The Reconstruction Gap: Boundary Noise and the Limits of Holographic Bulk Recovery in Deep Learning, with Implications for Black-Box AI Auditing

Maldacena’s conjecture holds that the interior (bulk) of an anti-de Sitter spacetime is encoded on its boundary. Holographic deep learning turns this idea into a learning problem: a network whose layers are radial slices of the spacetime learns the bulk metric from boundary data alone. This literature has asked whether the bulk can be recovered, not how much of it is lost when the boundary is observed imperfectly. A Scopus relaxation funnel finds no study of reconstruction under noisy boundary data, and none linking holographic reconstruction to AI auditing. This article defines the reconstruction gap, the relative error between the learned and the true metric by radial region, and measures it in two computational experiments with a known ground truth. A factorial design of 900 training runs varies boundary noise, sample size, depth and regularisation; a second experiment trains 400 networks from different initialisations on fixed data. With clean data, networks classify 99.1% of boundary points correctly while the near-horizon error remains about 30%. One per cent boundary noise costs half a percentage point of accuracy but nearly doubles the near-horizon error. A twenty-fold increase in sample size leaves that error unchanged, and the standard smoothness regulariser worsens it above roughly 7% noise. Among networks with indistinguishable in-distribution accuracy, interiors differ by a factor of more than three and out-of-distribution accuracy by up to 42 percentage points, while a global measure of structural error does not predict which networks fail. Read as a formal analogy, not an equivalence, the results quantify why audits restricted to black-box access cannot certify a model’s internal mechanism, and why white-box access helps only when it asks targeted questions. Replication package (code, run-level results for all 1,300 training runs, tables and figures): https://doi.org/10.5281/zenodo.23343342