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Multi-instance learning (MIL) is a form of weakly supervised learning where a single class label is assigned to a bag of instances while the instance-level labels are not available. Training classifiers to accurately determine the bag label and instance labels is a challenging but critical task in many practical scenarios, such as computational histopathology. Recently, MIL models fully parameterized by neural networks have become popular due to the high flexibility and superior performance. Most of these models rely on attention mechanisms that assign attention scores across the instance embeddings in a bag and produce the bag embedding using an aggregation operator. In this paper, we proposed a dual-stream maximum self-attention MIL model (DSMIL) parameterized by neural networks. The first stream deploys a simple MIL max-pooling while the top-activated instance embedding is determined and used to obtain self-attention scores across instance embeddings in the second stream. Different from most of the previous methods, the proposed model jointly learns an instance classifier and a bag classifier based on the same instance embeddings. The experiments results show that our method achieves superior performance compared to the best MIL methods and demonstrates state-of-the-art performance on benchmark MIL datasets.