Binary Numbers

binarynumbers

Modern computers today use a binary number representation system called 'Two's complement'. It is a fixed number of binary digits used in computer calculations. Basic math operations such as addition and subtraction can be performed using the binary rules of addition and subtraction. Two's complement is not a complex scheme and is rather very simple to work with. This system also helps overcome the shortcomings of having to deal with magnitudes. Two's complement can be characterized as: A fixed number of bits are used to represent numbers i.e 4 bits The most significant bit is called the sign bit (the leftmost bit) This notation can represent both negative and positive integers. The highest positive number that can be represented is 7; the lowest possible number that can be represented is -8 using a 4 bit string. Positive numbers have a 0 in the most significant (leftmost) position and negative numbers have a 1 in this position. This is why the most significant bit is also called the sign bit. 1101 = -3 0011 = 3 How to convert to Two’s complement? The process of converting a binary string to a Two’s complement consists of inverting all of the bits in the number, then adding 1 to the least significant bit (rightmost) position. For example: We wish to write out 28 in Two’s complement. Firstly we will write down 28 in binary form. 0001 1100 Then we invert the digits. 0 becomes 1, 1 becomes 0. 1110 0011 Then we add 1 to the least significant bit i.e the rightmost bit. 1110 0100 This is the way that one would write -28 in 8-bit binary. Note the leftmost bit is a 1 which means 28 is a negative integer in this example. This works both ways as well. You can start with a negative integer but to make our calculations easier we avoid the negative notation initially and then in our final answer adjust the bits to get the desired result. Take for example -30. We want to represent it in 2's complement, you take the binary representation of +30: 0001 1110 Invert the digits. 1110 0001 And add one. 1110 0010 The final output is the Two’s complement for -30. Inverting and adding one might sound like a very strange thing to do, but it is actually just a mathematical shortcut and a rather straightforward computation. Detecting an Overflow When we are dealing with binary digits, we are often limited in the number of bits we can use. There is usually a fixed number of bits allowed by the system. Therefore we need to stay vigilant in case an overflow occurs. Overflow mostly occurs when adding two binary numbers together. An overflow occurs if the two numbers being added have the same sign bit and the result has the opposite sign bit. For instance, 2 positive numbers when added together yield a negative answer. Another instance can be when the final output exceeds the range (?8 ? x ? +7). No overflow occurs when a positive number is added to a negative number. (-7)         1001 +(-6)         1010 --------    --------------- (-13)     1  0011 = 3 In this example, the leftmost 1 is an overflow bit. We also know an overflow has occurred here because the lowest possible number for a 4-bit binary string is -8. -13 obviously exceed the range. This is all there is to Two’s complement and you can now start solving your sums. Happy solving! Previously published at https://5amily.com/mathematics/blog/two-s-complement-how-to-calculate-and-convert-for-binary-numbers

A Guide to Two's Complement: Calculating And Converting For Binary Numbers

Authors:
(1) Ying Tang, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (tang@rowan.edu);
(2) Ryan Hare, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (harer6@rowan.edu). Table of Links Abstract and I. Introduction II. Overview of PING System and Gridlock III. Design Insights and Educational Impact IV. Conclusion and References III. DESIGN INSIGHTS AND EDUCATIONAL IMPACT A. Design Insights and Student Feedback When discussing design changes made in the game with regards to student feedback, the iterations focused on three main areas: Interface design, student testing, and tutorials/student assistance. 1) Interface Design For interface design, we had a few main considerations. First, the target audience for the game is highly generalized, and thus includes players who are and are not familiar with virtual games. For players who are familiar with virtual games, certain aspects such as a standard control scheme and familiar interface elements are enough for players to understand the goals, controls, and objective of the game. For example, the updated game features a system of objective markers shown in Figure 4, where students receive a visual indication of their current objective. Even among students who were less familiar with virtual games, a visual indicator marking their objective helps to significantly improve their ability to navigate the virtual environment. Outside of marking objectives, it was also very important to have both a stated objective and a guide on the control scheme of the game. For Gridlock, students can open up a “how to play” screen at any time that indicates the control scheme of the game. Additionally, students can also access a “current objectives” screen that has a written statement of their current objective. Among players experienced with virtual games, these features were largely ignored. However, their inclusion is crucial to help players who are unfamiliar with navigating virtual game environments. One final aspect that also helped students navigate the environment was “notification” markers on certain in-game utilities. For example, when students start the game, they have a notification on one of the menu options. This incentivizes them to click this option, thus taking them to the assistance menu, as shown in Figure 5. This way, students are already familiarized with this menu before it becomes relevant, allowing them to have a smoother experience in the latter parts of the game. 2) Student Testing Another modification that was well-received among students was the replacement of some testing methods with interactive mini-games or puzzles. In each of these basic games, students receive an instructional prompt before participating. These games are designed in such a way that we can gather data on the students’ knowledge while they play. For example, as shown in Figure 6, students are tested on their ability to convert binary numbers through a game where they are tasked with matching binary numbers to their decimal counterparts as quickly as possible. 3) Student Assistance Finally, the in-game tutorials were also modified as per student feedback. In prior iterations, accessing the personalized assistance provided to students was required for students to progress. Furthermore, the assistance was specifically tailored to a student’s issues. In the updated version of the game, the assistance is general-purpose, but students are directed to a specific area that addresses their issues. This way, students have the option to manually explore additional help materials. Additionally, students now must manually access the help materials, which prevents the help prompts from breaking the flow of the game. If a student is performing poorly, the game can also put a notification marker on the help menu to encourage the student to request help. With all these changes, students have much more freedom to either accept the help as given, explore additional content at their own pace, or to ignore the help entirely and attempt to solve problems on their own. This gives students guidance if they need it, and the freedom to explore and solve problems without being limited or interrupted by the system. B. Educational Impact Preliminary results for an evaluation of educational efficacy use a pre-test and a post-test administered before and after students played the game, respectively. These tests asked students to design a state machine for a vending machine; a task which has a similar required skill set as the traffic light problem in the game. Figure 7 shows a comparison of score improvement among students from our pre-test to the post-test. Students were graded on both assignments on a scale from 0 to 1, and the graph compares four scenarios: 1) The updated game with PING system integration, modified based on student feedback as per the design statements outlined in this paper (𝑁 = 13); 2) The prior version of the game with PING system integration (𝑁 = 20); 3) An old version of Gridlock that did not use the PING system (𝑁 = 14); and 4) Students who did not play the game (𝑁 = 8). As shown, students who played the updated game had greater improvement over students who played the prior version of the game. Additionally, there were a fewer number of students who regressed or showed little improvement compared to past classroom evaluations. This is likely due to the new quality of life features and easier-to-access help documentation making it both easier and less frustrating for students to learn with Gridlock. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Ying Tang, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (tang@rowan.edu); (2) Ryan Hare, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (harer6@rowan.edu). Authors: Authors: (1) Ying Tang, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (tang@rowan.edu); Dept. of Electrical and Computer Engineering, Rowan University, (2) Ryan Hare, Dept. of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA (harer6@rowan.edu). Dept. of Electrical and Computer Engineering, Rowan University, Table of Links Abstract and I. Introduction Abstract and I. Introduction II. Overview of PING System and Gridlock II. Overview of PING System and Gridlock III. Design Insights and Educational Impact III. Design Insights and Educational Impact IV. Conclusion and References IV. Conclusion and References III. DESIGN INSIGHTS AND EDUCATIONAL IMPACT A. Design Insights and Student Feedback A. Design Insights and Student Feedback When discussing design changes made in the game with regards to student feedback, the iterations focused on three main areas: Interface design, student testing, and tutorials/student assistance. 1) Interface Design 1) Interface Design For interface design, we had a few main considerations. First, the target audience for the game is highly generalized, and thus includes players who are and are not familiar with virtual games. For players who are familiar with virtual games, certain aspects such as a standard control scheme and familiar interface elements are enough for players to understand the goals, controls, and objective of the game. For example, the updated game features a system of objective markers shown in Figure 4, where students receive a visual indication of their current objective. Even among students who were less familiar with virtual games, a visual indicator marking their objective helps to significantly improve their ability to navigate the virtual environment. Outside of marking objectives, it was also very important to have both a stated objective and a guide on the control scheme of the game. For Gridlock, students can open up a “how to play” screen at any time that indicates the control scheme of the game. Additionally, students can also access a “current objectives” screen that has a written statement of their current objective. Among players experienced with virtual games, these features were largely ignored. However, their inclusion is crucial to help players who are unfamiliar with navigating virtual game environments. One final aspect that also helped students navigate the environment was “notification” markers on certain in-game utilities. For example, when students start the game, they have a notification on one of the menu options. This incentivizes them to click this option, thus taking them to the assistance menu, as shown in Figure 5. This way, students are already familiarized with this menu before it becomes relevant, allowing them to have a smoother experience in the latter parts of the game. 2) Student Testing 2) Student Testing Another modification that was well-received among students was the replacement of some testing methods with interactive mini-games or puzzles. In each of these basic games, students receive an instructional prompt before participating. These games are designed in such a way that we can gather data on the students’ knowledge while they play. For example, as shown in Figure 6, students are tested on their ability to convert binary numbers through a game where they are tasked with matching binary numbers to their decimal counterparts as quickly as possible. 3) Student Assistance 3) Student Assistance Finally, the in-game tutorials were also modified as per student feedback. In prior iterations, accessing the personalized assistance provided to students was required for students to progress. Furthermore, the assistance was specifically tailored to a student’s issues. In the updated version of the game, the assistance is general-purpose, but students are directed to a specific area that addresses their issues. This way, students have the option to manually explore additional help materials. Additionally, students now must manually access the help materials, which prevents the help prompts from breaking the flow of the game. If a student is performing poorly, the game can also put a notification marker on the help menu to encourage the student to request help. With all these changes, students have much more freedom to either accept the help as given, explore additional content at their own pace, or to ignore the help entirely and attempt to solve problems on their own. This gives students guidance if they need it, and the freedom to explore and solve problems without being limited or interrupted by the system. B. Educational Impact B. Educational Impact Preliminary results for an evaluation of educational efficacy use a pre-test and a post-test administered before and after students played the game, respectively. These tests asked students to design a state machine for a vending machine; a task which has a similar required skill set as the traffic light problem in the game. Figure 7 shows a comparison of score improvement among students from our pre-test to the post-test. Students were graded on both assignments on a scale from 0 to 1, and the graph compares four scenarios: 1) The updated game with PING system integration, modified based on student feedback as per the design statements outlined in this paper (𝑁 = 13); 2) The prior version of the game with PING system integration (𝑁 = 20); 3) An old version of Gridlock that did not use the PING system (𝑁 = 14); and 4) Students who did not play the game (𝑁 = 8). As shown, students who played the updated game had greater improvement over students who played the prior version of the game. Additionally, there were a fewer number of students who regressed or showed little improvement compared to past classroom evaluations. This is likely due to the new quality of life features and easier-to-access help documentation making it both easier and less frustrating for students to learn with Gridlock. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Enhancing Learning with Gamified Instruction: Design Insights and Educational Impact

