How humans and machines make sense of current inputs for relation reasoning and question-answering, and put the perceived information into context of our past memories, has been a challenging conundrum in cognitive science and artificial intelligence. Inspired by human brain's memory system and cognitive architectures, we propose a PMI framework that consists of perception, memory and inference components. Notably, the memory module comprises working and long-term memory, with the latter endowed with a higher-order structure to retain more accumulated knowledge and experiences. Through a differentiable competitive write access, current perceptions update working memory, which is later merged with long-term memory via outer product associations, averting memory overflow and minimizing information conflicts. In the inference module, relevant information is retrieved from two separate memory origins and associatively integrated to attain a more comprehensive and precise interpretation of current perceptions. We exploratively apply our PMI to improve prevailing Transformers and CNN models on question-answering tasks like bAbI-20k and Sort-of-CLEVR datasets, as well as relation reasoning and image classification tasks, and in each case, our PMI enhancements consistently outshine their original counterparts significantly. Visualization analyses reveal that memory consolidation, along with the interaction and integration of information from diverse memory sources, substantially contributes to the model effectiveness on inference tasks.