Nature Is Inside Art as Its Content Not Outside as Its Model

Abstract

Beyond a range of creative domains, individual careers are characterized past hot streaks, which are bursts of high-bear upon works clustered together in shut succession. However it remains unclear if there are whatsoever regularities underlying the kickoff of hot streaks. Here, we analyze career histories of artists, film directors, and scientists, and develop deep learning and network science methods to build high-dimensional representations of their creative outputs. We discover that across all 3 domains, individuals tend to explore diverse styles or topics before their hot streak, but become notably more focused after the hot streak begins. Crucially, hot streaks appear to be associated with neither exploration nor exploitation beliefs in isolation, but a particular sequence of exploration followed by exploitation, where the transition from exploration to exploitation closely traces the onset of a hot streak. Overall, these results may have implications for identifying and nurturing talents beyond a wide range of creative domains.

Introduction

A remarkable characteristic of creative careers is the beingness of hot streaks^1,2,iii. Despite the ubiquitous nature of hot streaks across artistic, cultural, and scientific domains, it remains unclear if there are any regularities underlying the beginning of a hot streak. Understanding the origin of hot streaks is not but crucial for our quantitative understanding of patterns governing artistic life cycles but it as well has implications for the identification and development of talent across a wide range of settings^iv,v. Deciphering what predicts hot streaks, however, remains a claiming, partly due to the complex nature of creative careers^{i,six,7,8,ix,10,11,12,13,14,15,xvi,17}. The lack of systematic explanations for hot streaks, combined with the randomness of when they occur within a career¹, paints an unpredictable, if incomplete, view of inventiveness across a diverse range of domains.

Of the myriad forces that might bear upon career progression and success, the strategies of exploration and exploitation have attracted indelible interests from a broad set of disciplines^{14,15,16,18,19,20,21,22}, prompting us to examine their potential human relationship with hot streaks. Indeed, according to the literature, exploitation allows individuals to build knowledge in a particular area and to refine their capabilities in that area over time. This could exist relevant for understanding hot streaks since exploitation allows individuals to "go deep" in a focal expanse to both institute expertise in that area and foster a reputation related to that expertise^{eighteen,nineteen}. Exploration, on the other hand, engages individuals in experimentation and search across their existing or prior areas of competency. Although exploration is more risky and consequently associated with larger variance in outcomes²³, it may besides increase one's likelihood of stumbling upon a groundbreaking thought through unanticipated combinations of disparate sources²⁴. In contrast, exploitation, as a conservative strategy, may stifle originality and, may over time, limit an individual'due south ability to consistently produce loftier-bear on work¹⁴. Taken together, the benefits and downsides to these contrasting approaches raise a fundamental question: Are career hot streaks reflective of exploration or exploitation behavior, or some combination of the two?

To answer this question, we develop computational methods using deep learning^25,26 and network science^27,28 and apply them to large-calibration datasets tracing the career outputs of artists, picture directors, and scientists. Specifically, nosotros build loftier-dimensional representations of the artworks, films, and scientific publications they produce (Supplementary Annotation i), which capture abstract concepts, styles, and topics represented therein, assuasive us to trace an individual's career trajectory on the underlying creative space (Supplementary Note 1). We further quantify the hot streak within each career by the bear on of works one produced^one, measured by auction price^1,29, IMDB ratings^1,30, and newspaper citations in 10 years^1,12, respectively. We then correlate the timing of hot streaks with the creative trajectories for each individual, assuasive the states to examine changes in the characteristics of the piece of work i produces around the beginning of a hot streak.

Results

To examine the art styles of each artist and their exploration and exploitation dynamics, we collected over 800 One thousand images of visual arts from museum and gallery collections, covering the career histories of 2128 artists^31,32. Building on recent advances in calculator vision^33,34, we utilise a transfer-learning approach³⁵ to construct an embedding for artworks using deep neural networks (Fig. 1a–c). Nosotros generate a 200-dimensional embedding of each artwork (run into "Methods" and Supplementary Annotation 1.1), and identify art styles through clusters on the 200-dimensional embedding space, allowing us to trace the development of fine art styles over the course of their careers (Fig. 2a–d).

