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Attention decay in science
Pietro Della Briotta Parolo, Raj Kumar Pan, Rumi Ghosh, Bernardo A. Huberman, Kimmo Kaski, Santo Fortunato
TL;DR
The paper addresses how the growth of scientific publishing affects the limited attention available to individual papers and their citation life cycles. It analyzes citation trajectories across disciplines and periods, comparing decay models and rescaling time by publication volume. Citation rates typically peak a few years after publication and then decline, with exponential fits preferred in most cases; although decay is faster in recent periods, it is comparatively stable when measured by the number of papers published.
Problem
Rapid growth in scientific publishing makes it harder to track relevant papers and limits attention available to individual publications.
Method
The study analyzes millions of papers across four disciplines and historical periods, fitting normalized citation trajectories with exponential and power-law models.
Results
Exponential fits are preferred for most papers, while citation rates usually peak 2–7 years after publication and then decline relatively rapidly.
Takeaways & Limitations
Citation decay is faster in recent periods in absolute time but occurs after an approximately constant number of published papers.
Abstract
from arXiv · showhide
The exponential growth in the number of scientific papers makes it increasingly difficult for researchers to keep track of all the publications relevant to their work. Consequently, the attention that can be devoted to individual papers, measured by their citation counts, is bound to decay rapidly. In this work we make a thorough study of the life-cycle of papers in different disciplines. Typically, the citation rate of a paper increases up to a few years after its publication, reaches a peak and then decreases rapidly. This decay can be described by an exponential or a power law behavior, as in ultradiffusive processes, with exponential fitting better than power law for the majority of cases. The decay is also becoming faster over the years, signaling that nowadays papers are forgotten more quickly. However, when time is counted in terms of the number of published papers, the rate of decay of citations is fairly independent of the period considered. This indicates that the attention of scholars depends on the number of published items, and not on real time.
1. Introduction
Scientific papers compete for limited scholarly attention, and their citation-based attention typically grows initially before decaying as knowledge becomes obsolete. This paper systematically studies whether that decay is exponential or follows a slower power law, and how it changes across fields and historical periods.
- Motivation: Scientific publishing creates an attention economy in which citations contribute to recognition, reputation, and career advancement.Attention also motivates productivity in other content domains, while limited capacity to attend to new material produces characteristic growth-and-decay patterns.
- Related work: Online attention typically rises rapidly and then decays, with power-law fits often outperforming exponential fits for online content.Stretched exponentials are preferable in some cases.
- Research problem: Scientific papers become obsolete as later papers surpass their results and attract citations that would otherwise go to earlier work.Prior scientometric studies disagree over whether citation decay is exponential or follows a slower power law.
- Study aim: The study systematically analyzes paper life cycles across scientific fields and historical periods using longitudinal bibliographic data.It compares exponential and power-law descriptions and examines whether faster recent decay reflects the expanding publication pool.
- Main findings: Exponential and power-law behaviors can both describe citation decay, but exponential fits are preferable in most cases; decay also accelerates over time.After rescaling time by the number of papers published, citation curves die out at comparable rates across periods.
2. Material and methods
The study uses Web of Science records to analyze citation trajectories across broad disciplines and evaluates temporal trends and competing fits statistically. Figure 1 compares normalized citation life cycles in Physics and Biology across publication periods, focusing on highly cited papers.
- Data: The dataset contains English-language articles and reviews published through 2010, categorized into Physics, Medicine, Chemistry, and Biology.Analyses mainly use papers in the top 10% by total citations.
- Statistical analysis: Citation-trajectory trends and competing statistical models are evaluated with least-squares fitting and F-statistics.F-statistics account for sample size and model degrees of freedom when comparing fit accuracy.
- Figure 1: Figure 1 compares normalized yearly citation trajectories for Physics and Biology papers across publication years and shows post-peak decay for top-decile papers.Normalization divides each citation count by the paper’s peak value; the lower panels focus on decay after the peak year.
3. Results and discussions
Citation trajectories typically rise for 2–7 years, peak, and then decay; the peak arrives sooner in more recent years. Exponential and power-law models can both fit decay, but exponential fits are preferred for most papers, while decay rates increase over time.
- Citation evolution: 2–7 years: citation rates typically rise after publication, peak, and then decline as older knowledge becomes obsolete.The trajectories are normalized by each paper’s maximum annual citation count.
- Time to peak: Recent papers reach peak attention sooner, with mean time-to-peak decreasing steadily across fields and citation percentiles.Biology has smaller time-to-peak values than Medicine, Physics, and Chemistry.
- Functional form: Exponential fits outperform power-law fits for most papers when the two decay models are compared using F-statistics.Both models often fit the decay adequately, but the exponential model generally has the stronger F-score.
- Ultradiffusion: An ultradiffusive citation process can produce exponential behavior for finite autocorrelation and power-law behavior otherwise.The model treats post-peak citations as a counting process with hierarchical temporal correlations.
- Decay rate: The median exponential decay rate increases over time, indicating that attention to papers is decaying faster in more recent years.The pattern holds across disciplines and for both the top 10% and [11-30] percentile groups.
3.5. Evolution of the decay exponent
The decay rate of scientific attention increases for papers peaking in later years, with the trend varying across disciplines and remaining independent of the fitted decay form.
