Chapter 27 Key Update Theorem



Jiang Yubai was right, the introductory class was about to begin.

Lin Zhixia didn't want to be late. She grabbed Jiang Yubai's wrist, pulled him forward, and confided in him: "Jiang Yubai, I encountered something that made me feel very uncomfortable. Are you willing to listen?"

Jiang Yubai replied in a gentle voice: "What is it? Just tell me directly."

Lin Zhixia turned her head and glanced at Lin Zeqiu. There was a hint of grievance in her eyes, and a flickering light. But her brother looked at her for a moment, then turned and left.

From Lin Zhixia's perspective, her brother's classmates quickly caught up with him, and their backs became farther and farther away, gradually disappearing at the stairs.

In fact, Lin Zeqiu absentmindedly stepped onto the stairs and held the handrail. He was about to look for Lin Zhixia when he remembered those horrible nightmares. In the dream, he was frightened to death, and when he woke up, his pajamas were soaked with cold sweat.

In addition, Lin Zeqiu believes that his sister is too young and lacks gender awareness, which is why she has such a close relationship with Jiang Yubai.

How could Lin Zhixia allow a boy to flirt with her in public at school? Lin Zhixia must understand one thing - in middle school, girls should play with girls and boys should play with boys. Students of different genders must keep a distance when interacting with each other.

School is not a good place to educate my sister.

Lin Zeqiu planned to capture Lin Zhixia personally after returning home and teach her a lesson so that she would understand what to do and what not to do.

Lin Zeqiu is still thinking about Lin Zhixia.

Lin Zhixia put aside all distractions and walked towards the classroom with determination.

Class 17 and Class 18 were almost all there. The students from the two classes sat on the left and right sides of the classroom respectively. The row of seats in the middle of the classroom was completely unoccupied, like a dividing line separating the two competition classes.

As soon as Lin Zhixia showed up, Han Peng shouted at her, "Team Leader Lin? Team Leader Lin! You and Jiang Yubai, come sit here! We've saved a seat for you!"

Lin Zhixia and Jiang Yubai walked over and sat down one after another.

The other students only brought a notebook, but Jiang Yubai carried a heavy schoolbag. Because his schoolbag contained the competition question bank that Lin Zhixia gave him - it was obviously a valuable item. He decided to keep it with him.

There was no one maintaining discipline in the classroom, and no one was making loud noises.

Lin Zhixia lowered her voice and whispered to Jiang Yubai: "Just now, the senior we met in the corridor, the one who was 1.8 meters tall..."

"Who is he?" Jiang Yubai asked casually.

Lin Zhixia introduced honestly: "That man is my brother, the kind of brother with the same father and mother. His name is Lin Zeqiu, and my name is Lin Zhixia. It is obvious that these are the names of a pair of siblings. He is Qiu Qiu, and I am Xia Tian... I don't understand why he doesn't acknowledge our blood relationship. This morning, he warned me that he didn't allow me to call him brother in school. He pretended not to know me in front of my classmates and treated me as a junior schoolmate in the competition class of the first grade..."

A raging fire burned in Lin Zhixia's heart, burning out all her emotions. The remaining ashes only left a feeling of resentment: "Why did he do this? Does he really hate me? I'm so angry! I grew up with him! He always complains about me, says I'm a chatterbox, and scolds me for wasting his time! I'm never going to talk to him again!"

"Lin Zeqiu often scolds you?" Jiang Yubai emphasized this point.

"Not really," Lin Zhixia held her chin with one hand, "I don't know how to put it... ah, now I know, he just says nasty things. I remember every word he said."

Jiang Yubai thought for a while and concluded rationally: "Don't blame yourself. Lin Zeqiu needs to adjust himself. My father said that you can't get angry with family members. Family members can discuss everything."

"What should we do if we can't reach an agreement?" Lin Zhixia asked humbly.

Jiang Yubai said calmly: "Kick him out of the house."

Lin Zhixia was stunned by Jiang Yubai's aura. She had a new understanding of Jiang Yubai's father's education methods.

At the same time, she felt more and more distressed and depressed. The method of "expelling her from home" would definitely not work - it was too cold-blooded and horrible. What else could she do? She didn't understand Lin Zeqiu's strange and peculiar psychological activities. Could it be that from now on, she and Lin Zeqiu were strangers? After returning home at noon today, what attitude should she take to face her brother?

