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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
This reminds me a lot of the problem of predicting an integer-valued output for an image or audio sequence, where you want to predict a value between 0 and 255, or even say 65536, but you want to help the model understand that the result is categorical, but some categories are closer to each other. I learned recently that one approach to this used in Tacotron 2 (speech synthesis) is called a Mixture of Logistics. There is a not very good blog post that goes over it, but links to a very in-depth explanation in a github issue of all places.. might be interesting for you.
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