Learning robust and generalisable abstractions from high-dimensional input data is a central challenge in machine learning and its applications to high-energy physics (HEP). Solutions of lower functional complexity are known to produce abstractions that generalise more effectively and are more robust to input perturbations. In complex hypothesis spaces, inductive biases make such solutions learnable by shaping the loss geometry during optimisation. In a HEP classification task, we show that a soft symmetry respecting inductive bias creates approximate degeneracies in the loss, which we identify as pseudo-Goldstone modes. We quantify functional complexity using metrics derived from first principles Hessian analysis and via compressibility. Our results demonstrate that solutions of lower complexity give rise to abstractions that are more generalisable, robust, and efficiently distillable.

翻译：从高维输入数据中学习鲁棒且可泛化的抽象表示是机器学习及其在高能物理（HEP）应用中面临的核心挑战。已知较低函数复杂度的解能够产生更有效泛化且对输入扰动更鲁棒的抽象表示。在复杂假设空间中，归纳偏置通过优化过程中塑造损失函数的几何形态，使得此类解可被学习。在一个HEP分类任务中，我们证明了一种尊重对称性的软归纳偏置会在损失函数中产生近似简并，我们将其识别为赝戈德斯通模。我们使用基于第一性原理海森矩阵分析推导的度量指标以及通过可压缩性来量化函数复杂度。我们的结果表明，较低复杂度的解能够产生更具泛化性、更鲁棒且可高效蒸馏的抽象表示。