The paper explores the application of machine learning, specifically neural networks, to identify phases and phase transitions in condensed matter systems. The authors demonstrate that a standard feed-forward neural network can be trained to detect multiple types of order parameters directly from raw state configurations sampled with Monte Carlo simulations. They show that this classification can be performed without knowledge of the Hamiltonian or the general locality of interactions. The study focuses on the ferromagnetic Ising model and a toy model of a neural network for the Ising model, achieving high accuracy in classifying states at various temperatures. The authors also extend their approach to more complex systems, such as Coulomb phases and topological phases, where conventional order parameters are absent. They use a convolutional neural network to classify states in the Ising lattice gauge theory, achieving 100% accuracy by detecting local constraints satisfied by the spin configurations. The results highlight the potential of machine learning as a powerful tool in condensed matter and statistical physics, offering a complementary approach to traditional methods and enabling the analysis of complex data sets.The paper explores the application of machine learning, specifically neural networks, to identify phases and phase transitions in condensed matter systems. The authors demonstrate that a standard feed-forward neural network can be trained to detect multiple types of order parameters directly from raw state configurations sampled with Monte Carlo simulations. They show that this classification can be performed without knowledge of the Hamiltonian or the general locality of interactions. The study focuses on the ferromagnetic Ising model and a toy model of a neural network for the Ising model, achieving high accuracy in classifying states at various temperatures. The authors also extend their approach to more complex systems, such as Coulomb phases and topological phases, where conventional order parameters are absent. They use a convolutional neural network to classify states in the Ising lattice gauge theory, achieving 100% accuracy by detecting local constraints satisfied by the spin configurations. The results highlight the potential of machine learning as a powerful tool in condensed matter and statistical physics, offering a complementary approach to traditional methods and enabling the analysis of complex data sets.