Structure–Residual Inductive Biases for Language Model Pretraining

Next-token prediction is relied upon to learn both predictive behavior and internal representations. We ask whether representation structure itself should be an explicit inductive bias. Motivated by the two-part coding view of Kolmogorov complexity, we study a structure–residual principle in which a representation separates structure from realization detail. We instantiate this principle in two complementary ways. Boundary Bottleneck Concept (BBC) routes information from token segments through boundary carriers while preserving local autoregressive computation. Continuous Concept (CC) regularizes representation geometry and induces a spectral decomposition into low-frequency structure and high-frequency residual. We derive coding bounds for both views and show that low CC energy controls the error of multiplicity-corrected BBC-style boundary attention. Empirically, BBC and CC exhibit strikingly different depth preferences: BBC works best in early layers, whereas CC is most effective in later layers. At 300M training tokens, combining BBC and CC improves NLL by 1.44% on GPT-2 Medium. These gains persist with training runs up to 20B tokens. Representation diagnostics show that BBC increases the relative predictive importance of boundary states, while CC reduces spectral residual energy. Together, these results suggest that structure–residual biases can improve language-model pretraining beyond next-token prediction.