CAUSALCITE: A Causal Formulation of Paper Citations (2024)

Abstract: Citation count of a paper is a commonly used proxy for evaluating the significance of a paper in the scientific community. Yet citation measures are widely criticized for failing to accurately reflect the true impact of a paper. Thus, we propose CAUSALCITE, a new way to measure the significance of a paper by assessing the causal impact of the paper on its follow-up papers. CAUSALCITE is based on a novel causal inference method, TEXTMATCH, which adapts the traditional matching framework to highdimensional text embeddings. TEXTMATCH encodes each paper using text embeddings from large language models (LLMs), extracts similar samples by cosine similarity, and synthesizes a counterfactual sample as the weighted average of similar papers according to their similarity values. We demonstrate the effectiveness of CAUSALCITE on various criteria, such as high correlation with paper impact as reported by scientific experts on a previous dataset of 1K papers, (test-of-time) awards for past papers, and its stability across various subfields of AI. We also provide a set of findings that can serve as suggested ways for future researchers to use our metric for a better understanding of the quality of a paper.1

heading: 1 Introduction
text: Recent years have seen explosive growth in the number of scientific publications, making it increasingly challenging for scientists to navigate the vast landscape of scientific literature. Therefore, identifying a good paper has become a crucial challenge for the scientific community, not only for technical research purposes, but also for making decisions, such as funding allocation (Carlsson, 2009), research evaluation (Moed, 2006), recruitment (Gary Holden and Barker, 2005), and university ranking and evaluation (Piro and Sivertsen, 2016).
A traditional approach to recognize paper quality is peer review, a mechanism that requires large efforts,
∗Equal contribution. 1Our code is available at https://github.com/
causalNLP/causal-cite.
Causal Effect Paper a Paper b
What is the impact of Paper a on its followup study b?
Paper topic Publication year ... Success metric: y
Attributes
Paper a Paper b Paper topic Publication year ...
Success metric: y'
Attributes
We make a counterfactual situation Had Paper a not existed... Yet Paper b still has the same topic, year, etc.
What would the counterfactual success metric y' be?
Figure 1: An overview of our research question.
and yet has inherent randomness and flaws (Cortes and Lawrence, 2021; Rogers et al., 2023; Shah, 2022; Prechelt et al., 2018; Resnik et al., 2008). Moreover, the number of papers after peer review is still overwhelmingly large for researchers to read, leaving the challenge of identifying truly impactful research unaddressed. Another commonly used metric is citations. However, this metric faces criticism for biases, such as a preference for survey, toolkit, and dataset papers (Zhu et al., 2015; Valenzuela-Escarcega et al., 2015). Together with altmetrics (Wilsdon et al., 2015), which incorporates social media attention to a paper, both metrics also bias towards papers from major publishing countries (Rungta et al., 2022; Gomez et al., 2022), with extensive publicity and promotion, and authored by established figures.
To provide a more equitable assessment of paper quality, we employ the causal inference framework (Hernán and Robins, 2010) to quantify a paper’s impact by how much of the academic success in the follow-up papers should be causally attributed to this paper. We introduce CAUSALCITE, an enhanced citation based metric that poses the following counterfactual question (also shown in Figure 1): “had this paper never been published, what would have happened to its follow-up studies?” To compute the causal attribution of each follow-up paper, we contrast its citations (the treatment group) with citations of papers that address a similar topic, but are not built on the paper of interest (the control group).
Traditionally, this problem is solved by using the match-
8395
ing method (Rosenbaum and Rubin, 1983) in causal inference, which discretizes the value of the confounder variable, and compares the treatment and control groups with regard to each discretized value of the confounder variable. However, this approach does not apply when the confounder variable is high-dimensional, e.g., text data, such as the content of the paper. Thus, we improve the matching method to adapt for textual confounders, by marrying recent advancement of large language models (LLMs) with traditional causal inference. Specifically, we propose TEXTMATCH, which uses LLMs to encode an academic paper as a high-dimensional text embedding to represent the confounders, and then, instead of iterating over discretized values of the confounder, we match each paper in the treatment group with papers from the control group with high cosine similarity by the text embeddings.
TEXTMATCH makes contributions in three different aspects: (1) it relaxes the previous constraint that the confounder variable should be binned into a limited set of intervals, and makes the matching method applicable for high-dimensional continuous variable type for the confounder; (2) since there are millions of papers, we enable efficient matching via a matching-and-reranking approach, first using information retrieval (IR) (Manning et al., 2008) to extract a small set of candidates, and then applying semantic textual similarity (STS) (Majumder et al., 2016; Chandrasekaran and Mago, 2022) for fine-grained reranking; and (3) we enable a more stable causal effect estimation by leveraging all the close matches to synthesize the counterfactual citation score by a weighted average according to the similarity scores of the matched papers.
CAUSALCITE quantifies scientific impact via a causal lens, offering an alternative understanding of a paper’s impact within the academic community. To test its effectiveness, we conduct extensive experiments using the Semantic Scholar corpus (Lo et al., 2020; Kinney et al., 2023), comprising of 206M papers and 2.4B citation links. We empirically validate CAUSALCITE by showing higher predictive accuracy of paper impact (as judged by scientific experts on a past dataset of 1K papers (Zhu et al., 2015)) compared to citations and other previous impact assessment metrics. We further show a stronger correlation of the metric with the test-of-time (ToT) paper awards. We find that, unlike citation counts, our metric exhibits a greater balance across various research domains in AI, e.g., general AI, NLP, and computer vision (CV). While citation numbers for papers in these domains vary significantly – for example, while an average CV paper has many more citations than an average NLP paper, CAUSALCITE scores papers across AI sub-fields more similarly.
After demonstrating the desirable properties of our metric, we also present several case studies of its applications. Our findings reveal that the quality of conference best papers is noisier on average than that of ToT papers
(Section 5.1). We then showcase and present CAUSALCITE for several well-known papers (Section 5.3) and utilize CAUSALCITE to identify high-quality papers that are less recognized by citation counts (Section 5.4).
In conclusion, our contributions are as follows:
1. We introduce CAUSALCITE, a counterfactual causal effect-based formulation for paper citations.
2. We develop TEXTMATCH, a new method that leverages LLMs and causal inference to estimate the counterfactual causal effect of a paper.
3. We conduct comprehensive analyses, including various performance evaluations and present new findings using our metric.