Fig. 1: Quantifying individual creative trajectories using high-dimensional representation techniques.

a The architecture of the deep neural network to build loftier-dimensional representation of artworks. Nosotros connect a pre-trained VGGNet with 3 fully connected layers and fine-tune the model with art way labels. The blue box indicates the convolutional layer and the yellow box the max pooling layer. The green bar shows the summit styles predicted by the model for the input image (Prototype reproduced nether Creative Commons Attribution three.0 Unported license). We construct the high-dimensional representation of artworks by combining the output from the beginning and 3rd convolutional layer (blue arrows) and the second fully continued layer (blood-red arrow). b An analogy of the 64 filters in the commencement convolutional layer. We highlight the first filter, the original image, and the output later the prototype passing through the filter. The red box represents the size of the filter (iii × iii pixel box). c The activation of 4 layers in VGGNet and the saliency map of the post-impressionism class. The saliency map visualizes the important pixels for predicting the post-impressionism. Layers close to the input capture depression-level features, such as castor strokes, whereas the layers close to the output capture high-level features such every bit the shape of objects. d Word embedding for film plots. Target words are encoded every bit a binary vector and passed to the neural network. We employ the hidden layer to represent the embedding of words and plots. e Node embedding for the co-casting network. We apply DeepWalk to the co-casting network of 79 Thousand films, to capture the co-occurrence of nodes from the trajectories of random walkers. We apply the hidden layer of the model to represent the cast data. We concatenate the word embedding from plots and the node embedding from casts to construct a 200-dimensional vector to represent each film. f An analogy of the co-citing network among papers published past a scientist. Two papers are connected if they have at least i common reference, with link weight measuring the total number of references they share. Following prior piece of work¹⁶, nosotros apply a community detection algorithm to the co-citing network and identify the topic of each paper as the community it belongs to.

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Fig. 2: Creative trajectories and hot-streak dynamics: three exemplary careers.

a, e, i We fit the hot-streak model to careers of a Jackson Pollock, eastward Peter Jackson and i John B. Fenn. The hot-streak model^one assumes that the affect of works produced in a career (\({{\log }}\,{{{{{\mathrm{price}}}}}}\) for artworks, IMDB rating for films and \({{\log }}{C}_{x}\) for papers) is fatigued from two normal distributions (\({\Gamma }_{0}\) and \({\Gamma }_{H}\)), where \({\Gamma }_{0}\) captures the typical operation and \({\Gamma }_{H}\) captures the performance during hot streak. The red line denotes the hot-streak model. \({t}_{\uparrow }\) and \({t}_{\downarrow }\) marks the beginning and the end of hot streak. To avoid mixing beyond the 2 periods, we measure out the entropy of styles or topics for works produced before and during hot streak by excluding those produced during the year of the transition. b–d We project the 200-dimensional representation of artworks produced by Jackson Pollock to a 3D t-SNE embedding space. Different styles are shown in different colors, and nodes with larger sizes denote those produced during hot streak. For Jackson Pollock, his hot streak is well aligned with the famous "drip period" (1946–1950). The entropy of works produced during this menstruation is substantially lower than typical (\(H=0.25\) vs \(H=0.43\)), suggesting an intensive focus on one item fashion (d). This exploitation behavior contrasts the work he produced in the catamenia leading up to hot streak, which was characterized by an unusual exploration of new and diverse styles (\(H=0.59\)) (c). f–h Nosotros project the films vectors produced by Peter Jackson to a t-SNE embedding space. Peter Jackson'due south hot streak covers "The Lord of the Rings" trilogy (\(H=0.31\)) (h). Before his hot streak, however, Jackson worked on diverse types of films including biography and horror-comedy (\(H=0.59\)) (one thousand). j–l For the career of John Fenn, we study the co-citing network of his papers. Earlier his hot streak, Fenn worked on numerous unlike topics from excitation on hot surfaces to dimers (\(H=0.55\)) (thou). But during his hot streak, Fenn intensively focused on electrospray ionization (\(H=0.25\)) (50), which eventually won him the chemistry Nobel in 2002.

