AI 资讯
AI 개발자가 실전에서 쓰는 필수 수학 개념 완전 정복
https://mdooai.com AI 모델을 다루다 보면 코드는 돌아가는데 왜 성능이 안 나오는지 이해하지 못하는 순간이 옵니다. 그 답은 대부분 수학에 있습니다. 실무 AI 개발자로 성장하기 위해 반드시 잡아야 할 최소한의 수학 개념과, 그것을 어떻게 공부해야 하는지를 구체적으로 살펴보겠습니다. 코딩만으로는 해결할 수 없는 AI 모델 성능의 열쇠 많은 주니어 개발자들이 비슷한 경험을 합니다. PyTorch나 TensorFlow로 튜토리얼 코드를 복사하고, 학습도 돌리고, 결과도 나옵니다. 그런데 모델이 왜 이렇게 예측하는지, 왜 학습이 멈추는지, 어떻게 하면 성능이 올라가는지는 설명할 수가 없습니다. 이 간극의 정체가 바로 수학입니다. 가령 모델이 과적합(overfitting)될 때 L2 정규화를 쓰라는 조언을 듣습니다. 코드 한 줄로 해결되지만, 그게 왜 작동하는지는 가중치 벡터의 크기를 제한한다는 선형대수와 확률론적 추론이 얽혀 있습니다. 이 원리를 이해하는 개발자와 모르는 개발자가 새로운 문제에서 만들어내는 솔루션의 질은 다를 수밖에 없습니다. 다행인 건, AI 개발에서 필요한 수학은 대학원 수준의 수리해석학이 아닙니다. 핵심 개념 몇 가지를 실용적 도구로 이해하는 것으로 충분합니다. 선형대수와 확률통계, 어떤 개념부터 공부해야 할까? 선형대수와 확률통계는 AI 수학의 두 축입니다. 그런데 이 두 분야 전체를 공부하려 들면 끝이 없습니다. 개발자 관점에서 실제로 반복해서 등장하는 개념만 추려내면 다음과 같습니다. 선형대수에서 우선해야 할 개념 벡터와 행렬의 연산 : 데이터는 사실상 전부 벡터와 행렬로 표현됩니다. 이미지는 픽셀값 행렬이고, 텍스트는 임베딩 벡터입니다. 행렬 곱(matrix multiplication)이 신경망의 순전파(forward pass) 그 자체입니다. 내적(dot product)과 유사도 : 추천 시스템, 어텐션 메커니즘(Transformer의 핵심)이 내적 연산 위에 서 있습니다. 고유값(eigenvalue)과 고유벡터(eigenvector) : PCA(주성분 분석)처럼 차원을 줄이는 기법을 이해하려면 반드시 필요합니다. 행렬 분해(SVD 등) : 추천 시스템과 자연어 처리의 기반 기술에 등장합니다. 확률통계에서 우선해야 할 개념 확률분포와 기댓값 : 모델의 출력이 확률인 이유, 소프트맥스(softmax)가 하는 일을 이해하는 기반입니다. 베이즈 정리 : 사전 지식을 데이터로 업데이트하는 논리 구조로, 생성 모델과 불확실성 추정에 직접 연결됩니다. 최대 우도 추정(MLE, Maximum Likelihood Estimation) : 모델 학습이 왜 손실 함수를 최소화하는 방향인지를 설명하는 원리입니다. 크로스 엔트로피 손실 : 분류 모델에서 가장 자주 쓰이는 손실 함수로, 확률론과 정보이론이 만나는 지점입니다. 분야 핵심 개념 AI 실무 연결 지점 선형대수 행렬 곱, 내적 신경망 순전파, 어텐션 선형대수 고유값·고유벡터 PCA, 차원 축소 선형대수 행렬 분해(SVD) 추천 시스템, NLP 확률통계 확률분포, 기댓값 소프트맥스, 분류 출력 확률통계 베이즈 정리 생성 모델, 불확실성 추정 확률통계 최대 우도 추정 손실 함수의 논리적 근거 확률통계 크로스 엔트로피 분류 모델 학습 활성화 함수와 역전파에서 미적분은 어떻게 작동하는가? 미적분은 신경망 학습의 핵심 메커니즘인 역전파(backpropagation)를 이해하는 데 필요합니다. 겁먹을 필요는 없습니다. AI 개발에서 실제로 필요한 미적분 개념은 크게 두 가지입니다. 1. 편미분과 기울기(gradient) 손실 함수는 모델의 가중치를 변수로 가지는 다변수 함수입니다. 학습이란 이 함수의 값을 줄이는 방향으로 가중치를 조금씩 조정하는 과정입니다. 이 '방향'을 계산하는 도구가 편미분이고, 모든 가중치에 대한 편미분을 모아놓은 것이 기울기(gradient)입니다. 경사하강법(gradient descent)은 이 기울기의 반대 방향으로 가중치를 업데이트합니다. 수식으로는 다음과 같습니다. 새 가중치 = 기존 가중치 − 학습률(lr) × 기
科技前沿
India's first privately-developed rocket reaches orbit on dramatic debut launch
"On the first attempt, reaching orbit, I never thought it was possible."
