A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain.causal analysis | functional connectivity | decoding | hidden Markov models | machine learning I n analyzing complex networks, there is a crucial need for tools to analyze interaction strength among nodes of the networks, extending from genetics to economics (1), demographics (2), and ecology (3). This need is newly pressing in neuroscience (4-6) ( Fig. 1A). State-of-the-art recording techniques now allow simultaneous measurement of the activity of hundreds of neurons (7,8). Interpreting these recorded data requires the identification of groups of neurons that strongly interact with each other, known as neural microcircuits, as well as the ability to link microcircuit activity to behavior (7, 9). Currently, Granger causality (GC) (1) and cross-correlation (7) are leading methods for interaction strength analysis (5,6,10). Neither method can effectively analyze the nonlinear interactions that are common in neural circuits and systems in other fields (1,(3)(4)(5).Network decoding is an important need in many fields as well, and again, there is need for improved tools. Hidden Markov model (HMM)-based approaches are a leading method in the decoding field (11-15), but these can only decode a single element at a time. Linear dynamical systems (LDSs) are another approach based on latent variables and are an effective way to model and characterize the behavior of populations of neurons (16). However, LDS models are designed for analyzing data from large populations of similar neurons: they are less appropriate for analyzing circuits made up of heterogeneous neurons. Moreover, LDS cannot use known interactions between populations of neurons to improve decoding and prediction for both populations.A further motivating point is that most analytic methods now used are either strictly tools for interaction strength analysis or tools for decoding (5,7,17). There is a significant advantage to combining the two processes, because identifying nodes that strongly interact with each other enables robust network decoding (13). Here, we introduce the nonlinear multidimensional hidden stat...