Recursive Self-Similarity in Deep Weight Spaces of Neural Architectures: A Fractal and Coarse Geometry Perspective

This paper conceptualizes the Deep Weight Spaces (DWS) of neural architectures as hierarchical, fractal-like, coarse geometric structures observable at discrete integer scales through recursive dilation. We introduce a coarse group action termed the fractal transformation, $T_{r_k} $, acting under the symmetry group $G = (\mathbb{Z}, +) $, to analyze neural parameter matrices or tensors, by segmenting the underlying discrete grid $\Omega$ into $N(r_k)$ fractals across varying observation scales $ r_k $. This perspective adopts a box count technique, commonly used to assess the hierarchical and scale-related geometry of physical structures, which has been extensively formalized under the topic of fractal geometry. We assess the structural complexity of neural layers by estimating the Hausdorff-Besicovitch dimension of their layers and evaluating a degree of self-similarity. The fractal transformation features key algebraic properties such as linearity, identity, and asymptotic invertibility, which is a signature of coarse structures. We show that the coarse group action exhibits a set of symmetries such as Discrete Scale Invariance (DSI) under recursive dilation, strong invariance followed by weak equivariance to permutations, alongside respecting the scaling equivariance of activation functions, defined by the intertwiner group relations. Our framework targets large-scale structural properties of DWS, deliberately overlooking minor inconsistencies to focus on significant geometric characteristics of neural networks. Experiments on CIFAR-10 using ResNet-18, VGG-16, and a custom CNN validate our approach, demonstrating effective fractal segmentation and structural analysis.

DataOps for Societal Intelligence: a Data Pipeline for Labor Market Skills Extraction and Matching

Big Data analytics supported by AI algorithms can support skills localization and retrieval in the context of a labor market intelligence problem. We formulate and solve this problem through specific DataOps models, blending data sources from administrative and technical partners in several countries into cooperation, creating shared knowledge to support policy and decision-making. We then focus on the critical task of skills extraction from resumes and vacancies featuring state-of-the-art machine learning models. We showcase preliminary results with applied machine learning on real data from the employment agencies of the Netherlands and the Flemish region in Belgium. The final goal is to match these skills to standard ontologies of skills, jobs and occupations.