Beyond Representation Similarity: Exchange-Diagram Residuals for Diagnosing Neural Network Module Compatibility: A Computational Proof-of-Concept Study

The email address of this preprint: [email protected]; [email protected] Neural network representations are commonly compared using similarity measures such as centered kernel alignment (CKA) and singular vector canonical correlation analysis (SVCCA). Although these methods characterize relationships between internal representations, representational similarity does not necessarily establish whether a previously trained downstream module remains compatible with an updated upstream module. This distinction becomes particularly important when a network undergoes fine-tuning, pruning, or function-preserving transformations. This study investigates whether exchange-diagram residuals can provide structural information relevant to neural network module compatibility. We distinguish two tasks: (1) mismatch detection, which determines whether a frozen downstream module can still be reused after an upstream representation update, and (2) downstream-damage prediction, which estimates the magnitude of performance degradation associated with such reuse. We introduce a fixed-coordinate exchange-diagram residual, calculated using a reference principal component analysis (PCA) coordinate system, and compare it with conventional functional and representational diagnostics. Experiments were conducted using multilayer perceptrons trained on synthetic group-operation tasks involving the cyclic group Z7 and the symmetric group S3. The confirmatory experiment included 40 random seeds, three macro-representation dimensions, and 11 update conditions, producing 2,640 experimental records. Of these, 1,920 satisfied predefined external-behavior-preservation criteria. In grouped cross-validation, adding the fixed-coordinate residual increased mismatch-detection AUROC from 0.927 to approximately 1.000. For continuous downstream-damage prediction, mean absolute error decreased from 1.793 to 1.228, while the coefficient of determination increased from 0.784 to 0.885. Two deliberately constructed counterexamples demonstrated that high exchange residuals can coexist with downstream compatibility, while nearly zero residuals can coexist with severe downstream incompatibility. Furthermore, leave-one-mechanism-out analyses revealed that the predictive relationship was not uniformly transferable across intervention mechanisms. These findings suggest that exchange-diagram residuals may serve as complementary structural diagnostics for neural network module compatibility. Their principal contribution is not to establish a universal compatibility criterion, but to highlight a distinction between representational consistency and downstream functional compatibility. Potential applications include modular model updating, component reuse, continual learning, and model maintenance, although these applications require validation in larger and more realistic architectures. The use of AI: AI was used for searching the resource, writting the experiment codes, and polishing the preprint.