Let's learn about via these 85 free stories. They are ordered by most time reading created on HackerNoon. Visit the to find the most read stories about any technology. Mathematics /Learn Repo I don't like math, but you might. The wonderous world of numbers awaits! 1. Implementing 3x+1 or Collatz Conjecture In Python 3x+1 or Collatz conjecture is a simple maths problem that can easily be implemented using a simple while loop in Python. 2. Why AI is a Fear-Driven Discipline People are scared of AI. According to Genpact research: 3. 69 Poem 69 was in his house 4. Java Program to Check for Right Angled Triangle A simple program in Java to check whether a triangle is right-angled or not. 5. Urpflanze JavaScript Library for Generative Art and Creative Coding Urpflanze is a javascript library to approach creative coding and generatve art 6. Formulas of Uniswap: A Deep Dive Find out the benefits of concentrated liquidity for multiple pooled assets in Uniswap. 7. You Can't Run from Math: Applications of Integration & Differentiation Learn all about Integration and differentiation with examples and understand their role in calculus. 8. A Guide to Two's Complement: Calculating And Converting For Binary Numbers Modern computers today use a binary number representation system called 'Two's complement'. It is a fixed number of binary digits used in computer calculations. Basic math operations such as addition and subtraction can be performed using the binary rules of addition and subtraction. Two's complement is not a complex scheme and is rather very simple to work with. This system also helps overcome the shortcomings of having to deal with magnitudes. Two's complement can be characterized as: 9. How to Calculate Cross Product and Rectangle Area in 3 Easy Steps Albeit the dot product of two vectors gives a scalar, in contrast, the resultant vector is a vector of cross-products. 10. Understanding Boolean Methods in Ruby With Examples Most programming languages have a Data Type called “Boolean”. This is
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Object Detection Using Single Shot MultiBox Detector (A Case Study Approach) This blog post delivers the fundamental principles behind object detection and it's algorithms with rigorous intuition. Thank you for checking out the 85 most read stories about Mathematics on HackerNoon. to find the most read stories about any technology. Visit the /Learn Repo

