Towards Defining, Measuring, and Leveraging Creativity in AI Applications

• Prior approaches often lack either a formal mathematical definition or careful examination of assumptions and validation on real data.Source: §1 · p. 1
• The proposed postulates and mathematical definition are grounded in Boden’s criteria of newness, value, and surprise.Source: §1 · p. 1
• The paper tests the same creativity formula on chess moves and paintings, adapting the criteria’s specific definitions to each domain.Source: §1 · p. 1
• The stated contributions combine formal postulates, a mathematical formula, and tests on chess and paintings.Source: §1 · p. 1

• Creativity research spans disciplines, yet proposed approaches have not reached consensus on what creativity is.Source: §2 · pp. 1–2
• The paper focuses on product creativity, applying it to paintings and chess from historical and personal perspectives.Source: §2 · p. 2
• The classical view uses originality and effectiveness, while Boden’s influential account adds surprise as a distinct criterion.Source: §2 · p. 2
• Computational creativity lacks uniform criteria; Ritchie’s dimensions are novelty, quality, and typicality.Source: §2 · p. 2
• Embedding-based score estimation, including CNN evaluation of drawing-task outputs, lacks interpretability into creativity’s underlying structure.Source: §2 · p. 2
• Prior multi-criterion approaches are criticized for weak theoretical grounding, counterintuitive additive formulas, absent implementation or validation, and ambiguous measurement.Examples include, [Franceschelli and Musolesi, 2022],, and [Franc¸a et al., 2016].Source: §2 · p. 2
• The paper contrasts these approaches with a psychologically and philosophically grounded formulation, concrete criterion measurements, and empirical validation in two domains.Source: §2 · p. 2

3 Definition of Creativity and Postulates

• Creativity is scored relative to pre-existing objects through a continuous, differentiable function of newness, value, and surprise, with domain-dependent weights.The reference set can contain historical objects for H-creativity or personally known objects for P-creativity.Source: §3 · pp. 2–3
• The creativity score and each component score are bounded, with bounds motivated by constraints on prior assumptions and available resources.For artwork valued by auction price, the total wealth available in that market bounds value.Source: §3 · p. 3
• An object is creative if and only if its newness, value, and surprise scores are all greater than zero.The postulate rejects additive formulations that could classify an object as creative based on only some components.Source: §3 · p. 3
• Newness measures difference from every object in the pre-existing set; what counts as identical must be defined for each domain.A Starry Night image reproduced on a T-shirt is treated as equivalent to the original because its content is unchanged.Source: §3 · p. 3
• Newness, value, and surprise are separable: the presence or absence of one does not determine the others.A newly made painting may lack value, while a valuable Van Gogh reprint is not new.Source: §3 · pp. 3–4
• The relationship between newness and surprise is discontinuous, so large changes in newness may yield little surprise and small changes may yield much.The films The Magnificent Seven and The Seven Samurai differ in setting but share similar narrative structures; a one-word change can sharply alter a joke’s surprise.Source: §3 · p. 4

4 Creativity Formula

• The closed-form formula is a special case of a generic creativity definition, with newness, value, and surprise measures specified for its components.The paper says these component measures must be tailored to each application's characteristics and constraints.Source: §4 · p. 4, §4.3 · p. 5

4.1 Measure of Newness

• Newness is the minimum distance between an object's embedding and embeddings of pre-existing objects in domain set T.The minimum is preferred to median, average, or distance to a cluster center because those alternatives may not satisfy Postulate (4).Source: §4.1 · p. 4

4.2 Measure of Value

• Intrinsic value may be estimated as the maximum business value over time, such as an artwork's maximum auction sale price.The paper assumes intrinsic value can be measured or estimated using various methods.Source: §4.2 · p. 4
• Value can also be estimated from domain-specific expert criteria, such as writing coherence or interestingness and chess moves' change in winning rate.When reliable intrinsic measures are available, the paper says to use them; otherwise, external values such as market prices or user feedback can serve as substitutes.Source: §4.2 · p. 5

