Micro–Macro Relations Under Developmental Compression: An Exploratory Study of Representation Drift, Group-Structure Readout, and Predictive Sufficiency

This project was finished by Yancheng Guo(email:yanchengguo423@gmail.com), and Yuanfei Hu(email:yuanfeihu_duke@outlook.com). This study examines how task performance, hidden-state similarity, readout of a prespecified group representation, and cross-stage prediction change when a multilayer perceptron is progressively pruned and further trained. A two-hidden-layer network (width 32) learned addition in the cyclic group Z₇ from one-hot operands plus eight Gaussian nuisance dimensions. The v4 experiment comprised 1,600 runs: 10 seeds crossed with five pruning targets (0%, 20%, 40%, 60%, and 80%), four development learning rates, two pruning methods, two widening conditions, and two parameter-anchoring coefficients. Across factorial conditions, mean test accuracy declined from 1.000 at 0% pruning to 0.503 at 80%; centered kernel alignment (CKA) between early and late hidden states declined from 0.952 to 0.436. The mean error of a newly fitted supervised group-representation probe increased from 0.133 to 0.471, while the selected micro-input predictor’s test-MSE advantage over the selected macro-only predictor increased from 0.0090 to 0.0905. Magnitude pruning preserved task accuracy better than random pruning, showing that pruning method materially affected outcomes. Synthetic known-truth controls illustrated the distinction between failure of a linear macro-predictor and failure of nonlinear factorization; a separate specified dynamical system showed that perturbations outside a macrostate can affect a later macrostate when explicit coupling is present. These results suggest that task performance and several internal representation diagnostics can change non-synchronously in this controlled setting. They do not establish a universal loss of macrostate sufficiency, a direct commutative-diagram residual, autonomous discovery of group structure, or a causal necessity of residual plasticity. Generalization beyond Z₇ and stronger capacity-matched tests remain open.