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In this paper, we address the task of determining whether a given utterance is directed towards a voice-enabled smart-assistant device or not. An undirected utterance is termed as a "false trigger" and false trigger mitigation (FTM) is essential for designing a privacy-centric non-intrusive smart assistant. The directedness of an utterance can be identified by running automatic speech recognition (ASR) on it and determining the user intent by analyzing the ASR transcript. But in case of a false trigger, transcribing the audio using ASR itself is strongly undesirable. To alleviate this issue, we propose an LSTM-based FTM architecture which determines the user intent from acoustic features directly without explicitly generating ASR transcripts from the audio. The proposed models are small footprint and can be run on-device with limited computational resources. During training, the model parameters are optimized using a knowledge transfer approach where a more accurate self-attention graph neural network model serves as the teacher. Given the whole audio snippets, our approach mitigates 87% of false triggers at 99% true positive rate (TPR), and in a streaming audio scenario, the system listens to only 1.69s of the false trigger audio before rejecting it while achieving the same TPR.