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Localization of acoustic sources using miniature microphone arrays poses a significant challenge due to fundamental limitations imposed by the physics of sound propagation. With sub-wavelength distances between the microphones, resolving acute localization cues become difficult due to precision artifacts. In this paper we propose a framework which overcomes this limitation by integrating signal-measurement (analog-to-digital conversion) with statistical learning (bearing estimation). At the core of the proposed approach is a min-max stochastic optimization of a regularized cost function that embeds manifold learning within ???? modulation. As a result, the algorithm directly produces a quantized sequence of the bearing estimates whose precision can be improved asymptotically similar to a conventional ???? modulators. In this paper we present a hardware implementation of a miniature acoustic source localizer which comprises of: (a) a common-mode canceling microphone array and (b) a ???? integrated circuit which produces bearing parameters. The parameters are then combined in an estimation procedure that can achieve a linear range from 0??-90??. Measured results from a prototype fabricated in a 0.5 ??m CMOS process demonstrate that the proposed localizer can reliably estimate the bearing of an acoustic source with a resolution less than 2?? while consuming less than 75 ??W of power.