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Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
Measuring the originality of intellectual property assets...
Sébastien Ragot · 2020-10-14 · via math.PR updates on arXiv.org

Originality criteria are frequently used to compare assets and, in particular, to assess the validity of intellectual property (IP) rights such as copyright and design rights. In this work, the originality of an asset is formulated as a function of the distances between this asset and its comparands, using concepts of maximum entropy and surprisal analysis. Namely, the originality function is defined according to the surprisal associated with a given asset. Creative assets can be justifiably compared to particles that repel each other via an electrostatic-like pair potential. This allows a very simple, suitably bounded formula to be obtained, in which the originality of an asset writes as the ratio of a reference energy to an interaction energy imparted to that asset. In particular, the originality of an asset can be expressed as a ratio of two average distances, i.e., the harmonic mean of the distances from this asset to its comparands divided by the harmonic mean of the distances between the sole comparands. Accordingly, the originality of objects such as IP assets can be simply estimated based on distances computed thanks to unsupervised machine learning techniques or other distance computation algorithms. Application is made to various types of assets, including emojis, typeface designs, paintings, and novel titles.