AI 资讯
DevLog #1: Re-entering the Matrix after years away
I’ve been out of context with my computer science degree for years, and honestly, it feels overwhelming. I want to change that, so I'm starting this log to document my comeback story, my failures, and my progress. What I did today: Acknowledged the starting line. Took 10 minutes to think about where I left off and what I need to tackle first. Decided to write daily logs. This is not my first attempt to finish the degree, but hopefully with some public eyes on it, it will be the last. 10 subject left. Starting with Mathematical analysis. The biggest challenge right now: Feeling completely out of context and fighting the urge to get distracted by everything else. Many things have changed since i was actively going to classes. My generation graduated many years ago and i feel like getting all the information I need will be extremely difficult since i don't know anyone. Getting information from the university websites and emailing professors will be slow. Next steps: Tomorrow, I'm going to try to overcome my overdramatic anxiety and post in the student groups I was in, in hope that somebody might have new information about the subjects. I will go start lesson #1. Goal is to ease into the material and start a habit, rather than pressuring myself to do everything at once. Come back tomorrow.
科技前沿
OPERATING SYSTEM
**🙄 فى كتاب chapter الصدمة دي هي بالظبط اللي حسيت بيها وأنا بقرأ أول “operating system: three easy Pieces “ ‘OSTEP’. 🖤اهلا بيكم ! يارب تكونوا بخير 💯 حابه اشارك معاكم رحلتى مع قراءة الكتاب ونستفيد منه سوا قبل ما نعرف هو !!!! ولا لا OS is virtual machine 🤔 !!!!دا يعنى ايه ووظيفته ايه OS تعالوا الاول نعرف ال موجودة فى الكمبيوتر ولا لا ؟؟؟؟ RAM وال CPUزى ال HARDWARE وهل هو قطعة ::هنبدأ من الاخر موجود على الكمبيوتر SW هو عبارة عن HW يسيدى مش قطعة OSال .على الجهازINSTALL ولازم يبقى ووظيفته ايه؟؟؟ OS طب يعنى ايه ‘OS’ اختصار “OPERATING SYSTEM”. .“يعنى نظام تشغيل “ .👁🗨👁🗨 تعالوا نعرف معنى ” نظام تشغيل” ونفسرها نظام تشغيل يعنى مسئول عن 1_ “HWالنظام “من غيره مش هيبقى فيه نظام خصوصا لقطع ال . يعنى بناخد منه الاذن للعمليات HW ببعضه وكمان بيدير ال HWيعنى هو بيربط ال 👏 . (Order)من الاخر بيخلق “النظام” 2_.”التشغيل “هو المسئول عن تشغيل البرامج Learn about Medium’s values هو اللي بيتحكم في دورة حياة البرنامج بالكامل؛هو اللي بيبدأ تشغيله في الذاكرة،OSيعني الـ وبيحدد هو محتاج إيه من إمكانيات الجهاز عشان يشتغل بكفاءة وبيفضل مراقبه ويحميه طول ما هوشغال ، ولحد ما تقفليه بنفسك 🌹 .ويقوم هو بتنظيف الذاكرة وتوفير المساحة لغيره 🧐::وظيفته بقا بيخلي البرنامج يشتغل بسهولة:1️⃣ لأنه بيخلق للبرنامج بيئة وهمية مريحة، وبيخفي عنه كل التعقيدات والأسلاك بتاعة الهاردوير عشان يشتغل بسلاسة 2️⃣: بيسمح للبرامج إنها تشارك الذاكرة بين كل البرامج بالعدل RAM بيشتغل كعسكري مرور بيوزع مساحة الـ . وبيحمي كل برنامج في مساحته الخاصة 3️⃣: بيمكن البرامج إنها تتعامل مع الأجهزة بيعمل كـ “وسيط” أو مترجم بيوصل كود البرنامج بالقطع الحقيقية (زي الشاشة أو الهارد) .عشان ينفذ أوامره فوراً بيعمل التلات حاجات دول إزاي في نفس الوقت وبمنتهى السلاسة؟ ؟؟؟OS طب الـ بيعملهم يسيدى عن طريق أكبر خدعة سحرية في عالم الكمبيوتروهي الـ Virtualization👌 كنت حابة جداً أكلمكم المرة دي عن خدعة الـ “Virtualization” 💎 😌👁👁اللي اتكلمنا عليها في العنوان، بس لقيت البوست هيبقى طويل أوي عليكم ✔🔥!!وعشان متعبكمش معايا.. هنخليها للبوست الجاي إن شاء الله 💯✅!!بيعمل الخدعة دي إزاي OSاستنوا البوست الجاى عشان نعرف الـ 💋.دمتم بخير **
AI 资讯
The Off Switch: Mammals May Have Been Hiding the Power to Regrow Themselves All Along
A salamander can lose a leg and grow a new one. Cut a zebrafish's fin and it simply builds another. Mammals, us included, got the consolation prize: a scar. For a century, biologists assumed that somewhere on the evolutionary road to becoming warm-blooded, fast-moving animals, we traded regeneration away for good. Two research teams working on opposite sides of the planet have just made that assumption look wrong. The headline is almost hard to believe: the ability to regrow lost body parts may not have been deleted from our biology at all. It may simply have been switched off, and switches can be flipped back on. The genetic "remote control" that stopped working The first clue comes from a team at the National Institute of Biological Sciences in