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To examine the career histories of film directors, nosotros collected our second dataset capturing plot description and cast information for each film recorded in the IMDB database (79 One thousand films by 4337 directors; see Supplementary Note 1.two for more than particular). We build a 200-dimensional representation of each film by combining its plot and bandage data (Fig. 1d, e, see "Methods," and Supplementary Annotation i.2), and identify the style of each motion-picture show based on clusters in the obtained embedding space, allowing us to investigate the dynamics of styles for film directors (Fig. 2e–h).

In the 3rd setting, nosotros analyze the career histories of 20,040 scientists by combining publication and citation datasets from the Spider web of Scientific discipline and Google Scholar^1,12, tracing the dynamics of research topics equally reflected in the publication history of each career. We use a method adult recently by Zeng et al.^sixteen, which identifies research topics within a career past finding communities in a weighted co-citing network of all publications by the private (Figs. 1f and 2i–l). To ensure that the results obtained for scientific careers are consequent with the embedding methods used to analyze the careers of artists and directors, we too applied a node embedding method to the co-citing network to identify research topics, and repeated our analyses, finding that the conclusions remain the same (Supplementary Annotation i.three).

To quantify the exploration and exploitation behaviors reflected in each individual'south career across the iii domains, we measure the manner or topic entropy for the work one produces, defined equally \(\widetilde{H}=-\mathop{\sum }\nolimits_{i=1}^{m}{p}_{i}\,{{\log }}\,{p}_{i}\), where \({p}_{i}\) is the frequency in which 1 devotes to an art mode or topic \(i\) and \(1000\) is the number of unique styles or topics. On one extreme, a pure exploitation strategy means that an private'southward piece of work is independent within only one mode or topic (\(\widetilde{H}=0\)); on the other extreme, \(\widetilde{H}={{\log }}\,n\) corresponds to the instance of pure exploration, where \(due north\) is the number of works one produced in the period, indicating that an individual's attention is evenly divided across a distribution of styles or topics (\({p}_{i}=1/n\)). For convenience, we normalize the entropy measure to obtain the rescaled entropy \(H=\widetilde{H}/{{\log }}\,north\). Figure 2 illustrates three notable careers every bit examples for identifying art styles, topics, and their entropies calculated using the methodologies described above also as in "Methods."

To test whether hot streaks are associated with exploration or exploitation, nosotros measure the distribution of entropy \(P(H)\) for works produced before and during a hot streak (Fig. 3a–c). To judge the expected magnitude of \(H\) around a hot streak, we farther construct a zippo model for each career by randomly designating the fourth dimension at which the hot streak begins¹. We calculate the average entropy \(\langle H\rangle\) measured in real careers before (Fig. 3d–f) and after the onset of the hot streak (Fig. 3g–i), and compare them with random careers, measured by the distribution of entropy, \(P\left(\langle H\rangle \correct)\), for chiliad realizations of the randomized careers. Figure 3d–i shows three primary findings. Showtime, before a hot streak, \(\langle H\rangle\) is systematically larger than expected (z-scores >ii), indicating that individuals tend to diversify the topics they piece of work on before a hot streak begins, consistent with an exploration strategy in the menses leading upwardly to hot streak. Second, following the onset of the hot streak, \(\langle H\rangle\) measured in existent careers becomes significantly smaller than expected (z-score <−2), suggesting that individuals get substantially more focused on what they work on, reflecting an exploitation strategy during hot streak. 3rd, despite the differences in the three types of careers nosotros study and the methodologies to examine their career outputs, the observed associations between exploration, exploitation, and hot streaks appear universal across all three domains we studied.

Fig. 3: Exploration, exploitation and career hot streaks.