85 Stories To Learn About Mathematics

154 Stories To Learn About Computer Science

Let's learn about via these 54 free stories. They are ordered by most time reading created on HackerNoon. Visit the to find the most read stories about any technology. Computers /Learn Repo 1. A Guide to Two's Complement: Calculating And Converting For Binary Numbers Modern computers today use a binary number representation system called 'Two's complement'. It is a fixed number of binary digits used in computer calculations. Basic math operations such as addition and subtraction can be performed using the binary rules of addition and subtraction. Two's complement is not a complex scheme and is rather very simple to work with. This system also helps overcome the shortcomings of having to deal with magnitudes. Two's complement can be characterized as: 2. Smaller, Faster, and Cheaper Coding Laptops via AWS My Coding Laptop is Smaller, Faster, and Cheaper than Yours and it lives in an AWS Data Center! 3. I Test, Therefore it Works To put it simply, programmers make it work and testers make it break. The benefits beat the costs in the long run. 4. What Is Bottleneck in PC World In the last article, which you can read here, I was talking about which PC components are crucial for programmers. Basically, I listed all the components to worry about, but I’ve also said that you need to keep the Bottleneck in mind. Because, there’re a lot of people who don’t know what is a bottleneck, in this article, I’ll try to explain what that is. 5. Raspberry Pi 400: $70 Cheapest PC of 2020 for Programming If you have ever wondered if there is any Desktop PC that comes at a very cheap price, you probably wouldn't have looked at Raspberry Pi, no one did. Until now, Raspberry Pi was a compact, small machine with limited performance but it has changed with the arrival of Raspberry Pi 400. Raspberry Pi 400 is a complete personal computer built into the Raspberry Pi Keyboard giving us the cheapest complete computer of all time. 6. Thinking of Humans as a Computer Program 7. Microsoft Urges Users Not to Remove Expired Windows 10 Root Certificate The root Windows certificate expires on December 31, but it is still required for the OS to function properly. 8. Nvidia Vs Amd Graphics Card: Where This Never-ending War Lead Us Photo by Uriel Soberanes on Unsplash 9. 5 Mac Apps with the Largest Service Files Merely removing apps on Mac OS X is not a hard thing to do: drag & drop or just delete to the Trash. But sometimes after such removal on your Mac, there could be left system files, caches, logs, and other debris – called app leftovers. That is why it is better to use special third-party app uninstallers for removing programs from your Mac with all their service files. 10. Linux Desktops and Hardware Enablement - It’s Time for a Change If you told me twenty years ago that Nvidia GPU's would still be a pain in the you-know-what to get working in Linux to this very day, I wouldn't believe you. 11. What is RS232 Communication? As many of you are no doubt aware, it’s not easy to find a modern consumer-grade computer today that would have a classic serial port. However, just because laptop makers stopped adding them doesn’t mean the legacy ports are no longer used nowadays. Being an essential part of medical and networking equipment, serial ports can still be found on a large number of old and new useful devices. 12. Windows 10 New File Recovery Application Microsoft released its own File Recovery Tool in the Windows Store, making it a lot simpler to choose which device you need on the off chance that you lose a significant bit of information on your PC. 13. How To Check What Motherboard I Have The knowledge of the motherboard is essential for you as it helps you to decide whether you should upgrade your drivers or not. And to what extent you can update your drivers. Someone might suggest you look for the information on your computer system, but that is not understandable to all. We will help you in figuring out your query. 14. 3 Best DVD Ripper Software for Windows and Mac We all know that a DVD ripping software works by transferring a video into DVDs, back up or edit a DVD content, as well as to convert a DVD video into the media player and mobile devices playback. 15. Computers on the Farm A computer can be very useful when repetitive analyses are needed or when data storage is important, as with financial records or daily milk output per cow. 16. What to Do Before Selling a Computer Planning to sell your computer? Here's everything you need to know to get it done right. 17. How to Choose a Microcomputer System Many computer experts strongly recommend against buying a computer first and then shopping for the software packages. 18. All You Need To Know About Computer Hardware PC equipment alludes to the physical segments that make up a PC framework. 19. How to Combat Cyber Security Threats and Attacks Progress in complex technology can result in the ‘progress’ of complex threats. 20. Easiest Ways to Fix ERR_CONNECTION_RESET Error [SOLVED] The "ERR_CONNECTION_RESET" error is a common error message that appears in Google Chrome when a website fails to load. This error is typically caused by a problem with the connection between your device and the website you're trying to access. 21. How to Generate Random Numbers - A Guide to TRNGs and PRNGs We'll take a look at how computers generate random numbers and the limitations of pseudo-random number generators. 22. Artificial Intelligence and Machine Learning: A Significant Game Changer in Healthcare A well-organized and trusted data source fosters a faster and more accurate healthcare system. 23. 17 Reasons Why Your Computer is so Slow If you're wondering why your computer is so slow and generally performing poorly, this article will give you 17 things that may be wrong and 8 ways to better optimize your PC. 24. What a Computer Can Do for You - Process Controllers Besides analyzing farm management problems and storing data, computers have another key use—as process controllers. 25. How to Solve: Nova Spatie 422 error "This disk is not configured as a backup disk" Spatie's Laravel Components are surely known to most and are great helpers to build any kind of Laravel application or website. I've been using the Spatie' Laravel Backup component on my projects. With my recent shift to Laravel Nova on my new project, I've started to look at the related Nova component. It worked fine, once I got over some initial trouble. 26. Download This Virus Donating Compute to Fight COVID-19 27. What are File Permissions and Why do they Matter? Each and every file on a computer has what we call file permissions. These are attributes of the file that determine who has permission to access that file and what they can do to that file. To understand what file permissions are we first need to determine what exactly a file is. 28. What a Computer Can Do for You  - Telecommunications With the computer hooked up to the telephone, you can get information quickly, receive it visually, and record it in detail if you wish. 29. Charging Up Your Debugging Skills After struggling with a finicky laptop charger, I learned some valuable lessons in software debugging 30. Circuit Boards: Motherboards, System Boards And Mainboards The motherboard serves to interface the entirety of the pieces of a PC together. The CPU, memory, hard drives, and different ports and extension cards all interface with the motherboard legitimately or through links. 31. WTF is Power Supply Unit? The Power Supply Unit is the bit of equipment that changes over the force gave from the outlet into usable force for the numerous parts inside the PC case. 32. A Comparison Of The Best Desktops vs Laptops For Coding Every programmer who is buying a new computer will ask themselves, ‘Should I buy a desktop or a laptop for coding’? Also, what computer should I buy if I also want to do other things besides coding, like playing games? 33. Mobile Devices Will Never Replace Desktops The future of technology makes a lot of people very curious. There are hundreds of new devices developed every day, each of them improving upon former models. 34. What are Microsoft Windows Display Drivers? - A Brief Overview Microsoft introduced the Windows Display Driver to drive the video cards installed in the Windows OS. 35. What if Malware isn’t Slowing Down Your Games? Most experienced gamers realize that many different kinds of malware can slow down their games. 36. Why RPA Is Attractive to Manufacturers As Kevin Ross from CyberArk puts it, “RPA is one of the hottest technologies in the IT market today, mainly due to its potential to deliver huge benefits to companies.” Many businesses are rushing to close the gap between production and demand for their services, especially after the COVID-19 disruptions. 37. Solar Home Systems: The Changing Paradigms of Electric Power From electric cars to recyclable plastics; there have been several moral responses to the earth's clarion call to caution, many have become a mainstream tech. The development of alternative energy is also bridging the gap between being a moral responsibility and being a much-needed technology that is clean and cost-effective. One of these much-needed technologies is the solar home system. 38. Real-Time Rendering Tool with Reconstructions Based on UE4 Raytracing Tech Direct use of UE4's pathtracing is a great yet not perfect solution, since UE4 uses BruteForce 39. 5 Best Budget Gaming Laptops Under $500 Lenovo, Asus, and Acer produce some of the best budget gaming laptops under 500 USD. The extensive features and a multitude of uses has led to gaming laptops being preferred over consoles in today’s gaming world. But as the demand for gaming laptops rose, so did their prices. 40. KFC Partners with Cooler Master to Launch Gaming Console with Chicken Warmer A new collaboration between fast-food chain giant KFC, Intel, and Cooler Master has birthed the perfect gaming console for the chicken lover. 41. Computers on the Farm by Deborah Takiff Smith - Table of Links Computers on the Farm, by Deborah Takiff Smith is part of the HackerNoon Books Series. Read this book online for free on HackerNoon! 42. BitBanged Serial Peripheral Interface in Go on Raspberry Pi [Explained] I’m going to focus mostly on some design decisions and also how I went about writing an SPI interface using Go on a Raspberry Pi. I assume my readers have a basic understanding of what a Raspberry Pi is, and how basic electronics work. If not, read on anyway and I will be sure to include some valuable resources below. 43. How Computer Recycling is Going to Save Your City E-waste makes up more than half of our toxic waste and it’s going to take all of us working together to make sure that the environmental impact is diminished. 44. How To Install Virtual Media On An iDrac Controller The iDRAC is a Dell remote access controller. This controller allows for remote power cycling, and a virutal console with keyboard, video, and mouse. It also provides a number of ways to roll out an operating system or vmware. 45. Introducing YALT: Because some people don’t like LLVM. We all wait for our program to compile (or someone else’s) and we keep thinking “This is it. It’s going to fail”. And sometimes it does. But sometimes (thankfully), it doesn’t. Then we discover a bug (Or two. Or three) and we all know how it goes from there. 46. An Intro to Quantum Computers Gordon Moore, the founder of Fairchild Semiconductor and former CEO of Intel in his 1965 paper, described that the number of transistors in a dense integrated circuit double about every two years and this statement is famously known as Moore's Law. Moore's law was consistent for the past 50 years, but with the current technological advancements, it is coming to an end. It is starting to become physically impossible to reduce transistor sizes to increase computational efficiency further, and hence this calls for alternate methods. 47. What a Computer Can Do for You  -  Other Uses Other Uses 48. How to Install Anthos Bare Metal on Intel NUCs: A Beginner's Guide Anthos on Bare Metal allows you to spin up a cluster from as few as 2 Intel NUCs. It’s a relatively straightforward process. 49. Port Forwarding for Noobs Port forwarding is used to enable a router to use a specific port to communicate with certain devices on a network. Learn more about how it is set up here. 50. How Big Data and Computers Leveled Up India in the 1950s When we think of computers, we think of the twenty-first century. But did you know that India started using them back in the 1950s? 51. Strategies for Getting Into Computers One way is to first buy the basic hardware and components you think you need, and then add memory and other components later 52. A Brief Introduction to System Drivers All computers operate with hardware, including; soundcards, video cards, USB ports, etc. Just about everything on your PC that ant a software program. 53. How To Choose A Laptop When You're A Software Developer So you’ve either decided to go into software development, you’ve been doing software development for a while and you’ve decided to pickup a laptop, or you want some insight into what might be some good options for your next computer. There are various reasons to want a personal laptop: 54. Everything You Need to Know About Refurbished Computers via TechSoup Explore the details of refurbished computers from TechSoup Thank you for checking out the 54 most read stories about Computers on HackerNoon. to find the most read stories about any technology. Visit the /Learn Repo