Beijing, working with genomics powerhouse BGI-Research. Publishing in Science , they zeroed in on a gene called ALDH1A2 , the instruction sheet for an enzyme that turns vitamin A into retinoic acid, a molecule that acts like a foreman on a construction site, telling cells where to go and what to build during tissue repair. Animals that regenerate freely crank this gene up at the wound site. Mice, it turns out, still carry the same gene. They've just lost the genetic "remote controls," the regulatory DNA that tells the gene to fire after an injury. The hardware is intact; the software command was disconnected somewhere in evolution. So the researchers reconnected it. By reactivating that dormant switch and restoring the flow of retinoic acid, they got mice to regenerate damaged outer-ear tissue, something a normal mouse simply cannot do. In their own words, they had found "a genetic switch involved in the evolution of regeneration." Meanwhile, in Texas, they regrew a limb joint The second piece of evidence lands the point with force. At Texas A&M, a group led by Dr. Ken Muneoka took a different route to the same destination. Instead of editing a genetic switch, they used a precisely timed sequence of two signaling proteins.
产品设计
As mosquito ranges expand, better monitoring is key to preventing disease
Monitoring is expensive and labor intensive. But it helps public health officials stop outbreaks.
产品设计
The grueling, 630-mile road race where the only fuel is sunlight
On July 19th, dozens of teams of high school students will begin a five-day, 630-mile road race from Fort Worth to Fort Stockton in Texas. But this is not your typical contest. The students design and build the cars themselves, using off-the-shelf parts and 3D printed materials. The winner is the team that accumulates the […]
科技前沿
The Search for Another Earth-Like Planet Just Took a Big Step Forward
Astronomers have discovered a rocky exoplanet that has an atmosphere and sits within the habitable zone of a solar system.
AI 资讯
LOD (Law of Demeter)
Introdução O nome do princípio vem do próprio nome do projeto de pesquisa (que remete a Deméter, deusa grega da agricultura — a metáfora era "cultivar" software que cresce de forma incremental e adaptável, não do princípio de acoplamento em si). O projeto Demeter investigava como reduzir o custo de manutenção de sistemas orientados a objetos observando que boa parte das mudanças de software quebrava código muito distante do ponto onde a mudança real acontecia — um efeito cascata causado por classes que conheciam profundamente a estrutura interna de outras classes. Essa observação foi confirmada empiricamente alguns anos depois: em 1994, Chidamber & Kemerer publicaram as famosas métricas CK ( A Metrics Suite for Object Oriented Design ), nas quais o CBO (Coupling Between Objects) — quão acoplada uma classe é a outras — se tornou um dos preditores mais fortes de defeitos e esforço de manutenção em estudos empíricos posteriores de engenharia de software. Ou seja: a intuição por trás da Law of Demeter (menos acoplamento = menos bugs ao mudar código) tem respaldo em dados de décadas de pesquisa empírica em qualidade de software. Definição Também chamada de "Principle of Least Knowledge" , a formulação clássica é: Um método M de um objeto O só deve chamar métodos de: O próprio O Os parâmetros recebidos por M Qualquer objeto que M crie/instancie internamente Os componentes diretos de O (seus atributos/campos) Variáveis globais acessíveis a O Resumo popular: "use apenas um ponto" — evite código como: pedido . getCliente (). getEndereco (). getCidade (). getNome () Isso é conhecido como "train wreck" (trem de vagões) — cada . é um vagão acoplado ao anterior. Se a estrutura interna de Cliente ou Endereco mudar, todo código que fez essa travessia quebra, mesmo estando em um módulo completamente não relacionado. Porque isso importa na prática? Quando o método M faz objeto.getX().getY().metodo() , ele passa a depender da estrutura interna de X e Y , não só da interface pública d
科技前沿
FIFA Doesn’t Have a Plan to Deal With Climate Change
This year’s World Cup has faced sweltering heat and humidity. Now it may need to deal with wildfire smoke.