a–c Career histories of a Jackson Pollock, b Peter Jackson, and c John Fenn illustrate the topics they worked on before and during their hot streak and the impacts of the piece of work. Color of the dots is consequent with the dots shown in Fig. 2b, f, j. d–f The distribution of entropy \(P\left(\langle H\rangle \right)\) earlier a hot streak for g realizations of the randomized careers for all individuals analyzed in our datasets. The vertical line indicates \(\left\langle H\right\rangle\) measured in real careers, showing that it is significantly larger than expected (z-scores are \(four.24\) for artists, \(two.94\) for directors, and \(13.90\) for scientists). chiliad–i Same as (d –f), but for the entropy of work produced during hot streak. \(\left\langle H\right\rangle\) in existent careers (vertical line) is significantly smaller than expected (z-scores are \(-2.42\) for artists, \(-8.54\) for directors, and \(-22.71\) for scientists). j–l The dynamics of topic entropy \(H\) surrounding the onset of hot streak for real and randomized careers, measured through a sliding window of half-dozen artworks, five films or five scientific papers. Error bars represent the standard error of the mean. m–o Cumulative entropy distribution \({P}_{\le }\left(H\correct)\) before and during hot streak in existent careers across the 3 domains. P values of the KS-test are \(iii.seven\times {x}^{-6}\) for artists, \(1.5\times {10}^{-5}\) for directors, and \(1.i\times {10}^{-64}\) for scientists. p–r Cumulative entropy distribution \({P}_{\le }\left(H\correct)\) earlier and during hot streak for the nil model. P- values are \(0.23\) for artists, \(0.77\) for directors, and \(0.06\) for scientists. s–u The probability to detect the onset of a hot streak at the end of an exploration episode lone (non followed past exploitation), or at the beginning of an exploitation episode alone (not proceeded by exploration), or at the transition from exploration to exploitation, or from exploitation to exploration. Nosotros then compare with the baseline probability of having a hot streak. Hither we calculate entropy with a sliding window of ii years for artists and scientists, and five works for directors, and define exploration and exploitation episodes as entropy above or below one'due south average.

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To systematically examine the temporal changes in entropy, nosotros align careers based on when their hot streak begins and measure the dynamics of \(H\) around the hot streak (Fig. 3j–50). We find that compared with randomized careers, \(H\) measured in real careers is systematically elevated before a hot streak begins, merely drops precipitously below expectation during the hot streak. We farther compare directly the entropy distribution \(P(H)\) earlier and later the hot streak begins, finding that, across all iii domains, \(H\) during a hot streak is systematically smaller than before (Fig. 3m–o, Kolmogorov–Smirnov (KS) examination, p value <0.001); this pattern is absent when we repeat the same measurement for randomized careers (Fig. 3p–r).

The exploitation behavior during hot streaks appears consistent with several famous examples, including painter Jackson Pollock's "baste period" (1946–1950) (Fig. second), director Peter Jackson's "The Lord of the Rings trilogy" (Fig. 2h), and the career of scientist John Fenn, whose hot streak arrived late in his career, only the work he produced during that period on electrospray ionization eventually won him the chemistry Nobel in 2002 (Fig. 2l). These examples heighten an intriguing question: can the exploitation behavior by itself predict career hot streaks? To test this, we identify episodes of exploitation in each career past tracing the dynamics of \(H\) beyond our three domains. Nosotros calculate the probability of initiating a hot streak with the onset of an exploitation episode, and compare it with the baseline probability measured in randomized careers (Fig. 3s–u). We find that when exploitation occurs by itself, non preceded by exploration, the take chances that such episodes coincide with a hot streak is significantly lower than expected, not college, across all three domains. These results indicate that exploitation by itself may not guarantee hot streaks, further suggesting the importance of prior exploration. Indeed, reexaminations of the careers of Jackson Pollock, Peter Jackson, and John Fenn reveal a phase of unusual exploration of new and diverse art styles, types of films, and research topics, respectively, for the period leading up to their hot streaks (Fig. 2c, g, k). This observation raises the question of whether exploration that precedes a hot streak is instead the crucial ingredient, prompting us to calculate the probability of initiating a hot streak following an exploration episode lone. Yet, we find that when the episode of exploration is not followed by exploitation, the risk for such exploration to coincide with a hot streak again reduces significantly. By contrast, exploration followed by exploitation appears consistently associated with a pregnant lift in the probability of initiating a hot streak: this configuration consistently outperforms the baseline across all 3 domains (20.v%, xiii.8%, and 19.2% over the baseline for artists, directors, and scientists, respectively), and represents the simply positive lift amidst all combinations of the two creative strategies (Fig. 3s–u). Figure S46 farther examines the exploration, exploitation, and normal phases, and explores all potential sequences of whatever two of the 3 phases (nine in full), reaching the same conclusions.

