2311.02790v3

# CausalCite: A Causal Formulation of Paper Citations > Equal contribution. ## 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 high-dimensional 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. Our code is available at https://github.com/causalNLP/causal-cite. ## 1 Introduction 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). <details> <summary>x1.png Details</summary>  ### Visual Description ## Conceptual Diagram: Causal Impact of a Prior Paper on a Follow-up Study ### Overview This image is a conceptual diagram illustrating a method for estimating the causal impact of a prior academic paper ("Paper a") on its follow-up study ("Paper b"). It uses a counterfactual framework to isolate the effect of Paper a's existence on a success metric of Paper b. The diagram is divided into two main sections: the real-world scenario at the top and the constructed counterfactual scenario at the bottom, connected by a large downward arrow. ### Components/Axes The diagram is not a chart with axes but a flow of conceptual components. **Top Section (Real World):** * **Main Title:** "What is the impact of **Paper a** on its **followup study b**?" (Text is black, with "Paper a" in red and "followup study b" in blue). * **Left Element:** A red oval labeled "**Paper a**" in bold red text. * **Right Element:** A blue oval labeled "**Paper b**" in bold blue text. * **Connecting Arrow:** A black arrow points from Paper a to Paper b, labeled "**Causal Effect**" above it. * **Attributes List:** To the right of Paper b, a list titled "**Attributes**" (bold black) includes: * "Paper topic" * "Publication year" * "..." (ellipsis indicating other attributes) * "Success *metric*: *y*" (where *y* is in italics). **Transition:** * A large, solid blue arrow points downward from the top section to the bottom section. **Bottom Section (Counterfactual Situation):** * **Section Title:** "We make a counterfactual situation" (bold black text). * **Descriptive Text:** Two lines of text: * Left: "Had **Paper a** not existed..." (in red). * Right: "Yet **Paper b** still has the same topic, year, etc." (in blue). * **Left Element:** The same red oval for "**Paper a**", but now with a large red "X" crossed over it. * **Right Element:** The same blue oval for "**Paper b**". * **Connecting Arrow:** A black arrow still points from the crossed-out Paper a to Paper b. * **Attributes List:** Identical to the top section, listing "Attributes" (Paper topic, Publication year, ...) and "Success *metric*: *y'*" (where *y'* is in italics and a different color, appearing brownish-orange). * **Final Question:** At the very bottom, in brownish-orange text: "What would the counterfactual success metric *y'* be?" ### Detailed Analysis The diagram presents a logical, step-by-step thought experiment: 1. **Factual World:** We observe Paper b, which has certain attributes (topic, year) and a measurable success metric *y* (e.g., citation count, impact factor). Paper a is posited to have a causal effect on Paper b. 2. **Counterfactual Construction:** We imagine a world identical to the factual one in all respects (Paper b's attributes remain constant) except for one key change: Paper a does not exist. This is visually represented by the red "X" over Paper a. 3. **Core Question:** In this imagined world, what would the success metric for Paper b be? This hypothetical value is denoted as *y'*. 4. **Implied Calculation:** The causal impact of Paper a on Paper b is then conceptualized as the difference between the observed success (*y*) and the counterfactual success (*y'*). The diagram's purpose is to frame the problem of estimating *y'*. ### Key Observations * **Color Coding:** Consistent use of red for Paper a and blue for Paper b aids visual tracking. The success metric changes color from black (*y*) to brownish-orange (*y'*) to emphasize its different, hypothetical nature. * **Visual Metaphor:** The red "X" is a clear, universal symbol for negation or removal, effectively communicating the counterfactual condition. * **Attribute Invariance:** The text explicitly states that Paper b's attributes (topic, year) are held constant between the factual and counterfactual worlds. This is a critical assumption for a valid causal comparison. * **Ellipsis (...):** Indicates that the list of attributes is not exhaustive; other confounding variables might need to be controlled for in a real analysis. ### Interpretation This diagram is a pedagogical tool explaining the **counterfactual framework for causal inference** in the context of academic influence. It translates the abstract question "What did Paper a contribute to Paper b's success?" into a more concrete, albeit hypothetical, question: "How successful would Paper b have been if Paper a had never been published?" The underlying principle is that a true causal effect can only be measured by comparing what actually happened with what would have happened under identical conditions except for the cause in question. Since we cannot observe both *y* and *y'* for the same Paper b, the challenge (implied but not solved by the diagram) is to *estimate* *y'* using methods like matching, regression, or instrumental variables. The diagram successfully isolates the core logical structure of the problem. It highlights that the goal is not merely to find a correlation between Paper a and Paper b's success, but to estimate the specific contribution of Paper a's existence, holding all other features of Paper b constant. This is a foundational concept in fields like econometrics, epidemiology, and, as shown here, the science of science (sciometrics). </details> Figure 1: An overview of our research question. A traditional approach to recognize paper quality is peer review, a mechanism that requires large efforts, 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 matching 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 $206$ M papers and $2.4$ B 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. 1. We develop TextMatch, a new method that leverages LLMs and causal inference to estimate the counterfactual causal effect of a paper. 1. We conduct comprehensive analyses, including various performance evaluations and present new findings using our metric. ## 2 Problem Formulation 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. 2.0.0.0.1 Citation Graph In the citation graph $\mathbb{G}\coloneqq(\mathbb{P},\mathbb{L})$ , $\mathbb{P}$ is a set of papers, and each edge $\ell_{i,j}\in\mathbb{L}$ indicates that an earlier paper ${p}_{i}$ influences (i.e., is cited by) a follow-up paper ${p}_{j}$ . 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. <details> <summary>x2.png Details</summary>  ### Visual Description ## Causal Diagram: Identifying Variables to Control for Estimating Causal Effect Size ### Overview The image is a technical diagram illustrating a causal inference framework. It aims to answer the question: "What is the causal effect size?" of a specific treatment on an outcome within academic research. The diagram uses a causal graph (Directed Acyclic Graph - DAG) to visually identify which variables should and should not be statistically controlled for to obtain an unbiased estimate of the causal effect. ### Components/Axes The diagram is structured in two main sections: **1. Top Section (Simplified Target):** * **Title/Question:** "Target: What is the causal effect size?" (Text in orange). * **Treatment Node (T):** A blue oval labeled "**Treatment T**" with the sub-text "**Building Paper *b* on Paper *a***". It is accompanied by an icon of a syringe with a question mark. * **Effect Node (Y):** An orange oval labeled "**Effect Y**" with the sub-text "**Success of Paper *b***". It is accompanied by an icon of a gold medal/ribbon. * **Causal Arrow:** A gray arrow points from Treatment T to Effect Y, with a thought bubble containing a question mark above it, symbolizing the unknown causal effect. **2. Bottom Section (Detailed Causal Graph):** * **Introductory Text:** "We use the causal graph to identify the correct variables to control for:" (Text in black). * **Nodes (Variables):** * **Treatment T (Blue Oval):** Same as above: "**Treatment T / Building Paper *b* on Paper *a***". * **Effect Y (Orange Oval):** Same as above: "**Effect Y / Success of Paper *b***". * **Confounders X (Green Oval):** Labeled "**Confounders X**". Contains the text "**Title+Abstract**" and "**Year**". Below, in smaller text: "incl., topic, research question". A green checkmark icon is placed to its right with the text "**Should be controlled for**". * **Mediators (Pink Oval):** Labeled "**Mediators**". Contains the text "**Performance**" (with example "e.g., '90%'") and "**Venue**" (with example "e.g., 'ACL'"). A red "X" icon is placed below it with the text "**Should *not* be controlled for**". * **Colliders (Pink Oval):** Labeled "**Colliders**". Contains the text "**Post-Hoc Award ...