Summary The BRAIN initiative is enabling ground-breaking techniques for brain recordings that will permit a unique view onto the dynamics of neural activity. However, inferring brain function from multi-channel physiological recordings is challenging. A key difficulty is that individual neurons and mesoscopic, often rhythmic, cell populations interact in complicated and recurrent ways. Such complex neuronal dynamics is hard to analyze but very likely important to the functioning of the brain. This proposal will address this problem by developing (1) tools for analyzing brain activity; (2) a theoretical framework for expressing underlying computations and generating experimental predictions. The starting point of the project is our earlier discovery that phase structure in oscillatory local field potentials (LFP) of hippocampal areas CA1/CA3 carry location information in exquisite detail (Agarwal et al. 2014). We will release software tools that make the methods for phase decoding and extracting meaningful LFP components available to the broader community. Further, in collaboration with experimental labs we will research the mechanistic underpinnings of this discovery in hippocampus (Buzsaki NYU, Foster, UC Berkeley), and explore how similar approaches can leverage phase diversity in cortical gamma oscillations (Fries, MPI Frankfurt). The research goal is to develop analysis tools for decoding and extraction of functional components (Aims 1 and 2), applicable to a broad range of multivariate brain recordings of hippocampal and cortical activity. Further, we will develop a flexible two-level theory framework with software tools (Aim 3) to help neuroscientists, in particular experimenters, to formulate putative abstract computations underlying a brain function under study, and build a concrete mechanistic circuit model of those computations. The computational description level will leverage ideas of vector symbolic architectures, a class of connectionist models originally proposed for describing cognitive reasoning (Plate, 1995; Kanerva, 1996). Models produced by the software tool will concisely encapsulate assumptions about the computation and its implementation of a brain function and produce predictions that can be tested in a next generation of recording experiments. The proposed theory framework will be tested in building models for navigation in hippocampus and for visual processing in areas V1 and V4 in cortex.