Taken together, these results advise that neither exploration nor exploitation alone is associated with the hot streak dynamics; rather, it is the shift from exploration to exploitation that closely traces the onset of a hot streak. One plausible explanation is that exploration, as a risky, variance-enhancing strategy, increases one'southward chances to stumble upon new, potentially groundbreaking ideas; the subsequent exploitation behavior allows the individual to focus, develop noesis and capabilities in that focal expanse, and build out their discoveries further. Importantly, our findings suggest that both ingredients of exploration and exploitation seem necessary. This supports the notion that not all explorations are fruitful, and that exploitation in the absence of promising new ideas may not be as productive. On the other hand, the sequence of exploration followed by exploitation may facilitate the emergence of high-touch on piece of work by incorporating new insights into a focused agenda. The positioning of exploration before exploitation may therefore serve to expand an private'due south artistic possibilities.

Nosotros test the robustness of our results across several dimensions. We carve up our samples of artists, directors, and scientists based on the timing of their hot streaks (Supplementary Annotation iii.i), the individual'due south level of touch on (Supplementary Note 3.ii), and different fields of studies (Supplementary Notation 3.3), and repeat our analyses in each subsample, arriving at consistent conclusions. We further control for individual fixed effects in their exploration–exploitation dynamics (Supplementary Annotation 3.4), and detect that artists, directors, and scientists predictably deviate from their typical creative behaviors effectually the get-go of a hot streak: individuals who tend to exploit go more exploratory before a hot streak begins, whereas individuals who tend to explore become particularly focused during their hot streak (Supplementary Annotation 3.4). We further use regression analysis to fit the relationship between hot streaks and the exploration–exploitation transition by controlling for the impact of an individual'southward work, their career phase, and other individual characteristics, and discover that our conclusions remain the aforementioned (Supplementary Note 3.5). For scientists who experience ii hot streaks, we perform our measurements for the first and second hot streak separately (Supplementary Annotation 3.six), and find that the exploration–exploitation dynamics hold true in both cases. For those having hot streaks at the showtime of their careers, while by structure we cannot notice their prior behaviors, we find that they consistently appoint in exploitation during their hot streaks (Supplementary Note 3.7). We further verify that these results are robust to using different community detection algorithms such as Infomap³⁶ (Supplementary Note 3.eight) and different means of accumulation data over fourth dimension (Supplementary Notation 3.9). We also replaced our entropy mensurate to quantify the exploration–exploitation dynamics by the Simpson diversity measure \((1-{\Sigma }_{i}{p}_{i}^{2})\) (Supplementary Note 3.10), the number of styles or topics (Supplementary Note 3.eleven), the fraction of works in the nearly popular mode or topic (Supplementary Notation 3.12), and probability of switching topics (Supplementary Annotation 3.13), and echo all our analyses, finding again the same conclusions.

To understand the potential forces that might facilitate the shift from exploration to exploitation, nosotros further examine the organization of innovative activeness. Motivated by the literature on science teams^8,37,38, hither we focus on scientific careers only, asking whether there are detectable changes in collaboration patterns around the exploration–exploitation transition. We discover that scientists are more likely to explore with minor teams earlier a hot streak, merely exploit with big teams afterwards a hot streak begins. Indeed, we quantify the modify in team size through two measures. Nosotros trace the dynamics of team size around the beginning of a hot streak (Fig. 4a). We also calculate the team size distribution observed in real careers normalized past the randomized careers (\({R}\left({{{{{\rm{team}}}}}}\; {{{{{\rm{size}}}}}}\right)\); Fig. 4b). Both results show that squad size drops significantly before the hot streak yet becomes substantially larger than expected during the hot streak (Fig. 4a, b). We further find that the onset of hot streaks appears to mark an increment in new collaborators (Supplementary Note 4), consequent with the advantages of fresh teams³⁸. Note that the role and definition of teams vary essentially across the iii domains, hence this analysis is applicative to scientific careers but. Given the observational nature of our study, we cannot dominion out potential omitted variables that might mediate these patterns. Nonetheless, these results are in line with the findings that small and large teams are differentially positioned for innovation³⁷: large teams tend to excel at furthering existing ideas and pattern, whereas pocket-sized teams tend to disrupt current ways of thinking with new ideas and opportunities. We further test the robustness of these results beyond different disciplines, adjusting for cocky-citations, and controlling for the publication year, research field, and career stage using regression analysis, all arriving at the same conclusions (Supplementary Note 4).