heading: 2 Problem Formulation
text: Our problem formulation involves a citation graph and a causal graph. We use lowercase letters for specific papers and uppercase for an arbitrary paper treated as a random variable.
Citation Graph In the citation graph G := (P,L), P is a set of papers, and each edge ℓi,j ∈ L indicates that an earlier paper pi influences (i.e., is cited by) a follow-up paper pj . To obtain the citation graph, we use the Semantic Scholar Academic Graph dataset (Kinney et al., 2023) with 206M papers and 2.4B citation edges.
Treatment T Building Paper b on Paper a
Effect Y Success of Paper b
What is the causal effect size?
We use the causal graph to identify the correct variables to control for:
Target:
Causal Graph. The causal graph, shown in Figure 2, highlights the contribution of a paper a to a follow-up paper b. We use a binary variable T to indicate if a influences b and an effect variable Y to represent the success of b. We use log10 of citation counts to quantify Y , although other transformations can also be used. We introduce two sets of variables in this causal graph: (i) The set of confounders, which are the common causes of T and Y . For instance, the research area of b impacts both the likelihood of a paper citing a and its own citation count. (ii) Descendants of the treatment, comprising mediators (e.g., paper a influencing the quality of paper b and subsequently influencing its citations) and colliders (e.g., both the influence from a and the citations of b influencing later awards received by b).

heading: 2.1 CAUSALCITE Indices
text: In this section, we introduce various indices that measure the causal impact of a paper.
Two-Paper Interaction: Pairwise Causal Impact (PCI). To examine the causal impact of a paper a on a follow-up paper b, we define the pairwise causal impact PCI(a, b) by unit-level causal effect:
PCI(a, b) := yt=1 − yt=0 , (1)
where we compare the outcomes Y of the paper b had it been influenced by paper a or not, denoted as the actual yt=1 and the counterfactual yt=0, respectively. Note that the counterfactual yt=0 can never be observed, but only estimated by statistical methods, as we will discuss in Section 3.2.
Single-Paper Quality Metrics: Total Causal Impact (TCI) and Average Causal Impact (ACI). Let S denote the set of all follow-up studies of paper a. We define total causal impact TCI(a) as the sum of the pairwise causal impact index PCI(a, b) across all b ∈ S. That is,
TCI(a) := ∑
b∈S PCI(a, b) . (2)
This definition provides an aggregated measure of a paper’s influence across all its follow-up papers.
As the causal inference literature is usually interested in the average treatment effect, we further define the average causal impact (ACI) index as the average per paper PCI:
ACI(a) := TCI(a) |S| = 1 |S| ∑
b∈S
( yt=1 − yt=0 ) . (3)
We note that ACI(a) is equal to the average treatment effect on the treated (ATT) of paper a (Pearl, 2009).

heading: 3 The TEXTMATCH Method
text: As illustrated in Figure 1, the objective of our study is to quantify the causal effect of the treatment T (i.e., whether paper b is built on paper a) on the effect Y (i.e., the outcome of paper b). To approach this, we envision a counterfactual scenario: what if paper a had never been published, yet certain key characteristics of paper b remain unchanged? The critical question then becomes: which key characteristics of paper b should be controlled for in this hypothetical situation?

heading: 3.1 What Does Causal Inference Tell Us about
text: What Variables to Control for, and What Not?
In causal inference, selecting the appropriate variables for control is a delicate and crucial process that affects the accuracy of the analysis. Pearl’s seminal work on causality guides us in differentiating between various types of variables (Pearl, 2009).
Firstly, we must control for confounders – variables that influence both the treatment and the outcome. Confounders can create spurious correlations; if not controlled, they can lead us to mistakenly attribute the effect of these external factors to the treatment itself. For example, in assessing the impact of one paper on another, if both papers are in a trending research area, the apparent influence might be due to the popularity of the topic rather than the papers’ content.
However, not all variables warrant control. Mediators and colliders should be explicitly avoided in control. Mediators are part of the causal pathway between the treatment and outcome. By controlling them, we would block the very effect we are trying to measure. Colliders, affected by both the treatment and the outcome, can introduce bias when controlled. Controlling a collider can inadvertently create associations that do not naturally exist. In general, this also includes not controlling for the descendants of the treatment, as it could obscure the direct impact we intend to study.
Lastly, variables that do not share a causal path with both the treatment and outcome, known as unshared ancestors, are less critical in our analysis. They do not contribute to or confound the causal relationship we are exploring, and thus, controlling for them does not add value to our causal understanding.