AI 资讯
How a Bookstore in Finland Reaches the Whole World
Week 0 of my DevOps Micro Internship was about the foundations—the parts of the internet you use every day without thinking about them. The exercise that made it click was a simple scenario: a friend launches an online bookstore called EpicReads, hosted on a server in Finland, and asks how people anywhere in the world can open it. The answer is a short chain of technologies working together. The Chain of Technologies Packet Switching: When someone opens the site, their request does not travel as one big lump. Packet switching breaks the data into small packets that each take the best available path across the network and get reassembled at the other end. This is what keeps the internet fast and resilient even across continents. IP Addresses & TCP/IP: Every device on the way has a unique IP address, like a postal address, so the user's computer and the Finland server can actually find each other. The TCP/IP suite runs the conversation: IP handles addressing and routing, while TCP makes sure the packets arrive complete and in the right order, asking again for anything that went missing. HTTP & HTTPS: On top of that sits HTTP and HTTPS, which define how the browser and server actually exchange the web pages. HTTPS adds encryption, so a customer's details and payment stay private. DNS: The last piece is DNS. Nobody wants to type an IP address, so DNS acts as the internet's phonebook, translating epicreads.com into the server's IP. To point a domain at an IPv4 address, you use an A record . The Biggest Takeaway The biggest lesson for me was not any single term. It was seeing how these layers hand off to each other so cleanly that the whole thing feels instant to a user. Understanding that chain is the groundwork for everything else in DevOps, because once you know how a request really travels, troubleshooting stops being guesswork. P.S. This post is part of the DevOps Micro Internship with Agentic AI Cohort 3 by Pravin Mishra. You can begin your DevOps journey by joining
创业投融资
İlk İnsanlı Katı-Hal Uçuşunun Mühendisliği: Elektrikli Uçakta Duvar Neden Hep Batarya?
İlk insanlı katı-hal uçuşu manşetlere düştüğünde çoğu haber "yeni motor" diye başladı. Oysa bir mühendisin gözünde olay motorda değil. Elektrik motoru bu denklemde en çözülmüş parça: hafif, sessiz, yüksek verimli. Asıl kararların döndüğü yer, o motoru besleyen enerjinin nasıl depolandığı. Bu yazı, duvarın neden onlarca yıl boyunca hep aynı yerde — bataryada — durduğunu sistem mühendisliği açısından ele alıyor. Sistem kısıtı: enerjiyi değil, ağırlığı taşırsınız Bir uçağı tasarlarken bütçeniz enerji değil, kütledir. Depoladığınız her watt-saat bir ağırlıkla gelir ve bu ağırlık kaldırma kuvvetiyle ödenmek zorundadır. Ölçüt enerji yoğunluğu , yani Wh/kg. Kerosen bu metrikte devasa bir avantaja sahip olduğu için jetler onlarca yıl tartışmasız kazandı. Elektrikli havacılığın tüm hikâyesi, bu tek sayıyı yukarı çekme mücadelesidir. Neden hep batarya? Kısır döngünün matematiği Menzili artırmak için daha fazla batarya eklersiniz. Ama batarya ağırdır; eklediğiniz kütle daha fazla kaldırma, dolayısıyla daha fazla enerji ister. O ek enerji için yine batarya eklersiniz ve döngü kendini besler. Buna ağırlığın kısır döngüsü denir ve bir sistem sınırıdır: hücrenin Wh/kg değeri belli bir eşiği aşmadıkça, motoru ne kadar iyileştirirseniz iyileştirin duvar yerinde durur. Kararın kaldıraç noktası bu yüzden hücre kimyasıdır. Kimyayı değiştiren tasarım kararı Bugünün lityum-iyon hücreleri pratikte ~260 Wh/kg dolayında bir tavana oturur. Bu tavanın altında yatan iki bileşen sıvı elektrolit ve grafit anottur. Katı-hal yaklaşımı burada iki radikal karar verir: sıvı elektroliti katı bir iletkenle değiştirir ve anodu lityum-metale taşır. Sonuç ~410 Wh/kg, yani mevcut tavanın %60'tan fazla üstü. Yan kazanım da en az ana kazanım kadar önemli: yanıcı sıvı ortadan kalkınca termal kaçış riski düşer, hücre daha kararlı olur ve 15 dakikanın altında %80 şarj operasyonel olarak mümkün hâle gelir. Bu üç sayı tek başına değil, birlikte anlam kazanır. Havacılıkta bir aracın yerde geçirdiği süre doğrudan m