**" (with example "e.g., 'Test of Time'"). A red "X" icon is placed above it. * **T's Ancestors (Gray Oval, faded):** Labeled "**T's Ancestors (but not Y's)**". Contains the text "**Paper *a*'s venue, publicity, ...**". * **Y's Ancestors (Gray Oval, faded):** Labeled "**Y's Ancestors (but not T's)**". Contains the text "**Paper *b*'s efforts into PR ...**". * **Causal Relationships (Arrows):** * **Gray Arrows (from faded nodes):** An arrow points from "T's Ancestors" to "Treatment T". An arrow points from "Y's Ancestors" to "Effect Y". * **Black Arrows (main graph):** * From "Confounders X" to both "Treatment T" and "Effect Y". * From "Treatment T" to "Mediators". * From "Mediators" to "Effect Y". * From "Treatment T" to "Colliders". * From "Effect Y" to "Colliders". ### Detailed Analysis The diagram explicitly defines the variables involved in the research question: * **Treatment (T):** The act of a new paper (*b*) building upon a prior paper (*a*). * **Outcome (Y):** The success of the new paper (*b*). * **Confounders (X):** Variables that influence both the treatment (whether paper *b* builds on *a*) and the outcome (success of *b*). The diagram specifies these include the **Title+Abstract** (encompassing topic and research question) and the **Year**. These **must be controlled for** to block backdoor paths and isolate the causal effect. * **Mediators:** Variables on the causal pathway from T to Y. The diagram lists **Performance** (e.g., a metric like "90%") and **Venue** (e.g., a conference like "ACL"). Controlling for these would block the very effect one wants to measure, so they **should not be controlled for**. * **Colliders:** Variables caused by both T and Y. The example given is a **Post-Hoc Award** (e.g., "Test of Time"). Conditioning on colliders opens spurious paths, so they **should not be controlled for**. * **Ancestors:** Variables that are causes of only T or only Y, but not both (faded in the diagram). These are not confounders and are generally not the focus for control in this specific identification strategy. ### Key Observations 1. **Clear Visual Coding:** The diagram uses color (green for "control", pink/red for "do not control") and icons (checkmark vs. X) to reinforce the analytical rules. 2. **Emphasis on Identification:** The core message is about *variable selection for causal identification*, not measurement. It answers "what to adjust for" before running an analysis. 3. **Contextual Examples:** Abstract concepts are grounded with concrete academic examples (e.g., "ACL" for venue, "Test of Time" for award), making the diagram applicable to scientometrics or research analysis. 4. **Spatial Layout:** The confounders are placed centrally above the main T->Y pathway, visually representing their role in creating a "backdoor" path. Mediators are placed directly on the pathway, and colliders are placed below, receiving arrows from both T and Y. ### Interpretation This diagram is a pedagogical tool for applying causal inference principles to study the impact of academic lineage (building on prior work) on paper success. It argues that to estimate the true causal effect of "building on paper *a*" on "the success of paper *b*", a researcher must statistically adjust for shared causes like the paper's topic (from Title+Abstract) and its publication year. Adjusting for mediators like the eventual performance score or publication venue would be a mistake, as these are part of the mechanism through which the lineage might exert its effect. Similarly, adjusting for a post-hoc award (a collider) would introduce bias. The underlying assumption is that the causal effect is identifiable from observational data if the correct set of confounders (X) is measured and adjusted for. The diagram effectively translates a complex statistical concept into a visual map for research design, highlighting common pitfalls (controlling for mediators/colliders) in causal analysis. </details> Figure 2: The causal graph of our study. 2.0.0.0.2 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 $\log_{10}$ 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 $b$ ). ### 2.1 CausalCite Indices In this section, we introduce various indices that measure the causal impact of a paper. 2.1.0.0.1 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 $\mathrm{PCI}(a,b)$ by unit-level causal effect: $$ \displaystyle\mathrm{PCI}(a,b)\coloneqq y^{t=1}-y^{t=0}~{}, \tag{1} $$ where we compare the outcomes $Y$ of the paper $b$ had it been influenced by paper $a$ or not, denoted as the actual $y^{t=1}$ and the counterfactual $y^{t=0}$ , respectively. Note that the counterfactual $y^{t=0}$ can never be observed, but only estimated by statistical methods, as we will discuss in Section 3.2. 2.1.0.0.2 Single-Paper Quality Metrics: Total Causal Impact (TCI) and Average Causal Impact (ACI). Let $\bm{S}$ denote the set of all follow-up studies of paper $a$ . We define total causal impact $\mathrm{TCI}(a)$ as the sum of the pairwise causal impact index $\mathrm{PCI}(a,b)$ across all $b\in\bm{S}$ . That is, $$ \mathrm{TCI}(a)\coloneqq\sum_{b\in\bm{S}}\mathrm{PCI}(a,b)~{}. \tag{2} $$ 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: $$ \mathrm{ACI}(a)\coloneqq\frac{\mathrm{TCI}(a)}{|\bm{S}|}=\frac{1}{|\bm{S}|} \sum_{b\in\bm{S}}\left(y^{t=1}-y^{t=0}\right)~{}. \tag{3} $$ We note that $\mathrm{ACI}(a)$ is equal to the a verage t reatment effect on the t reated (ATT) of paper $a$ (Pearl, 2009). ## 3 The TextMatch Method 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? ### 3.1 What Does Causal Inference Tell Us about 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. ### 3.2 Can Existing Causal Inference Methods Handle This Control? 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. 3.2.0.0.1 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. 3.2.0.0.2 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 $\bm{x}$ of the adjustment variables $\bm{X}$ and obtain the difference between the treatment group $\mathcal{T}$ and control group $\mathcal{C}$ : $$ \widehat{\mathrm{ACI}}(a)=\sum_{\bm{x}}P(\bm{x})\left(\frac{1}{|\mathcal{T}_{ \bm{x}}|}\sum_{i\in\mathcal{T}_{\bm{x}}}y_{i}-\frac{1}{|\mathcal{C}_{\bm{x}}|} \sum_{j\in\mathcal{C}_{\bm{x}}}y_{j}\right)~{}, \tag{4} $$ where for each value $\bm{x}$ , 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. 3.2.0.0.3 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 $\bm{C}$ , where each paper $c_{i}$ has a citation count $y_{i}$ , and vector representation $\bm{t}_{i}$ of the confounders (e.g., research topic). One-to-one matching estimates PCI as $$ \begin{split}\widehat{\mathrm{PCI}}(a,b)&=y_{b}-y_{\operatorname*{argmax}_{c_{ i}\in\bm{C}}m_{i}}\\ &=y_{b}-y_{\operatorname*{argmax}_{c_{i}\in\bm{C}}\mathrm{sim}(\bm{t}_{b},\bm{ t}_{i})}~{},\end{split} \tag{5} $$ where we approximate the counterfactual sample by the paper $c_{i}\in\bm{C}$ which is the most similar to paper $b$ by the matching score $m_{i}$ , which is obtained by the cosine similarity $\mathrm{sim}$ 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? #### 3.3.1 Theoretical Formulation of TextMatch : Stabilizing Text Matching by Synthesis 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 $c_{i}\in\bm{C}$ with high matching scores $m_{i}$ to the paper $b$ , and synthesize the counterfactual sample by an interpolation of them: $$ \displaystyle\widehat{\mathrm{PCI}}(a,b)=y_{b}-\sum_{c_{i}\in\bm{C}}w_{i}y_{i} =y_{b}-\sum_{c_{i}\in\bm{C}}\frac{m_{i}}{\sum_{c_{i}\in\bm{C}}m_{i}}y_{i}~{}, \tag{6} $$ where the weight $w_{i}$ of each paper $c_{i}$ is proportional to the matching score $m_{i}$ and normalized. The contributions of our method are as follows: (1) we adapt the traditional matching methods from low-dimensional 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 $w_{i}$ 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. #### 3.3.2 Overall Algorithm 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 27, 28, 29, 30, 31, 32, 33, 34, 35 and 36. 