Machine-learning systems usually model external data, while their internal functional organization is analyzed by external observers. This work introduces Self-Interventional Learning (SIL), in which a neural system perturbs its own functional structure, observes consequences, learns a predictive self-model, generalizes to unexecuted interventions, and uses predictions to guide later structural action. In a construction-known synthetic system, SIL recovered critical structure, redundancy, and replaceability, while synergy was not reliably recovered. Across 30 fresh confirmatory seeds, increasing the pairwise intervention budget from 4 to 56 reduced held-out prediction error from 0.0335 to 0.0148 and increased Spearman correlation from 0.629 to 0.883. In a matched ablation, preserving the correct intervention--consequence mapping reduced prospective prediction error by 81.3%, while using the same learned self-model for action reduced normalized regret by 31.7% relative to ignoring it. However, model-guided action did not significantly outperform a direct empirical-memory policy, and powered CIFAR-10/ResNet validation showed no robustness advantage over equal-budget direct repair search. These results support SIL as an intervention-driven framework for learning predictive knowledge about a network's own functional organization, while showing that the self-model remains incomplete and is not universally superior to simpler direct strategies.
This paper introduces a categorical account of infinitesimal causality in Frobenius Markov categories equipped with tangent-bundle semantics. IDC captures the infinitesimal layer in which interventions act as tangent deformations of copy/discard structure. Two distinct Frobenius structures interact: (1) the categorical Frobenius algebra on classical variables encoding copying, comparing, and discarding; and (2) the geometric Frobenius integrability condition, namely involutive closure of the intervention distribution, distinct from the algebraic Frobenius structure. Categorical causal sufficiency is defined as the compatibility of these two notions. A key observation is that, for structural causal models, infinitesimal causality is most naturally formulated in the slice of deterministic mechanisms over exogenous variables, with visible stochastic kernels obtained only after pushforward. Interventions are tangent vectors that deform the Frobenius copy/discard operations; their Lie brackets measure whether this deformation preserves classical information-flow structure. Pearl's do-calculus is used as a guiding example of intervention identities: ignoring irrelevant interventions corresponds to counit invariance, action/observation exchange to coproduct compatibility with pushforward, and independence to involutive bracket closure of the visible intervention distribution.