Fig. 4: Authorship structure and hot streaks in scientific discipline.

a The boilerplate team size effectually the beginning of a hot streak for real and randomized careers in science. Team size shows a pregnant driblet before a hot streak begins, but a notable increment during hot streak. b Nosotros summate squad size for papers published before and during hot streak, and compare the distribution to that of randomized careers for 500 realizations, denoted every bit R(team size). R decreases with team size from in a higher place to below ane for papers published before a hot streak but increases with team size for papers published during a hot streak. Both measures in (a) and (b) suggest that scientists tend to engage with smaller teams before hot streak, and with larger teams during the hot streak. Error bars represent the standard mistake of the mean.

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Our side by side analysis probes potential connections between phases of exploration and exploitation surrounding a scientist'due south hot streak. We examine properties of the topics that are explored during the period leading upward to hot streak, ranging from recency to citation touch on to popularity, asking which topics tend to exist called for subsequent exploitation. We find that the topic that was eventually exploited is less likely to be the one explored the most recently, or the highest cited, or the almost pop among the topics explored before (see Supplementary Note 5). These findings imply that, more than simply chasing after discovery through exploration, individuals appear to seek out new opportunities by deliberating over dissimilar possibilities, and and then harvesting promising directions through exploitation. To test if these potential connections can help united states of america amend understand which direction to exploit post-obit exploration, we fix upward a uncomplicated prediction task to predict which topic to exploit using the features discussed in a higher place that characterize the exploration phase, including team size and topic properties (Supplementary Note 5); this practise yielded substantial predictive power (accuracy of 0.89 and area under the curve of 0.83). Overall, these results propose intriguing connections between phases of exploration and exploitation surrounding a hot streak, which may take implications for science funding, peculiarly given hot streaks and inquiry grants tend to terminal for a similar duration.

Finally, we consider career trajectories post-obit the end of a hot streak. We measure the average entropy \(\langle H\rangle\) later on the end of a hot streak and compare the measurements in existent careers with the distribution of entropy \(P\left(\left\langle H\right\rangle \right)\) from the randomized careers (Fig. 5a–c). We find that, after the hot-streak menstruation, \(\langle H\rangle\) becomes statistically duplicate from the randomized careers (−1 ≤z-score ≤ 1). Nosotros farther examine the temporal changes in entropy at the end of a hot streak by aligning careers based on when their hot streaks end (Fig. 5d–f). We find again a lack of difference betwixt data and the null model. Together, these analyses propose that individuals return to "normal" after their hot streak ends, showing an absenteeism of exploration or exploitation patterns.

Fig. 5: When hot streak ends.

a–c The distribution of entropy \(P\left(\langle H\rangle \right)\) later a hot streak for yard realizations of the randomized careers for all individuals analyzed in our datasets. The vertical line indicates \(\left\langle H\correct\rangle\) measured in real careers, showing that it is statistically duplicate from the randomized careers. d–f The dynamics of entropy \(H\) surrounding the terminate of hot streaks for real and randomized careers, measured through a sliding window of six artworks, five films, or five scientific papers. Error confined stand for the standard fault of the mean.

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Discussions

Taken together, these results unveil identifiable regularities underlying the onset of career hot streaks, which appear to apply universally across a wide range of creative domains. Overall, our results highlight the important role of both exploration and exploitation in individual careers. Curiously, beyond all 3 domains we studied, a major turning point for private careers appears most closely linked with neither exploration nor exploitation behavior in isolation, simply rather with the particular sequence of exploration followed by exploitation. Indeed, extant literature has documented the key role of exploration and exploitation in creativity (Supplementary Notation 2.2 and Supplementary Table 1). Notwithstanding as creative behaviors, they have traditionally been considered either in isolation or in combination but rarely in succession^14,22; this is especially the case for career-level assay. Our results suggest a sequential view of artistic strategies that remainder experimentation and implementation may exist particularly powerful for producing long-lasting contributions. These findings may hold broad relevance for identifying, grooming, and nurturing artistic talents, especially given the various forces that sometimes appear in tension with the exploration–exploitation dynamics, ranging from the intensifying pressure level to publish^39,40 to the increasing trend of exploration over a career^xvi, from the specialization of individual expertise¹⁰ to how such specialization is favored in personnel evaluations^41,42.

