Standard neural networks can locate the percolation threshold but miss the percolating cluster itself, learning local density proxies rather than scale-dependent connectivity. We recently introduced a scale-shared encoder–decoder that applies the same learned coarse-graining map at every scale (arXiv:2608.26764). Trained on small lattices, it extrapolates to L = 1024, reconstructs the spanning cluster, reproduces the critical exponents of 2D percolation, and its latent space displays an empirical RG flow between two stable phases. The internship aims to turn this empirical flow into a quantitative RG: locating the fixed points of the learned map and extracting exponents from its linearization, building in lattice symmetries, testing universality (bond percolation, other lattices), and extending the approach to other critical systems such as directed percolation or the Ising model. Profile: M2 student in theoretical, statistical or computational physics, with a solid background in statistical mechanics. Machine learning experience is a plus. Possible PhD continuation.