heading: 3.2 Can Existing Causal Inference Methods Handle This Control?
text: Several causal inference methods have been proposed to address the problem of estimating treatment effects while controlling for confounders. Next, we will discuss the workings and limitations of three classical methods.
Randomized Control Trials (RCTs) Assumes Intervenability. The ideal way to obtain causal effects is through randomized control trials (RCTs). For example, when testing a drug, we randomly split all patients into two groups, the control group and the treatment group, where the random splitting ensures the same distribution of the confounders across the two groups such as gender and age. However, RCTs are usually not easily achievable, in some cases too expensive (e.g., tracking hundreds of people’s daily lives for 50 years), and in other cases unethical (e.g., forcing a random person to smoke), or infeasible (e.g., getting a time machine to change a past event in history).
For our research question on a paper’s impact, utilizing RCTs is impractical as it is infeasible to randomly divide researchers into two groups, instructing one group to base their research on a specific paper a while the other group does not, and then observe the citation count of their papers years later.
Ratio Matching Iterates over Discretized Confounder Values. In the absence of RCTs, matching is as an alternate method for determining causal effects from observational data. In this case, we can let the
treatment assignment happen naturally, such as taking the naturally existing set of papers and running causal inference by adjusting for the variables that block all paths. Given a set of naturally observed papers, one of the most commonly used causal inference methods is ratio matching (Rosenbaum and Rubin, 1983), whose basic idea is to iterate over all possible values x of the adjustment variables X and obtain the difference between the treatment group T and control group C:
‘ACI(a) = ∑
x
P (x)
Ñ 1
|Tx| ∑
i∈Tx yi −
1 |Cx| ∑
j∈Cx yj
é ,
(4) where for each value x, we extract all the units corresponding to this value in the treatment and control sets, compute the average of the effect variable Y for each set, and obtain the difference.
While ratio matching is practical when there is a small set of values for the adjustment variables to sum over, its applicability dwindles with high-dimensional variables like text embeddings in our context. This scenario may generate numerous intervals to sum over, presenting numerical challenges and potential breaches of the positivity assumption.
One-to-One Matching Is Susceptible to Variance. To handle high-dimensional adjustment variables, one possible way is to avoid pre-defining all their possible intervals, but, instead, iterating over each unit in the treatment group to match for its closest control unit (e.g., McGue et al., 2010; Sato et al., 2022). Consider a given follow-up paper b, and a set of candidate control papers C, where each paper ci has a citation count yi, and vector representation ti of the confounders (e.g., research topic). One-to-one matching estimates PCI as
‘PCI(a, b) = yb − yargmaxci∈C mi = yb − yargmaxci∈C sim(tb,ti) ,
(5)
where we approximate the counterfactual sample by the paper ci ∈ C which is the most similar to paper b by the matching score mi, which is obtained by the cosine similarity sim of the confounder vectors. A limitation of the one-to-one matching method is that it might induce large instability in the result, as only taking one paper with similar contents may have a large variance in citations when the matched paper slightly differs.
3.3 How Do We Extending Causal Inference to Text Variables?

heading: 3.3.1 Theoretical Formulation of TEXTMATCH: Stabilizing Text Matching by Synthesis
text: To fill in the aforementioned gap in the existing matching methods, we propose TEXTMATCH, which mitigates the instability issue of one-to-one matching by replacing it with a convex combination of a set of matched samples to form a synthetic counterfactual sample. Specifically, we identify a set of papers ci ∈ C with
high matching scores mi to the paper b, and synthesize the counterfactual sample by an interpolation of them:
‘PCI(a, b) = yb − ∑
ci∈C wiyi = yb −
∑
ci∈C
mi∑ ci∈C mi yi ,
(6)
where the weight wi of each paper ci is proportional to the matching score mi and normalized.
The contributions of our method are as follows: (1) we adapt the traditional matching methods from lowdimensional covariates to any high-dimensional variables such as text embeddings; (2) different from the ratio matching, we do not stratify the covariates, but synthesize a counterfactual sample for each observed treated units; (3) due to this iteration over each treated unit instead of taking the population-level statistics, we closely control for exogenous variables for the ATT estimation, which circumvents that need for the structural causal models; (4) we further stabilize the estimand by a convex combination of a set of similar papers. Note that the contribution of Eq. (6) might seem to bear similarity with synthetic control (Abadie and Gardeazabal, 2003; Abadie et al., 2010), but they are fundamentally different, in that synthetic control runs on time series, and fit for the weights wi by linear regression between the time series of the treated unit and a set of time series from the control units, using each time step’s values in the regression loss function.

heading: 3.3.2 Overall Algorithm
text: To operationalize our theoretical formulation above, we introduce our overall algorithm in Algorithm 1. We briefly give an overview of the the algorithm with more details to be elaborated in later sections. We use the weighted average of the matched samples following our TEXTMATCH method in Eq. (6) through lines 25 to 34. In our experiments, we use the interpolation of up to top 10 matched papers. We encourage future work to explore other hyperparameter settings too. Given the PCI estimation, the main spirit of the GETACIANDTCI(a) function is to average or sum over all the follow-up studies of paper a, following the theoretical formulation in Eqs. (2) and (3) and implemented in our algorithm through lines 7 to 12.

heading: 3.3.3 Key Challenges and Mitigation Methods
text: We address several technical challenges below.