54 Stories To Learn About Computers

"Our Intelligence is what makes us human and AI is an extension of that Quality" -Yan LeCun Since the advent of (also known as artificial neural networks), the AI industry has enjoyed unparalleled success. Neural Networks are the driving force behind modern AI systems and they are modeled after the human brain. Modern AI research involves creating and implementing algorithms that aim to mimic the neural processes of the human brain to create systems that learn and act in ways similar to human beings. Neural Networks In this article, we will attempt to understand the brain-inspired approach to building It is worth noting that while this topic is an inherently broad one, I will be as brief and succinct as possible. I plan to treat sub-topics that have more intricate sub-branches as standalone articles, and I will, of course, leave references at the end of the article. AI systems. Content breakdown How I hope to approach this: Here we'll discuss how scientists Norman Weiner ann Warren McCulloch brought about the convergence of neuroscience and computer science, how Frank Rosenblatt's Perceptron was the first real attempt to mimic human intelligence, and how its failure brought about ground-breaking work which would serve as the platform for Neural Networks. History of the brain-inspired approach to AI: In this section, we'll dive into the biological basis for the brain-inspired approach to AI. We will discuss the basic structure and functions of the human brain, understand its core building block, the neuron, and how they work together to process information and enable complex actions. How the human brain works and how it relates to AI systems: Here we will discuss the fundamental concepts behind the brain-inspired approach to AI. We will explain how concepts such as; Neural networks, Hierarchical processing, and plasticity and how techniques of parallel processing, distributed representations, and recurrent feedback aid AI in mimicking the brain's functioning. The Core Principles behind the Brain-inspired Approach to AI: Here we will talk about the challenges and limitations inherent in attempting to build systems that mimic the human brain. Challenges such as; the complexity of the brain, and the lack of a unified theory of cognition explore the ways these challenges and limitations are being addressed. Challenges in building AI systems modeled after the human brain: Let us begin! The History of the brain-inspired Approach to AI The drive to build machines that are capable of intelligent behavior owes much of its inspiration to MIT Profesor, . Norbert Weiner was a child prodigy who could read by the age of three. He had a broad knowledge of various fields such as Mathematics, Neurophysiology, medicine, and physics. Norbert Weiner Norbert Weiner believed that the main opportunities in science lay in exploring what he termed as -areas of study that are not clearly within a certain discipline but rather a mixture of disciplines like the study of medicine and engineering coming together to create the field of Medical Engineering-, he was quoted saying: Boundary Regions "If the difficulty of a physiological problem is mathematical in nature, ten physiologists ignorant of mathematics will get precisely as far as one physiologist ignorant of mathematics" In the year 1934, Weiner and a couple of other academics gathered monthly to discuss papers involving boundary region science. It was a perfect catharsis for half-baked ideas, insufficient self-criticism, exaggerated self-confidence and pomposity - Norman Weiner From these sessions and from his own personal research, Weiner learned about new research on biological nervous systems as well as about pioneering work on electronic computers, and his natural inclination was to blend these two fields. And so, a relationship between neuroscience and computer science was formed. This relationship became the cornerstone for the creation of artificial intelligence, as we know it. After World War II, Wiener began forming theories about intelligence in both humans and machines and this new field was named . Wiener’s foray into Cybernetics successfully got scientists talking about the possibility of biology fusing with engineering. One of the said scientists was a neurophysiologist named , who then proceeded to drop out of Haverford University to study philosophy and psychology at Yale. Cybernetics Warren McCulloch While attending a scientific conference in New York, he came in contact with papers written by colleagues on biological feedback mechanisms. The following year, in collaboration with his brilliant 18-year-old protege named Walter Pitts, McCulloch proposed a theory about how the brain works -a theory that would help foster the widespread perception that computers and brains function essentially in the same way. They based their conclusions on research by McCulloch on the possibility of neurons processing Binary Numbers (for the unknowledgeable, computers communicate via binary numbers). This theory became the foundation for what became the first model of an artificial neural network, which was named the McCulloch-Pitts Neuron(MCP). The MCP served as the foundation for the creation of the first-ever neural network which came to be known as . The Perceptron was created by Psychologist, who, inspired by the synapses in the brain, decided that as the human brain could process and classify information through synapses(communication between neurons) then perhaps a digital computer could do the same via a neural network. the perceptron Frank Rosenblatt The Perceptron essentially scaled the MCP neuron from one artificial neuron into a network of neurons, but, unfortunately, the perceptron had some technical challenges which limited its practical application, most notable of its limitations was its inability to perform complex operations(like classifying between more than one item, for example, a perceptron could not perform classification between a cat, a dog, and a bird). In the year 1969, a book published by and titled lay out in detail the flaws of the Perceptron and due to that, research on Artificial Neural Networks stagnated until the proposal of Back Propagation by . Marvin Minsky Seymour Papert Perceptron Paul Werbos Back Propagation hopes to solve the issue of classifying complex data that hindered the industrial application of Neural Networks at the time. It was inspired by synaptic plasticity; the way the brain modifies the strengths of connections between neurons and as such improves performance. Back Propagation was designed to mimic the process in the brain that strengthens connections between neurons via a process called weight adjustment. Despite the early proposal by Paul Werbos, the concept of backpropagation only gained widespread adoption when researchers such as , , and published papers that demonstrated the effectiveness of backpropagation for training neural networks. The implementation of backpropagation led to the creation of Deep Learning which powers most of the AI systems available in the world. David Rumelheart Geoffrey Hinton Ronald Williams "People are smarter than today's computers because the brain employs a basic computational architecture that is more suited to deal with a central aspect of the natural information processing tasks that people are so good at." - Parallel Distributed Processing How the human brain works and how it relates to AI systems We have discussed how researchers began to model AI to mimic the human brain, let us now look at how the brain works and define the relationship between the brain and AI systems. How the brain works: A simplified description The human brain, essentially processes thoughts via the use of neurons, a neuron is made up of 3 core sections; The Dendrite, Axon, and the Soma. The Dendrite is responsible for receiving signals from other Neurons, The Soma processes information received from the Dendrite, and the Axon is responsible for transferring the processed information to the next Dendrite in the sequence. To grasp how the brain processes thought, imagine you see a car coming towards you, your eyes immediately send electrical signals to your brain through the optical nerve and then the brain forms a chain of neurons to make sense of the incoming signal. The first neuron in the chain collects the signal through its and sends it to the to process the signal after the Soma finishes with its task it sends the signal to the which then sends it to the Dendrite of the next neuron in the chain, the connection between Axons and Dendrites when passing on information is called a Synapse. The entire process continues until the brain finds a t(that's scientific lingo for; the brain continues processing until it finds an optimal response to the signal sent to it) and then it sends signals to the necessary effectors eg, your legs and then the brain sends a signal to your legs to run away from the oncoming car. Dendrites Soma Axon Sapiotemporal Synaptic Inpu The relationship between the brain and AI systems The relationship between the brain and AI is largely mutually beneficial with the brain being the main source of inspiration behind the design of AI systems and advances in AI leading to a better understanding of the brain and how it works. There is a reciprocal exchange of knowledge and ideas when it comes to the brain and AI, and there are several examples that attest to the positively symbiotic nature of this relationship: Arguably the most significant impact made by the human brain to the field of Artificial