A few months ago, my aunt sent an email to her colleague with the subject "Mathematical puzzle! What is the answer?", which contained a puzzle: She thinks her answer is obviously correct, but her colleagues think their own answer is correct - but the two answers are different. Is that one of their answers is wrong? Or is there a problem with the puzzle itself? My aunt and her colleague accidentally discovered a basic problem in machine learning. We expect all the learning done by computers and our own human learning to summarize the information into basic patterns and then use it to infer the unknown. Her puzzles are no exception. As human beings, the challenge we face is to discover all models. Of course, we have the intuition to limit our guesses. But computers don't have this intuition. From a computer perspective, the challenge in pattern recognition is to use only one mode: What determines which mode is "correct" in the case where multiple modes are actually feasible? Are the other modes "wrong"? This issue has only recently become a practical consideration for people. Before the 1990s, artificial intelligence systems hardly did much learning. For example, DeepBlue's predecessor chess system, DeepThought, did not master chess well by learning from successes and failures. Instead, chess masters and programmers carefully write rules that teach the computer which position is good or bad. Such a large amount of manual work is a typical method in the era of "expert system". To solve this puzzle, the expert system approach requires a human to discover the patterns of the first three rows of problems: 1*(4+1)=5 2*(5+1)=12 3*(6+1)=21 Then, people can order the computer to follow the x*(y+1)=z mode. Apply the rule to the last question, the answer is 96. Although early expert systems were successful, they required manual design, adjustment, and updating of the system, which made them cumbersome. Instead, the researchers turned their attention to designing machines that could infer their own patterns. That is, a program can check thousands of pictures or market transaction data and extract statistical signals indicating a face or an emergency price peak. This approach quickly became mainstream, and it has since enhanced tasks ranging from automated mail sorting to spam filtering and credit card fraud detection. Today, despite so many successes, these machine learning systems still require engineers. Going back to the puzzle above, we assume that each equation has three related components (three values ​​in the equation). But there is also a potential fourth element: the result of the previous equation. The attribute of an equation, also known as the feature of machine learning, is also taken into account, which creates another reasonable pattern: 0+1+4=5 5+2+5=12 12+3+6=21 According to this logic, the final answer should be 40. So which model is correct? Both are correct, of course or both are incorrect. This is entirely determined by which mode is allowed. You can even do this: multiply the first number by the second number, then add the answer to the previous line plus one-fifth of the number three, and then take the nearest integer. (This is weird, but effective) And, if we allow features that contain numerical visual forms, we may still get some patterns about glyphs and fonts. This pattern matching depends on the observer's assumptions. Wuxi Lerin New Energy Technology Co.,Ltd. , https://www.lerin-tech.com