The Secret CIO

#digitaltransformation Expert #CIO

[Dhanian 🗯️ @e_opore]

THE MATH YOU NEED TO START UNDERSTANDING LLMS

THE FOUNDATION BEHIND MODERN AI MODELS

Large Language Models (LLMs) are powered by mathematics. Behind every prediction, embedding, and generated response is a combination of linear algebra, probability, calculus, and optimization. You do not need a PhD in mathematics to start learning LLMs, but understanding the core concepts gives you a major advantage.

LINEAR ALGEBRA — THE LANGUAGE OF LLMS

→ VECTORS
Vectors represent words, tokens, and embeddings inside neural networks.

→ MATRICES
Matrices store and transform large amounts of numerical data efficiently.

→ DOT PRODUCT
Used to measure similarity between embeddings and power attention mechanisms.

→ MATRIX MULTIPLICATION
Core operation behind neural network computations and transformer architectures.

→ EIGENVECTORS & DIMENSIONALITY
Help models compress and organize information in high-dimensional spaces.

PROBABILITY & STATISTICS — HOW MODELS PREDICT

→ PROBABILITY DISTRIBUTIONS
LLMs predict the probability of the next token in a sequence.

→ CONDITIONAL PROBABILITY
Used to estimate the likelihood of words based on previous context.

→ MEAN, VARIANCE & STANDARD DEVIATION
Important for normalization and understanding data distributions.

→ BAYESIAN THINKING
Helps explain uncertainty and prediction confidence in AI systems.

→ SOFTMAX FUNCTION
Converts model outputs into probabilities for token prediction.

CALCULUS — HOW MODELS LEARN

→ DERIVATIVES
Measure how changes in parameters affect model outputs.

→ GRADIENTS
Guide neural networks toward lower error during training.

→ CHAIN RULE
Critical for backpropagation across deep neural networks.

→ OPTIMIZATION FUNCTIONS
Used to minimize loss and improve prediction accuracy.

OPTIMIZATION — TRAINING LARGE MODELS

→ GRADIENT DESCENT
The foundation of neural network training.

→ LEARNING RATE
Controls how fast or slow a model updates weights.

→ LOSS FUNCTIONS
Measure how wrong the model’s predictions are.

→ REGULARIZATION
Helps prevent overfitting and improves generalization.

INFORMATION THEORY — UNDERSTANDING TOKENS

→ ENTROPY
Measures uncertainty in predictions.

→ CROSS-ENTROPY LOSS
Common loss function used in transformer-based models.

→ TOKENIZATION
Breaks text into smaller units for model processing.

THE MOST IMPORTANT CONCEPT FOR TRANSFORMERS

→ ATTENTION MECHANISM
Allows models to focus on relevant words in a sequence.

The attention mechanism heavily relies on matrix multiplication, vector similarity, and probability distributions.

WHY THIS MATH MATTERS

→ Helps you understand how transformers actually work
→ Makes debugging and fine-tuning easier
→ Improves your understanding of embeddings and token prediction
→ Gives you a strong foundation for AI engineering and research

BEST WAY TO LEARN THE MATH

→ Start with linear algebra basics
→ Learn probability before deep learning
→ Understand derivatives conceptually before advanced calculus
→ Practice with small neural network examples
→ Focus on intuition before equations

TOOLS THAT MAKE LEARNING EASIER

→ NumPy for matrix operations
→ PyTorch for tensor computations
→ Jupyter Notebook for experiments
→ Visualization tools for gradients and embeddings

FINAL THOUGHT

You do not need to master every mathematical field before building with LLMs. Start with the fundamentals, connect the concepts to real AI systems, and learn progressively as you build projects.

MASTER LLMS IN DEPTH
Grab the complete LLMs Handbook here:
https://t.co/ljEMt0UNUI

[Brett Adcock @adcock_brett]

In the last 120 days, Figure scaled manufacturing 24x - from 1 robot/day to 1 robot/hour

We will manufacture 55 humanoid robots this week

[Neo Kim @systemdesignone]

If you're serious about system design (in 2026), learn these 26 case studies:

1 How Stock Exchange Works:
↳ https://t.co/iFNSX9TM9O

2 How YouTube Works:
↳ https://t.co/kHk3g6jz6t

3 How Kafka Works:
↳ https://t.co/8rOy9KgCMo

4 How Google Docs Works:
↳ https://t.co/W57IkAjXpT

5 How URL Shortener Works:
↳ https://t.co/tGndgdhH0V

6 How WhatsApp Works:
↳ https://t.co/VScq8QwHMr

7 How Airbnb Works:
↳ https://t.co/Bi5SAjfv5S

8 How Spotify Works:
↳ https://t.co/BxrH3oHIFS

9 How Slack Works:
↳ https://t.co/eIo29uOQOJ

10 How Reddit Works:
↳ https://t.co/o6Pw2hhj3T

11 How Bluesky Works:
↳ https://t.co/2rLYlRlky0

12 How Tinder Works:
↳ https://t.co/4E1zfgfvlw

13 How Twitter Timeline Works:
↳ https://t.co/pF2RYmPaIG

14 How Uber Finds Nearby Drivers:
↳ https://t.co/kJ2t8dtmch

15 How Pastebin Works:
↳ https://t.co/8NSUNlYM7q

16 How Amazon S3 Works:
↳ https://t.co/iReWAEHwmj

17 How Do Apple AirTags Work:
↳ https://t.co/upWcgsXwKh

18 How LLMs Actually Work:
↳ https://t.co/5lCKxq2g4N

19 How Uber Computes ETA:
↳ https://t.co/hw1hYJqQmj

20 How Real Time Leaderboard Works:
↳ https://t.co/HEChNTOHWb

21 How ChatGPT Apps Work:
↳ https://t.co/BJTYYnAwO1

22 How Nginx Works:
↳ https://t.co/JTeQTJvyrf

23 How ChatGPT Works:
↳ https://t.co/TZYZ3iddYH

24 How Meta Serverless Works:
↳ https://t.co/NSt6jovxu5

25 How YouTube Was Able to Support 2.49 Billion Users With MySQL:
↳ https://t.co/4VDJ5cs6fL

26 How Google Search Works:
↳ https://t.co/jwOaC4bhnv

What else should make this list?

