somewhat insufficient. It would be beneficial to explore different LLM variants (e.g., open-source models), and to elaborate on the prompt design—such as whether few-shot prompting is necessary.\n3.\tThe paper lacks analysis of important hyperparameters, such as the influence of alpha.", "was_revised": true, "final_justification": "I am positive about this work from the very beginning. The clarification made by the author further justifies my decision. I keep my score.", "rebuttal": "We are deeply grateful for the positive comments and insightful feedback. We hope that the following clarifications are helpful for your concerns.\n\n---\n\n### **[W1&Q2] Role of Causal Framework**\n\nThe causal framework is integral to our model's design. We clarify the additional role of the causal framework in MILD and the concrete do-operation in the model architecture.\n\n**1. MILD Under Causal Framework:**\n\nMILD is strictly designed to satisfy three front-door criteria in the causal framework to make a more accurate diffusion prediction. (C1) $Z$ intercepts all directed paths from $C$ to $Y$. When $Z$ can represent the information diffusion itself, $Z$ can intercept all directed paths from $C$ to $Y$. To achieve it, MILD captures almost all necessary and sufficient diffusion information to derive $Z$ based on communication theories to make sure that $Z$ can represent the nature of the information cascade. (C2) there is no unblocked back-door path from $C$ to $Z$, and (C3) all backdoor paths from $Z$ to $Y$ are blocked by $C$. MILD extract observed information cascades from the real-world social platform as $C$ to block the backdoor path from $Z$ to $Y$, which is $Z\\leftarrow C\\leftarrow U\\rightarrow Y$, satisfying (C2) and (C3).\n\n\n**2. Do-operation analysis:**\n\n$P(Y|do(C))$ contains two do-operations, which can be formulated as $P(Y|do(C))=\\sum\\limits_{z\\in Z} P(Y|do(Z))P(Z|do(C))$ based on the front-door criterion (C1). In MILD, $do(C)$ is to select several users who can form an observed information cascade, forcing $C=c$. $do(Z)$ operation is to derive diffusion influence representation $z$ based on given interventions, which are designed potential diffusion paths $P_C$, temporal order $T$, user influence and activity levels $O$, and comments $B$ from specific cascade $c$, forcing LLM to derive $Z=z$. In the $Z$ space, given the observed cascade $c$ without interventions, $Z$ contains all possible random diffusion processes. Thus, $P(Z|do(C))$ can be assumed as $P(z|do(C))=\\frac{1}{|Z|}, z\\in Z$. With interventions of $Z$, $P(Y|do(Z))$ is the probability of Transformer prediction $Y$ conditioned on our derived diffusion influence graph $z=G_I$. \n\nAdditionally, we also conducted an ablation study (in Table 3) of the comparison of our $do(Z)$ operation and other random $z\\in Z$. We replaced our $do(Z)$ operation with random $z\\in Z$ (*w/o Influence bias*) and with social graph $U$ (*w Social bias*), leading to a significant drop in performance, confirming the critical role of $do(Z)$ operation and our causal framework. More detailed analysis can be found in _Appendix C.1 and C.2_.\n\n---\n\n### **[W2 & Q1] Adaptability to LLM Variants and Prompting Strategy**\n\nThank you for your professional suggestions! Following your advice, we conducted additional experiments on LLM variants and few-shot prompting, and we will include these results in the final manuscript.\n\n**1. Performance on Diverse LLMs:**\n\nMILD can be effectively adapted to a wide range of LLMs. We evaluated its performance using six different models, including four open-source alternatives. The results below show that the performance is robust across all variants.\n\n| **News Dataset**      | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n| --------------------- | -------- | -------- | --------- | -------- | -------- | --------- |\n| **GPT-4o (reported)** | 24.08    | 31.31    | 35.50     | 15.49    | 15.87    | 15.92     |\n| Gemini 2.5            | 23.91    | 31.13    | 35.32     | 15.38    | 15.71    | 15.82     |\n| Claude 4-Sonnet       | 23.97    | 31.19    | 35.42     | 15.46    | 15.78    | 15.86     |\n| LLaMA3-70B            | 23.58    | 30.28    | 34.36     | 15.21    | 15.31    | 15.34     |\n| Qwen-turbo            | 22.92    | 30.06    | 34.08     | 14.74    | 15.24    | 15.29     |\n| Qwen3                 | 22.89    | 29.87    | 33.88     | 14.69    | 15.02    | 15.16     |\n| DeepSeek R1           | 22.56    | 29.91    | 33.94     | 14.68    | 15.11    | 15.17     |\n\n\n| **Weibo Dataset**     | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n| --------------------- | -------- | -------- | --------- | -------- | -------- | --------- |\n| **GPT-4o (reported)** | 14.73    | 23.34    | 28.18     | 8.70     | 9.09     | 9.15      |\n| Gemini 2.5            | 14.66    | 23.33    | 28.12     | 8.64     | 9.06     | 9.16      |\n| Claude 4-Sonnet       | 14.65    | 23.31    | 28.07     | 8.63     | 9.08     | 9.10      |\n| LLaMA3-70B            | 14.25    | 22.92    | 28.00     | 8.40     | 9.00     | 9.06      |\n| Qwen-turbo            | 14.20    | 22.61    | 27.93     | 8.24     | 8.66     | 8.73      |\n| Qwen3                 | 14.28    | 22.73    | 27.90     | 8.13     | 8.14     | 8.23      |\n| DeepSeek R1           | 14.31    | 22.80    | 27.94     | 8.08     | 8.11     | 8.14      |\n\n\n\n**2. Few-Shot Prompting:**\n\nWe further conducted experiments of few-shot prompt engineering and found that **few-shot prompting is an effective prompt engineering technique, but may not be necessary for our MILD**.