Title: S$^6$-DAMON: Bridging Self-Supervised Speech Models and Real-time Speech Recognition. Abstract: There has been an growing demand for deep neural network (DNN) powered automatic speech recognition (ASR) on mobile platforms for real-time speech recognition. However, ubiquitous on-device ASR systems are still hindered by two bottlenecks: (1) the lack of large-scale transcribed speech data especially for low-resource spoken languages and (2) the large gap between DNNs' prohibitive complexity and mobiles' limited resources. In parallel, speech models pretrained via self-supervised learning (SSL) have emerged to reduce the reliance on the availability of transcribed speech data, which however further enlarges the efficiency gap because they often adopt large transformers to ensure expressive speech representations. Thus, it is highly desired to trim down the complexity of speech SSL models to enable real-time on-device ASR. This is particularly challenging since only structured sparsity can favor hardware efficiency in commercial devices, under which the speech representation learned by SSL could easily be demolished. To this end, we develop a framework dubbed S$^6$-DAMON to pursue structured sparsity in speech SSL models via data-model co-compression. On the data side, leveraging both the duration of each phoneme and the pauses between the words/phonemes of human utterances, we propose a salient audio token detector, dubbed SALAD, to remove input audio tokens that are redundant; On the model side, we identify that the failure of the SOTA ASR pruning method under structured sparsity is caused by the sparsity discrepancy between finetuning/deployment and their limited learnability of sparsity distributions, and then tackle it via a new ASR pruning pipeline dubbed SAFARI, which adopts a three-step pipeline - sparsify, finetune, and adjust sparsity. Extensive experiments validate that S$^6$-DAMON can enable real-time ASR with limited transcribed speech data requirements while maintaining decent recognition performance. All source codes will be released upon acceptance.