GM

[Reso @Resorcinolworks]

I still think about this.

[Alex Zajac (🍔,🧠) @itsalexzajac]

An engineer built an interactive book on data structures and algorithms of 680 pages:

[tut_ml @tut_ml]

Best CNN Courses- https://t.co/ep7RM3P809

[Marcos Alvarado @marcosalvarado_]

No AI. Just acrylic paint and canvas and a deep love for symbolism

[Jonathan Sánchez Pérez 🚀⭐️ @Mexican_Space]

Cada clic y cada compartida me acerca más al espacio 🚀🌌.
Apóyame en esta carrera para que un mexicano llegue más allá de las estrellas 🇲🇽✨.
#BlueOrigin #SERASpace #MexicanoEspacial @seraspaceage @blueorigin

[Brian Roemmele @BrianRoemmele]

Fast Fourier Analysis.

[ani @anirudhbv_ce]

We finally know why LLMs hallucinate. It's not the model. It's the geometry.

@OpenAI text-embedding-3-large: 91/3072 dimensions do real work.

@GeminiApp gemini-embedding-001: 80/3072 dimensions do real work.

~97% of your vector database is mathematically empty. Your RAG system is retrieving from noise.

@ashwingop and I present "The Geometry of Consolidation" - a proof that RAG compression has a hard floor no algorithm can beat, set by a single spectral number your embedding model cannot escape.

Every hallucination your RAG pipeline produces? This is why.

Paper + results: https://t.co/zut8pdoPbH

[Mushtaq Bilal, PhD @MushtaqBilalPhD]

Sci-Hub, the evil website that pirated 88M+ research papers and made them freely available has added another evil feature.

If you run a DOI and open a paper, Sci-Hub can give you similar and related papers.

Click on the three horizontal dots or the arrow and it will show you similar papers.

Don't do it.

[Vivek Galatage @vivekgalatage]

Algorithms by Jeff Erickson - one of the best algorithm books out there.

The illustrations make complex concepts surprisingly easy to follow. Highly recommend this.

https://t.co/8G06RjGnMA

[Michael Pyrcz🌻 @GeostatsGuy]

When I teach Principal Component Analysis (PCA), I explain it from three complementary perspectives:

1. Best-fit lines, planes, and hyperplanes
2. Coordinate rotation
3. Eigenvalues and eigenvectors

For the second perspective, I use an interactive Python dashboard to perform PCA by hand, showing how rotating the coordinate system maximizes the variance captured by the first component while producing uncorrelated components. Stoked!

[GM @enrigm20]

@miniapeur Bayesian inference + mcmc is top tier

[Elias @iam_elias1]

MIT just made every AI company's billion dollar bet look embarrassing.

They solved AI memory. Not by building a bigger brain. By teaching it how to read.

The paper dropped on December 31, 2025. Three MIT CSAIL researchers. One idea so obvious it hurts. And a result that makes five years of context window arms racing look like the wrong war entirely.

Here is the problem nobody solved.

Every AI model on the planet has a hard ceiling. A context window. The maximum amount of text it can hold in working memory at once. Cross that line and something ugly happens — something researchers have a clinical name for.

Context rot.

The more you pack into an AI's context, the worse it performs on everything already inside it. Facts blur. Information buried in the middle vanishes. The model does not become more capable as you feed it more. It becomes more confused. You give it your entire codebase and it forgets what it read three files ago. You hand it a 500-page legal document and it loses the clause from page 12 by the time it reaches page 400.

So the industry built a workaround. RAG. Retrieval Augmented Generation. Chop the document into chunks. Store them in a database. Retrieve the relevant ones when needed.

It was always a compromise dressed up as a solution.

The retriever guesses which chunks matter before the AI has read anything. If it guesses wrong — and it does, constantly — the AI never sees the information it needed. The act of chunking destroys every relationship between distant paragraphs. The full picture gets shredded into fragments that the AI then tries to reassemble blindfolded.

Two bad options. One broken industry. Three MIT researchers and a deadline of December 31st.

Here is what they built.

Stop putting the document in the AI's memory at all.

That is the entire idea. That is the breakthrough. Store the document as a Python variable outside the AI's context window entirely. Tell the AI the variable exists and how big it is. Then get out of the way.