4.3 Measure of Surprise

• The paper focuses on probabilistic and observation mismatch for surprise, since belief mismatch can be insensitive when prior knowledge is large.Under belief mismatch, the shift between prior and posterior distributions becomes negligible as the prior knowledge grows.Source: §4.3 · p. 5
• Probabilistic mismatch measures surprise using an object's likelihood under a prior distribution, including Shannon's Surprise and Bayesian Factor Surprise.Shannon's Surprise is the negative log probability under a prior distribution that can be modeled with Gaussian Mixture Models.Source: §4.3 · p. 5
• Observation mismatch measures the distance between a predicted object and its actual observation, but iteratively updating a generative model can be computationally intensive.A chess dictionary can infer predictions because its legal board-state space is finite; dictionary methods are unsuitable for infinite spaces such as artwork and storytelling.Source: §4.3 · p. 5
• The paper applies its formula to chess and paintings, adapting component measurements to each domain's characteristics and constraints.Its discussion presents this domain-specific tailoring as necessary when computing newness, value, and surprise.Source: §4.3 · p. 5

5 Framework Validation on Two Applications

• The framework is applied to chess games and painting artworks as two validation applications.The passages provided here do not give outcome values for the applications.Source: §5 · p. 5

5.1 Chess Game

• The chess dataset contains 94,565 cleaned games and 7,711,327 moves, with expert comments used to identify creativity assessments.The games span 1610–2024, and comments also cover strategy, move analysis, tactical implications, and endgames.Source: §5.1 · p. 5
• Chess newness is binary, Stockfish depth-15 evaluation supplies value, and surprise compares a move embedding with a frequency-weighted average of prior moves at that position.The prior set begins with games before 1960 and is updated yearly; the surprise lookup stores prior move counts by board position.Source: §5.1 · pp. 5–6
• The chess labels comprise 639 moves, and three LLMs filter expert comments using agreement and justification-consistency criteria.The pairwise cosine distance between CLIP embeddings of the justifications must exceed 0.70, and all three LLMs must return the same result.Source: §5.1 · p. 6

5.2 Painting Artworks

• The painting data contains 355,551 cleaned auction records for Western artists active from 500AD through 2024, including 2,802 paintings with multiple records.The records include painting, artist, price in USD, and verified creation-date information.Source: §5.2 · p. 6
• Painting newness uses minimum embedding distance to prior paintings, value uses inflation-adjusted maximum auction price, and surprise uses low likelihood under a GMM fitted to prior embeddings.The painting domain uses the probabilistic mismatch approach because observation mismatch is computationally harder there.Source: §5.2 · p. 7
• Painting evaluation uses consistent LLM comments for works by Kollwitz, Renoir, and Picasso, producing 1,862 labeled samples for a normalized-feature regression model.Comments are retained when their pairwise CLIP-embedding cosine distance exceeds 0.70; the non-linear model uses a degree-4 spline transformer with 8 knots.Source: §5.2 · p. 7

6.1 Chess Games

• Table 1 reports chess performance across five-fold cross-validation, with averages and standard deviations across accuracy, AUC, precision, recall, and F1.Source: §6.1 · p. 7
• Chess creativity estimation achieved an AUC of 0.6357, higher than the 0.60 AUC reported for a difficult clinical prediction task.The authors note that no directly comparable baseline for chess creativity was identified.Source: §6.1 · pp. 7–8
• Chess correlations were 0.4785 for newness–surprise, −0.0290 for surprise–value, and −0.1513 for newness–value; newness and surprise were distinct, not collinear.Source: §6.1 · p. 8

6.2 Painting Artworks

• Because painting labels represent estimated creativity probabilities, evaluation includes JSD and WD alongside MAE and RMSE.JSD near zero indicates similar true and predicted creativity distributions; WD measures the probability mass needed to transform one distribution into the other.Source: §6.2 · p. 8
• For paintings, the basic model performed better on MAE, RMSE, and JSD, while the nonlinear model performed better on WD across the three embeddings.With CLIP, the basic model improved MAE by 4%, RMSE by 9%, and JSD by 20% versus the nonlinear model; the nonlinear model improved WD by 10%.Source: §6.2 · p. 8, Table 2 · p. 8
• Painting correlations were 0.2986 for newness–surprise, 0.0308 for surprise–value, and 0.0421 for newness–value using CLIP; newness and surprise were not collinear.Source: §6.2 · p. 8

• The paper formally defines creativity using newness, value, and surprise, and validates its formula on chess moves and paintings.Source: §7 · p. 8
• The formula stays the same across chess and paintings, but domain-specific definitions of the three criteria make the resulting measure application-dependent.Source: §7 · p. 8
• Future work includes applying the method to storytelling, music, and advertising, developing domain-specific solutions, and investigating whether a canonical formula exists.The current formula is described as one instantiation within the broader postulate framework.Source: §7 · p. 8