提出一种保持中间表示一致性的动态建模方法，让模型自适应停止更合理。
Scale-Consistent State-Space Dynamics via Fractal of Stationary Transformations
- 引入分形诱导偏置，确保状态空间模型在迭代中保持尺度一致性。
- 实验验证在ImageNet-100上中间状态呈现分形结构，且自适应效率提升。
- 适合关注模型可解释性与高效推理的开发者和研究者。
当前深度学习模型日益依赖深度，但缺乏对中间表示有效性的结构保证，导致早停和自适应计算失去意义。本文提出状态空间模型应具备跨迭代优化的尺度一致性潜在动态结构，并推导出平稳变换的分形（FROST），通过分形归纳偏置强制实现自相似表示流形。在此几何下，中间状态对应同一表示的不同分辨率，我们提供了几何分析，证明迭代过程中的收缩性与稳定收敛。由此产生的尺度一致性结构使得早停可自然表述为基于内在特征质量的排序问题。在ImageNet-100上的受控实验验证了预测的尺度一致性行为，表明自适应效率源于对齐的潜在几何结构。
原文摘要 · Abstract (English)
Recent deep learning models increasingly rely on depth without structural guarantees on the validity of intermediate representations, rendering early stopping and adaptive computation ill-posed. We address this limitation by formulating a structural requirement for state-space model's scale-consistent latent dynamics across iterative refinement, and derive Fractal of Stationary Transformations (FROST), which enforces a self-similar representation manifold through a fractal inductive bias. Under this geometry, intermediate states correspond to different resolutions of a shared representation, and we provide a geometric analysis establishing contraction and stable convergence across iterations. As a consequence of this scale-consistent structure, halting naturally admits a ranking-based formulation driven by intrinsic feature quality rather than extrinsic objectives. Controlled experiments on ImageNet-100 empirically verify the predicted scale-consistent behavior, showing that adaptive efficiency emerges from the aligned latent geometry.
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