\n\nWe evaluate 0-shot, 3-shot, and 5-shot prompting on the News Dataset as follows:\n\n| **Prompt Type** | **H@50** | **M@50** |\n| :-------------- | :------- | :------- |\n| 0-shot          | 0.3133   | 0.1585   |\n| 3-shot          | 0.3029   | 0.1501   |\n| 5-shot          | 0.3016   | 0.1467   |\n\nWe observed a moderate performance decrease with few-shot examples for two primary reasons:\n\n*   **Confused by Noisy Patterns:** The complexity of real-world information diffusion cannot be easily captured in a few examples. Providing shots may bias the LLM toward simplified or incorrect patterns.\n*   **Increased Hallucination:** We found that with few-shot examples, the LLM was more likely to hallucinate user IDs or relationships from the examples rather than reasoning based on the provided cascade data.\n\nGiven these findings, our zero-shot prompt, which is carefully designed based on communication theories, proves to be the most robust and effective approach.\n\n---\n\n### **[W3 & Q3] Hyperparameter $\\alpha$ and Injection Formulation**\n\nThank you for your careful reading and the insightful question about the injection formulation in Eq.(10) in Section 3.4. \n\n**1. Hyperparameter Analysis for $\\alpha$:**\nWe recognize the importance of this hyperparameter. In **Appendix A.1 (Figure 9)**, we have provided a sensitivity analysis for $\\alpha$. The results show the model's performance across a reasonable range of $\\alpha$ values (0.5 to 1.5).\n\n**2. Rationale for $+\\alpha A$ Formulation:**\nWe chose to inject the influence graph $A_I$ via an additive combination ($(X + \\alpha A_I)H$) rather than a hard mask for two primary reasons:\n\n*   *Preserving Implicit Correlation:* A mask would completely discard the implicit correlation (e.g., shared interests) for user pairs not present in $A_I$. Our additive approach allows the model to leverage both the explicit LLM-inferred influence paths and the implicit user correlation, treating them as complementary sources of information.\n    - Example: Two people are not causally influenced, but liking the same content implies that they have the same interests (such implicit correlations are also useful for prediction).\n*   *Flexibility and Gradient Flow:* The $+\\alpha A$ formulation creates a \"soft\" augmentation, allowing the model to learn the relative importance of the two different semantics. This provides a smoother optimization landscape compared to the hard constraints imposed by masking.\n\n**3. Empirical Comparison with Masking:**\n\nMasking operation is a reasonable observation. We provide an experiment to compare adding with a masking strategy, and we will add this experiment to the final version.\n\n| **Strategy**           | **H@50 (News)** | **M@50 (News)** | **H@50 (Weibo)** | **M@50 (Weibo)** |\n| :--------------------- | :-------------- | :-------------- | :-------------- | :-------------- |\n| Masked $A$             | 29.02           | 13.75           | 20.53           | 7.96            |\n| **+$\\alpha A$ (Ours)** | **31.33**       | **15.85**       | **23.37**       | **9.10**        |\n\nThe performance drop with masking suggests that even if some user-pairs do not represent the primary causal path for a given cascade, it may still contain useful relational information (e.g., shared interests). Discarding this information entirely is detrimental.\n\n---\n\n\n**[Typos]** Thank you for your careful proofreading. We will correct the figure references in Lines 218 and 228 and conduct a more thorough proofread of the revised manuscript.\n\n---\n\nSincerely thanks for the encouraging and valuable feedback, and we hope these clarifications are helpful for addressing your concerns :)"}, {"review_id": "F6uiz8tgie", "reviewer": "Reviewer_2ybE", "summary": "This paper proposes a causal framework based on LLMs called MILD to predict information diffusion on social platforms. The framework integrates four key factors (social connections, activity timelines, user profiles, and comments) to infer a diffusion influence graph, which explicitly illustrates the relationships and influences among users involved in information cascades. Unlike traditional models, MILD harnesses the strong reasoning capabilities of LLMs to provide a more accurate and explainable diffusion prediction structure. Experiments show that the graphs constructed by MILD improve the representation of real-world diffusion paths by 12% over traditional social network structures and outperform eight state-of-the-art methods in diffusion prediction performance by approximately 7%.", "questions": "Please refer to Strengths and Weaknesses.", "limitations": "No. In fact, Weibo is a large-scale dataset, but it is unclear whether the authors only obtained a subset or performed data reduction. If experiments could be conducted on the complete dataset, it could effectively address the limitations of this work.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "## Strengths  \n1. Innovative causal framework. A novel framework that combines LLMs and multiple factors is proposed to address the issue that traditional methods cannot clearly identify key influential connections.\n  2. Solid theoretical foundation. Provides detailed theoretical analysis and proofs, including complexity analysis of the problem and the theoretical basis for the solution.\n  3. Strong empirical results. Experiments on real-world datasets demonstrate the effectiveness of the method, with performance significantly surpassing existing state-of-the-art approaches.