heading: 3.3.3.1 Confounders of Various Types
text: First, as we mentioned in the causal graph in Figure 2, the confounder set consists of a text variable (title and abstract concatenated together) and an ordinal variable (publication year). Therefore, the similarity operation Sim between two papers should be customized. For our specific use case, we first filter by the publication year in line 16, as it is not fair to compare the citations of papers published in different years. Then, we apply the cosine similarity method paper embeddings as in line 22. As a
Algorithm 1 Get causal impact indices ACI and TCI 1: Input: Paper a. 2: procedure GETACIANDTCI(a) 3: D ← GetDesc(a) ▷ Get descendants by DFS 4: B ← GetChildren(a) 5: B′ ← SampleSubset(B) ▷ See Section 3.3.3.4 6: C ← EntireSet\{D ∪ {a}} ▷ Get non-descendants 7: ACI← 0 8: for each bi in B′ do 9: Ii ← GETPCI(a, bi,C) 10: ACI← ACI + 1|B′| · Ii 11: end for 12: TCI← ACI · |B| 13: return ACI and TCI 14: end procedure
15: procedure GETPCI(a, b,C) 16: CsameYear ← FilterByYear(C, byear) 17: for each pi in CsameYear ∪ {b} do 18: ti ← RemoveMediator(TitleAbstracti) 19: end for 20: Ccoarse ← BM25(b,CsameYear, topk = 100) 21: for each ci in Ccoarse do 22: mi ← Sim(tb, ti) 23: end for 24: Ctop10 ← argmax10m(Ccoarse)

heading: 25: M ← 0
text: 26: for each ci in Ctop10 do ▷ For the normalization later 27: M ←M +mi 28: end for 29: ŷt=0 ← 0 30: for each ci in Ctop10 do 31: wi ← miM 32: ŷt=0 ← ŷt=0 + wi · yi ▷ Apply Eq. (6) 33: end for 34: return yb − ŷt=0 35: end procedure
general solution, we recommend to separate hard logical constraints, and soft matching preferences, where the hard constraints should be imposed to filter the data first, and then all the rest of the variables can be concatenated to apply the similarity metric on.

heading: 3.3.3.2 Excluding the Mediators from Confounders
text: Another key challenge to highlight is that the text variable we use for the confounder might accidentally include some mediator information. For example, the quality or performance of a paper could be expressed in the abstract, such as “we achieved 90% accuracy.” Therefore, we conduct a specific preprocessing procedure before feeding the text variable to the similarity function. For the RemoveMediator function in line 18, we exclude all numerical expressions such as percentage numbers, as well as descriptions such as “state-of-theart.” For generalizability, the essence of this step is a entanglement action to separate the confounder variable (in this case, the research content) and all the descendants of the treatment variable (in this case, mentions of the performance). For more complicated cases in future work, we recommend a separate disentanglement model to be applied here.

heading: 3.3.3.3 Efficient Matching-and-Reranking Method
text: Since we use one of the largest available paper databases, the Semantic Scholar dataset (Kinney et al., 2023) containing 206M papers, we need to optimize our algorithm for large-scale paper matching. For example, after we filter by the publication year, the number of candidate papers CsameYear could be up to 8.8M. In order to conduct text matching across millions of papers, we use a matching-and-reranking approach, by combining two NLP tasks, information retrieval (IR) (Manning et al., 2008) and semantic textual similarity (STS) (Majumder et al., 2016; Chandrasekaran and Mago, 2022).
Specifically, we first run large-scale matching to obtain 100 candidates papers (line 20) using the common IR method, BM25 (Robertson and Zaragoza, 2009). Briefly, BM25 is a bag-of-words retrieval function that uses term frequencies and document lengths to estimate relevancy between two text documents. Deploying this method, we can find a set of candidate papers for, for example, two million papers, at a speed 250x faster than the text embedding cosine similarity matching. Then, we conduct a fine-grained reranking using cosine similarity (lines 21 to 23). In the cosine similarity matching process, we use the MPNet model (Song et al., 2020) to encode the text of each paper ci into an embedding ti, with which we get the matching score mi according to Eq. (5) in line 22, and the normalized weight wi by Eq. (6) in line 31.

heading: 3.3.3.4 Numerical Estimation
text: Given the large number of papers, it is numerically challenging to aggregate the TCI from individual PCIs, because the number of follow-up papers for a study can be up to tens of thousands, such as the 57,200 citations by 2023 for the ImageNet paper (Deng et al., 2009). To avoid extensively running PCI for all follow-up papers, we propose a new numerical estimation method using a carefully designed random paper subset.
A naive way to achieve this aggregation is Monte Carlo (MC) sampling. However, unfortunately, MC sampling requires very large sample sizes when it comes to estimating long-tailed distributions, which is the usual case of citations. Since citations are more likely to be concentrated in the head part of the distribution, we cannot afford the computational budget for huge sample sizes that cover the tails of the distribution. Instead, we propose a novel numerical estimation method for sampling the follow-up papers, inspired by importance sampling (Singh, 2014; Kloek and van Dijk, 1976).
Our numerical estimation method works as follows: First, we propose the formulation that the relation between ACI and TCI is an integral over all possible paper b’s. Then, we formulated the above sampling problem as integral estimation or area-under-the-curve estimation. We draw inspiration from Simpson’s method, which estimates integrals by binning the input variable into small intervals. Analogously, although we cannot run
through all PCIs, we use citations as a proxy, bin the large set of follow-up papers according to their citations into n equally-sized intervals, and perform random sampling over each bin, which we then sum over. In this way, we make sure that our samples come from all parts of the long-tailed distribution and are a more accurate numerical estimate for the actual TCI.

heading: 4 Performance Evaluation
text: The contribution of a paper is inherently multidimensional, making it infeasible to encapsulate its richness fully through a scalar. Yet the demand for a single, comprehensible metric for research impact persists, fueling the continued use of traditional citations despite their known limitations. In this section, we show how our new metrics significantly improve upon traditional citations by providing quantitative evaluations comparing the effectiveness of citations, Semantic Scholar’s highly influential (SSHI) citations (Valenzuela-Escarcega et al., 2015), and our CAUSALCITE metric.