开源项目
Taylor Farms pulls iceberg lettuce from the US market after cyclosporiasis outbreak
Food producer Taylor Farms released a statement on the Cyclospora outbreak Friday, confirming that it's "voluntarily removing all iceberg lettuce sourced from central Mexico from the US market." Reuters reports that, according to a source, Taylor Farms told customers like Yum Brands owner Taco Bell and the food distributor Sysco on Thursday to pull shredded […]
AI 资讯
What Cities From Chicago to Washington, DC, Look Like Under a Blanket of Wildfire Smoke
The US is home to some of the most polluted air on the planet as smoke from 120 out-of-control Canadian wildfires drifts across the border.
AI 资讯
Troubling new details emerge on diabetes ouster controversy
American Diabetes Association blocked publication of op-ed articles so the authors posted them as a preprint.
AI 资讯
How to Scrape Airbnb Listings and Prices in 2026 (No Code Required)
Heads-up: this post references a tool I built. It's a genuinely useful walkthrough either way — the technique applies to any Airbnb scraping project. If you've ever tried to scrape Airbnb, you already know the two walls you hit: the pages are rendered by JavaScript, and Airbnb aggressively blocks datacenter IPs. Below is the reliable way to get clean Airbnb data in 2026 — listing prices, ratings, coordinates, and discounts — without running a headless browser or babysitting proxies. The key insight: Airbnb ships its data in the HTML You don't need to render the page. Every Airbnb search response embeds the full result set as JSON inside a <script id="data-deferred-state-0"> tag. Parse that and you get structured data straight away — no DOM scraping, no selectors that break on the next redesign. The path to the results is: niobeClientData[*][1].data.presentation.staysSearch.results ├── searchResults[] // ~18 listings per page └── paginationInfo.pageCursors[] // all page cursors, upfront Each listing carries a base64-encoded ID in demandStayListing.id (decode it, take the segment after the last colon, and you have the numeric listing ID for airbnb.com/rooms/<id> ), a price line with discounts, avgRatingLocalized ("4.95 (123)"), and GPS coordinates. The two gotchas Datacenter IPs get blocked. You need residential proxies. If a response comes back without the data-deferred-state marker, you've been served a bot check — rotate to a fresh IP and retry. ~270 result cap per search. Airbnb won't paginate past ~15 pages. To cover a whole market, split into narrower searches (by price band or neighborhood) and dedupe by listing ID. The no-code way If you'd rather not maintain proxy pools and parsers, I published an Airbnb Scraper on Apify that does exactly the above. Paste a location or a full Airbnb search URL (every filter is honored), and get flat JSON/CSV back. curl -X POST "https://api.apify.com/v2/acts/ethanteague~airbnb-scraper/run-sync-get-dataset-items?token=YOUR_TOKE
开发者
The manosphere’s testosterone fever is coming for the troops
This is Optimizer, a weekly newsletter sent from Verge senior reviewer Victoria Song that dissects and discusses the latest gizmos and potions that swear they're going to change your life. Opt in for Optimizer here. I was in the middle of writing a different Optimizer column this week when I learned that Pete Hegseth is […]
开源项目
The report oil companies are worried about: Climate attribution science
New report says our ability to tie weather damages to climate change is improving.
科技前沿
The war on ‘woke science’ comes for space research
The Trump administration is waging a culture war on science, and the latest salvo is in the form of a dry, bureaucratic proposal from the Office of Management and Budget (OMB) that could threaten the future of US science as we know it. The proposal would give political appointees unprecedented control over grant funding, the […]
开发者
The CDC Has a Cyclospora Lab. DOGE Downsized It Last Year
“Based on simple math, these outbreak responses—which require rapid, timely responses—are going to be greatly diminished,” the former CDC lab director tells WIRED.