It is important to annotation that while our results demonstrate meaning and consistent relationships across domains, the overall effect size seems modest. On the 1 mitt, this suggests that additional controls might further tighten the human relationship. For instance, after we control for authorship and the effect of collaborations, the outcome size seems to magnify (Supplementary Notation four.five). On the other manus, it also suggests opportunities to examine other potential processes that may also underlie the onset of hot streaks. Indeed, existent careers are circuitous, with heterogeneous influences operating across domains as well as a multitude of individual and institutional factors. Hence, it is plausible that additional factors may also be at work. In this written report, we likewise tested several alternative explanations for the onset of hot streaks (Supplementary Note half dozen). Although each of these hypotheses we tested appears plausible past itself, nosotros discover that none of them shows consequent associations, indicating that none of these alternative hypotheses lone can business relationship for the hot-streak dynamics nosotros studied. It is also likely that on an individual basis, the exploration–exploitation transition is further influenced by other external factors, such as shifting market conditions⁴³, social network structure^38,44, and disciplinary culture^18,19. Individuals may also receive curt-term feedback (e.yard., art critiques or peer reviews) that may offer additional signals shaping their career focus. As such, the patterns of exploration and exploitation may reverberate personal initiatives as well as responses to external forces. Nevertheless, our results suggest that, despite the obvious heterogeneity in the settings we examined and the myriad factors that may impact career progression and success, the exploration–exploitation dynamics appears consistently associated with the onset of hot streaks across rather various domains.

The information-driven nature of our study indicates that it is not immune to 2 limitations mutual in this type of analysis. Get-go, while the datasets nosotros assembled in this paper represent big collections of career histories and outputs across a variety of domains, they are express to individuals who have had sufficiently long careers providing enough data points for statistical analyses (Supplementary Note i). Second, this paper presents correlational show, whose primary goal is to investigate empirical regularities associated with the onset of hot streaks. Hereafter work using causal research designs may improve causative interpretations of the regularities reported here.

Furthermore, while this piece of work mainly focuses on universal patterns related to the onset of hot streaks, in that location could be important domain-specific differences in the role of exploration, exploitation, and success that are worth investigating farther. For example, our preliminary analysis suggests that the level of exploration and exploitation in science appears much stronger than in art or film directing (Fig. 3). The number of styles/topics within each career besides varies essentially across domains (Supplementary Fig. 30). While these cantankerous-domain differences could flow from inherent differences in data and methods, assessing domain-specific patterns is an important direction for future piece of work.

Notably, the sequence of exploration followed by exploitation closely resembles strategies observed in a wide range of natural and socio-technical settings, from creature foraging⁴⁵ to homo cognitive search⁴⁶, from multi-armed bandits and reinforcement learning⁴⁷ to role oscillation betwixt brokerage and closure in social network⁴⁸ to irresolute innovation strategies over business cycles⁴⁹. It thus suggests that the sequential strategies of exploration followed past exploitation uncovered in this study may accept broad relevance that goes beyond individuals' careers. Lastly, the representation techniques used in this paper could open up up promising avenues for inquiry on creativity^fifty,51,52, offer a quantitative framework to probe the characteristics of the creative products themselves. Futurity advances in deep learning may enable researchers to incorporate more artistic dimensions, and hence more fruitfully contribute to a computationally enhanced understanding of creativity.