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 $\textsc{GetACIandTCI}(a)$ 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 7, 8, 9, 10, 11 and 12. Algorithm 1 Get causal impact indices $\mathrm{ACI}$ and $\mathrm{TCI}$ 1: Input: Paper $a$ . 2: procedure GetACIandTCI ( $a$ ) 3: $\bm{D}\leftarrow\mathrm{GetDesc}(a)$ $\triangleright$ Get descendants by DFS 4: $\bm{B}\leftarrow\mathrm{GetChildren}(a)$ 5: $\bm{B}^{\prime}\leftarrow\mathrm{SampleSubset}(\bm{B})$ $\triangleright$ See Section 3.3.3 6: $\bm{C}\leftarrow\mathrm{EntireSet}\backslash\{\bm{D}\cup\{a\}\}$ $\triangleright$ Get non-descendants 7: $\mathrm{ACI}\leftarrow 0$ 8: for each $b_{i}$ in $\bm{B}^{\prime}$ do 9: $I_{i}\leftarrow\textsc{GetPCI}(a,b_{i},\bm{C})$ 10: $\mathrm{ACI}\leftarrow\mathrm{ACI}+\frac{1}{|\bm{B}^{\prime}|}\cdot I_{i}$ 11: end for 12: $\mathrm{TCI}\leftarrow\mathrm{ACI}\cdot|\bm{B}|$ 13: return $\mathrm{ACI}$ and $\mathrm{TCI}$ 14: end procedure 15: 16: procedure GetPCI ( $a,b,\bm{C}$ ) 17: $\bm{C}_{\mathrm{sameYear}}\leftarrow\mathrm{FilterByYear}(\bm{C},b_{\mathrm{ year}})$ 18: for each $p_{i}$ in $\bm{C}_{\mathrm{sameYear}}\cup\{b\}$ do 19: $\bm{t}_{i}\leftarrow\mathrm{RemoveMediator}(\mathrm{TitleAbstract}_{i})$ 20: end for 21: $\bm{C}_{\mathrm{coarse}}\leftarrow\mathrm{BM25}(b,\bm{C}_{\mathrm{sameYear}}, \text{topk}=100)$ 22: for each $c_{i}$ in $\bm{C}_{\mathrm{coarse}}$ do 23: $m_{i}\leftarrow\mathrm{Sim}(\bm{t}_{b},\bm{t}_{i})$ 24: end for 25: $\bm{C}_{\mathrm{top10}}\leftarrow\mathrm{argmax10}_{m}(\bm{C}_{\mathrm{coarse}})$ 26: 27: $M\leftarrow 0$ 28: for each $c_{i}$ in $\bm{C}_{\mathrm{top10}}$ do $\triangleright$ For the normalization later 29: $M\leftarrow M+m_{i}$ 30: end for 31: $\hat{y}^{t=0}\leftarrow 0$ 32: for each $c_{i}$ in $\bm{C}_{\mathrm{top10}}$ do 33: $w_{i}\leftarrow\frac{m_{i}}{M}$ 34: $\hat{y}^{t=0}\leftarrow\hat{y}^{t=0}+w_{i}\cdot y_{i}$ $\triangleright$ Apply Eq. 6 35: end for 36: return $y_{b}-\hat{y}^{t=0}$ 37: end procedure #### 3.3.3 Key Challenges and Mitigation Methods We address several technical challenges below. Confounders of Various Types 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 $\mathrm{Sim}$ between two papers should be customized. For our specific use case, we first filter by the publication year in 17, 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 23. As a 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. Excluding the Mediators from Confounders 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 $\mathrm{RemoveMediator}$ function in 19, we exclude all numerical expressions such as percentage numbers, as well as descriptions such as “state-of-the-art.” 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. Efficient Matching-and-Reranking Method 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 $\bm{C}_{\mathrm{sameYear}}$ 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 (21) 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 (22, 23 and 24). In the cosine similarity matching process, we use the MPNet model Song et al. (2020) to encode the text of each paper $c_{i}$ into an embedding $\bm{t}_{i}$ , with which we get the matching score $m_{i}$ according to Eq. 5 in 23, and the normalized weight $w_{i}$ by Eq. 6 in 33. Numerical Estimation 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. ## 4 Performance Evaluation The contribution of a paper is inherently multi-dimensional, 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. ### 4.1 Experimental Setup Dataset We use the Semantic Scholar dataset (Lo et al., 2020; Kinney et al., 2023) https://api.semanticscholar.org/api-docs/datasets 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. 4.1.0.0.1 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 general-domain models such as BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019), we consider LLM variants Note that we follow the standard notion by Yang et al. (2023) to refer to BERT and its variants as LLMs. 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 Section A.3, according to which MPNet outperforms the other two models. Implementation Details We deploy the all-mpnet-base-v2 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 the top ten most similar papers above the 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, https://dask.org/ which optimizes for data processing and distributed computing. We optimize our program to take around 100GB RAM, and on average 25 minutes for each $\mathrm{PCI}(a,b)$ after matching against up to millions of candidates. More implementation details are in Section 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 Section A.2. ### 4.2 Author-Identified Paper Impact 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 Section 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. ### 4.3 Test-of-Time Paper Analysis | 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). <details> <summary>x3.png Details</summary>  ### Visual Description \n ## Violin Plot: CausalCite Distribution for Non-ToT vs. ToT Papers ### Overview The image is a violin plot comparing the distribution of a metric called "CausalCite" between two categories of academic papers: "Non-ToT Papers" and "ToT Papers". The plot visualizes the probability density of the data at different values, with the width of each "violin" representing the frequency of data points at that y-axis value. ### Components/Axes * **Y-Axis:** Labeled "CausalCite". The scale is linear, ranging from 0 to 7000, with major tick marks at intervals of 1000 (0, 1000, 2000, 3000, 4000, 5000, 6000, 7000). * **X-Axis:** Contains two categorical labels: * **Left Category:** "Non-ToT Papers" * **Right Category:** "ToT Papers" * **Plot Elements:** Each category has a corresponding violin shape and internal box plot elements (median line, interquartile range bar, and whiskers). * **Non-ToT Papers Violin:** Colored light pink/salmon. Positioned on the left side of the chart. * **ToT Papers Violin:** Colored light blue/lavender. Positioned on the right side of the chart. ### Detailed Analysis **1. Non-ToT Papers (Left, Pink Violin):** * **Trend/Shape:** The distribution is extremely right-skewed. The vast majority of data points are concentrated very close to 0, creating a wide, flat base. The violin tapers extremely rapidly into a very thin, long tail extending upward. * **Key Data Points (Approximate):** * **Median (Central horizontal line within the violin):** Very close to 0, approximately at 50-100 on the CausalCite scale. * **Interquartile Range (Thicker central bar):** Very narrow, spanning from near 0 to approximately 200-300. * **Range (Whiskers/Full extent):** The lower whisker is at 0. The upper whisker extends to approximately 4500, indicating a maximum outlier value in this group. * **Density:** The highest density (widest part of the violin) is at the very bottom, near 0. Density becomes negligible above ~500. **2. ToT Papers (Right, Blue Violin):** * **Trend/Shape:** The distribution is also right-skewed but is much more spread out and has a significantly higher central tendency compared to the Non-ToT group. It has a broad base, a pronounced bulge in the lower-middle range, and a long, thin tail extending to the top of the chart. * **Key Data Points (Approximate):** * **Median (Central horizontal line):** Located at approximately 1200-1300 on the CausalCite scale. * **Interquartile Range (Thicker central bar):** Spans from approximately 500 to 2500. * **Range (Whiskers/Full extent):** The lower whisker is at 0. The upper whisker extends to the top of the chart, at approximately 6800-6900, indicating a maximum value near the upper limit of the axis. * **Density:** The distribution shows significant density from 0 up to about 3000, with the widest point (highest density) occurring around 800-1500. The tail remains visible but very thin all the way to the maximum value. ### Key Observations 1. **Stark Contrast in Central Tendency:** The median CausalCite for ToT Papers (~1250) is over an order of magnitude higher than the median for Non-ToT Papers (~75). 