heading: 4.1 Experimental Setup
text: Dataset We use the Semantic Scholar dataset (Lo et al., 2020; Kinney et al., 2023)2 which includes a corpus of 206M scientific papers, and a citation graph of 2.4B+ citation edges. For each paper, we obtain the title and abstract for the matching process. We list some more details of the dataset in Appendix B, such as the number of papers reaching 8M per year after 2012.
Selecting the Text Encoder When projecting the text into the vector space, we need a text encoder with a strong representation power for scientific publications, and is sensitive towards two-paper similarity comparisons regarding their abstracts containing key information such as the research topics. For the representation power for scientific publications, instead of generaldomain models such as BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019), we consider LLM variants3 pretrained on large-scale scientific text, such as SciBERT (Beltagy et al., 2019), SPECTER (Cohan et al., 2020), and MPNet (Song et al., 2020).
To check the quality of two-paper similarity measures, we conduct a small-scale empirical study comparing human-ranked paper similarity and model-identified semantic similarity in Appendix A.3, according to which MPNet outperforms the other two models.
Implementation Details We deploy the all-mpnet-basev2 checkpoint of the MPNet using the transformers Python package (Wolf et al., 2020), and set the batch size to be 32. For the set of matched papers, we consider papers with cosine similarity scores higher than 0.81, which we optimize empirically on 100 random paper pairs. We take the top ten most similar papers above the
2https://api.semanticscholar.org/api-docs/datasets 3Note that we follow the standard notion by Yang et al.
(2023) to refer to BERT and its variants as LLMs.
threshold. In special cases where there is no matched paper above the threshold, it means that no other paper works on the same idea as Paper b, and we make the counterfactual citation number to be zero, which also reflects the quality of Paper b as its novelty is high.
To enable efficient operations on the large-scale citation graph, we use the Dask framework,4 which optimizes for data processing and distributed computing. We optimize our program to take around 100GB RAM, and on average 25 minutes for each PCI(a, b) after matching against up to millions of candidates. More implementation details are in Appendix A.1. For the estimation of TCI, we empirically select the sample size to be 40, which is a balance between the computational time and performance, as found in Appendix A.2.

heading: 4.2 Author-Identified Paper Impact
text: In this experiment, we follow the evaluation setup in Valenzuela-Escarcega et al. (2015) to use an annotated dataset (Zhu et al., 2015) comprised of 1,037 papers, annotated according to whether they serve as significant prior work for a given follow-up study. Although paper quality evaluation can be tricky, this dataset was cleverly annotated by first collecting a set of follow-up studies and letting one of the authors of each paper go through the references they cite and select the ones that significantly impact their work. In other words, for a given paper b, each reference a is annotated as whether a has significantly impacted b or not.
Table 1 reports the accuracy of our CAUSALCITE metric, together with two existing citation metrics: citations, and SSHI citations (Valenzuela-Escarcega et al., 2015). See the detailed derivation of the accuracy scores in Appendix C.2. From this table, we can see that our CAUSALCITE metric achieves the highest accuracy, 80.29%, which is 5 points higher than SSHI, and 9 points higher than the traditional citations.

heading: 4.3 Test-of-Time Paper Analysis
text: The test-of-time (ToT) paper award is a prestigious honor bestowed upon papers that have made substantial and enduring impacts in their field. In this section, we collect a dataset of 792 papers, including 72 ToT papers, and a control group of 10 randomly selected non-ToT papers from the same conference and year as each ToT paper. To collect this ToT paper dataset, we look into ten leading AI conferences spanning general AI (NeurIPS, ICLR, ICML, and AAAI), NLP (ACL, EMNLP, and NAACL), and CV (CVPR, ECCV, and ICCV), for which we go through each of their websites to identify all available ToT papers.5
In Table 2, we show the correlations of various metrics with the ToT awards. In this table, CAUSAL-
4https://dask.org/ 5We get this list by selecting the top conferences on Google Scholar using the h5-Index ranking in each of the above domains: general AI (link), CV (link), and NLP (link).
Metric Accuracy Citations 71.33 SSHI Citations 75.25 CAUSALCITE 80.29
Table 1: Accuracy of all three citation metrics.
Metric Corr. Coef. Citations 0.491 SSHI Citations 0.317 TCI 0.640
Table 2: Correlation coefficients of each metric and ToT paper award by Point Biserial Correlation (Tate, 1954).
CITE achieves the highest correlation of 0.639, which is +30.14% better than that of citations. Furthermore, we visualize the correspondence of our metric and ToT, and observe a substantial difference between the CAUSALCITE distributions of ToT vs. non-ToT papers in Figure 3. We also show three examples of ToT papers in Figure 4, where the ToT papers differ from the non-ToT papers by one or two orders of magnitude.

heading: 4.4 Topic Invariance of CAUSALCITE
text: A well-known issue with citations is their inconsistency across different fields. What might be considered a large number of citations in one field might be seen as average in another. In contrast, we show that our ACI index does not suffer from this issue. We show this using our ToT dataset, where we control for the quality of the papers to be ToT but vary the domain by the three fields: general AI, CV, and NLP. We observe in Table 3 that even though some domains have significantly more citations (for instance, CV ToT papers have, on average, 4.05 times more citations than NLP), the ACI remains consistent across various fields.

