What Really is Deep Learning Doing?

Deep learning has achieved a great success in many areas, from computer vision to natural language processing, to game playing, and much more. Yet, what deep learning is really doing is still an open question. There are a lot of works in this direction. For example, [5] tried to explain deep learning by group renormalization, and [6] tried to explain deep learning from the view of functional approximation. In order to address this very crucial question, here we see deep learning from perspective of mechanical learning and learning machine (see [1], [2]). From this particular angle, we can see deep learning much better and answer with confidence: What deep learning is really doing? why it works well, how it works, and how much data is necessary for learning. We also will discuss advantages and disadvantages of deep learning at the end of this work

Algebraic Expression of Subjective Spatial and Temporal Patterns

Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern of learning machine. In [2,4], we discussed subjective spatial pattern, and established a powerful tool -- X-form, which is an algebraic expression for subjective spatial pattern. However, as the initial stage of study, there we only discussed spatial pattern. Here, we will discuss spatial and temporal patterns, and algebraic expression for them

Sampling and Learning for Boolean Function

In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We proved the fundamental relationship between proper sampling set and complexity of boolean circuit. Armed with this set of tools, we then introduce much more effective learning strategies. We show that with such learning strategies and learning dynamics, universal learning can be achieved, and requires much less data