Jiang Yubai suggested to her: "If you have time, find an opportunity to talk to Lin Zeqiu."

"Let's talk?" Lin Zhixia asked, "Should I take the initiative to communicate with him?"

"Yes." Jiang Yubai agreed.

Lin Zhixia shook her head frantically: "No, no, no, you don't understand..." She lay on the table and whispered softly: "He doesn't know me now and doesn't like me. He must be very cruel to me. I hate my brother being cruel to me."

Jiang Yubai tapped the table with his fingers: "He may have something to say to you. Let your father sit in on the conversation. He won't dare to harm you."

"My dad is different from your dad," Lin Zhixia explained. "My dad is very gentle. My brother has no respect for my dad. But my brother is very obedient at home. He can sweep the floor, mop the floor, wash dishes, and do laundry. The washing machine in my house is a double-tub washing machine, the kind with double tubs... you know? One tub is for washing, and the other tub is for dehydrating."

Jiang Yubai had no idea about housework. He had never done any dirty or hard work. But he knew that Lin Zhixia's brother had made a lot of contributions to the family. Thinking of this, Jiang Yubai's impression of Lin Zeqiu improved a little.

But only a little.

Jiang Yubai believes that as a brother, Lin Zeqiu should set a better example. Even if Lin Zeqiu really dislikes Lin Zhixia, he can't keep saying "my sister is annoying" every day.

Jiang Yubai's father once told his son that a mature man should be shrewd, broad-minded and courageous, and should not let others easily guess what he is thinking. It can be seen that Lin Zeqiu is not mature enough, and Jiang Yubai hopes that he can grow up.

Jiang Yubai thought about it and reluctantly said something good for his brother: "Lin Zeqiu has a strong sense of family responsibility."

Afterwards, Jiang Yubai continued to comfort Lin Zhixia: "You should talk to Lin Zeqiu, appeal to his emotions and reason with him, and ask him why he pretended not to know you."

The Dean of Studies has already walked into the front door.

The dean was probably in his fifties. He had a unique hairstyle, with his sparse hair forming a circle and a bald patch in the middle of his head. Several students in Class 18 whispered to each other and secretly gave the dean a nickname, "Mediterranean".

The Dean of Studies noticed that the students sitting in the front row were making fun of his hairstyle. But he didn't show that he minded at all. He coughed and said in a calm voice: "Students, raise your heads. Everyone should listen carefully to this introductory class. It is related to your choices in the next three years and your development path in the Provincial No. 1 Middle School Competition Class. My first PPT has a NetEase 126 email address and password. I uploaded the brief document and overview materials of the competition class training as attachments to the email. After you go home, if your family has the conditions, you can go online and download the electronic version. The school will give you a printed version. You can take it out and read it when you have nothing to do, okay?"

"Okay!" Lin Zhixia said in a low voice.

Lin Zhixia had just untied the knot in her heart. Jiang Yubai's analysis and advice were very helpful to her, and he passed on the courage to her.

She will talk to her brother after she returns home today! Just like Jiang Yubai said, she should give it a try first, no matter what the result is.

Lin Zhixia secretly concluded in her heart: Jiang Yubai is fearless, Jiang Yubai is organized, Jiang Yubai is knowledgeable, Jiang Yubai is indeed Lin Zhixia's forever friend and best friend.

He could listen to her, help her plan, and give her advice, which made her feel safe. The emotional value he brought was always positive. In Lin Zhixia's memory, Jiang Yubai's every move and every word had never hurt her.

Lin Zhixia suddenly realized: "No wonder, no wonder..."

Jiang Yubai took notes and asked her, "What's so strange?"

"No wonder I'm happy every day when I see you," Lin Zhixia analyzed rationally and calmly, "I'm just an ordinary deeplearning artificial neural network, and my goal function is to make my life happier. When I lean towards you, I can get positive feedback, and I will definitely get closer and closer to you."

Jiang Yubai's handwriting was neat and smooth. He looked forward and made a request: "Lin Zhixia, please speak human language."

Lin Zhixia immediately spoke in human language: "You are so nice."

Jiang Yubai paused with his pen tip.