heading: 5 Findings
text: Having demonstrated the effectiveness of our metrics, we now explore some open-ended questions: (1) Do best papers have high causal impact? (Section 5.1) (2) How does the CAUSALCITE value distribute across papers? (Section 5.2) (3) What is the impact of some famous papers evaluated by CAUSALCITE? (Section 5.3) (4) Can we use this metric to correct for citations? (Section 5.4).

heading: 5.1 Do Best Papers Have High Causal Impact?
text: Selecting best paper awards is an arguably much harder task than ToT papers, as it is difficult to predict of the impact of a paper when it is just newly published. There-
fore, we are interested in the actual causal impact of best papers. Similar to our study on ToT papers, we collect a dataset of 444 papers including 74 best papers and a control set of random 5 non-best papers from the same conference in the same year, using the same set of the top ten leading AI conferences. We find that the correlation of the CAUSALCITE metric with best papers is 0.348, which is very low compared to the 0.639 correlation with the ToT papers. This shows that the best papers do not necessarily have a high causal impact. One interpretation can be that the best paper evaluation is a forecasting task, which is much more challenging than the retrospective task of ToT paper selection.

heading: 5.2 What Is the Nature of the CAUSALCITE Distribution?
text: We explore how the CAUSALCITE scores are distributed across papers in general. We plot Figure 5 using a random set of 100 papers from the Semantic Scholar dataset, which is a reasonably large size given the computation budget mentioned in Section 4.1. From this plot, we can see a power law distribution with a long tail, echoing with the common belief that the paper impact follows the power law, with high impact concentrated in a relatively small portion of papers.

heading: 5.3 Selected Paper Case Study
text: In addition to the shape of the overall distribution, we also look at our metric’s correspondence to some selected papers shown in Table 4. For example, we know that the Transformer paper (Vaswani et al., 2017) is a
more foundational work than its follow-up work BERT (Devlin et al., 2019), and BERT is more foundational than its later variant, RoBERTa (Liu et al., 2019). This monotonic trend is confirmed in their TCI and ACI values too. Again, this is a preliminary case study, and we welcome future work to cover more papers.

heading: 5.4 Discovering Quality Papers beyond Citations
text: Another important contribution of our metric is that it can help discover papers that are traditionally overlooked by citations. To achieve the discovery, we formulate the problem as outlier detection, where we first use a linear projection to handle the trivial alignment of citations and CAUSALCITE, and then analyze the outliers using the interquartile range (IQR) method (Smiti, 2020). See the exact calculation in Appendix C.1. We show the three subsets of papers in Table 5, where the two outlier categories, the overcited and undercited papers, correspond to the false positive and false negative oversight by citations, respectively. An additional note is that, when we look into some characteristics of the three categories, we find that the citation frequency in result section, i.e., the percentage of times they are cited in results section compared to all the citations, correlates with these categories. Specifically, we find that the undercited papers tend to have more of their citations concentrated in the results section, which usually indicates that this paper constitutes an important baseline for a follow-up study, while the overcited papers tend to be cited out of the results section, which tends to imply a less significant citation.

heading: 6 Related Work
text: The quantification of scientific impact has a rich history and continuously evolves with technology. Bibliometric analysis has been largely influenced by early methods that relied on citation counts (Garfield et al., 1964; Garfield, 1972, 1964). Hou (2017) investigate the evolution of citation analysis, employing reference publication year spectroscopy (RPYS) to trace its historical development in scientometrics. Donthu et al. (2021) provide practical guidelines for conducting bibliometric
analysis, focusing on robust methodologies to analyze scientific data and identify emerging research trends.
Indices such as the h-index, introduced by Hirsch (2005), are established tools for measuring research impact. The more recent Relative Citation Ratio (RCR), developed by Hutchins et al. (2016), provides a field-normalized alternative to traditional metrics. Valenzuela-Escarcega et al. (2015) introduced SSHI, an approach to identify meaningful citations in scholarly literature. However, these metrics are not without limitations. As Wróblewska (2021) discussed, conventional citation-based metrics often fail to capture the multidimensional nature of research impact. In this context, Elmore (2018) discussed the Altmetric Attention Score, which evaluates the broader societal and online impact of research.
With the increasing availability of large datasets and the advent of digital technologies, new opportunities for bibliometric analysis have emerged. Iqbal et al. (2021) highlighted the role of NLP and machine learning in enhancing in-text citation analysis. Similarly, Umer et al. (2021) explored the use of textual features and SMOTE resampling techniques in scientific paper citation analysis. Jebari et al. (2021) analyzed citation context to detect research topic evolution, showcasing data analysis for scientific discourse. Chang et al. (2023) explored augmenting citations in scientific papers with historical context, offering a novel perspective on citation analysis. Manghi et al. (2021) introduced scientific knowledge graphs, an innovative method for evaluating research impact. Bittmann et al. (2021) explored statistical matching in bibliometrics, discussing its utility and challenges in post-matching analysis. The use of AI in bibliometric analysis is highlighted in research by Chubb et al. (2022) and the systematic review of AI in information systems by Collins et al. (2021). Network analysis approaches, as discussed by Chakraborty et al. (2020) in the context of patent citations and by Dawson et al. (2014) in learning analytics, further illustrate the diverse applications of advanced methodologies in understanding citation patterns.

