The presence of a second critical point in water has been a topic of intense investigation, with the molecular origins typically attributed to the competition between local high-density (HD) and low-density (LD) structures. However, identifying these structures often requires human intervention. This study employs unsupervised learning to discover structures in atomistic simulations of water near the Liquid-Liquid Critical Point (LLCP). By encoding environmental information using local descriptors, no evidence for two distinct thermodynamic structures is found. In contrast, when non-local descriptors that probe nanometer-scale heterogeneities are used, LD and HD domains emerge, rationalizing the microscopic origins of density fluctuations near criticality. The method involves encoding local environments using Smooth Overlap of Atomic Positions (SOAP) descriptors, extracting the Intrinsic Dimension (ID), and constructing a high-dimensional point-dependent probability density function to infer thermodynamic information. The results show that the free energy landscape in the space of local descriptors consists of a single minimum despite pronounced density fluctuations, while non-local information reveals bimodality. A statistical test, the Information Imbalance (IB), is used to evaluate the coupling between different descriptors and macroscopic density fluctuations, showing that the mapping is strongest when descriptors include information on a nanometer length scale. The study also characterizes the formation of LD and HD domains, which are identified at the same thermodynamic state point, and discusses the implications for understanding water's structural and dynamic properties in various scenarios.The presence of a second critical point in water has been a topic of intense investigation, with the molecular origins typically attributed to the competition between local high-density (HD) and low-density (LD) structures. However, identifying these structures often requires human intervention. This study employs unsupervised learning to discover structures in atomistic simulations of water near the Liquid-Liquid Critical Point (LLCP). By encoding environmental information using local descriptors, no evidence for two distinct thermodynamic structures is found. In contrast, when non-local descriptors that probe nanometer-scale heterogeneities are used, LD and HD domains emerge, rationalizing the microscopic origins of density fluctuations near criticality. The method involves encoding local environments using Smooth Overlap of Atomic Positions (SOAP) descriptors, extracting the Intrinsic Dimension (ID), and constructing a high-dimensional point-dependent probability density function to infer thermodynamic information. The results show that the free energy landscape in the space of local descriptors consists of a single minimum despite pronounced density fluctuations, while non-local information reveals bimodality. A statistical test, the Information Imbalance (IB), is used to evaluate the coupling between different descriptors and macroscopic density fluctuations, showing that the mapping is strongest when descriptors include information on a nanometer length scale. The study also characterizes the formation of LD and HD domains, which are identified at the same thermodynamic state point, and discusses the implications for understanding water's structural and dynamic properties in various scenarios.