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Future wireless networks may operate at millimeter-wave (mmW) and sub-terahertz (sub-THz) frequencies to enable high data rate requirements. While large antenna arrays are critical for reliable communications at mmW and sub-THz bands, these antenna arrays would also mandate efficient and scalable initial beam alignment and link maintenance algorithms for mobile devices. Low-power phased-array architectures and phase-less power measurements due to high frequency oscillator phase noise pose additional challenges for practical beam tracking algorithms. Traditional beam tracking protocols require exhaustive sweeps of all possible beam directions and scale poorly with high mobility and large arrays. Compressive sensing and machine learning designs have been proposed to improve measurement scaling with array size but commonly degrade under hardware impairments or require raw samples respectively. In this work, we introduce a novel long short-term memory (LSTM) network assisted beam tracking and prediction algorithm utilizing only phase-less measurements from fixed compressive codebooks. We demonstrate comparable beam alignment accuracy to state-of-the-art phase-less beam alignment algorithms, while reducing the average number of required measurements over time.