Methods

Loftier-dimensional representation of artworks

We utilise a pre-trained VGGNet algorithm³³, one of the all-time-known algorithms for image recognition, to images of artworks, and connect it with an boosted neural network with fully connected layers to allocate the fine art fashion labels recorded in our dataset (Fig. 1a). The convolutional layers in the pre-trained VGGNet use iii × 3 filters to detect local patterns from the artwork (Fig. 1b). The filters in the beginning layer capture spatial patterns such as line orientations and brushstrokes (Fig. 1b), whereas those in higher layers combine outputs of filters from lower layers to capture more circuitous features, such as shapes and objects (Fig. 1c). To leverage VGGNet's image recognition capabilities, here we practise not railroad train the VGGNet layers, but instead railroad train the fully connected layers to repurpose VGGNet to identify art styles (Fig. 1a), helping the beginning ii fully connected layers to find an abstract representation of concepts and themes by grouping together related outputs of the VGGNet layers. Prior research shows that fine art style may exist decoded from both brush strokes and the overall concepts, subjects, and themes^34,53, suggesting that both low- and high-level features are important for capturing art styles. Nosotros combine the outputs from the commencement and 3rd convolutional layers in VGGNet with the fully connected layer earlier the final classification layer (see Supplementary Notation 1.1 for several example studies showing how art styles are interpreted past our deep learning framework). We apply our deep neural network to the career outputs of each creative person in the dataset, and then utilize principal component analysis for dimensionality reduction to generate a 200-dimensional embedding of each artwork.

Loftier-dimensional representation of films

We build loftier-dimensional representations of films by combing the plot and casting information of each film. Nosotros showtime train discussion embeddings⁵¹ in the description of the plot to learn a 100-dimensional text representation of a film from the co-occurrence of words (Fig. 1d and Supplementary Note 1.2). To comprise casting information, we construct a weighted co-casting network among all actors and utilize a node embedding method DeepWalk⁵⁴ to obtain a 100-dimensional casting vector for each pic (Fig. 1e and Supplementary Notation ane.2). We then concatenate the vectors for plot and bandage, assuasive us to develop a 200-dimensional embedding space to stand for all films. Despite the myriad factors that may affect the artistic and fiscal success of a film⁵⁵, ranging from the screenplay to interim, nosotros observe that the learned high-dimensional representation can successfully predict film genre with an accuracy of 0.948 (Supplementary Note one.2).

Reporting summary

Further information on research design is bachelor in the Nature Research Reporting Summary linked to this article.

Data availability

The data used in this study have been deposited in the GitHub repository https://kellogg-cssi.github.io/onsethotstreaks.

Code availability

The code used in this study has been deposited in the GitHub repository https://kellogg-cssi.github.io/onsethotstreaks.

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Acknowledgements

We give thanks A.-L. Barabási, West. Ocasio, B. Uzzi, J. Evans, K. Rao, C. Candia, S. Medya, Chiliad. Tripodi, and all members of the Centre for Science of Scientific discipline and Innovation (CSSI) for invaluable comments. This work is supported past the Air Force Office of Scientific Research under award numbers FA9550-15-i-0162, FA9550-17-one-0089, and FA9550-19-one-0354.

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Affiliations

1. Center for Science of Science and Innovation, Northwestern University, Evanston, IL, USA

   Lu Liu, Nima Dehmamy, Jillian Chown & Dashun Wang

2. Northwestern Found on Complex Systems, Northwestern University, Evanston, IL, The states

   Lu Liu, Nima Dehmamy & Dashun Wang

3. Kellogg School of Management, Northwestern Academy, Evanston, IL, USA

   Lu Liu, Nima Dehmamy, Jillian Chown & Dashun Wang

4. College of Information Sciences and Technology, Pennsylvania State Academy, University Park, PA, United states of america

   Lu Liu & C. Lee Giles

5. Department of Computer science and Engineering, Pennsylvania State University, University Park, PA, USA

   C. Lee Giles

6. McCormick Schoolhouse of Engineering, Northwestern University, Evanston, IL, USA

   Dashun Wang

Contributions

D.W. conceived the project and designed the experiments; L.L. and N.D. collected information and performed empirical analyses with help from J.C., C.L.G. and D.W.; all authors discussed and interpreted results; D.W., Fifty.L. and Northward.D. wrote the manuscript; all authors edited the manuscript.

Corresponding author

Correspondence to Dashun Wang.

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Liu, L., Dehmamy, North., Chown, J. et al. Understanding the onset of hot streaks across artistic, cultural, and scientific careers. Nat Commun 12, 5392 (2021). https://doi.org/10.1038/s41467-021-25477-8

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• Received: 22 Feb 2021

• Accepted: 04 August 2021

• Published: thirteen September 2021

• DOI : https://doi.org/10.1038/s41467-021-25477-viii

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