Researchers have addressed the problem of "Barren Plateaus" in Quantum Machine Learning (QML), a phenomenon that hinders the training of Parameterized Quantum Circuits (PQCs). This issue arises when the gradient landscape becomes exponentially flat, preventing effective optimization. The study proposes that the large Hilbert space capacity of PQCs, often seen as an advantage, is the direct mathematical cause of these plateaus, leading to "quantum underfitting" in unstructured architectures.

This work establishes a framework linking the algebraic dimension of circuit generators to their optimization dynamics. To achieve this, recent advances in Dynamical Lie Algebras (DLAs) and Geometric QML have been integrated. This approach reveals a quantum manifestation of the bias-variance tradeoff: while unstructured architectures can achieve near-perfect training accuracy via unscalable parameterization (which could be considered "quantum overfitting"), embedding group-theoretic geometric priors acts as a structural regularizer.

By restricting DLA growth to a polynomial regime, the proposed method sacrifices raw memorization capacity. However, this strategy guarantees scalable, gradient-rich training landscapes, which is crucial for the development of scalable quantum neural networks. The results were empirically validated on a non-linear binary classification task, demonstrating the feasibility of a "Trainability-by-Design" approach in QML systems.