\n## Weaknesses\n  1. Dataset limitations. The experiments mainly focus on two datasets, which may not fully reflect the characteristics of information diffusion on different types of social platforms. Could additional experiments on larger-scale datasets be provided? Furthermore, as far as I know, Weibo is a large-scale dataset with over 1.7 million users, as cited in reference [1]. Why are there only about 30,000 users in the dataset used by the authors? This suggests that the authors performed data reduction, but the paper does not explain this. It is recommended that the authors provide a detailed explanation of how and why the data was reduced.\n  2. High computational complexity. The path search problem in the paper is proven to be NP-hard, and the heuristic-based solution may face computational challenges in large-scale applications. Could the authors provide a comparison of the time costs among various methods or showcase the time cost of MILD on larger-scale datasets?\n  3. Heavy reliance on LLMs. The method is highly dependent on the reasoning ability of LLMs, and different LLMs may produce different results, affecting the stability of the approach. However, the paper only presents results based on GPT-4o and does not compare with other types or versions of LLMs, which may limit the generalizability and applicability of the results. It is suggested to add experimental results using more LLMs.\n\n[1] Social influence locality for modeling retweeting behaviors. IJCAI 2013.", "was_revised": true, "final_justification": "The author has added a larger dataset and conducted more experiments on various LLMs, addressing concerns about insufficient dataset size and the generalizability of the method. However, I still have doubts regarding the efficiency of MILD because only MILD's efficiency data is provided, without any comparison to other methods. Therefore, I am unable to assess the relative efficiency of MILD. For this reason, I have decided to raise the score to Borderline accept.", "rebuttal": "We sincerely appreciate your valuable comments and hope the following responses help address your concerns.\n\n---\n\n### **[W1] Dataset Selection and Scalability**\n\nIn the submission paper's Appendix D.1 (Lines 687-699), we have provided how and why we reduce the data. The size of reduced data is commonly adapted (~10k) [1,2,3]. Moreover, we have conducted new experiments on large networks (original Weibo) with 1.7M nodes as advised, reflecting that our approach achieves better performance against other methods. \n\n**1. Data Subsetting based on Localized Information Diffusion:**\n\nOur approach to subsetting the Weibo dataset, which is detailed in Appendix D.1 of our submission (Lines 687-699), is a standard and methodologically sound practice in network analysis [1,2,3]. The rationale is grounded in the principle that **information diffusion is typically a localized phenomenon**. A single cascade rarely engages all 1.7 million users on the platform; instead, it propagates within specific communities, often driven by Key Opinion Leaders (KOLs).\n\nTherefore, we first identify influential KOLs and then construct a representative subgraph of these KOLs and the users who actively engage with their content. This ensures our dataset captures a dense and relevant set of real-world diffusion cascades, which is a common practice for creating focused yet realistic benchmarks.\n\n  * As shown in Table 5 (Appendix D), the four commonly used benchmark datasets (without meta-text data) also have similar sizes (~10k).\n\n[1] Wang et al. Information Diffusion Prediction With Graph Neural Ordinary Differential Equation Network. In MM 2024.\n\n[2] Zhong et al. Information Diffusion Prediction via Cascade-Retrieved In-Context Learning. In SIGIR 2024.\n\n[3] Jiao et al. Enhancing Multi-Scale Diffusion Prediction via Sequential Hypergraphs and Adversarial Learning. In AAAI 2024.\n\n**2. Experiments on the Original 1.7M-Node Weibo Dataset**\n\nWe conducted new experiments using the original Weibo graph with 1.7 million nodes. The results demonstrate that MILD remains both effective and efficient.\n\n*   **Effectiveness is Maintained:** We evaluated the same test set of cascades on both our subset and the full graph. The performance is nearly identical, confirming that our localized subgraph is highly representative and does not lead to a loss of predictive power.\n\n| **Graph Used for Evaluation**   | **H@50**   | **M@50**   |\n| :---------------------------------- | :--------- | :--------- |\n| Selected Weibo Subgraph (31k nodes) | **0.2337** | **0.0910** |\n| Original Weibo Graph (1.7M nodes)   | 0.2319 | 0.0903 |\n\n*   **Efficiency is Scalable:** The runtime of our path-finding algorithm, the most computationally intensive step, shows only a moderate increase, confirming MILD's practicality for large-scale networks.\n\n| **Dataset**| **# Nodes** | **Avg. Node Degree** | **Avg. Runtime per Cascade** | **Runtime Growth** |\n|:-| :---------- | :------------------- | :--------------------------- | :----------------- |\n| Selected Weibo | 31,061  | 32.63| 0.0198s | 1x|\n| Original Weibo | 1,776,950   | 170.7| 0.1290s | ~6.5x  |\n\n**3. Data Diversity:**\n\nWe sincerely appreciate your thoughtful feedback. As discussed in the \"Limitations\" Section in our paper, the availability of such datasets is limited, composed of complete user profiles, social relationships, diffusion dynamics, and users' comments. As far as we know, Weibo is a popular Chinese social media platform that is well-representative. We are actively seeking additional datasets and will gladly incorporate them in future work. We would appreciate it if you could provide more data resources or links to enhance our work.