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The spatial distribution of matter at late time in the Universe depicts a complex pattern commonly referred to as the cosmic web. In this web-like structure, massive nodes are linked together by elongated bridges of matter, the filaments, themselves found at the intersections of mildly-dense walls forming the borders of vast and underdense volumes called voids. In this presentation, I will start by giving a broad introduction to the cosmic web together with some motivations for extracting compressed summaries from matter fields. I will then focus on the definition and exploitation of the several cosmic web environments to improve the constraints on the cosmological parameters over the traditionally-used two-point statistics in large N-body simulations from the Quijote suite. If time permits, I will also take a few minutes to discuss another part of my recent research activity aimed at using developments from theoretical physics to better understand the learning procedure of some neural networks.