2. **Difference in Spread:** The ToT Papers group exhibits vastly greater variability. Its interquartile range (~2000 units wide) is many times larger than that of the Non-ToT group (~250 units wide). 3. **Presence of Extreme Values:** Both groups contain high-value outliers, but the maximum value for ToT Papers (~6850) is substantially higher than the maximum for Non-ToT Papers (~4500). 4. **Distribution Shape:** While both are right-skewed, the ToT Papers distribution has a much more substantial "body" in the 500-2500 range, whereas the Non-ToT Papers distribution is almost entirely collapsed near zero. ### Interpretation This chart strongly suggests that papers categorized as "ToT Papers" are associated with a significantly higher "CausalCite" metric compared to "Non-ToT Papers". The data indicates this is not merely a shift in the average but a fundamental difference in distribution: * **Impact:** The ToT methodology or topic (whatever "ToT" signifies) appears to be linked to papers that achieve much higher causal citation counts. The typical (median) ToT paper has a CausalCite score comparable to a high-performing outlier in the Non-ToT group. * **Consistency vs. Potential:** The Non-ToT group is highly consistent, with nearly all papers clustering near zero impact, punctuated by rare exceptions. The ToT group shows a broader range of outcomes, but even its lower quartile performs better than the vast majority of Non-ToT papers. This suggests the ToT category either enables higher impact or attracts research with inherently higher causal citation potential. * **Underlying Question:** The plot visualizes a dramatic disparity but does not explain its cause. It prompts investigation into what "ToT" represents (e.g., a specific research paradigm, topic, or methodology) and why it correlates so strongly with this measure of causal influence in the literature. The long tails in both distributions also highlight the presence of exceptional papers in both categories that achieve very high CausalCite scores. </details> Figure 3: Distributions of ToT (mean: 142) and non-ToT papers (mean: 1,623). <details> <summary>x4.png Details</summary>  ### Visual Description \n ## Scatter Plot: CausalCite Values for Non-ToT vs. ToT Methods Across Three Research Papers ### Overview This image is a scatter plot comparing the "CausalCite" metric for two categories of methods—labeled "Non-ToT" and "ToT"—across three distinct research papers. The y-axis uses a logarithmic scale. The plot visually demonstrates a significant disparity in CausalCite values between the two method categories for each paper. ### Components/Axes - **Y-Axis:** - **Label:** `CausalCite` - **Scale:** Logarithmic (base 10). Major tick marks are at `10^1`, `10^2`, `10^3`, and `10^4`. - **X-Axis:** - **Categories (from left to right):** 1. `Random Features for Large-Scale Kernel Machines (NeurIPS 2017)` 2. `BLEU Metric (NAACL 2018)` 3. `ImageNet Dataset (CVPR 2019)` - **Legend:** - **Position:** Top-right corner of the plot area. - **Categories:** - `Non-ToT`: Represented by pink/salmon-colored circles. - `ToT`: Represented by light blue/periwinkle-colored circles. ### Detailed Analysis Data points are plotted as circles. For each x-axis category, multiple "Non-ToT" points are shown, while only one "ToT" point is visible. **1. Random Features for Large-Scale Kernel Machines (NeurIPS 2017)** - **Non-ToT (Pink):** A cluster of approximately 6-7 points. Their approximate CausalCite values range from just above `10^1` (~20) to just above `10^2` (~150). The points are densely packed between `10^1.5` (~30) and `10^2`. - **ToT (Blue):** A single point located significantly higher, at approximately `10^3.4` (~2500). **2. BLEU Metric (NAACL 2018)** - **Non-ToT (Pink):** A cluster of approximately 8-9 points. Values range from `10^1` (10) to approximately `10^2.4` (~250). One outlier point is near the bottom at `10^1` (10). - **ToT (Blue):** A single point located very high, at approximately `10^3.8` (~6300). **3. ImageNet Dataset (CVPR 2019)** - **Non-ToT (Pink):** A cluster of approximately 7-8 points. Values range from below `10^1` (~7) to approximately `10^2.8` (~630). The spread is wider here, with points near the bottom and top of this range. - **ToT (Blue):** A single point located at the highest position on the entire chart, at approximately `10^4.3` (~20,000). ### Key Observations 1. **Consistent Disparity:** For all three papers, the single "ToT" data point has a CausalCite value one to two orders of magnitude (10x to 100x) higher than the cluster of "Non-ToT" points. 2. **Logarithmic Scale Necessity:** The use of a log scale is essential to visualize both the low-value "Non-ToT" cluster and the high-value "ToT" point on the same chart. 3. **Clustering vs. Singularity:** "Non-ToT" methods are represented by multiple data points per paper, suggesting a distribution of results or multiple studies. "ToT" is represented by a single, dominant point per paper. 4. **Trend Across Papers:** The CausalCite value for the "ToT" point appears to increase from the first paper (NeurIPS 2017) to the third (CVPR 2019). ### Interpretation The chart presents a strong visual argument that methods or concepts associated with "ToT" (the exact meaning of the acronym is not defined in the image) have a dramatically higher "CausalCite" metric compared to "Non-ToT" approaches within the context of these three influential machine learning papers. - **What it suggests:** "CausalCite" likely measures some form of impact, influence, or causal attribution within the academic literature. The data implies that the "ToT" element in each paper is considered far more causally significant or foundational by the metric's definition. - **Relationship between elements:** The plot isolates and contrasts two classes of contribution within each paper. The stark separation suggests "ToT" is not just marginally better but represents a different tier of impact as measured by CausalCite. - **Notable pattern:** The increasing CausalCite value for the "ToT" point across the three papers (from ~2500 to ~20,000) could indicate that the concept or method labeled "ToT" gained increasing recognition or became more foundational in subsequent, high-profile research (from NeurIPS to CVPR). - **Underlying question:** The chart raises a critical question about the nature of "ToT." Is it a specific technique, a theoretical framework, or a key finding? Its consistent, outsized impact across different sub-fields (kernel methods, NLP metrics, computer vision datasets) suggests it may be a broadly applicable and highly influential concept. The chart effectively argues for the paramount importance of the "ToT" component in these works. </details> Figure 4: The CausalCite values of three example ToT papers from general AI, NLP, and CV. 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. We 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). In Table 2, we show the correlations of various metrics with the ToT awards. In this table, CausalCite 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 4. 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. ### 4.4 Topic Invariance of CausalCite | Research Area | ACI | Citations | SSHI | | --- | --- | --- | --- | | General AI (n=16) | 0.748 | 2,024 | 267 | | CV (n=36) | 0.734 | 7,238 | 1,088 | | NLP (n=20) | 0.763 | 1,785 | 461 | Table 3: The average of each metric by research area on our collected set of 72 ToT papers. 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. ## 5 Findings 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). ### 5.1 Do Best Papers Have High Causal Impact? 