\n\n---\n\n\n### **[W2] Computational Complexity**\n\nWe provide a detailed time complexity analysis of MILD and new experiments evaluating the practical time cost of heuristic-based solutions and MILD, demonstrating that our heuristic algorithm achieves high efficiency on million-level large dense graphs.\n\n**1. Theoretical Time Complexity Analysis:**\nAs proven in Section 3.2, the time complexity of our heuristic-based solution is $\\mathcal{O}(|V_C|d_{\\max}^r + |V_C||E_C|)$, which is not directly determined by the scale of the entire social network. $|V_C|$ and $|E_C|$ are the number of nodes and edges in the cascade graph $G_C$. $d_{\\max}^r$ is the maximum out-degree in the cascade graph. $r$ is the graph density, which is a fixed hyperparameter. Thus, $O(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid\\mid E_C\\mid)$ is in polynomial time. For the whole MILD framework, the time complexity is $O(|V_C| d_{max}^r+|V_C||E_C|)+N\\ O_{\\text{LLM}}(L)$, where $L$ is the token length of prompts. $N$ is the number of prompts, which is a controllable parameter we set. Thus, the complexity of MILD is minimally affected by the overall size of the social network, further supporting the efficiency of our approach in large‐scale graphs.\n\n\n\n\n**2. Time Cost of MILD on Larger-Scale Datasets:**\nWe added new experiments evaluating our heuristic solution on a range of graphs with varying scales and graph densities. Moreover, we conducted experiments evaluating the overall runtime of MILD on larger and more complex social networks (original Weibo).\n\nRemarkably, even for large-scale dense graphs with millions of nodes and an average degree of 120, our heuristic solution achieves millisecond-level efficiency (0.0334s per cascade). On the real-world Weibo dataset with 1.7 million users, our heuristic solution can still achieve 0.1290s, further supporting the significance of our contribution.\n\nThe overall runtime of MILD is acceptable and can be reduced easily by setting a small number of LLM reasoning prompts for various downstream requirements.\n\n**2.1 Runtime of Heuristic Algorithm per Cascade:**\n\n| Datasets   | #Node | Avg. Node Degree | Avg. Runtime per cascade |\n|:-|-|-|-|\n| News   | 10,255| 16.90| 0.0126s |\n| Our Weibo  | 31,061| 32.63| 0.0198s |\n| Original Weibo | 1,776,950 | 170.7| 0.1290s |\n\n\nFor different scaled graphs with average node degree 40: \n\n| **Graph Scale**  | **Avg. Runtime per cascade (s)** | **Runtime Growth** |\n|-|-|-|\n| Graph with 50000 nodes   | 0.0050  | - |\n| Graph with 100000 nodes  | 0.0049  | ~1.0x  |\n| Graph with 300000 nodes  | 0.0070  | ~1.4x  |\n| Graph with 1000000 nodes | 0.0086  | ~1.7x  |\n\nFor different scaled graphs with average node degree 120:\n\n| **Graph Scale**  | **Avg. Runtime per cascade (s)** | **Runtime Growth** |\n|-|-|-|\n| Graph with 50000 nodes   | 0.0139  | - |\n| Graph with 100000 nodes  | 0.0145  | ~1.0x  |\n| Graph with 300000 nodes  | 0.0162  | ~1.2x  |\n| Graph with 1000000 nodes | 0.0334  | ~2.4x  |\n\n**2.2 Total Time Cost of MILD per Cascade**:\n\n| **Datasets**   | **#Node** | **Avg. Runtime per cascade (s)** |\n|:-| ---------- |-|\n| News   | 10,255 | 39.77s  |\n| Our Weibo  | 31,061 | 54.39s  |\n| Original Weibo | 1,776,950  | 92.53s  |\n\nIn MILD, the LLM reasoning step introduces additional computational cost. However, we believe this latency is acceptable for several reasons: \n\n- The LLM inference is a one-time, preliminary analysis whose results can be cached and reused for multiple downstream tasks (e.g., diffusion prediction, popularity prediction). As it is performed before downstream tasks, it does not affect their real-time efficiency. Moreover, the rapid evolution of LLMs is continuously reducing inference times, which will further improve the efficiency of MILD. \n\n- Especially for diffusion prediction, the time cost of the LLM reasoning process is a worthwhile trade-off for the ~7% improvement in prediction accuracy and, crucially, the novel explainability our MILD framework provides. As we validated in Section 3.3, MILD is consistent with real public opinion.\n\nThus, MILD achieves an effective balance between computational efficiency and the gains in performance and explainability, thereby offering strong practical utility.\n\n---\n\n### **[W3] Generalization of MILD on Diverse LLMs**\n\nWe thank the reviewer for highlighting this key consideration, which is indeed crucial for the robustness of any LLM-based approach. We conducted extensive new experiments using **six different prominent LLMs**, covering both advanced open-source and closed-source models. *Results show remarkable consistency across different LLMs on most metrics.*\n\n**Performance of MILD with Different LLMs:**\n\n| **News Dataset**  | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n|-|-|-|-|-|-|-|\n| **GPT-4o (reported)** | 24.08| 31.31| 35.50 | 15.49| 15.87| 15.92 |\n| Gemini 2.5| 23.91| 31.13| 35.32 | 15.38| 15.71| 15.82 |\n| Claude 4-Sonnet   | 23.97| 31.19| 35.42 | 15.46| 15.78| 15.86 |\n| LLaMA3-70B| 23.58| 30.28| 34.36 | 15.21| 15.31| 15.34 |\n| Qwen-turbo| 22.92| 30.06| 34.08 | 14.74| 15.24| 15.29 |\n| Qwen3| 22.89| 29.87| 33.88 | 14.69| 15.02| 15.16 |\n| DeepSeek R1   | 22.56| 29.91| 33.94 | 14.68| 15.11| 15.17 |\n\n\n| **Weibo Dataset** | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n|-|-|-|-|-|-|-|\n| **GPT-4o (reported)** | 14.73| 23.34| 28.18 | 8.70 | 9.09 | 9.15  |\n| Gemini 2.5| 14.66| 23.33| 28.12 | 8.64 | 9.06 | 9.16  |\n| Claude 4-Sonnet   | 14.65| 23.31| 28.07 | 8.63 | 9.08 | 9.10  |\n| LLaMA3-70B| 14.25| 22.92| 28.00 | 8.40 | 9.00 | 9.06  |\n| Qwen-turbo| 14.20| 22.61| 27.93 | 8.24 | 8.66 | 8.73  |\n| Qwen3| 14.28| 22.73| 27.90 | 8.13 | 8.14 | 8.23  |\n| DeepSeek R1   | 14.31| 22.80| 27.94 | 8.08 | 8.11 | 8.14  |\n\n\n---\n\nWe sincerely hope that these clarifications are helpful, and we will improve further on all the mentioned questions."