- Papers peaking in recent years have broader decay-rate distributions and systematically higher median exponential decay rates.The faster decay is independent of the paper group selected for analysis and of the fitting ansatz.
- Physics and Chemistry exhibit faster citation decay than Biology and Medicine.Both the decay rates and their relative increase over time are field dependent.
- Later peak years imply shorter paper life cycles and faster decay of scientific attention in absolute time.
3.6. Exponential increase in number of publications
Scientific publication volume has grown exponentially, increasing competition for researchers’ limited attention and making older results easier to replace or update.
- All examined fields show an exponential increase in publication numbers over time.The growth is modeled with Np = N0 expδt.
- Rapid publication growth can make older scientific results easier to replace or update.
- Rising publication volume increases competition among scientific products for scholars’ attention.Researchers must filter which papers to attend to and cite from an increasingly broad selection.
3.7. Half-life
The paper uses citation-rate half-life to assess whether the observed acceleration in attention decay is robust. Half-life is defined by the last time a paper’s normalized citation rate remains above the threshold.
- Half-life measures the time after which a paper’s normalized citation rate never rises above 1/2.The measure is used to test whether citation decay becomes faster for recent papers.
- Other citation-rate thresholds σ can be used instead of 1/2.
- The half-life is defined using the last sub-peak at which a paper gathers sufficient attention.
- Mean absolute half-life decreases linearly with time across all four fields.The result is consistent with a linear increase in citation-decay rate.
3.8. Rescaling time
Rescaling half-life from calendar time to publication volume shows that papers become obsolete after a roughly stable number of subsequent publications, despite shorter absolute-time half-lives in recent years.
- 3.8. Rescaling time: The rescaled half-life is constructed from the number of publications in a paper’s discipline between its peak year and half-life.The publication count is based on field-specific output over that interval.
- 3.8. Rescaling time: Absolute-time half-life decreases linearly, whereas publication-count-rescaled half-life remains relatively constant.This contrast indicates that the apparent acceleration in calendar time is offset by publication growth.
- 3.8. Rescaling time: Figure 7 compares absolute and renormalized half-life over time across four fields and two paper percentiles.Linear fits and 95% confidence intervals are shown, with separate absolute-time and renormalized-time coefficients.
- 3.8. Rescaling time: Using the first crossing below 1/2 instead produces an increasing renormalized half-life, unlike the last-crossing measure.The alternative measure captures the first lowest drop of attention and behaves differently across years.
- 3.8. Rescaling time: The approximately constant publication-count distance to obsolescence suggests that each additional paper contributes similarly regardless of the focal paper’s age.
4. Conclusions
Across millions of papers in four disciplines, citations typically peak a few years after publication and then decay, with exponential fits generally preferred. Decay has accelerated over time, which the paper links to the growing publication volume and scholars’ finite capacity to track literature.
- 4. Conclusions: Citations typically peak a few years after publication and then decline relatively rapidly across four scientific disciplines.The study examines millions of papers and attributes the decline to knowledge obsolescence.
- 4. Conclusions: Exponential decays are generally preferred over power-law decays, although power laws describe recent data increasingly well.
- 4. Conclusions: Citation decay is getting faster, indicating that scholars forget papers more easily now than in the past.
- 4. Conclusions: The paper links faster turnover to exponential publication growth and scholars’ finite capacity to track scientific literature.
Appendix A. Description of the categories
The paper classifies publications into broader scientific fields by aggregating Thomson Reuters subject categories. Table A.1 provides the detailed category mapping.
- Appendix A. Description of the categories: Publications are categorized using Thomson Reuters subject categories and then aggregated into broader scientific fields.
- Appendix A. Description of the categories: Table A.1 contains the detailed aggregation of Thomson Reuters subject categories into broader fields.
Appendix B. Evolution of the number of citations for other decile
For papers in the [11-30]% citation window, citation trajectories peak earlier and decay more rapidly than those for the top decile, ending at a lower plateau.
- Appendix B. Evolution of the number of citations for other decile: The [11-30]% papers accumulate fewer citations than the top-decile papers.
- Appendix B. Evolution of the number of citations for other decile: Their average citation peak is more concentrated in the initial years and is followed by a more rapid decay.
- Appendix B. Evolution of the number of citations for other decile: The citation trajectories of the [11-30]% papers reach a plateau significantly lower than the top-decile plateau.
Appendix C. Evolution of half-life for different values of σ and alternative definition of half-life
Alternative half-life definitions and a lower threshold alter the observed temporal patterns. With σ = 0.3, most reported trends remain, while the alternative definition yields field-specific or increasing values.
- Appendix C. Evolution of half-life for different values of σ and alternative definition of half-life: Using σ = 0.3 retains the paper’s main pattern for other parameter choices.Physics shows a slight decreasing pattern, while Medicine and Biology retain increasing trends.
- Appendix C. Evolution of half-life for different values of σ and alternative definition of half-life: The alternative half-life definition treats a paper’s half-life as the first year when citations fall below a specified threshold.
- Appendix C. Evolution of half-life for different values of σ and alternative definition of half-life: Under the alternative definition, half-life values lose their decreasing pattern and instead show field-specific values retained across publication years.
- Appendix C. Evolution of half-life for different values of σ and alternative definition of half-life: The alternative half-life also deviates from the previously constant pattern toward a significant increase.