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. Therefore, 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. ### 5.2 What Is the Nature of the CausalCite Distribution? <details> <summary>x5.png Details</summary>  ### Visual Description ## Bar Chart: TCI Distribution by Percentile ### Overview The image displays a bar chart illustrating the distribution of a metric labeled "TCI" across percentiles from 0 to 100. The chart reveals an extremely right-skewed (or heavy-tailed) distribution, where a very small proportion of cases at the lowest percentiles have exceptionally high TCI values, while the vast majority of cases have low TCI values that gradually taper off. ### Components/Axes * **Chart Type:** Vertical bar chart. * **X-Axis:** * **Label:** "Percentile" * **Scale:** Linear scale from 0 to 100. * **Major Tick Marks:** Located at 0, 25, 50, 75, and 100. The labels are rotated approximately 45 degrees. * **Y-Axis:** * **Label:** "TCI" * **Scale:** Linear scale from 0 to 700. * **Major Tick Marks:** Located at intervals of 100 (0, 100, 200, 300, 400, 500, 600, 700). * **Data Series:** A single series represented by solid blue bars. There is no legend, as only one data category is present. * **Spatial Layout:** The chart area is bounded by a simple black frame. The axes labels are centered along their respective axes. The bars are tightly packed, suggesting each bar represents a small percentile increment (e.g., 1st, 2nd, 3rd percentile, etc.). ### Detailed Analysis * **Trend Verification:** The visual trend is a dramatic, near-vertical drop from the first bar, followed by a steady, monotonic decrease in bar height as the percentile increases. The slope is extremely steep at the beginning and becomes very gradual after approximately the 10th-15th percentile. * **Data Point Extraction (Approximate Values):** * **Percentile 0 (First Bar):** The TCI value is at the maximum of the scale, approximately **700**. * **Percentile ~1-2 (Second Bar):** There is a precipitous drop. The TCI value is approximately **110-120**. * **Percentile ~3-5:** Values continue to fall quickly to the range of **80-100**. * **Percentile 25:** The bar height corresponds to a TCI value of approximately **40-50**. * **Percentile 50 (Median):** The TCI value is approximately **20-25**. * **Percentile 75:** The TCI value is approximately **10-15**. * **Percentile 100 (Final Bar):** The TCI value is very close to **0**, possibly slightly negative or at the baseline. ### Key Observations 1. **Extreme Skew:** The distribution is dominated by a single, massive outlier at the 0th percentile. The first bar is over 6 times taller than the second bar. 2. **Rapid Initial Decay:** The most significant change in TCI occurs within the first 5-10 percentiles. 3. **Long Tail:** From roughly the 20th percentile onward, the TCI values decrease very slowly, forming a long, flat tail that approaches zero. 4. **No Central Tendency:** The median (50th percentile) value is very low relative to the range, indicating that half of all cases have a TCI below ~25. ### Interpretation This chart demonstrates a classic "power law" or "Pareto" distribution pattern. The data suggests that the "TCI" metric is not evenly distributed but is instead highly concentrated in a tiny fraction of cases. * **What it means:** A very small percentage of entities (those in the lowest percentiles) account for an overwhelmingly large proportion of the total TCI. Conversely, the vast majority of entities have minimal TCI. This is common in phenomena like wealth distribution, city populations, or website traffic, where a few "superstars" or "black swan" events dominate the total. * **Why it matters:** For analysis or intervention, focusing on the low-percentile, high-TCI outliers would yield the greatest impact on the aggregate TCI. The median or mean would be poor representations of a "typical" case due to the extreme skew. The system or phenomenon being measured is likely driven by rare, high-impact events rather than consistent, average performance. * **Underlying Question:** The chart prompts investigation into what defines the group at the 0th-5th percentile. What unique characteristics cause their TCI to be orders of magnitude higher than the norm? The near-zero values at the high percentiles suggest a baseline or minimal possible TCI for most observations. </details> Figure 5: The distribution of TCI values by percentile of 100 random papers, which shows a long tail indicating that high impact is concentrated in a relatively small portion of papers. 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 4.1.0.0.1. 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. ### 5.3 Selected Paper Case Study | Paper Name | TCI | Citations | ACI | | --- | --- | --- | --- | | Transformers | 52,507 | 68,064 | 0.771 | | BERT | 40,675 | 59,486 | 0.683 | | RoBERTa | 6,932 | 14,434 | 0.480 | Table 4: Case study of some selected NLP papers. 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. ### 5.4 Discovering Quality Papers beyond Citations 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 Section 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. | Paper Category | Result Citations | Residual | | --- | --- | --- | | Overcited Papers (7.04%) | 1.26 | -1.792 | | Aligned Papers (91.20%) | 1.51 | 0.118 | | Undercited Papers (1.76%) | 1.90 | 1.047 | Table 5: We use our CausalCite metric to discover outlier papers that are overlooked by citations. For each paper category, we include their portion relative to the entire population, the percentage of citations occurred in the result section (Result Citations), and average residual value by linear regression. ## 6 Related Work 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. ## 7 Conclusion 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 multi-faceted 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 loack 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. ## Acknowledgment 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. ## References - Abadie et al. 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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 small-scale study, first obtaining the TCI using our upper-bound 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. $0 0$ $20$ $40$ $60$ $80$ $100$ $0 0$ $50$ $100$ $150$ Sample Size $n$ Error Percentage TCI error $0 0$ $1{,}000$ $2{,}000$ $3{,}000$ Minutes Computational time Figure 6: We show the trade-off of two curves: the error curve (orange), and the time cost curve (blue). For the error curve, we see an elbow point at around $n=40$ , when the error starts to be small. The curve for the computational time is linear, taking 25 minutes for each paper. Balancing the trade-offs, we decided to choose the sample size $n=40$ . ### 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 open-sourced our annotated data in the codebase. | Paper Index | Title | SciBERT | SPECTER | MPNet | | --- | --- | --- | --- | --- | | Pivot Paper: GPT-3 (Brown et al., 2020) | | | | | | 1 (Most similar) | PaLM (Chowdhery et al., 2022) | 0.9787 | 0.8689 | 0.7679 | | 2 | GPT-2 (Radford et al., 2019) | 0.9346 | 0.9064 | 0.8196 | | 3 | GPT (Radford and Narasimhan, 2018) | 0.9488 | 0.8778 | 0.7790 | | 4 | BERT (Devlin et al., 2019) | 0.9430 | 0.8321 | 0.6784 | | 5 | Transformers (Vaswani et al., 2017) | 0.9202 | 0.8644 | 0.6385 | | 6 | SciBERT (Beltagy et al., 2019) | 0.8396 | 0.8112 | 0.5667 | | 7 | Latent Diffusion Models (Rombach et al., 2021) | 0.9586 | 0.7755 | 0.4567 | | 8 | Sentiment Analysis Using DL (Fang and Zhan, 2015) | 0.7775 | 0.7298 | 0.2911 | | 9 | Sentiment Analysis Using ML (Zainuddin and Selamat, 2014) | 0.6462 | 0.6403 | 0.2563 | | 10 (Least similar) | New High Energy Accelerator (Courant et al., 1952) | 0.8033 | 0.5617 | 0.0359 | Table 6: An example collection of papers with monotonically decreasing similarity to the pivot paper. As can be seen from the similarities scores produced by the three text embedding methods, MPNet corresponds to the ground truth the most, and also shows clear score distinctions