arXiv:2607.06048v1 Announce Type: cross Abstract: We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension. The networks we consider employ a fixed monomial nonlinearity and no pooling, so that the only design variable is the frame generated by the network filters. For data modeled as rectifiable sets, we first characterize and bound the separation capacity of general feature extractors in terms of the geometry of the dataset. We then particularize to scattering networks and obtain two design criteria: (i) the filters should
This paper in 2026 contributes to the ongoing theoretical work in optimizing AI architectures, specifically scattering networks, which are gaining renewed interest for their interpretability and efficiency on certain data types.
Improving the theoretical understanding and design criteria for neural networks, like scattering networks, is crucial for developing more efficient, robust, and explainable AI systems, impacting future applications in various fields.
The identification of specific design criteria based on dataset geometry could lead to more targeted and performant scattering network architectures for low-dimensional data tasks.
- · AI researchers
- · Machine learning engineers
- · Sectors with low-dimensional data (e.g., specific sensor data analysis, medical
- · Developers of less optimized general-purpose neural architectures
Further research will build upon these design criteria to develop more effective scattering network models.
Improved scattering networks could lead to advancements in specific AI applications requiring high interpretability or efficiency on low-dimensional inputs.
These theoretical insights might eventually influence broader neural network design principles, even for deep learning models operating on high-dimensional data.
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Read at arXiv cs.LG