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Probabilistic Topic Modeling with hundreds of its models and applications has been an efficient text analysis technique for almost twenty years. This research area has evolved mostly within the frame of the Bayesian learning theory. For a long time, the possibility of learning topic models with a simpler conventional (non-Bayesian) regularization remained underestimated and rarely used. The framework of Additive Regularization for Topic Modeling (ARTM) fills this gap. It dramatically simplifies the model inference and opens up new possibilities for combining topic models by just adding their regularizers. This makes the ARTM a tool for synthesizing models with desired properties and gives rise to developing the fast online algorithms in the BigARTM opensource environment equipped with a modular extensible library of regularizers. In this paper, a general iterative process is proposed that maximizes a smooth function on unit simplices. This process can be used as inference mechanism for a wide variety of topic models. This approach is believed to be useful not only for rethinking probabilistic topic modeling, but also for building the neural topic models increasingly popular in recent years.