between less similar and more similar papers. ## Appendix B Dataset Overview <details> <summary>extracted/5624611/fig/paperVsYearTitles.png Details</summary>  ### Visual Description ## Bar Chart: Number of Papers per Year from 1684 to 2023 ### Overview This is a vertical bar chart illustrating the annual volume of published academic or scientific papers over a 339-year period, from 1684 to 2023. The chart demonstrates a dramatic, exponential increase in publication output, particularly in the late 20th and early 21st centuries. ### Components/Axes * **Chart Title:** "Number of Papers per Year from 1684 to 2023" (centered at the top). * **X-Axis (Horizontal):** * **Label:** "Year" (centered below the axis). * **Scale:** Linear scale from approximately 1684 to 2023. * **Major Tick Marks:** Labeled at 50-year intervals: 1700, 1750, 1800, 1850, 1900, 1950, 2000. * **Y-Axis (Vertical):** * **Label:** "Number of Papers" (centered to the left of the axis). * **Scale:** Linear scale from 0 to 8,000,000 (8e6). * **Major Tick Marks:** Labeled at intervals of 2,000,000: 0, 2e6, 4e6, 6e6, 8e6. The axis uses scientific notation (1e6) at the top to indicate the scale multiplier. * **Data Series:** A single series represented by green vertical bars. Each bar's height corresponds to the number of papers for a specific year. There is no legend, as only one data category is presented. * **Spatial Layout:** The plot area is framed by the axes. The title is positioned above the plot. The x-axis labels are below the axis line, and the y-axis labels are to the left of the axis line. ### Detailed Analysis * **Trend Verification:** The data series shows a clear, accelerating upward trend. The line formed by the tops of the bars is nearly flat for the first two centuries, begins a very gradual rise in the late 19th century, and transitions into a steep, exponential climb from the mid-20th century onward. * **Data Point Extraction (Approximate):** * **1684 - ~1850:** The number of papers per year is visually negligible on this scale, appearing as a flat line at or very near zero. * **~1850 - 1900:** A very slight, barely perceptible rise begins. Values are likely in the low thousands or less per year. * **~1900 - 1950:** A visible but still modest increase. By 1950, the annual count appears to be in the range of tens of thousands (approx. 0.05e6 to 0.1e6). * **1950 - 2000:** Growth accelerates significantly. * ~1970: Approximately 0.5e6 (500,000) papers. * ~1990: Approximately 1.5e6 to 2e6 (1.5-2 million) papers. * **2000 - 2023:** Exponential growth phase. * ~2005: Crosses the 4e6 (4 million) mark. * ~2010: Reaches approximately 6e6 (6 million). * **Peak (~2020-2022):** The highest bars appear just before the end of the series, reaching close to or slightly above 9e6 (9 million) papers per year. * **2023 (Final Bar):** The last bar is slightly shorter than the peak, suggesting a value around 8.5e6. This may indicate incomplete data for the most recent year at the time of chart creation. ### Key Observations 1. **Exponential Growth:** The most dominant feature is the hockey-stick curve, indicating that the rate of scientific publication has itself been increasing exponentially for several decades. 2. **Historical Baseline:** For over 200 years (1684-~1900), the annual output was minuscule compared to modern volumes, reflecting the smaller scale of the formal scientific community. 3. **Inflection Points:** Notable acceleration begins around the early 20th century and again, more dramatically, around the 1960s-1970s. 4. **Recent Peak and Dip:** The peak in the early 2020s followed by a slight dip in 2023 is a notable short-term feature, potentially an artifact of data collection lag. ### Interpretation This chart is a powerful visualization of the "knowledge explosion." It quantitatively demonstrates the massive and accelerating expansion of human scientific endeavor over the past century. The data suggests several underlying factors: * **Institutional Growth:** The proliferation of universities, research institutes, and funding bodies globally. * **Technological Enablement:** Advances in communication (internet, digital publishing), laboratory equipment, and data processing have lowered barriers to conducting and publishing research. * **Population and Economic Growth:** A larger global population and increased GDP dedicated to R&D. * **Cultural Shift:** The increasing emphasis on publication as a metric for academic career progression ("publish or perish"). The near-zero baseline for centuries underscores how recent this explosion is in the context of recorded history. The steepness of the curve in recent decades raises questions about sustainability, information overload, and the quality versus quantity of research output. The slight dip in 2023 is likely not a reversal of the trend but a data artifact, as compiling global publication statistics for the most recent year is often incomplete. </details> Figure 7: The number of papers published per year from 1684 to 2023. We can see that in recent years since 2010, there are more than 7 million papers each year. <details> <summary>extracted/5624611/fig/yearwise_average_referenceCount.png Details</summary>  ### Visual Description \n ## Bar Chart: Yearwise Average Reference Count ### Overview The image displays a bar chart illustrating the trend in the average number of references per academic publication over time, spanning from approximately 1700 to the early 21st century. The chart demonstrates a dramatic, exponential increase in reference counts, particularly in the latter half of the 20th century. ### Components/Axes * **Chart Title:** "Yearwise Average Reference Count" (centered at the top). * **X-Axis (Horizontal):** * **Label:** "Year" (centered below the axis). * **Scale:** Linear scale from approximately 1700 to just past 2000. * **Major Tick Marks:** Labeled at 50-year intervals: 1700, 1750, 1800, 1850, 1900, 1950, 2000. * **Y-Axis (Vertical):** * **Label:** "Average Reference Count" (centered to the left, rotated 90 degrees). * **Scale:** Linear scale from 0 to 25. * **Major Tick Marks:** Labeled at intervals of 5: 0, 5, 10, 15, 20, 25. * **Data Series:** A single series represented by vertical green bars. There is no legend, as only one category of data is presented. ### Detailed Analysis The chart shows a clear, non-linear growth pattern in the average reference count per publication over three centuries. * **1700 - ~1800:** The average reference count is extremely low, visually near zero. Bars are sparse and barely visible, indicating that publications from this era typically contained very few, if any, formal citations. * **~1800 - ~1900:** A very gradual, almost imperceptible increase begins. The average count remains below 1 for most of this period, with minor fluctuations. A slight uptick is visible around 1900, where the average may approach 0.5 to 1. * **~1900 - ~1950:** The growth rate begins to accelerate. The average count rises from approximately 1 in 1900 to roughly 2 by 1950. The bars become consistently visible and show a steady upward slope. * **~1950 - ~2000:** This period exhibits explosive, exponential growth. * By 1960, the average is approximately 3-4. * By 1970, it reaches approximately 5-6. * By 1980, it climbs to around 8-9. * By 1990, it surpasses 10. * By the year 2000, the average reference count is approximately 12-13. * **Post-2000:** The trend continues sharply upward. The final bars on the right (estimated to represent the early 2000s to circa 2010-2015) show the highest values, peaking at or just above the 25 mark on the y-axis. **Trend Verification:** The visual trend is one of accelerating growth. The slope of the "line" formed by the bar tops is shallow for the first 200 years, becomes moderately steep from 1900-1950, and then becomes very steep from 1950 onward, confirming the exponential nature of the increase. ### Key Observations 1. **Exponential Growth:** The most striking feature is the dramatic, exponential rise in reference counts, which begins in earnest around the mid-20th century. 