Lin Zhixia was afraid that he didn't understand. She emphasized again: "You are so good. Even if there are many things in life that cannot be obtained, at least I met you, which is something that can only be encountered by chance. Really, friendship between friends is priceless."

After saying this, Lin Zhixia nodded.

Jiang Yubai's notebook page was crumpled by his grip. He lowered his head and raised one side of the notebook to cover half of his face. He thought he was thinking about the "competition class training mode", but what he wrote down was "friendship is priceless".

Last year at the Experimental Primary School, Jiang Yubai had already received the evaluation of "You are super awesome".

Today in the auditorium of the Provincial No. 1 Middle School, Jiang Yubai heard again “You are so nice, you are so nice…” and a series of other words that he was too embarrassed to recall carefully.

Perhaps, Lin Zhixia is both his competitor and his true friend. These two identities are not contradictory, but can also urge him to constantly improve himself.

Jiang Yubai's fighting spirit was ignited.

He took note of the teaching methods of the competition class, the course selection direction of the students, and the training programs of previous years. This weekend, he will discuss countermeasures with his tutor team and formulate an effective plan as soon as possible. He and Lin Zhixia want to drive together to sweep all major awards in the province, the country, and even the world.

The dean of students on the podium stood with his hands behind his back, gazing at the many students in the competition class.

The slides were at the end. The introductory class was almost over. The dean did not take up too much time. He was very skillful, detailed, and impressive. One of his principles in life was not to say nonsense to students.

The students were looking at him.

Those students have young faces. One day, they will grow up to be the pillars of the country.

"Okay, everyone, pay attention," the Dean of Education said loudly, "Next, please give a round of applause to the two head teachers of Class 17 and Class 18 - Teacher Zhang and Teacher Wang!"

A round of enthusiastic applause broke out in the lecture hall. The sound was so powerful that it was like a surging wave, stirring up thousands of waves and breaking the originally quiet atmosphere.

Teacher Zhang and Teacher Wang both walked up to the podium.

Teacher Zhang, the head teacher of Class 17, bent down, manipulated the mouse, and opened a Word document called "Mathematics Warm-up Quiz". There were a total of 40 questions in the document, and each question occupied a page.

Mr. Wang, the head teacher of Class 18, pulled out a small whiteboard. He picked up a black marker and wrote on the whiteboard: Class 17, zero points. Class 18, zero points.

Teacher Wang briefly introduced the rules of the competition: "Students! This is a race to answer questions. If you answer correctly, you earn one point. If you answer incorrectly, you lose one point. If a student from a certain class answers the question and gets it wrong, we will draw another student from another class."

Will I lose points if I answer incorrectly?

After hearing the bad news, the students present all became cautious, and even a small number of them decided not to participate in the competition, not to drag down the group, and to remain quiet from beginning to end. Even if they become dumb, it is much better than "a bad apple spoils the whole pot of porridge".

Mr. Zhang, the head teacher of Class 17, smiled knowingly. He stood up straight, opened the first question in the Word document, and read aloud: "What are the degrees of the interior and exterior angles of a regular octagon?"

Lin Zhixia raised her hand immediately.

However, a female student from Class 18 suddenly stood up and answered directly: "The inner angle is 135 degrees, the outer angle is 45 degrees, and the sum of the inner angles is 1080 degrees."

This female student wore glasses, had short hair, was neatly dressed, and had an unobtrusive appearance. Her tone of voice was very steady, like a calm river.

Teacher Wang criticized her in a gentle tone: "Jin Baihui, you should raise your hand first. When we call your name, you should stand up and respect the rules of the game..."

Teacher Zhang offered a favor instead: "Oh? She is Jin Baihui from Class 18? No problem, Jin Baihui is very good at mental arithmetic, and other students may not be better than her. That's it! Class 18 gets one point."

Based on what?

Lin Zhixia muttered, "I can do mental arithmetic, too. I'm faster than her."

Shen Qixuan hissed and whispered, "Jin Baihui! She is Jin Baihui!"

Lin Zhixia asked back: "Who is Jin Baihui? Is she very good? Her name did not appear on the ranking list of the entrance examination."

"She was the first last year, didn't you know?" Shen Fuxuan turned to Lin Zhixia and said, "Jin Baihui took the entrance exam for the provincial No. 1 Middle School's junior high school competition class last year. She was also admitted to a young talent class in Beijing. She went to Beijing to study for more than half a year, but she didn't adapt well..."