heading: 7 Conclusion
text: In this study, we propose CAUSALCITE, a novel causal formulation for paper citations. Our method combines traditional causal inference methods with the recent advancement of NLP in LLMs to provide a new causal outlook on paper impact by answering the causal question: ”Had this paper never been published, what would be the impact on this paper’s current follow-up studies?”. With extensive experiments and analyses using expert ratings and test-of-time papers as criteria for impact, our new CAUSALCITE metric demonstrates clear improvements over the traditional citation metrics. Finally, we use this metric to investigate several open-ended questions like “Do best papers have high causal impact?”, conduct a case study of famous papers, and suggest future usage of
our metric for discovering good papers less recognized by citations for the scientific community.
Limitations and Future Work There are several limitations for our work. For example, as mentioned previously, our metric has a high computational budget. Future work can explore more efficient optimization methods. Also, we model the content of the paper by its title and abstract, it could also be possible for future work to benefit from modeling the full text, given appropriate license permissions.
As for another limitation, our study is based on data provided by the Semantic Scholar corpus. This corpora has certain properties such as being more comprehensive with computer science papers, but less so in other disciplines. Its citation data also has a delay compared to Google Scholar, so for the newest papers, the citation score may not be accurate, making it more difficult to calculate our metric.
Additionally, our study provides a general framework for causal inference given a causal graph that involves text. It is totally possible that for a more fine-grained problem, the causal graph will change, in which case, we undersuggest future researchers to derive the new backdoor adjustment set, and then adjust the algorithm accordingly. An example of such a variable could be the author information, which might also be a confounder.
Finally, since quality evaluation of a paper is a multifaceted task, theoretically, a single number can never give more than a rough approximation, because it collapses multiple dimensions into one and loses information. Our argument in this paper is just to show that our formulation is theoretically more accurate than the citation formulation. We take one step further, instead of solving the quality evaluation problem which is much more nuanced. Some intrinsic problems in citations that we can also not solve (because our metrics still rely on using citations, just contrasting them in the right away) include (1) if a paper is newly published, with zero citations, there is no way to obtain a positive causal index, and (2) we do not solve the fair attribution problem when multiple authors share credit of a paper, as our metric is not sensitive towards authors.
Ethical Considerations Data Collection and Privacy The data used in this work are all from Open Source Semantic Scholar data, with no user privacy concerns. The potential use of this work is for finding papers that are unique and innovative but do not get enough citations due to lack of popularity or awareness of the field. This metric can act as an aid when deciding impact of papers, but we do not suggest its usage without expert involvement. Through this work, we are not trying to demean or criticize anyone’s work we only intend to find more papers that have made a valuable contribution to the field.
CS-Centric Perspective The authors of this paper work in Computer Science (mostly Machine Learning) hence a lot of analysis done on the quality of papers that required sanity checks are done on ML papers. The conferences selected for doing the ToT evaluation were also CS Top conferences, hence they might have induced some biases. The metric in general has been created generically and should be applicable to other domains as well, the Author Identified Most Influential Papers study is also done on a generalized dataset, but we encourage readers in other disciplines to try out the metric on papers from their field.
Author Contributions
This project originates as part of the AI Scholar series of projects that Zhijing Jin started since 2021, as she identified that causal inference over papers is a valuable research setting with sufficient data and rich causal phenomena. Bernhard Schölkopf came up with the formulation that the action of citation itself has a causal nature, and can thus be formulated as a causal inference question. Zhijing, Bernhard, and Siyuan Guo settled down the overall project design.
After the initial idea formulation, Ishan Kumar and Zhijing Jin operationalized the entire project, with vast efforts in identifying the data source; improving the theoretical formulation (together with Ehsan Mokhtarian, and Bernhard); speeding up the code efficiency; designing the evaluation and analysis protocols (with the insightful supervision from Mrinmaya Sachan and Bernhard, and suggestions from Siyuan); and implementing all the evaluations (with the help of Yuen Chen). In the writing stage, Mrinmaya gave substantial guidance to structure the storyline of the paper, and Zhijing, Ehsan, Ishan, and Mrinmaya contributed significantly to the writing, with various help and suggestions from all the other authors.

heading: Acknowledgment
text: During the idea formulation stage, we are grateful for the research discussions with Kun Zhang on the vision of the AI Scholar series of projects. During the implementation of our paper, we thank Zhiheng Lyu for his suggestions on efficient computer algorithm over massive graphs and large data. We also thank labmates from Max Planck Institute for constructive feedback and help on data annotation. We thank Vincent Berenz, Felix Leeb, and Luigi Gresele for their generous support with computation resources.
This material is based in part upon works supported by the German Federal Ministry of Education and Research (BMBF): Tübingen AI Center, FKZ: 01IS18039B; by the Machine Learning Cluster of Excellence, EXC number 2064/1 – Project number 390727645; by the John Templeton Foundation (grant #61156); by a Responsible AI grant by the Haslerstiftung; and an ETH Grant
(ETH-19 21-1). Zhijing Jin is supported by PhD fellowships from the Future of Life Institute and Open Philanthropy, as well as the travel support from ELISE (GA no 951847) for the ELLIS program.