Intelligence is the creation of Neural Networks. In essence, Neural Networks are computational models that mimic the function and structure of biological neurons, the architecture of neural networks and their learning algorithms are largely inspired by the way neurons in the brain interact and adapt. Neural Networks: AI systems have been used to the human brain and study its interactions with the physical world. For example, researchers have Machine Learning techniques to simulate the activity of biological neurons involved in visual processing, and the result has provided insight into how the brain handles visual information. Brain Simulations: simulate Researchers have begun using Machine Learning Algorithms to analyze and gain insights from brain data, and fMRI scans. These insights serve to identify patterns and relationships which would otherwise have remained hidden. The insights gotten can help in the understanding of internal cognitive functions, memory, and decision-making, it also aids in the treatment of brain-native illnesses such as Alzheimer's. Insights into the brain: Core Principles Behind the brain-inspired Approach to AI Here we will discuss several concepts which aid AI in imitating the way the human brain functions. These concepts have helped AI researchers create more powerful and intelligent systems which are capable of performing complex tasks. Neural Networks As discussed earlier, neural networks are arguably the most significant impact made by the human brain to the field of Artificial Intelligence. In essence, Neural Networks are computational models that mimic the function and structure of biological neurons, the networks are made up of various layers of interconnected nodes, called artificial neurons, which aid in the processing and transmitting of information, similar to what is done by dendrites, somas, and axons in biological neural networks. Neural Networks are architected to learn from past experiences the same way the brain does. Distributed Representations Distributed representations are simply a way of encoding concepts or ideas in a neural network as a pattern along several nodes in a network in order to form a pattern. For example, the concept of smoking could be represented(encoded) using a certain set of nodes in a neural network and so if that network comes along an image of a man smoking it then uses those selected nodes to make sense of the image (it's a lot more complex than that but for the sake of simplicity), this technique aids AI systems in remembering complex concepts or relationships between concepts the same way the brain recognizes and remembers complex stimuli. Recurrent Feedback This is a technique used in training AI models where the output of a neural network is returned as input to allow the network to integrate its output as extra data input in training. This is similar to how the brain makes use of feedback loops in order to adjust its model based on previous experiences. Parallel Processing Parallel processing involves breaking up complex computational tasks into smaller bits in an effort to process the smaller bits on another processor in an attempt to improve speed. This approach enables AI systems to process more input data faster, similar to how the brain is able to perform different tasks at the same time(multi-tasking). Attention Mechanisms This is a technique used which enables AI models to focus on specific parts of input data, it is commonly employed in sectors such as Natural Language Processing which contains complex and cumbersome data. It is inspired by the brain's ability to attend to only specific parts of a largely distracting environment; like your ability to tune into and interact in one conversation out of a cacophony of conversations. Reinforcement Learning Reinforcement Learning is a technique used to train AI systems, it was inspired by how human beings learn skills through trial and error. It involves an AI agent receiving rewards or punishments based on its actions, this enables the agent to learn from its mistakes and be more efficient in its future actions (this technique is usually used in the creation of games). Unsupervised Learning The brain is constantly receiving new streams of data in the form of sounds, visual content, sensory feelings to the skin, etc and it has to make sense of it all and attempt to form a coherent and logical understanding of how all these seemingly disparate events affect its physical state. Take this analogy as an example, you feel water drop on your skin, you hear the sound of water droplets dropping quickly on rooftops, you feel your clothes getting heavy and in that instant, you know rain is falling, you then search your memory bank to ascertain if you carried an umbrella and if you did, you are fine, else, you check to see the distance from your current location to your home if it is close, you are fine, else you try to gauge how intense the rain is going to become if it is a light drizzle you can attempt to continue the journey back to your home, but if it is priming to become a shower, then you have to find shelter. The ability to make sense of seemingly disparate data points(water, sound, feeling, distance) is implemented in Artificial intelligence in the form of a technique called Unsupervised Learning. It is an AI training technique where AI systems are taught to make sense of raw, unstructured data without explicit labeling ( no one tells you rain is falling when it is falling, do they/). Challenges in Building Brain-Inspired AI Systems We have spoken about how the approach for using the brain as inspiration for AI systems came about, how the brain relates to AI, and the core principles behind brain-inspired AI. In this section, we are going to talk about some of the technical and conceptual challenges inherent in building AI systems modeled after the human brain. Complexity This is a pretty daunting challenge. The brain-inspired approach to AI is based on modeling the brain and building AI systems after that model, but the human brain is an inherently complex system with 100 billion neurons and approximately 600 trillion synaptic connections(each neuron, has on average, 10,000 synaptic connections with other neurons), and these synapses are constantly interacting in dynamic and unpredictable ways. Building AI systems that are aimed to mimic, and hopefully exceed, that complexity is in itself a challenge and requires equally complex statistical models. Data Requirements for Training Large Models Open AI's GPT 4, which is, at the moment, the cutting edge of text-based AI models requires 47 GigaBytes of data, in comparison, its predecessor GPT3 was trained on 17 Gigabytes of data, which is approximately 3 orders of magnitude lower, imagine how much GPT 5 will be trained on. As has been proven in order to get acceptible results, Brain-Inspired AI systems require vast amounts of data and data for tasks especially auditory and visual tasks and this places a lot of emphasis on the creation of data collection pipelines, for instance, Tesla has 780 million miles of driving data and its data collection pipeline adds another million every 10 hours. Energy Efficiency Building brain-inspired AI systems that emulate the brain's energy efficiency is a huge challenge. the human brain consumes approximately 20 watts of power, in comparison, 's Autopilot, on specialized chips, consumes about 2,500 watts per second and 7.5-megawatt hours(MWh) to train an AI model the size of . Tesla it takes around ChatGPT The Explainaibility Problem Developing brain-inspired AI systems that can be trusted by users is crucial to the growth and adoption of AI, but therein lies the problem, the brain, which AI systems are meant to be modeled after, is essentially a black box. The inner workings of the brain are not easy to understand, this is due to the lack of information surrounding how the brain processes thought. There is no lack of research on how the biological structure of the human brain but there is a certain lack of empirical information on the functional qualities of the brain, that is, how thought is formed, how deja vu occurs, etc, and this leads to a problem in the building of brain-inspired AI systems. The Interdisciplinary Requirements The act of building brain-inspired AI systems requires the knowledge of experts in different fields, such as; Neuroscience, Computer Science, Engineering, Philosophy, and Psychology. But there lies a challenge there both logistical and foundational, in the sense that getting experts from different fields very financially tasking, and also there lies the problem of knowledge conflict; it is really difficult to get an engineer to care about the psychological effects of what he/she is building, not to talk of the problem of colliding egos. Summary In Conclusion, while the brain-inspired approach is the obvious route to building AI systems(we have discussed why), it is wrought with challenges but we can look to the future with the hope that efforts are being made to solve these problems. Also published here. References FreeCode Camp Machine Learning Tesla's Vehicle Safety Report Basic Neural Units of the Brain: Neurons, Synapses and Action Potential When Brain-inspired AI meets AGI Perceptron: The artificial Neuron (An Essential Upgrade To The McCulloch-Pitts Neuron) McCulloch-Pitts Neuron — Mankind’s First Mathematical Model Of A Biological Neuron BackPropagation through Time: What it does and How to do it The History of AI BrainOS: A Novel Artificial Brain-Alike Automatic Machine Learning Framework