"So, Jin Baihui returned to the Provincial No. 1 Middle School?" Jiang Yubai asked.

"Yes," Shen Fuxuan covered his mouth with one hand and told them secretly, "The head teacher of Class 18 particularly values ​​Jin Baihui. I heard from my mother that the head teacher of Class 18 would rather give Lin Zhixia to Teacher Zhang than accept Jin Baihui as a student."

"Your mother? How does your mother know what the head teacher of Class 18 thinks?" Lin Zhixia noticed this.

Shen Fuxuan stretched out his legs and sat like a lazy old man. He answered without hesitation: "My mother is the principal of the Provincial No. 1 Middle School. I chose to go to Class 17. You are the first, so I will go wherever you go. If you go to Class 18, I will go with you."

His mother is the principal of the Provincial No. 1 Middle School...

Then isn’t his grandmother Professor Shen Zhaohua?

Lin Zhixia finally understood the cause and effect relationship and was extremely surprised. She learned a lot of inside information from Shen Fuxuan. She paid more attention to Jin Baihui.

While Lin Zhixia, Jiang Yubai, and Shen Fuxuan were chatting, Teacher Zhang asked another question. Jin Baihui raised her hand and answered it again. Her mental arithmetic ability is indeed not to be underestimated.

Class 17 is two points behind.

Jin Baihui glanced sideways at the students in Class 17. Her jaw was slightly tilted, her expression was cold and provocative.

Jin Baihui's seat was close to the dividing line between Class 17 and Class 18. Duan Qiyan also happened to be sitting nearby.

Duan Qiyan folded his arms and glanced secretly at Jin Baihui. Jin Baihui raised her little finger at him, and he was so angry that he almost exploded on the spot.

All these little actions were seen by Teacher Zhang.

Teacher Zhang read slowly, "For the third question, we know that the first five terms of an arithmetic sequence are all prime numbers. What is the minimum possible value of the fifth term?"

Jin Baihui raised her hand high.

Lin Zhixia stood up and answered: "The minimum value of the fifth term is 5. The arithmetic progression is 29, 23, 17, 11, 5."

Teacher Zhang smiled and said, "Lin Zhixia, you are right, but you should raise your hand first."

Lin Zhixia admitted her mistake perfunctorily: "I'm sorry, teacher, I was too anxious. I will raise my hand next time."

Teacher Wang smoothed things over: "You are Lin Zhixia from Class 17? Not bad, not bad. Although I didn't interview you, other teachers all speak highly of you. We look forward to you bringing honor to the Provincial No. 1 Middle School. OK! Class 17 gets one point. After this round, everyone has to raise their hands! We can't disrespect the rules, okay?"

All the students responded in unison.

Teacher Zhang scrolled the mouse wheel, and Teacher Wang read out the fourth question: "Students, please listen to the question. Suppose n is a decimal digit. Now there is another decimal digit. This digit is nq in base 58 and (n-1)g in base 62. What is this digit?"

Jiang Yubai raised his hand first.

Lin Zhixia noticed that he was about to make a move, so she stopped competing with him. She began to worry whether Jiang Yubai could answer correctly. She held her breath and heard Jiang Yubai say, "The three-digit number is 512, and n is equal to 9."

Lin Zhixia stretched out her two index fingers, touched their fingertips together, and applauded him in a low-key manner.

Teacher Zhang praised happily, "Not bad! You answered quickly and well! Class 17 gets another point! Teacher Wang and I were worried that the questions were too difficult and wouldn't motivate everyone. Now it seems that students from both classes are enjoying it! Very good! Keep it up!"

Han Peng, who was sitting in front of Lin Zhixia, couldn't help but say, "I give up... So far, only Jin Baihui, Lin Zhixia, and Jiang Yubai have answered the questions, and Teacher Zhang thinks we all enjoy it."

Han Peng leaned back in his chair, tilted his head back, and asked Jiang Yubai: "How did you solve that problem just now?"

"Rapid base conversion," Jiang Yubai unexpectedly replied, "very basic stuff."

Jiang Yubai had learned base conversion two years ago, and this year he took six months of mental and oral arithmetic. Even though he spent the entire summer playing, he still retained his math skills.