}, {"review_id": "T9p1iR8Tro", "reviewer": "Reviewer_iynN", "summary": "This paper proposes a novel multi-step framework to predict information diffusion in social networks, namely, MILD (LLM-based Causal Framework for Diffusion Influence Derivation). One of the novelties of the proposed method is that inlike existing methods that are mainly based on GNNs and sequence models, it uses LLMs to explain underlying influence and infer a \"who-influences-whom\" diffusion graph. Experiments have been conducted to demonstrate that the proposed framework achieves SOTA accuracy as well as explainable representation of the diffusion mechanism.", "questions": "I am very curious to see authors' response to my comment that I posed earlier on the weaknesses of the method.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Paper is well-written and easy to follow. \n2. LLM used in the method helps with the explainability of the information diffusion process which is at the core of the paper's innovations.\n3. The proposed method uses different types of inputs and information which make the method more reliable and stronger.\n4. Also extensive experiments (including ablation studies) have been performed to support the proposed idea. Furthermore, experiments have been supported by rigorous theoretical discussions.\n5. Extensive evaluations have been performed to show the superiority of the results and the proposed method in general.\n\nWeaknesses:\n1. Although this is a nice paper, I have two major concerns regarding (1) computational costs and (2) reproducibility of the results. First of all, the method is comprised of multiple steps that make the method very expensive and the process quite time-consuming. Second, because of LLM and numerous parameters, reproducibility is very challenging due to underlying LLM's reasoning abilities.", "was_revised": true, "final_justification": "I have read authors responses and my concerns about time complexity and reproducibility have been addressed.", "rebuttal": "We sincerely appreciate your constructive feedback. In response to the concerns regarding (1) computational costs and (2) reproducibility of LLMs, we add more experiments and theoretical analysis to mitigate your concerns.\n\n### **[W1] Computational Costs**\n\nThank you for this crucial question. We provide a theoretical analysis of time complexity and conduct new experiments evaluating the time cost of MILD. Results show that MILD remains SOTA effectiveness with low computational cost.  We will enhance the discussion in the final version and provide the experiments and analysis as follows:\n\n**1. Time Complexity**\n\nThe time complexity of MILD mainly involves three modules, which can be conducted in polynomial time.\n\n\n|**Module**|**Time complexity**|\n|-|-|\n| Prompt Construction | $\\mathcal{O}(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid\\mid E_C\\mid)$|\n| LLM Reasoning       | $\\mathcal{O}_{\\text{LLM}}(L)$   |\n|Transformer Prediction    | $\\mathcal{O}_{\\text{Trans}}(\\mid V_C \\mid)$ |\n|Overall MILD|$\\mathcal{O}(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid\\mid E_C\\mid)+N\\mathcal{O}_{\\text{LLM}}(L)$|\n\nIn our heuristic algorithm, $|V_C|$ and $|E_C|$ denote the size of the cascade graph. $d_{\\max}^r$ is the maximum out-degree in the cascade graph. $r$ is the graph density, which is a fixed hyperparameter. Thus, $O(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid \\mid E_C\\mid)$ is in polynomial time. For the LLM reasoning process, for each query, the complexity is determined by the token length of prompts $L$ and the LLM function itself $O_{\\text{LLM}}(\\cdot)$, which will decrease as prompts shorten and LLMs evolve. For Transformer-based prediction, the complexity is determined by the size of the cascade $|V_C|$ and the function $O_\\text{Trans}(\\cdot)$. In summary, as $O_{\\text{Trans}}(\\mid V_C\\mid)\\subseteq O_{\\text{LLM}}(L)$, the time complexity of MILD is $O(|V_C| d_{max}^r+| V_C||E_C|)+N\\ O_{\\text{LLM}}(L)$. $N$ is the number of prompts, which is a controllable parameter.\n\n**2. Runtime Evaluation**\n\nWe further evaluate the efficiency and token costs as follows.\n\n**2.1 Average Runtime (in seconds per cascade):**\n\n| **Module** | **News Runtime**| **Weibo Runtime** |\n| :- | :- | :- |\n| Prompt Construction|0.012s|0.019s|\n| LLM Reasoning (per prompt)|1.53s|1.62s|\n| Transformer Prediction|0.38s|0.33s|\n| Total Time|39.77s|54.39s|\n| Avg. #Prompts|25.77|33.36|\n\nBoth prompt construction and Transformer prediction are highly efficient, with average runtimes well under 1 second. While the LLM reasoning step introduces additional computational overhead, we think this latency is acceptable for several reasons: \n\n- The number of prompts is controllable, which can be reduced for requirements in diverse scenarios.\n- The LLM reasoning process serves as a preliminary analysis step, and its results can be leveraged across various downstream applications (such as diffusion prediction and public opinion analysis). As it is performed before downstream tasks, it does not affect their real-time efficiency. Moreover, the rapid evolution of LLMs is continuously reducing inference times, which will further improve the efficiency of MILD. \n- Especially for diffusion prediction, the time cost of the LLM reasoning process is a worthwhile trade-off for the ~7% improvement in prediction accuracy and, crucially, the novel explainability our MILD framework provides. As we validated in Section 3.3, MILD is consistent with real public opinion.