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It all started when we ordered an actuator, with an encoder, from China for a project. But something went wrong, and a month later, we received actuators without an encoder. It was necessary to complete the project code urgently, but it would not be possible to control the actuators without encoders. For the project, you need to know the rod extension length, and for this, you need to know the number of engine rotations. So we decided to spend one day and make our encoder for actuators. At first, we thought to put a multi-turn potentiometer. But there can be a lot of rotations, and we didn’t have such an encoder at hand. Then we wanted to use an encoder like , EC11 but such encoders have a very small resource of work.
And in the end, we chose the option: of two digital hall sensors and magnets. SS443A The SS443A hall sensor outputs a logic HIGH on one polarity of magnets and a logic LOW on the other and retains that value even when the magnet is removed. If briefly: We take two hall sensors and put them at an angle of 45 degrees to each other. We glue two magnets to the motor axis, with different poles, and when the motor is spinning, each sensor turns on and off in turn. If each sensor turned on and off one time, then there was one turn of the engine. With two sensors, we can count a quarter of a turn. And knowing the sequence of turning on and off the sensors, we can determine the direction of rotation. We dismantled the actuator to find a place to mount the magnets. No place was there, and magnets could not be glued because everything was oily with grease. Then we decided to throw away the original cap of the actuator, which will have a built-in gear with magnets and two hall sensors. The gear will be driven, and we will place the gear on a separate axis. And the gear will spin without load from the drive gear of the engine. We took two magnets with a diameter of 5mm and a thickness of 4mm. In SolidWorks, with the help of the “GearTrax” plugin, we drew the gear of the required size and drew the case cap for the actuator with a 6-pin GX16 connector. We printed the case on a 3D printer from PETG plastic, and on the 3rd attempt, we got a working mechanism. It took about 11 hours for all these, along with 3D printing. All that’s left is to write the code to calculate the length of the rod extension. For the test, we took the Arduino MEGA 2560 board; there are six pins with hardware interrupts. You can make the code without interruptions, but if at least one pulse (a quarter of a turn) is skipped, the error will be 1.6mm, and this is already a lot for our task. Tests have shown that without interruptions, the error can accumulate to large values with active use. Therefore, we use two interrupt pins for each actuator. 1 pin = 1 hall sensor. The code, in the end, turned out to be quite simple, but I decided to leave it here as a cheat sheet for the future, or maybe it will come in handy for someone else: const byte M1_HALL1_pin = 20; //connect pintout Hall sensor 1
const byte M1_HALL2_pin = 21;	//connect pintout Hall sensor 2

const byte M1_HALL1_pin_interupt = 3; //Interrupt pin3 match Pin20 Arduino Mega
const byte M1_HALL2_pin_interupt = 2; //Interrupt pin2 match Pin21 Arduino Mega

volatile byte M1_HALL_cur_state = B00; //Current state hall sensors. If Hall1 and Hall2 is LOW then variable value is B00
volatile byte M1_HALL_last_state = B00; //Last state hall sensors. If Hall1 is HIGH and Hall2 is LOW then variable value is B10

volatile long countPulsesM1 = 0; //Counter

/*
Arrays dirUpM1 and  dirDownM1 have directions of rotation.
*/
byte dirUpM1[] = {1,3,0,2}; 	//01 11 00 10
byte dirDownM1[] = {2,0,3,1}; 	//10 00 11 01

void setup(void){
  attachInterrupt(M1_HALL1_pin_interupt, countRotationInteruptsM1, CHANGE);
  attachInterrupt(M1_HALL2_pin_interupt, countRotationInteruptsM1, CHANGE);

  //Be sure to pullup the pins to avoid noises
  pinMode(M1_HALL1_pin, INPUT_PULLUP); 
  pinMode(M1_HALL2_pin, INPUT_PULLUP); 

  Serial.begin(9600);
}

void loop(void){
  Serial.println(countPulsesM1);
}

void countRotationInteruptsM1(){
  //Present cur status of hall sensor as binary number
  M1_HALL_cur_state = digitalRead(M1_HALL1_pin);  //Read HALL1 state (for example: if HALL1 is HIGH then value is  B01)
  M1_HALL_cur_state = M1_HALL_cur_state << 1; //Shift the bit to make room for the second value (for example: value is  B10)
  M1_HALL_cur_state += digitalRead(M1_HALL2_pin); //Read HALL2 state and ADD it to HALL1 value (for example: if HALL2 is HIGH too, then value is B11)