2. **Inflection Point:** The period around 1950 serves as a clear inflection point where the growth rate shifts from gradual to rapid. 3. **Recent Peak:** The highest average reference counts are observed in the most recent years represented on the chart (early 21st century), reaching approximately 25. 4. **Historical Baseline:** For the first two centuries shown (1700-1900), the practice of extensive citation was either non-existent or extremely rare, with averages hovering near zero. ### Interpretation This chart visually quantifies the evolution of scholarly communication and the formalization of academic discourse. The data suggests: * **The Rise of Modern Academia:** The slow start reflects an era before the standardized practice of citation was established. The gradual increase from 1800-1950 correlates with the professionalization of science and academia. * **The Information Explosion:** The exponential growth post-1950 aligns with the "Big Science" era, the massive expansion of published literature, and the development of digital databases. As the volume of available literature grew, so did the necessity and ability to reference prior work. * **Changing Norms:** The trend indicates a fundamental shift in scholarly norms, where comprehensive literature reviews and explicit attribution became standard, expected components of research publication. * **Potential Implications:** While demonstrating increased scholarly rigor and connectivity, such a trend also raises questions about information overload, the pressure to cite excessively, and the challenges of keeping abreast of the literature in any given field. The peak at ~25 references per paper in the early 2000s sets a modern baseline for citation density in academic writing. </details> Figure 8: The year-wise average of the number of references per paper, also with a sharply increasing trend. 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, and 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. ## Appendix C Additional Analyses ### 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 $\log(\mathrm{TCI})=1.026\log(\mathrm{Cit})-0.541$ , 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. <details> <summary>x6.png Details</summary>  ### Visual Description ## Scatter Plot with Regression Line: Relationship between Citations and GCI Value ### Overview The image is a scatter plot displaying the relationship between two logarithmic variables: the base-10 logarithm of citation counts and the base-10 logarithm of a "GCI Value." A linear regression line with a shaded confidence interval is overlaid on the data points. The plot suggests a strong, positive correlation between the two metrics. ### Components/Axes * **X-Axis:** Labeled "log₁₀ of the Citations". The scale runs from 0 to 10, with major tick marks at intervals of 2 (0, 2, 4, 6, 8, 10). * **Y-Axis:** Labeled "log₁₀ of the GCI Value". The scale runs from approximately -1 to 11, with major tick marks at intervals of 2 (0, 2, 4, 6, 8, 10). * **Data Series:** Represented by semi-transparent purple circles. There is no legend, indicating a single data series. * **Regression Line:** A solid red line running diagonally from the lower-left to the upper-right of the plot area. * **Confidence Interval:** A light red, semi-transparent shaded band surrounding the regression line, representing the uncertainty of the fit. ### Detailed Analysis * **Trend Verification:** The data points form a clear, upward-sloping cloud from the bottom-left to the top-right. The red regression line follows this trend precisely, confirming a strong positive linear relationship between the log-transformed variables. * **Data Distribution:** The majority of data points are clustered tightly around the regression line, particularly in the central region of the plot (x-axis values between 2 and 8). The density of points appears highest in the range of x=3 to x=7. * **Regression Line Path:** The line originates near the coordinate (0, 0) and terminates near (10, 10). This suggests a slope close to 1, indicating that a one-unit increase in log₁₀(Citations) is associated with approximately a one-unit increase in log₁₀(GCI Value). * **Confidence Interval Width:** The shaded confidence interval is narrowest in the center of the data cloud (around x=5) and widens noticeably at both the lower (x < 2) and upper (x > 8) extremes of the x-axis, where data points are sparser. * **Outliers:** Several data points lie outside the main cluster and the confidence band. Notable outliers include: * A point near (x=3, y=-1.2), significantly below the trend. * A point near (x=4.5, y=0.5), also well below the trend. * A point near (x=6, y=7.5), above the trend. * A point near (x=7.5, y=5), below the trend. ### Key Observations 1. **Strong Positive Correlation:** The primary observation is the robust, positive linear relationship between the logarithm of citations and the logarithm of the GCI Value. 2. **Log-Log Relationship:** The use of logarithmic scales on both axes implies the underlying relationship between the raw (non-log) variables is likely multiplicative or power-law in nature. 3. **Heteroscedasticity:** The widening of the confidence interval at the extremes suggests the variance of the residuals (the scatter of points around the line) may not be constant across all values, a condition known as heteroscedasticity. 4. **Data Sparsity at Extremes:** There are fewer data points at the very low and very high ends of the citation scale (log₁₀ values < 2 and > 8). ### Interpretation The data demonstrates that the GCI Value is strongly and positively associated with the number of citations. The near 1:1 slope on the log-log plot suggests that the GCI Value scales proportionally with citations across several orders of magnitude. This implies that the GCI metric is likely designed to reflect or is inherently linked to scholarly impact as measured by citation counts. The presence of outliers indicates that while the general trend is very strong, there are individual cases where the GCI Value is either unexpectedly high or low relative to the citation count. These could represent interesting anomalies—for instance, a paper with few citations but a high GCI might indicate high quality or influence in a niche field, while a highly cited paper with a low GCI might suggest different types of impact or methodological considerations in the GCI calculation. The widening confidence interval at the extremes is a standard statistical artifact due to fewer data points, but it also serves as a caution that predictions based on this model are less reliable for entities with extremely low or extremely high citation counts. Overall, the chart provides compelling visual evidence that citations and the GCI Value are deeply interconnected metrics. </details> Figure 9: The scatter plot between our CausalCite and citations, with the fitted function as $\log(\mathrm{TCI})=1.026*\log(\mathrm{Cit})-0.541$ , and a non-outlier band width of 0.8809. ### 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 non-significant 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 $n_{\mathrm{lower}}/|\mathrm{Sig}|$ of conformity, where $n_{\mathrm{lower}}$ is the number of significant papers which it is lower than, and $|\mathrm{Sig}|$ is the total number of significant papers. Then we report the overall accuracy for each score by averaging the accuracy numbers on each non-significant paper. To illustrate the idea better, we show the calculated accuracy numbers for all three metrics on our example batch in Table 7. | References of the Paper “Sorting improves word-aligned bitmap indexes” | Label | PCI | Citations | SSHI | | --- | --- | --- | --- | --- | | - A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces | 0 | 3.519 | 1777 | 156 | | - Optimizing bitmap indices with efficient compression | 0 | 3.519 | 375 | 40 | | - Data Warehouses And Olap: Concepts, Architectures And Solutions | 0 | 3.526 | 187 | 11 | | - Histogram-aware sorting for enhanced word-aligned compression in bitmap indexes | 0 | 3.543 | 17 | 1 | | - CubiST++: Evaluating Ad-Hoc CUBE Queries Using Statistics Trees | 0 | 3.543 | 5 | 1 | | - Improving