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Neuromorphic computing mimicking the functionalities of mammalian brain holds the promise for cognitive capabilities enabling new intelligent applications. However, research efforts so far mainly focused on using analog and digital CMOS technologies to emulate neural activities, and are yet to achieve expected benefits. They suffer from limited scalability, density overhead, interconnection bottleneck and power consumption related constraints. In this paper, we present a transformative approach for neuromorphic computing with Wave Interference Functions (WIF). This is a framework using emerging non-equilibrium wave phenomenon such as spin waves. WIF leverages inherent wave attributes for multi-dimensional, multi-valued data representation and communication, resulting in reduced connectivity requirements and efficient neural function implementations. It also yields a compact implementation of an artificial neuron. Moreover, since WIF computation and communication are in the spin domain, extremely low-power operation is possible. Our evaluations indicate up to 57x higher density, 775x lower power and 2x better performance when compared to an equivalent 8-bit 45nm CMOS neuron. Our scalability study using arithmetic circuits for higher bit-width neuron implementations indicate up-to 63x density, 884x power and 3x performance benefits in comparison to a 32- bit CMOS equivalent design at 45nm.