\n\n**Hard resources requirement:** One Tesla V100 32GB is enough for our evaluation.\n\n\n\n\n-----\n\n### **[W2] LLM Reproducibility**\n\nThank you for highlighting the fundamental importance of reproducibility. In our evaluation, we have taken corresponding measures to ensure reproducibility.\n\n**1. _0-temperature_ Setting for Reproducibility**\nWe fully agree with the reviewer's concern and have specifically addressed it in our work. As described in *Section 4, line 301*, we set the \"temperature\" hyperparameter to **0** to ensure reproducibility during all LLM reasoning steps.\n\n\"Temperature\" parameter directly controls the variability in LLM-generated responses. **As confirmed in the GPT-4 official technical report [1]**, temperature=0 ensures deterministic and stable outputs for the same input prompt. This practice is widely adopted in the research community to guarantee result consistency [2][3]. By following this standard, MILD can **guarantee the reproducibility** of the \"who-influences-whom\" diffusion graph.\n\nWe have released the source code in the supplemental materials, and *we also promise to provide a verification code for LLM reproducibility.*\n\n[1] Gpt-4 technical report. arXiv preprint arXiv:2303.08774 (2023).\n\n[2] The effect of sampling temperature on problem solving in large language models. EMNLP (2024).\n\n[3] A survey of large language models. arXiv preprint arXiv:2303.18223 1.2 (2023).\n\n\n\n**2. Robustness across different LLMs**\n\nWe evaluate MILD on six different state-of-the-art LLMs (four open-source models and two closed-source models). We will add these experiments to the final version.\n\n*Summary:* The results below show that MILD achieves stable performance across six LLMs. (1) MILD is broadly generalizable, working effectively with a range of open-source and closed-source LLMs. (2) The success of MILD is determined by the causal framework and prompting strategy, not relying on the reasoning ability of a single LLM, such as GPT-4o. (3) Open-source LLMs (e.g., LLaMA 3, Qwen Turbo, Deepseek R1) deliver comparable results, making MILD both widely accessible and cost-effective for the broader research community.\n\n**Performance with Various LLMs:**\n\n| **News Dataset**      | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n| --------------------- | -------- | -------- | --------- | -------- | -------- | --------- |\n| **GPT-4o (reported)** | 24.08    | 31.31    | 35.50     | 15.49    | 15.87    | 15.92     |\n| Gemini 2.5            | 23.91    | 31.13    | 35.32     | 15.38    | 15.71    | 15.82     |\n| Claude 4-Sonnet       | 23.97    | 31.19    | 35.42     | 15.46    | 15.78    | 15.86     |\n| LLaMA3-70B            | 23.38    | 30.28    | 34.36     | 15.01    | 15.31    | 15.34     |\n| Qwen-turbo            | 22.92    | 30.06    | 34.08     | 14.74    | 15.24    | 15.29     |\n| Qwen3                 | 22.89    | 29.87    | 33.88     | 14.69    | 15.02    | 15.16     |\n| DeepSeek R1           | 22.56    | 29.91    | 33.94     | 14.68    | 15.11    | 15.17     |\n\n\n| **Weibo Dataset**     | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n| --------------------- | -------- | -------- | --------- | -------- | -------- | --------- |\n| **GPT-4o (reported)** | 14.73    | 23.34    | 28.18     | 8.70     | 9.09     | 9.15      |\n| Gemini 2.5            | 14.66    | 23.33    | 28.12     | 8.64     | 9.06     | 9.16      |\n| Claude 4-Sonnet       | 14.65    | 23.31    | 28.07     | 8.63     | 9.08     | 9.10      |\n| LLaMA3-70B            | 14.25    | 22.92    | 28.00     | 8.40     | 9.00     | 9.06      |\n| Qwen-turbo            | 14.20    | 22.61    | 27.93     | 8.24     | 8.66     | 8.73      |\n| Qwen3                 | 14.28    | 22.73    | 27.90     | 8.13     | 8.14     | 8.23      |\n| DeepSeek R1           | 14.31    | 22.80    | 27.94     | 8.08     | 8.11     | 8.14      |\n\n---\n\nWe would like to improve the paper for all questions, and we hope these clarifications and additional results are helpful for your concerns."}, {"review_id": "jGspA9G0An", "reviewer": "Reviewer_CJaf", "summary": "This paper proposes an information diffusion prediction framework (MILD) based on large language models (LLMs). Unlike previous methods that focus only on social structure and propagation sequence, MILD leverages LLMs to infer the causal relationships of “who influences whom” within cascades. It comprehensively integrates multi-dimensional data such as social network structure, user activity, comment content, and temporal information to explicitly construct a directed diffusion influence graph, which is then incorporated into downstream diffusion prediction tasks.", "questions": "Can the authors further analyze or provide information on the inference efficiency and resource consumption of MILD when applied to larger-scale, longer cascades, or more complex social networks?\n\nIs there any further external data or human-annotated experiments to validate the causal validity of the “who influences whom” chains inferred by the LLM?\n\nSince the model utilizes sensitive user attributes and comment content, how can privacy and data compliance be ensured in practical applications? Is it possible to anonymize or obfuscate sensitive information?", "limitations": "The authors have discussed some limitations, such as inference cost and the verifiability of LLM outputs, but the analysis of privacy and ethical risks is insufficient. It is recommended to include statements regarding data collection compliance and to further analyze the method's resource consumption and practical applicability in large-scale scenarios.