	//If in an array dirUpM1 of sequences, the previous value is followed by the current, means the actuator moves up
	if(dirUpM1[M1_HALL_cur_state] == M1_HALL_last_state){
		countPulsesM1++;
	//else  the actuator moves up
	} else if(dirDownM1[M1_HALL_cur_state] == M1_HALL_last_state){
		countPulsesM1--;
		if(countPulsesM1 < 0){
			countPulsesM1 = 0;
		}
	}
} Arrays dirUpM1 and  dirDownM1 have directions of rotation.
As the gear turns, the hall sensors will turn on and off one after the other. For example: at first, HALL1 and HALL2 is LOW. This can be written as binary B00 then HALL1 is LOW, and HALL2 is HIGH. This can be written as binary B01 then HALL1 and HALL2 are HIGH. This can be written as binary B11 then HALL1 is HIGH, and HALL2 is LOW. This can be written as binary B10 and then the cycle repeats 00 - 01
01 - 11
11 - 10
10 - 00 This can be represented as a combination: 0 - 1
1 - 3
3 - 2
2 - 0 If you convert binary numbers to decimals, it will look like this: Now let's represent it as an array: arrD[0] = 1; arrD[1] = 3; arrD[3] = 2; arrD[2] = 0; byte dirUpM1[] = {1,3,0,2}; And finally: If suddenly the connection of the hall sensors changes, the array with the direction can be “trained”: void setDerectionUp(){	
  if(M1_HALL_cur_state != M1_HALL_last_state){
    dirUpM1[M1_HALL_last_state] = M1_HALL_cur_state;
    M1_HALL_last_state=M1_HALL_cur_state;
  }
  if(M2_HALL_cur_state != M2_HALL_last_state){
  	dirUpM2[M2_HALL_last_state] = M2_HALL_cur_state;
  	M2_HALL_last_state=M2_HALL_cur_state;
  }
} The factory actuator with an encoder costs: $41
Actuator without encoder + homemade encoder costs: $26 + $4 = $30 PS:

My Experience with Length Control for a DC Actuator

Character Encoding Demystified: Everything you Need to Know About ASCII, Unicode, UTF-8

AI and machine learning are very hot topics these days. Self-driving cars, real-time automatic translation, voice recognition, etc. These are only some of the applications that cannot exist without machine learning. But how can machines learn? I will show you how the magic works in this article, but I won’t talk about neural networks! I will show you what is in the deepest deep of machine learning. One of the best presentations about machine learning is . Fei Fei Li’s TED talk As Li said in her talk, in the early days, programmers tried to solve computer vision tasks by algorithms. These algorithms were looking for shapes and tried to identify things by preprogrammed rules. But they could not solve it in this way. Computer vision is a very complex problem, and we cannot solve it algorithmically. So, here comes machine learning into the picture. If we cannot write the program, let’s write a program that writes it instead of us. Machine learning algorithms do this. If we have enough data, they can write the algorithm that calculates the expected output from the inputs for us. In the case of image recognition, the input is the image, and the output is a label or a description of the content of the image. This is why Li and her team worked really hard to build ImageNet, which was the biggest labeled image database in the world, with 15 million images and 22,000 categories. Thanks to ImageNet, we had enough data, but how did programmers use it to solve the problem of image recognition? This is the point where I should talk about neural networks like Li does, but I won’t. The biological brain indeed inspires neural networks, but today’s transformers are far from the biological model. This is why I think the name “neural network” is misleading. But what would be a better name? My favorite is Karpathy’s (head of AI @ Tesla) . Software 2.0 As Karpathy said , Software 1.0 is the classical software, where the programmer writes the code, but in the case of Software 2.0, another software finds it based on big data. But how can a software write another software? in this talk Let me quote Karpathy: “Gradient descent can write code better than you. I’m sorry.” is the name of the magic that is used by most machine learning systems. To understand it, let’s imagine a machine learning system. It’s a black box with inputs and outputs. If the purpose of the system is image recognition, then the input is an array of pixels, and the output is a probability distribution vector. Gradient descent If the system can identify cats and dogs, and the input is an image of a cat, the output will be like 10% dog and 90% cat. So, the inputs are numbers, the outputs are also numbers, and the content of the black box is a giant (really huge) mathematical expression. The black box calculates the output vector from the pixel data. I promised to talk about programs writing programs, and now I’m talking about mathematical expression. But in fact, programs are mathematical expressions. CPUs are built from logic gates. They use the binary representation of numbers and logic operators. Any existing algorithm can be implemented by these logical expressions, so a long logical expression can represent any program that can run on classical computers. As you see, classical programs are also not more than binary calculations from a binary input to a binary output. Machine learning systems use real numbers and operators instead of binary numbers and operators, but basically, these mathematical expressions are also “programs.” Alan Turing about “B-type unorganized machines.” These machines are built from interconnected logical NAND gates and can be trained by enabling/disabling the wires between the nodes. In binary algebra, NAND is a universal operator, because every other operator can be expressed by it. These B-type unorganized machines are universal computers because every algorithm can be implemented on them. wrote a paper in 1948 These B-type machines are similar to nowadays neural networks, but they are implemented upon logic gates like today’s CPUs, so the algorithms that are implemented by these B-type machines would be more like our today’s algorithms. Unfortunately, Turing never published the paper, this is why we do not know him as an inventor of early neural networks. The problem with these B-type networks is that they cannot be trained efficiently. If we have a set of inputs and outputs and a parameterized expression, how can we find the correct parameters that calculate the outputs from the inputs with the fewest error? It is something like a black box that has many potentiometers. Every combination of the potentiometer positions is a program, and we are searching for the correct positions. To solve this problem, let’s imagine the error function. It looks like a landscape with hills and valleys. Every single parameter of the expression is a dimension of the landscape, and the height of the current point is the error with the given parameters. When we initialize the expression with random numbers, we are at a random location on the landscape. To minimize the errors, we have to come down to the lowest point (that represents the lowest error). The problem is that we are completely blind. How can we come down from the hill? We can grope around to find the steepest slope and go there. But how can we determine the slope of a function? Here comes the gradient in the picture. Gradient shows how steep the slope on the function is at a given point. This is why we call this method “gradient descent.” The gradient at the given point can be calculated by partial derivation. A function has to satisfy some requirements to be derivable. If we want to use gradient descent for optimization, we have to use these types of functions. If the functions are derivable, then the chain of functions will also be derivable, and there is an algorithmic method to calculate the gradient. Now we have all the knowledge to understand how and (the two most popular machine learning frameworks) find the correct parameters for our expression. TensorFlow PyTorch First, let’s look at TensorFlow. In Tensorflow, there is a gradient registry where gradient functions are registered for the operators by the method. In the learning phase, in every step, a has to be started. is something like a video recorder. When TensorFlow does any operation, the gradient tape logs it. RegisterGradient GradientTape GradientTape After the end of the forward phase (when the output is generated from the input), we stop the gradient tape that goes backward on the log by using the error and calculating the gradients using the registered gradient functions. We can modify the parameters and repeat the process until we reach the minimum error by using the gradients. Let’s look at the code in Python: # Linear regression using GradientTape
# based on https://sanjayasubedi.com.np/deeplearning/tensorflow-2-linear-regression-from-scratch/

