Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data

The paper presents a clear logical flow, starting from the problem, introducing the tool (BID), describing the methods (simulations, binarization, fitting), presenting the results (scaling analysis, data collapse), and discussing the interpretation and future directions. The connection between BID scaling and Family-Vicsek universality is well-articulated.

Strengths: Numerical simulations performed on established models (RSOS, RDSD)., Sufficient number of realizations (N=2000) used for statistical averaging., Clear description of the binarization procedure and reference point., Use of Kullback-Leibler divergence for rigorous model fitting., Verification of results with different binarization rules (in supplementary material)., Demonstration of data collapse to support scaling hypothesis., Code availability mentioned.
Weaknesses: Specific optimization parameters (amin, amax, Nsteps, step size) for BID fitting are given in supplementary material, but the main text does not fully elaborate on their sensitivity impact on final BID values, beyond stating results were not highly sensitive for reasonable variations (though supplementary material notes sensitivity to Nsteps for RD model)., The discrepancy in the 2D saturation exponent relation and sensitivity to binarization rule require further investigation that is noted but not fully resolved in the presented work.

The claims are strongly supported by extensive numerical simulation results presented in multiple figures (Figs. 2, 3, 4, and supplementary figures). The data collapse plots provide compelling visual evidence for the Family-Vicsek scaling of the BID.

Applying the concept of Intrinsic Dimension, specifically the Binary Intrinsic Dimension, to study scaling phenomena in nonequilibrium growth dynamics is novel. Demonstrating that a metric from data science exhibits fundamental physical universality classes (Family-Vicsek scaling) is a significant original finding.

The work establishes a new connection between data science metrics and fundamental physical phenomena in nonequilibrium systems. This opens up new avenues for characterizing complex systems using data-driven approaches and suggests potential applications in fields like machine learning. The finding that even heavily compressed data retains universal scaling properties is potentially impactful.

Strengths: Precise academic terminology is used., Key concepts are introduced and explained (e.g., ID, BID, Family-Vicsek scaling)., Methodology is described clearly, including simulation details and binarization rule., Results are presented clearly and linked to the figures., The discussion synthesizes findings and outlines future work effectively.
Areas for Improvement: None