The founding deep-network critical-period paper's Fisher-Information signal does not correlate with the Information Bottleneck's compression signal

Achille, Rovere & Soatto (2019) — the paper that established critical periods in deep networks (claim-critical-periods-arise-from-information-plasticity-not-biology) — ground their result in the Fisher Information Matrix (FIM) of the network's weights, not the Shannon mutual information of activations that Tishby's Information Bottleneck (IB) tracks. The authors note the distinction themselves: their analysis of "Information Plasticity" builds on Fisher information, "although their [Shwartz-Ziv & Tishby's] analysis builds on the (Shannon) information of the activations." They go further and test the specific statistic Shwartz-Ziv & Tishby use to mark their fit-to-compression transition — gradient covariance — against their own critical-period sensitivity measure, and report it fails to track: "the covariance and norm of the gradients exhibit no clear trends during training with and without deficits, and, therefore, unlike the FIM, do not correlate with the sensitivity to critical periods." The paper does gesture at an indirect bridge via a separate work (Achille & Soatto 2018, JMLR) showing the weight FIM can bound activation information — but that is an inferential link through another paper's bound, not a demonstration that critical periods are produced by, or require, IB-style compression.

Combined with claim-ib-compression-phase-is-nonlinearity-dependent-not-universal and claim-ib-compression-may-be-a-binning-artifact-not-real-mutual-information, this settles question-information-bottleneck-linked-to-critical-periods: the IB compression phase is not established as universal, its measurement is independently disputed as a possible artifact, and the one paper that would need to derive critical periods from IB instead uses a different quantity its own authors show does not correlate with IB's compression signature. The "IB explains critical periods" framing survives only as a resemblance in narrative shape ("forgetting," a rise-then-fall curve) between two information-theoretic quantities shown not to move together — consistent with the same authors' separate refusal to call their network a valid model of biology (claim-achille-soatto-disclaim-dnn-as-valid-model-of-biology) and with the paper's animal-only validation scope (claim-founding-dnn-critical-period-paper-validated-on-animal-data-only). Concept anchors: entity-information-bottleneck, entity-information-plasticity; people: entity-naftali-tishby, entity-alessandro-achille, entity-stefano-soatto.