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt

class Model:
    def __init__(self):
        self.W = tf.Variable(16.0)
        self.b = tf.Variable(10.0)

    def __call__(self, x):
        return self.W * x + self.b

TRUE_W = 3.0 # slope
TRUE_b = 0.5 # intercept

NUM_EXAMPLES = 1000

X = tf.random.normal(shape=(NUM_EXAMPLES,))
noise = tf.random.normal(shape=(NUM_EXAMPLES,))
y = X * TRUE_W + TRUE_b + noise

model = Model()

plt.figure()
plt.scatter(X, y, label="true")
plt.scatter(X, model(X), label="predicted")
plt.legend()
plt.show()

def loss(y, y_pred):
    return tf.reduce_mean(tf.square(y - y_pred))

def train(model, X, y, lr=0.01):
    with tf.GradientTape() as t:
        current_loss = loss(y, model(X))

    dW, db = t.gradient(current_loss, [model.W, model.b])
    model.W.assign_sub(lr * dW)
    model.b.assign_sub(lr * db)

Ws, bs = [], []
epochs = 20
for epoch in range(epochs):
    Ws.append(model.W.numpy()) # eager execution allows us to do this
    bs.append(model.b.numpy())

    current_loss = loss(y, model(X))

    train(model, X, y, lr=0.1)
    print(f"Epoch {epoch}: Loss: {current_loss.numpy()}")

plt.figure()
plt.plot(range(epochs), Ws, 'r', range(epochs), bs, 'b')
plt.plot([TRUE_W] * epochs, 'r--', [TRUE_b] * epochs, 'b--')
plt.legend(['W', 'b', 'true W', 'true b'])
plt.show()

plt.figure()
plt.scatter(X, y, label="true")
plt.scatter(X, model(X), label="predicted")
plt.legend()
plt.show() This code shows how we can solve the simplest problem (linear regression) by using gradient descent in TensorFlow. The aim of linear regression is to find the parameters of a line that is closest to each point, where closest means that the sum of squares of the distances is minimal. TensorFlow uses tensor operations for the calculations. Tensors are generalizations of matrices. From the programmer’s perspective, tensors are simple arrays. A zero-dimensional tensor is a scalar, a one-dimensional tensor is a vector, a two-dimensional tensor is a matrix, and from third dimension, tensors are simply tensors. Tensor operations can be done in parallel to run efficiently, especially on GPUs or TPUs. At the beginning of the code, we define our model, which is a linear expression. It has two scalar parameters, and , and the expression is . The default value of is , and is . This is in our black box, our code will change the and the to minimize the error. Real-world models have millions or billions of parameters, but these two parameters are enough to understand the method. W b y=W*x+b W 16 b 10 W b From line 21 to line 23, we define the random point set. The method generates a vector with 1,000 random numbers in a normal distribution, and we use that to generate the points near a line. tf.random.normal The loss function is defined in line 34. and parameters are vectors. is the actual output of our model, and is the expected output. The square function calculates the square of every vector element, and the output is also a vector with the squares. The function calculates the mean of elements, and its result is a scalar. This is the error itself that we want to minimize. y y_pred y_pred y reduce_mean The gradient descent is from line 36 to line 42. This is the essence of the code where the learning happens. The in line 37 is a Python expression. It calls the parameter object’s method at the beginning of the block and at the end. with __enter__ __exit__ In the case of , the method starts the recording, and stops it. In the block (line 38), we calculate the model output by and the error. In line 40, the calculates the gradients for the parameters ( and ), and in lines 41 and 42, modify the parameters. GradientTape __enter__ __exit__ model(X) GradientTape dW db There are different optimization strategies. We are using the simplest, where the gradients are multiplied by a fixed learning rate ( ). lr In a nutshell, this is how gradient descent and TensorFlow’s work. You can find many . Neural networks for image recognition, reinforcement learning, etc., but keep in your mind, there are always tensor operations and a GradientTape. GradientTape tutorials on TensorFlow’s webpage Now, let’s see how gradient descent works in the other big framework, PyTorch. PyTorch uses the system for gradient calculation, which is embedded into the torch tensors. If a tensor is a result of an operator, it contains a back pointer to the operator and the source tensors. The source tensors also contain back pointers, etc., and the full operator chain is traceable. autograd Every operator can calculate its own gradient. When you call the backward method on the last tensor, it goes back on the chain and calculates the gradients to the tensors. Let’s see the previous linear regression code in PyTorch: import torch
import matplotlib.pyplot as plt
from torch.autograd import Variable


class Model:
    def __init__(self):
        self.W = Variable(torch.as_tensor(16.), requires_grad=True)
        self.b = Variable(torch.as_tensor(10.), requires_grad=True)

    def __call__(self, x):
        return self.W * x + self.b


TRUE_W = 3.0  # slope
TRUE_b = 0.5  # intercept

NUM_EXAMPLES = 1000

X = torch.normal(0.0, 1.0, size=(NUM_EXAMPLES,))
noise = torch.normal(0.0, 1.0, size=(NUM_EXAMPLES,))
y = X * TRUE_W + TRUE_b + noise

model = Model()

plt.figure()
plt.scatter(X, y, label="true")
plt.scatter(X, model(X).detach().numpy(), label="predicted")
plt.legend()
plt.show()


def loss(y, y_pred):
    return torch.square(y_pred - y).mean()


def train(model, X, y, lr=0.01):
    current_loss = loss(y, model(X))
    current_loss.backward()

    with torch.no_grad():
        model.W -= model.W.grad.data * lr
        model.b -= model.b.grad.data * lr

    model.W.grad.data.zero_()
    model.b.grad.data.zero_()


Ws, bs = [], []
epochs = 20
for epoch in range(epochs):
    with torch.no_grad():
        Ws.append(model.W.numpy().item())
        bs.append(model.b.numpy().item())

        current_loss = loss(y, model(X))

    train(model, X, y, lr=0.1)
    print(f"Epoch {epoch}: Loss: {current_loss.numpy()}")

plt.figure()
plt.plot(range(epochs), Ws, 'r', range(epochs), bs, 'b')
plt.plot([TRUE_W] * epochs, 'r--', [TRUE_b] * epochs, 'b--')
plt.legend(['W', 'b', 'true W', 'true b'])
plt.show()

plt.figure()
plt.scatter(X, y, label="true")
plt.scatter(X, model(X).detach().numpy(), label="predicted")
plt.legend()
plt.show() The model and the loss part are very similar to TensorFlow. You find the difference in the method from line 37 to line 46. After the calculation of the tensor, we call the backward method on it. It recursively goes back on the chain and calculates the gradient for the and tensors. train current_loss W b From line 41 to line 43, we modify the and tensors. It’s important that this calculation is in a block. The method temporarily disables the gradient calculation for the operators, which is not needed when we modify the parameters. W b torch.no_grad() no_grad() At the end of the method calling the zero method clears the gradients. Without this, PyTorch will sum up the gradients, which results in strange behavior. The other parts of the code are very similar to TensorFlow. Like TensorFlow, PyTorch also has good tutorials, community, and documentation. train You will find everything to build any neural network, but the most important part is the autograd system, which is the base of the training. Next time, when you see a picture that DALL-E generates, a car that drives itself, or simply wonder how Google Assistant understands what you say, you will know how the magic works, and how an algorithm (the gradient descent) wrote these cool algorithms for us. First Published here

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