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n\nIt skillfully integrates social relationships, temporal order, user profiles, and comment content, resulting in comprehensive and well-structured information utilization.\n\nIn addition to ablation studies, the paper also conducts empirical analyses from perspectives such as robustness and attention visualization.\n\nWeaknesses：\n\nMILD relies on large language model inference, which may incur excessive deployment and computational costs in ultra-large-scale social networks or real-time prediction scenarios, posing challenges for practical application.\n\nAlthough LLMs can infer “who influences whom,” the inferred causal chains are difficult to fully verify in real-world scenarios and may introduce subjectivity or hallucinations.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate your valuable feedback. We hope that the following clarifications help address your concerns.\n\n### **[W1&Q1] Inference Efficiency**\n\nThank you for your valuable feedback. We provide time complexity analysis and conduct new experiments evaluating the time cost of MILD. Results show that MILD remains SOTA effectiveness with low computational cost. \n\n**1. Theoretical Time Complexity**\n\nWe provide a breakdown time complexity of each module as follows.\n\n|**Module**|**Time complexity**|\n|-|-|\n| Prompt Construction | $\\mathcal{O}(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid\\mid E_C\\mid)$|\n| LLM Reasoning| $\\mathcal{O}_{\\text{LLM}}(L)$ |\n|Transformer Prediction| $\\mathcal{O}_\\text{Trans}(\\mid V_C\\mid)$ |\n|Overall MILD|$\\mathcal{O}(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid\\mid E_C\\mid)+N\\mathcal{O}_{\\text{LLM}}(L)$|\n\n$|V_C|$ and $|E_C|$ denote the size of the cascade graph. $d_{\\max}^r$ is the maximum out-degree in the cascade graph. $r$ is the graph density, which is a fixed hyperparameter. Thus, $O(\\mid V_C\\mid d_{max}^r+\\mid V_C\\mid \\mid E_C\\mid)$ is in polynomial time. For the LLM reasoning process, for each query, the complexity is determined by the token length of prompts $L$ and the LLM function itself $O_{\\text{LLM}}(\\cdot)$, which will decrease as prompts shorten and LLMs evolve. For Transformer-based prediction, the complexity is determined by the size of the cascade $|V_C|$ and the function $O_\\text{Trans}(\\cdot)$. In summary, as $O_{\\text{Trans}}(\\mid V_C\\mid)\\subseteq O_{\\text{LLM}}(L)$, the time complexity of MILD is $O(|V_C| d_{max}^r+| V_C||E_C|)+N\\ O_{\\text{LLM}}(L)$. $N$ is the number of prompts, which is a controllable parameter.\n\n**2. Runtime Evaluation**\n\n**2.1 Efficiency on Larger-Scaled and More Complex Graphs**:\n\nWe conducted new experiments to evaluate the time cost of MILD, showing that the overall runtime of MILD is acceptable and can be reduced easily by setting a small number of LLM reasoning prompts for various downstream requirements. Thus, MILD achieves an effective balance between computational efficiency and the gains in performance and explainability, thereby offering strong practical utility.\n\n|Datasets|#Node|Avg. Node Degree|Avg. Runtime per cascade|\n|:-|-|-|-|\n| News| 10,255| 16.90  | 39.77s |\n| Our Weibo | 31,061| 32.63  | 54.39s |\n| Original Weibo | 1,776,950  | 170.7  | 92.53s |\n\nIn MILD, the LLM reasoning step introduces additional computational cost. However, we think this latency is acceptable for several reasons: \n\n- In practice, the number of prompts is controllable, which can be reduced for requirements in diverse scenarios.\n- The LLM reasoning process serves as a preliminary analysis step, and its results can be leveraged across various downstream applications (such as diffusion prediction and public opinion analysis). As it is performed before downstream tasks, it does not affect their real-time efficiency. Moreover, the rapid evolution of LLMs is continuously reducing inference times, which will further improve the efficiency of MILD. \n- Especially for diffusion prediction, the time cost of the LLM reasoning process is a worthwhile trade-off for the ~7% improvement in prediction accuracy and, crucially, the novel explainability our MILD framework provides. As we validated in Section 3.3, MILD is consistent with real public opinion.\n\n\n**2.2 Heuristic Algorithm Runtime on Larger-Scaled and More Complex Graphs:**\n\nWe evaluate the time cost of our heuristic algorithm on a range of graphs with varying *scales* and *densities*, and *longer cascades*, demonstrating that our heuristic solution achieves strong efficiency. Specifically, it achieves 0.0334s per cascade, even for synthetic large-scale dense graphs with millions of nodes and an average degree of 120. On the Weibo platform with 1.7 million users, our heuristic solution can still achieve 0.1290s.\n\n| Datasets | News | Our Weibo | Original Weibo |\n| :- |-|-|-|\n| Avg. Runtime per cascade (s) | 0.0126s | 0.0198s| 0.1290s|\n\n**For different scaled graphs with different node degree:**\n\n| Degree 40 | Avg. Runtime per cascade (s) | Runtime Growth |\n|-|-|-|\n| Graph with 50000 nodes | 0.0050 |- |\n| Graph with 100000 nodes  | 0.0049 | ~1.0x|\n| Graph with 300000 nodes  | 0.0070 | ~1.4x|\n| Graph with 1000000 nodes | 0.0086 | ~1.7x|\n\n| Degree 80 | Avg. Runtime per cascade (s) | Runtime Growth |\n|-|-|-|\n| Graph with 50000 nodes | 0.0095 |- |\n| Graph with 100000 nodes  | 0.0100 | ~1.0x|\n| Graph with 300000 nodes  | 0.0115 | ~1.2x|\n| Graph with 1000000 nodes | 0.0124 | ~1.3x|\n\n| Degree 120 | Avg. Runtime per cascade (s) | Runtime Growth |\n|-|-|-|\n| Graph with 50000 nodes | 0.0139 | - |\n| Graph with 100000 nodes  | 0.0145 | ~1.0x|\n| Graph with 300000 nodes  | 0.0162 | ~1.2x|\n| Graph with 1000000 nodes | 0.0334 | ~2.4x|\n\n**2.3 Heuristic Algorithm Runtime on Longer Cascades:**\n\n| **Cascade Length** | **News Dataset** | **Weibo Dataset** |\n| :- | :- | :- |\n| 1-50 | 0.002s| 0.013s|\n| 50-100 | 0.002s| 0.013s|\n| 101-200| 0.012s| 0.020s|\n| 201-300| 0.029s| 0.044s|\n| 301-500| 0.217s| 0.212s|\n\n\nOverall, the above results indicate that MILD shows good efficiency across larger-scale and denser graphs, longer cascades, and more complex social networks.  \n\n**3. Cost-Effective Deployment with Open-Source LLMs**\n\nWe further conducted experiments with four open-sourced and two closed-source LLMs. Results show that open LLMs perform comparably to commercial ones, validating that MILD can be effectively deployed without reliance on costly commercial LLMs.\n\n| **News Dataset** | **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n|-|-|-|-|-|-|-|\n| **GPT-4o (reported)** | 24.08| 31.31| 35.50| 15.49| 15.87| 15.92|\n| Gemini 2.5| 23.91| 31.13| 35.32| 15.38| 15.71| 15.82|\n| Claude 4-Sonnet| 23.97| 31.19| 35.42| 15.46| 15.78| 15.86|\n| LLaMA3-70B| 23.58| 30.28| 34.36| 15.21| 15.31| 15.34|\n| Qwen-turbo| 22.92| 30.06| 34.08| 14.74| 15.24| 15.29|\n| Qwen3 | 22.89| 29.87| 33.88| 14.69| 15.02| 15.16|\n| DeepSeek R1| 22.56| 29.91| 33.94| 14.68| 15.11| 15.17|\n\n\n| **Weibo Dataset**| **H@10** | **H@50** | **H@100** | **M@10** | **M@50** | **M@100** |\n|-|-|-|-|-|-|-|\n| **GPT-4o (reported)** | 14.73| 23.34| 28.18| 8.70| 9.09| 9.15 |\n| Gemini 2.5| 14.66| 23.33| 28.12| 8.64| 9.06| 9.16 |\n| Claude 4-Sonnet| 14.65| 23.31| 28.07| 8.63| 9.08| 9.10 |\n| LLaMA3-70B| 14.25| 22.92| 28.00| 8.40| 9.00| 9.06 |\n| Qwen-turbo| 14.20| 22.61| 27.93| 8.24| 8.66| 8.73 |\n| Qwen3 | 14.28| 22.73| 27.90| 8.13| 8.14| 8.23 |\n| DeepSeek R1| 14.31| 22.80| 27.94| 8.08| 8.11| 8.14 |\n\n\n**3.2 MILD Token Cost:**\n\nMILD is efficient and keeps token usage low, showing faster and cheaper use in real-world scenarios. Besides, MILD with open-source LLMs can achieve SOTA performance with 0 dollars.\n\n|Datasets|Avg. #Input tokens| **Avg. #Output tokens** |\n|-|-|-|\n| News  | 285.67 | 12.25|\n| Weibo | 647 | 24 |\n\n**Hard resources requirement:** In our evaluation, One Tesla V100 32G is enough.\n\n---\n\n### **[W2 & Q2] Validation of LLM-derived Chains**\n\nThank you for emphasizing the validation of the LLM-derived $G_I$, which is the key in our MILD. \n\nIn the submission paper's Sections 3.3, 4.1, and 4.2, we have conducted experiments with human-annotated and external data to verify \"who influences whom\" chains, validating the causal validity of this. Here, we clarify it more detailedly as follows.\n\n**[Sections 4.1 and 4.2]** Downstream Performance as the Primary Validation of $G_I$\n\nThe most powerful evidence for the validity of the LLM-inferred influence graph ($G_I$) is its direct impact on the primary downstream task: **diffusion prediction**. Our framework significantly outperforms eight state-of-the-art baselines. A more accurate diffusion influence graph directly translates to more accurate predictions, and our SOTA results serve as strong empirical validation that $G_I$ is capturing meaningful, real diffusion dynamics that are overlooked by other models.\n\n**[Section 3.3]** Real-world Diffusion Pathways and Key Interactions as External Validation\n\n> **Real-world diffusion pathways as external data:**\n\nIn Section 3.3 (E1), we carefully extracted actual diffusion chains on the real-world social platform as external data for evaluations. Specifically, real-world diffusion pathways always appear in reply comments, in the form of $\\{A:\\text{[comment]} @B:\\text{[comment]}@C:\\text{[comment]}\\}$. Thus, we can extract these as the ground truth. Results (shown in Figure 4 in Section 3.3) indicate that our diffusion influence graph $G_I$ can truly capture these real-world information diffusion pathways.\n\n>  **Key interaction as external data:**\n\nIn Section 3.3 (E2), we also manually extracted key interactions among users during the information diffusion process. Specifically, as the well-known communication theory, the Strength of Weak Ties, posits, \\emph{\"the strength of any tie is a function of the frequency and duration of interaction\"}, we assessed whether $G_I$ observes participant interactions among participants within cascades. Key interactions are high-frequency interactions that happen in the real-world social platform. \n\n---\n\n### **[Q3] Data Privacy**\n\nWe take data privacy and the ethical implications of our work with the utmost seriousness. \n_**All datasets are public research datasets**_ and have been processed with strict privacy-preserving measures. The prompts fed to the LLM contain only these anonymized or public IDs, timestamps, and comments, with no other Personally Identifiable Information (PII). Furthermore, the datasets used in our study have been **widely used by the research community**. Our use of this data is strictly for academic research purposes and complies with the terms of service under which the data was released. We will add a dedicated **\"Ethics and Privacy Statement\"** section to the paper to make these commitments explicit.\n\n---\n\nSincerely thank you again for the thoughtful and valuable comments."}]

Author rebuttal:

Meta-review: The paper introduces an LLM-based causal framework to predict information diffusion on social platforms. All the reviewers are mildly positive or positive about the paper after rebuttal.
Decision: Accept (poster)