"Yes, Jiang Yubai is right. That kind of transformation is more basic." Lin Zhixia particularly agreed with him.

Han Peng stretched his neck and almost suffocated. He held on to the table and sat back down, lowering his head and coughing madly.

Life is really not easy, Han Peng thought.

The competition was still going on. Lin Zhixia gradually felt that it was unfair. She was always the first to raise her hand. However, sometimes, Teacher Wang would not call on her. Teacher Wang tended to call out "Jin Baihui" by name. The math warm-up questions for the first graders were not too difficult. There were almost no particularly complicated knowledge points. It was not surprising that Jin Baihui could do it.

"Is an unfair competition worthy of being called a competition?" Lin Zhixia asked doubtfully.

Jiang Yubai had seen through everything. He gave Lin Zhixia some advice: "The dean is sitting at the back of the classroom. Teacher Wang can't let the dean think that Class 18 is too much worse than Class 17. You and Jin Baihui raised your hands one after the other, and there was a two-second gap in between, which is not obvious. Also, if Class 18 loses too badly, it will severely dampen their morale and is not conducive to cultivating self-confidence."

Lin Zhixia lay on the table. She unilaterally gave up the game and expressed silent protest.

Her cheek was pressed against her arm, making her look both pitiful and lovely.

Jiang Yubai noticed Lin Zhixia's condition, and his heart was filled with a sense of mission. He found that Teacher Wang deliberately ignored Lin Zhixia, which was equivalent to the referee on the basketball court deliberately favoring and blocking the other side's main players.

He had seen this kind of plot in "Slam Dunk".

He remained undaunted and responded calmly.

Teacher Wang is still reading the question: "Throw a dice and add up the points on the dice. If the points are greater than 10,000, it is considered a failure. If the points are equal to 10,000, it is considered a success. If the points are less than 10,000, continue to throw the dice. What is the probability of success?"

The classroom was silent for more than ten seconds, and Jiang Yubai and Jin Baihui raised their hands at the same time.

Before Teacher Wang said anything, the dean of students sitting in the last row said, "I saw these two students raised their hands almost at the same time. Let them both answer. What we are holding today is a small competition, not a big contest. Friendship comes first, competition comes second."

Teacher Wang first asked Jiang Yubai: "What is the probability?"

Jiang Yubai calmly replied, "Two-sevenths."

Jin Baihui suddenly spoke up and questioned Jiang Yubai: "How did you calculate it? Your method is not as fast as mine. I wrote an equation and I can get two-sevenths of the result."

Teacher Wang nodded repeatedly: "What equation? Jin Baihui, go to the blackboard and write it for everyone to see."

Jin Baihui's face seemed to be covered with a layer of frost, cold and arrogant. She cared more about winning than Jiang Yubai. She wrote on the blackboard: "Toss the dice six times, the expected value is 3.5. I will first use the formula to prove that the sequence will eventually converge..." She realized that her logic was not rigorous enough, and immediately applied L'Hôpital's rule.

Just as Jin Baihui was about to give her conclusion, Lin Zhixia's voice suddenly came over: "This question is not difficult, I believe you can solve it quickly. But I think you don't need to write out the general formula. There is a situation called the ttice case in Blackwell's key update theorem, and the dice game just meets its restrictions. At this time, each term of the random variable can be expressed by a constant divided by the expected value. The constant of the dice game is one, and the result is one divided by three and a half, which is equal to two-sevenths."

Jiang Yubai said nothing.

Because his method is the most low-level.

He assumed that the probability of success is p, and the probability of failure is (1-p), and several failure scenarios can be listed. For example, in one scenario, when the total number of points on the dice adds up to 9995, and a number other than 5 is thrown, it is considered a loss... and so on, the answer can be calculated.

The mathematical theorems used by Jin Baihui and Lin Zhixia are much more complicated than his.

However, Professor Zhang said: "Jin Baihui's algorithm is very rigorous, and she has a solid grasp of advanced mathematics knowledge. I also appreciate Jiang Yubai and Lin Zhixia's algorithms, and the Blackwell update theorem is concise and powerful."

Lin Zhixia nodded proudly.

She sat in her seat and quietly stretched out a hand. Jiang Yubai followed her example and she seized the opportunity to high-five him.

Jiang Yubai was very encouraged. He lowered his head and smiled silently.

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