I engineer systems where advanced hardware physics meets real-time intelligent software. 🛰️💻🧠Backed by a PhD track & 4 specialized Master's degrees, I map complex mathematics into deterministic, bare-metal production code.Below is a breakdown of my engineering focus: 👇
"A Mathematical Explanation of Transformers" is a recent paper that develops a rigorous mathematical framework for understanding the architecture behind Transformers and large language models.
It interprets the Transformer as a discretization of a continuous integro-differential equation, with self-attention represented as a non-local integral operator, layer normalization as a projection onto a constrained set, and feedforward layers and activation functions incorporated into the same mathematical framework, then uses operator splitting and numerical discretization to recover the standard Transformer architecture and extend the formulation to multi-head attention, Vision Transformers, and convolutional Transformers.
I've already shared several resources on the mathematics behind neural networks, Transformers, and LLMs, but there always seems to be something new and interesting to explore in this area.
https://t.co/18IZwRRDZS
Here is a beautiful integral I worked on today. Just observe the different closed-forms of this integral
It looks complicated, but periodicity removes the distracting triple oscillation. Reflection symmetry simplifies the inverse-tangent terms, while a complex logarithm reveals the hidden factorization. A classical logarithmic cosine identity then gives an explicit algebraic closed form. The same approach also produces elegant binomial, gamma, and hypergeometric representations.
instead of watching 2 hours of Netflix tonight, watch this Stanford lecture
it's the clearest explanation I've seen of how ChatGPT and Claude actually work
useful whether you've never touched AI in your life or have been using it every day for the past year
i took the key ideas and turned them into a practical guide on how to actually get 100% out of AI
you can find it below with ready-to-copy prompts and solutions
Free PDF of my new Optimization book:
https://t.co/2QQMQMJqr2
If you like it, check it out on Amazon or at Cambridge University Press!
Please leave a review and email me with any typos/corrections.
"Introduction to Machine Learning" by Laurent Younes
If you already know the core ML concepts, this textbook is a great next step to learn or refresh the math behind them.
It explains:
- optimization, SGD, and Adam
- bias–variance
- regression, SVMs, and kernels
- decision trees
- neural networks
- graphical and generative models
- clustering
- generalization bounds
Though it’s a math book, it still covers the key ML methods along the way.
Check out my production-ready flight code and firmware nodes on GitHub: https://t.co/DZxMO3hzBt Let's connect! Academic publications can be tracked via my ORCID and Google Scholar profiles
I engineer systems where advanced hardware physics meets real-time intelligent software. 🛰️💻🧠Backed by a PhD track & 4 specialized Master's degrees, I map complex mathematics into deterministic, bare-metal production code.Below is a breakdown of my engineering focus: 👇
3/ Structural Energy Storage 🔋
Bridging materials science with flight vehicle efficiency. My doctoral research focuses on high-tensile multifunctional composites for ambient-temperature structural sodium-ion batteries and supercapacitors
For #Pi day. Here are some beautiful integrals that can produce (π/e)^n. They connect analysis and number theory, hinting at fresh routes toward proving irrationality.
#mathematics#piday
A free comprehensive textbook – Linear Algebra for Computer Vision, Robotics, and Machine Learning
Covers both, essential theory and computation:
- vector spaces, matrices, norms
- eigenvalues, SVD, numerical algorithms
- applications like PCA, graphs, wavelets, and 3D rotations
Happy to share my new published paper (third and final paper of my PhD)
Fabrication and characterization of high-tensile-strength PEO–PVP blend-based multifunctional composites for sodium-ion structural batteries - now published in Materials Advances https://t.co/CLdBeyNWxJ