===

👋 PS - Want my System Design Playbook for FREE?

Join my newsletter with 200K+ software engineers now:
→ https://t.co/ByOFTtOihX

===

1 Save & RT to help other software engineers ace system design.
2 Follow @systemdesignone + turn on notifications.

[McKinsey Global Institute @McKinsey_MGI]

AI won’t make most human skills obsolete, but it will change how they’re used.

Negotiation, problem solving, and leadership will matter more than ever as people work alongside agents and robots.

Our new Skill Change Index shows which skills will be most, and least, exposed to automation in the next five years: https://t.co/fRXfHF1k56

[Python Programming @PythonPr]

Convolutional Neural Network
Image Credit- Aqeel Anwar

[Giuliano Liguori @ingliguori]

30 AI algorithms that power modern AI 👇

📊 Linear & Logistic Regression
🌲 Random Forest
⚡ XGBoost
🎯 SVM
🔍 k-Means / DBSCAN
📉 PCA / t-SNE
🎮 Q-Learning / DQN
🧠 ANN / CNN / RNN / LSTM
🔁 Transformers
🧬 Genetic Algorithms

Master the foundations → master AI.

[McKinsey & Company @McKinsey]

#GenAI is here—and it’s poised to transform businesses across industries. But there are risks to consider, too.

Learn how companies can manage the risks of gen AI—starting with an honest conversation about what risks they are willing to take. https://t.co/pWNKhJyUac

[Enrico Molinari #VivaTech2025 @enricomolinari]

#GenerativeAI in the Finance function of the Future

Source @BCG

📌 #GenerativeAI #GenAI #marketing #fintech #AI #govtech #finserv #ehealth #insurtech #web3 #neobanks #payments #ModelOps #DevOps #RStats #flutter #Metaverse #TensorFlow #Python #CyberSecurity #blockchain #NFTs #smartcities #ESG #SDGs #innovation #bigdata #MachineLearning #cloud #ehealth #marketing #ChatGPT #ML #DataScience #CloudComputing #Robotics #programming #enricomolinari @EvanKirstel @sonu_monika @chidambara09 @tlloydjones @danfiehn @sebbourguignon @MaiaGabunia @smaksked @LavaletteAstrid @arlenenewbigg @RosyCoaching @mdrechsler @sim010101 @pierrepinna @pierrecappelli @GlenGilmore @pchamard @thierry_pires @vanivina9 @KanezaDiane @mary_gambara @drsharwood @Sharleneisenia @1OFFGINGER @andresvilarino @mdrechsler @fernandolofrano @gvalan @HeinzVHoenen @EstelaMandela @FmFrancoise @Hana_ElSayyed @DanielleLargier @Ym78200 @aure79lien @SANDDELA @tewoz @Gaellepicardabe @Nad_Alves @AzurFlorian @NadiaCalvino @jesuisdigital @ELCavalos @HervePoussineau

[ipfconline @ipfconline1]

The 6 Stages for a Successful Digital Transformation [Infographic]
#DigitalTransformation #DigitalMarketing #Business

[Alex & Books 📚 @AlexAndBooks_]

The best place to read or write a book is on a plane with no wifi.

[Aryan Rakib @tec_aryan]

The future is here and it looks like science fiction.

Here are 15 Mind-Blowing Inventions that will shock you.

Number 12 is Truely Impressive:

[Harvard Business Review @HarvardBiz]

“No one can teach you how to lead; you need to be willing and able to learn how to lead. Mostly we learn from our experiences and facing adversity. Stepping outside of the spaces where we feel safe — is a powerful teacher.” https://t.co/wP1BqqQmnt

[Harvard Business Review @HarvardBiz]

In a study of 60 leaders, those who were most successful in overcoming resistance were the ones who diagnosed the root of a disagreement before trying to persuade. https://t.co/wA4ll3N7MG

[Harvard Business Review @HarvardBiz]

The best way to build a successful career is to put in the work right now: Grow your skills, take on lateral responsibilities, and work at companies and with people who will build up your credibility. https://t.co/Hh8pTNWL6a

[Harvard Business Review @HarvardBiz]

Many leaders think that they’re coaching their employees, but they’re just telling them what to do. https://t.co/4cZOpK9cwJ

[Harvard Business Review @HarvardBiz]

Leaders must always be learning and adapting — and inspiring their employees to do the same. https://t.co/c310Extej8

[Harvard Business Review @HarvardBiz]

"Acumen, allocation, and action — the ability to think, plan, and do — are what separate strategic thinkers from the rest." https://t.co/WUcRr7MYsG

[Microsoft @Microsoft]

That's a wrap on Day 1 of #MSIgnite ✨

[Harvard Business Review @HarvardBiz]

Smart people often forget that relationship-building is important, too. https://t.co/DYbMXfSUHf

[Deep Psychology @DeepPsycho_HQ]

If you have ego, read this :