Performance of Sparse Matrix-Vector Multiplication | 0 | 3.543 | 114 | 11 | | - Binary Gray Codes with Long Bit Runs | 0 | 3.543 | 53 | 4 | | - Analysis of Basic Data Reordering Techniques | 0 | 3.543 | 16 | 1 | | - Tree Based Indexes Versus Bitmap Indexes: A Performance Study | 0 | 3.543 | 24 | 0 | | - Secondary indexing in one dimension: beyond b-trees and bitmap indexes | 0 | 3.543 | 10 | 1 | | - A comparison of five probabilistic view-size estimation techniques in OLAP | 0 | 3.543 | 24 | 1 | | - Compression techniques for fast external sorting | 0 | 3.543 | 16 | 0 | | - A Note on Graph Coloring Extensions and List-Colorings | 0 | 3.543 | 33 | 1 | | - Using Multiset Discrimination to Solve Language Processing Problems Without Hashing | 0 | 3.543 | 52 | 2 | | - Monotone Gray Codes and the Middle Levels Problem | 0 | 3.543 | 80 | 5 | | - The Art in Computer Programming | 0 | 3.543 | 9242 | 678 | | - An Efficient Multi-Component Indexing Embedded Bitmap Compression for Data Reorganization | 0 | 3.543 | 8 | 2 | | - The LitOLAP Project: Data Warehousing with Literature | 0 | 3.543 | 8 | 0 | | - Multi-resolution bitmap indexes for scientific data | 0 | 3.583 | 96 | 3 | | - Notes on design and implementation of compressed bit vectors | 0 | 3.583 | 81 | 12 | | - Compressing Large Boolean Matrices using Reordering Techniques | 0 | 3.595 | 88 | 7 | | - Compressing bitmap indices by data reorganization | 1 | 3.595 | 53 | 4 | | - Model 204 Architecture and Performance | 0 | 3.635 | 238 | 10 | | - On the performance of bitmap indices for high cardinality attributes | 1 | 3.654 | 196 | 10 | | - A performance comparison of bitmap indexes | 0 | 3.655 | 86 | 9 | | - Minimizing I/O Costs of Multi-Dimensional Queries with Bitmap Indices | 0 | 3.692 | 16 | 0 | | - Evaluation Strategies for Bitmap Indices with Binning | 0 | 3.692 | 69 | 3 | | - C-Store: A Column-oriented DBMS | 0 | 3.710 | 1241 | 111 | | - Byte-aligned bitmap compression | 0 | 3.793 | 209 | 48 | | - Bit Transposed Files | 0 | 3.837 | 84 | 10 | | - Space efficient bitmap indexing | 0 | 4.011 | 96 | 16 | Table 7: All the reference papers for a given study “Sorting improves word-aligned bitmap indexes.” Among all its 31 references, we boldface the reference papers that are annotated to be significant influencers. For the three metrics, PCI, citations, and SSHI, we report their impact scores for each reference paper on the given study, where we mark a score in green when it conforms to the rule that a non-significant paper’s value should be lower than that of a significant paper, and mark a score in dark green if it conforms to the rule to have a lower score than one of the significant paper, but violates the rule, i.e., having a higher score than the other significant paper. In this example, our PCI metric has an accuracy score of 79.3%, which is higher than both citations (68.1%), and SSHI (65.0%). ### 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 $\mathrm{PCI}(\cdot,b)$ 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 $a_{1}$ to $a_{2}$ 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 $a_{1}$ , and adding the constraint that they cannot cite $a_{2}$ . <details> <summary>x7.png Details</summary>  ### Visual Description \n ## Line Chart: PCI vs. Unlabeled X-Axis ### Overview The image displays a simple line chart plotting a variable labeled "PCI" against an unlabeled numerical x-axis. The chart shows a single data series represented by a blue line with circular markers at each data point. The overall trend is a gradual increase, followed by a plateau, and concluding with a sharp, significant spike at the final data point. ### Components/Axes * **Y-Axis:** * **Label:** "PCI" (positioned vertically on the left side). * **Scale:** Linear scale ranging from approximately 4.8 to 7.5. * **Major Tick Marks:** Labeled at 5.0, 5.5, 6.0, 6.5, 7.0, and 7.5. * **X-Axis:** * **Label:** None present. * **Scale:** Linear scale ranging from 0 to approximately 28. * **Major Tick Marks:** Labeled at 0, 5, 10, 15, 20, and 25. * **Data Series:** * **Representation:** A single blue line connecting circular blue markers. * **Legend:** None present. * **Chart Area:** White background with a standard rectangular frame. ### Detailed Analysis The data series consists of 29 distinct points (from x=0 to x=28). The following table reconstructs the approximate values, with uncertainty noted due to visual estimation from the chart's scale. | X-Value (Approx.) | PCI Value (Approx.) | Trend Description | | :--- | :--- | :--- | | 0 | 4.8 | Starting point. | | 1 | 4.85 | Slight increase. | | 2 | 4.87 | Very slight increase. | | 3 | 5.03 | Noticeable increase. | | 4 | 5.05 | Slight increase. | | 5 | 5.15 | Increase. | | 6 | 5.20 | Increase. | | 7 | 5.25 | Increase. | | 8 | 5.27 | Slight increase. | | 9 | 5.28 | Very slight increase. | | 10 | 5.30 | Slight increase. | | 11 | 5.38 | Increase. | | 12 | 5.40 | Slight increase. | | 13 | 5.62 | **Notable increase.** | | 14 | 5.68 | Increase. | | 15 | 5.68 | Plateau begins. | | 16 | 5.68 | Plateau. | | 17 | 5.68 | Plateau. | | 18 | 5.68 | Plateau. | | 19 | 5.68 | Plateau. | | 20 | 5.68 | Plateau. | | 21 | 5.68 | Plateau. | | 22 | 5.68 | Plateau. | | 23 | 5.68 | Plateau. | | 24 | 5.75 | Slight increase, plateau ends. | | 25 | 5.75 | Stable. | | 26 | 5.78 | Slight increase. | | 27 | 7.48 | **Dramatic, sharp spike.** | **Trend Verification:** 1. **Phase 1 (x=0 to x=14):** The line shows a consistent, gradual upward slope. The rate of increase is modest but steady. 2. **Phase 2 (x=15 to x=23):** The line becomes perfectly horizontal, indicating a stable plateau where the PCI value remains constant at approximately 5.68. 3. **Phase 3 (x=24 to x=27):** The line resumes a slight upward trend before an extreme, near-vertical ascent at the final point (x=27). ### Key Observations 1. **The Plateau:** A prolonged period of stability (9 consecutive data points) where the PCI metric shows no change is a dominant feature of the chart. 2. **The Final Spike:** The most significant event is the abrupt and massive increase in PCI at the last recorded x-value (27). The value jumps from ~5.78 to ~7.48, an increase of approximately 1.7 units (or ~29%) in a single step. 3. **Lack of Context:** The chart lacks a title, a label for the x-axis, and a legend. This makes it impossible to determine what "PCI" represents (e.g., a performance index, a chemical property, a financial metric) or what the independent variable on the x-axis is (e.g., time, iterations, temperature, concentration). ### Interpretation The data suggests a system or metric that experiences slow, incremental growth, enters a phase of equilibrium or saturation, and then undergoes a sudden, transformative change. * **The Plateau** could represent a system reaching a steady state, a process hitting a limit, or a period of consolidation where no new inputs or changes affect the output (PCI). * **The Dramatic Spike** is the critical anomaly. It indicates a phase transition, a breakthrough, a failure point, or the introduction of a powerful new variable at x=27. Without context, it's impossible to know if this spike is desirable (e.g., a performance breakthrough) or undesirable (e.g., a system failure or error condition). * **Relationship Between Elements:** The long plateau makes the final spike even more dramatic by contrast. It suggests that the factor causing the spike was either absent or inactive during the plateau phase and was triggered or introduced at the final step. The initial gradual rise may represent a warm-up or learning phase before the stable plateau. **In summary, the chart tells a story of stability followed by sudden, extreme change. The primary investigative question raised by this visual is: What specific event, condition, or input changed at x=27 to cause the PCI metric to surge so dramatically after a long period of constancy?** </details> Figure 10: We take an example paper $b$ , Sentence BERT (Reimers and Gurevych, 2019), and plot its PCI values with all its reference paper $a$ ’s. We can see clearly that there is a plateau in the curve, showing a step function-like nature.