Grok 4.5, based on our 1.5T V9 foundation model, with Cursor data added in supplemental training, is now in private beta at SpaceX & Tesla. Early evals show performance close to, perhaps exceeding Opus.
RL is continuing to significantly improve the model, and the Grok Build harness gets better every day.
Nice work by all those involved!
Completely trained from scratch new models will be released by @SpaceX every month this year.
Nancy Lynch's Distributed Algorithms is the kind of book where you read one page, stare at the wall for 10 minutes, and come back smarter.
Genuinely one of the best things you can read if you work in distributed systems.
The entire core of a neural network on four cards.
Neuron, forward pass, activations, backprop. Learn these four and you understand how every model from a perceptron to a transformer predicts and learns.
The beauty of C
If you want to understand how things works in your pc just read the C code, elegant, clear and straight to the point.
fcopy implementation (how to copy a file).
a hash map in 25 lines of C
FNV-1a handles the hashing, start with a fixed value and XOR each byte multiply by a prime and repeat
the interesting part is the last line
instead of using hash % cap it uses hash & (cap - 1)
same result when the capacity is a power of two
and a bitwise AND is generally cheaper than a modulo operation
another neat detail is the use of void pointers for values
the hash map does not care what type you store
integers strings structs anything works
the caller handles the casting when storing and retrieving data
Little software design decisions have a big impact on performance.
Array-of-Structs vs Struct-of-Arrays is a neat example. This "small" difference for in-memory state organization drastically changes cache utilization and hit rate. In turn, you can get order-of-magnitude performance differences.
It's similar to the row-oriented vs column-oriented layouts for data systems. Which to choose depends on expected access patterns (OLTP vs OLAP).
Farad's article on this is quick read and easy to follow. Link below.
FREE Math Book. 598 pages.
"A Computational Introduction to Number Theory and Algebra" by Shoup.
Contents:
Basic properties of the integers
Congruences
Computing with large integers
Euclid’s algorithm
The distribution of primes
Abelian groups
Rings
Finite and discrete probability distributions
Probabilistic algorithms
Probabilistic primality testing
Finding generators and discrete logarithms
Quadratic reciprocity and computing modular square roots
Modules and vector spaces
Matrices
Subexponential-time discrete logarithms
More rings
Polynomial arithmetic and applications
Linearly generated sequences and applications
Finite fields
Algorithms for finite fields
Deterministic primality testing
"All of the mathematics required beyond basic calculus is developed 'from scratch.' Moreover, the book generally alternates between 'theory' and 'applications.' The choice of topics covered in this book was motivated primarily by their applicability to computing and communications, especially to the specific areas of cryptography and coding theory. Thus, the book may be useful for reference or self-study by readers who want to learn about cryptography, or it could also be used as a textbook in a graduate or upper-division undergraduate course on (computational) number theory and algebra, perhaps geared towards computer science students."
Link: https://t.co/9bUumLgYpZ
Virtual Machine vs Container vs Serverless
𝗩𝗶𝗿𝘁𝘂𝗮𝗹 𝗠𝗮𝗰𝗵𝗶𝗻𝗲𝘀 run a full operating system on top of virtualized hardware. They give you strong isolation and more control over the environment, but they are heavier because each VM carries its own OS.
𝗖𝗼𝗻𝘁𝗮𝗶𝗻𝗲𝗿𝘀 package an application with its dependencies and run as isolated processes on a shared host kernel. They are lighter than VMs, easier to move across environments, and commonly used for deploying microservices.
𝗦𝗲𝗿𝘃𝗲𝗿𝗹𝗲𝘀𝘀 𝗙𝘂𝗻𝗰𝘁𝗶𝗼𝗻𝘀 let you deploy small units of code without managing the underlying servers. The cloud provider handles provisioning, scaling, and execution, which makes them useful for event-driven tasks like APIs, scheduled jobs, and queue processing.
Modern systems rarely pick one. It's common to see containers running inside VMs while serverless functions handle specific event-driven tasks, with each technology used for the workloads it suits best.
What else would you add?
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"Elementary Calculus: An Infinitesimal Approach" is an interesting introduction to calculus that presents familiar topics from a different perspective.
The book covers limits, derivatives, integrals, and infinite series, but develops them using infinitesimals rather than the approach found in most standard calculus textbooks. Even for readers already familiar with calculus, it offers a fresh way of thinking about some of its central concepts.
It is a worthwhile read for anyone interested in calculus, mathematical foundations, and alternative viewpoints on limits, derivatives, and integrals.
https://t.co/SxDEgCXQ0Y