When you ask a question, the AI does not try to remember anything. It behaves like a human expert dropped into a library with a computer. It writes code. It searches the document with regular expressions. It slices to the exact section it needs. It scans the structure. It navigates. It finds precisely what is relevant and pulls only that into its active window.

Then it does something that makes this recursive.

When the AI finds relevant material, it spawns smaller sub-AI instances to read and analyze those sections in parallel. Each one focused. Each one fast. Each one reporting back. The root AI synthesizes everything and produces an answer.

No summarization. No deletion. No information loss. No decay. Every byte of the original document remains intact, accessible, and queryable for as long as you need it.

Now here are the numbers.

Standard frontier models on the hardest long-context reasoning benchmarks: scores near zero. Complete collapse. GPT-5 on a benchmark requiring it to track complex code history beyond 75,000 tokens — could not solve even 10% of problems.

RLMs on the same benchmarks: solved them. Dramatically. Double-digit percentage gains over every alternative approach. Successfully handling inputs up to 10 million tokens — 100 times beyond a model's native context window.

Cost per query: comparable to or cheaper than standard massive context calls.

Read that again. One hundred times the context. Better answers. Same price.

The timeline of the arms race makes this sting harder. GPT-3 in 2020: 4,000 tokens. GPT-4: 32,000. Claude 3: 200,000. Gemini: 1 million. Gemini 2: 2 million. Every generation, every company, billions of dollars spent, all betting on the same assumption.

More context equals better performance.

MIT just proved that assumption was wrong the entire time.

Not slightly wrong. Fundamentally wrong. The entire premise of the last five years of context window research — that the solution to AI memory was a bigger window — was the wrong answer to the wrong question.

The right question was never how much can you force an AI to hold in its head.

It was whether you could teach an AI to know where to look.

A human expert handed a 10,000-page archive does not read all 10,000 pages before answering your question. They navigate. They search. They find the relevant section, read it deeply, and synthesize the answer.

RLMs are the first AI architecture that works the same way.

The code is open source. On GitHub right now. Free. No license fees. No API costs. Drop it in as a replacement for your existing LLM API calls and your application does not even notice the difference — except that it suddenly works on inputs it used to fail on entirely.

Prime Intellect — one of the leading AI research labs in the space — has already called RLMs a major research focus and described what comes next: teaching models to manage their own context through reinforcement learning, enabling agents to solve tasks spanning not hours, but weeks and months.

The context window wars are over.

MIT won them by walking away from the battlefield.

Source: Zhang, Kraska, Khattab · MIT CSAIL · arXiv:2512.24601
Paper: https://t.co/ngovOSNrCQ
GitHub: https://t.co/gT0ootCNoa

[Matt Dancho (Business Science) @mdancho84]

Understanding regression models is essential in data science.

In 4 minutes, I'll demolish your confusion. Let's go:

[How To Prompt @HowToPrompt__]

Researchers just proved that every single elementary function, sin, exp, log, sqrt, comes from one single binary operator.

It is like finding the “God Particle" for calculus.

In computer science, every complex program breaks down to a single logical operator: the NAND gate. It is the fundamental building block of all digital reality.

But for continuous math, physics, engineering, machine learning, we thought we needed a massive toolbox.

Addition. Subtraction. Trigonometry. Logarithms.

Every scientific calculator and neural network has to juggle all of them.

Until today.

But this paper proved that every single mathematical function can be generated by a single, bizarre binary operator.

eml(x,y) = exp(x) - ln(y).

Combine that with the number 1, and you can build everything.

Pi. The square root. Sine and Cosine. Arithmetic.

It is all just the exact same operator, repeating over and over again in a binary tree.

Nobody anticipated this existed. It was found by systematic exhaustive search.

But the implications for AI are massive.

Instead of an AI struggling to combine different mathematical rules to discover a new scientific law, it can just use a single, uniform architecture.

One trainable circuit. One repeatable node.

We thought the language of the universe was complex.

It turns out, it's just one equation repeating in the dark.

[gabrielle @legitimatetiger]

how it feels to accept that reality is just a carbon-based simulation where your infinite consciousness gets to play as a human avatar and remember itself as the creator of all experience despite the inherent limitations of a fragile physical existence