heading: A Additional Implementation Details
text: A.1 Time and Space Complexity Details For the time cost of running the causal impact indices, each PCI(a, b) takes around 1,500 seconds, or 25 minutes. Multiplying this by 40 samples per paper a, we spend 16.67 hours to calculate each ACI or TCI for the paper’s overall impact. For a fine-grained division into the time cost, the majority of the time is spend on the BM25 indexing (800s) and the sentence embedding cosine similarities calculation (400s). The rest of the time-consuming steps are the BFS search (150-200s every time) to identify descendants and non-descendants of a paper.
For the space complexity, we loaded the 2.4B edges of the citation graph into a parquet gzip format for faster loading, and use Dask’s lazy load operation to load it part by part to RAM for better parallelization. The program can fit into different sizes of RAMs by modifying the number of partitions and reducing the number of workers in Dask, at the cost of an increased computation time. On the hard disk, citation graph takes up 19G space, and paper data takes 11G.
A.2 Numerical Estimation Method: Finding the Sample Size
For our numerical estimation method, we first calculate the ACI on a subset of carefully sampled papers and then aggregate it to TCI. One design choice question is how to decide the size of this random subset. In our case, we need to balance both the computation time (25 minutes per pairwise paper impact) and the estimation accuracy. To identify the best sample size, we conduct a smallscale study, first obtaining the TCI using our upperbound budget of n = 100 samples and then gradually decreasing the number of samples to see if there is a stable point in the middle which also leads to a result close to that obtained with 100 samples. In Figure 6, we show the trade-off of the two curves, the error curve and time cost, where we can see n = 40 seems to be a good point balancing the two. It is at the elbow of the arrow curve, making it relatively close to the estimation result of n = 100, and also in the meantime vastly saving our computational budget, enabling us to run efficient experiments for more analyses.
A.3 Experiment to Select the Best Embedding Method
When selecting the text encoder for our TEXTMATCH method, we compare among the three LLMs pre-trained on scientific papers, SciBERT, MPNet, and SPECTER. Specifically, we conduct a small-scale experiment to see how much the similarities scores based on the embedding of each model align with human annotations. As for the annotation process, we first collect a set of random papers, and for each such paper (which we call
a pivot paper), we identify ten papers, from the most similar to the least, with monotonically decreasing similarity. We collect a total of 100 papers consisting of ten such collections, for which we show an example in Table 6. Then we see how the resulting similarity scores conform to this order by deducting the percentage of papers that are out of place in the ranking.
We find that MPNet correlates the best with human judgments, achieving an accuracy of 82%, which is 10 points better the second best one, SPECTER, which gets 72%, and 18 points better than SciBERT with a score of 64%. It also gives more distinct scores to papers with different levels of similarity. This capability advantage may be attributed to its Siamese network objectives in the training process (Song et al., 2020). We opensourced our annotated data in the codebase.

heading: B Dataset Overview
text: For the Semantic Scholar dataset (Kinney et al., 2023; Lo et al., 2020), we obtain the set of 206M papers using the “Papers” endpoint to get the Paper Id, Title, Abstract, Year, Citation Count, Influential Citation Count (Valenzuela et al., 2015), and the Reference Count for each paper. The papers come from a variety of fields such as law, computer science, linguistics, chemistry, material science, physics, geology, etc. For the citation network with 2.4B edges, we use the Semantic Scholar Citations API to get each edge of the citation graph in a triplet format of (fromPaper, toPaper, isInfluentialCitations).
In general, the number of publications shows an explosive increase in recent years. Figure 7 shows the number of papers publish the per year, which reaches on average 7.5M per year since 2010. Figure 8 shows the number of references each paper cites, which also increases from less than five before 1970s, to around 25 in recent years. Both statistics support the need of our paper, which helps distinguish the quality of scientific studies given such massive growths of papers.

heading: C Additional Analyses
text: C.1 Citation Outlier Analysis
For the outlier detection, we first visualize the scatter plot between our CAUSALCITE and citations. Then, we
fit a log-linear regression to learn the line log(TCI) = 1.026 log(Cit)−0.541, as shown in Figure 9, with a root mean squared error (RMSE) of 0.6807. After fitting the function, we use the interquartile range (IQR) method (Smiti, 2020), which identify as outliers any samples that are either lower than the first quartile by over 1.5 IQR, or higher than the third quartile by more than 1.5 IQR, where IQR is the difference between the first and third quartile.
We denote as overcited papers the ones that are identified as outliers by the IQR method due to too many citations than what it should have deserved given the CAUSALCITE value. Symmetrically, we denote as undercited papers the ones that are identified as outliers by the IQR method due to too few citations than what it should have deserved given the CAUSALCITE value. And we denote the non-outlier papers as the aligned ones.
C.2 Additional Information for the Author-Identified Paper Impact Experiment
As mentioned in the main paper, the dataset is annotated by pivoting on each paper b, and going through each of its references a to label whether a has a significant influence on b or not. We show an example of paper b and all its 31 references in Table 7. We calculate the accuracy of each metric with the spirit that each nonsignificant paper’s impact value should be lower than a significant paper’s. Specifically, we go through the score of each non-significant paper, and count its accuracy as 100% if it is lower than all the significant papers’, or the more general form nlower/|Sig| of conformity, where nlower is the number of significant papers which it is lower than, and |Sig| is the total number of significant papers. Then we report the overall accuracy for each score by averaging the accuracy numbers on each nonsignificant paper. To illustrate the idea better, we show the calculated accuracy numbers for all three metrics on our example batch in Table 7.
C.3 Step Curve for PCI Values Given a Fixed Paper b
Apart from the long-tailed curve shape of TCI in Section 5.2, we also look into the pairwise paper impacts by PCI. If we fix the paper b, we can see that PCI(·, b) often has a step curve shape in Figure 10. The reason behind it lies in the nature of PCI, which is calculated based on the top K papers that are similar in content with paper b, but do not cite paper a. When we go through different references, e.g., from a1 to a2 of the same paper b, the semantically matched top K papers could still be largely the same pool, and only change when some papers in the pool need to be swapped when releasing the constraint to be that they can cite a1, and adding the constraint that they cannot cite a2.

heading: Future Work
text: Zhijing Jin is supported by PhD fellowships from the Future of Life Institute and Open Philanthropy, as well as the travel support from ELISE (GA no 951847) for the ELLIS program