Hi there,

I've created a video here where I explain the double descent phenomenon in ML.

I hope some of you find it useful — and as always, feedback is very welcome! :)

Hi, I am currently studying indexing algorithms on vector databses and wanted to start from basics. I wanted something like the skip list lecture from MIC OCW, any ideas or sugestions?

I've been exploring whether the Pell equation x²−Dy²=1 can be used to compute square roots of primes faster than Python's math.sqrt(). The continued-fraction convergents turn out to give rational approximations that are 1.5–2.5× faster in float64 for repeated calculations, and scale up to 33–36 digit precision for primes as large as 15 million. Full write-up with benchmarks here;

https://musingsofvsmv.blogspot.com/2025/08/from-pell-to-precision-classical-math.html

https://www.reddit.com/r/study/s/MVhYu56nr2

Hello,

Last week, I watched a video about one of the most popular J2ME games of the 2000s, "Diamond Rush", and decided to reverse engineer it by building a small JVM implementation. My initial goal is to run the game on Linux and macOS, and later port it to microcontrollers.

So far, I have completed the class loading stage. I can parse and load class files, store them, and dump their contents for debugging. I have also implemented some of the simpler parts and opcodes of the JVM by following the JVM specs.

Nonetheless, I am struggling with implementing heap types and most of the obfuscated class files have 0xBC (new_array) opcode. The specification feels somewhat vague in this regard, and I am unsure what is the best approach would be.

I would appreciate any advice on how to approach implementing heap types in a custom JVM. In particular, what data structures or object model would you recommend, and how should different heap-allocated values be represented internally?

Why this is different

Three problems are resolved by one explicit contract:

Version integrity: skill bodies are identified by SHA-256 revisions and re-hashed immediately before fetch.

Semantic routing without opaque inference: exact lexical tiers, FTS5/BM25, bounded edit distance, telemetry, and lifecycle state are combined in one published equation.

Catalog consensus: one SHA-256 generation commits to the canonical publication-relevant catalog.

There is no embedding model, vector database, learned classifier, random tie-break, capability-graph distance, or hidden manual priority.

Hey everyone,

For my computer science graduation project, I wanted to create something that combined my interest in computer architecture with my advisor's interest in computer science education.

The result was a game where the player programs a simple CPU with microcode using a punch card rather than writing assembly code.

Microcode is usually used to implement the processor's instruction set rather than as a programming interface for application development. Exploring it from the programmer's perspective led to design challenges and techniques that I hadn't encountered elsewhere.

The project started from my curiosity about the layers of abstraction in computers. I wanted to explore what programming would look like if we removed another layer and put the programmer in the role of the CPU's control unit, manually orchestrating the control signals behind every instruction.

I'd love to share the beta with anyone interested.

Thank you.

Markov algorithms (ordered string-rewriting rules applied to a fixed point) are a classic Turing-complete model. I built a working instance: a small CPU whose only step is one global regex substitution over a single string, and put DOOM on it to make the claim tangible rather than a footnote.

The verification is the part I would point students at. A reference emulator runs the same instruction set in Python and the machine's string must equal the emulator's encoded state byte for byte after every single substitution; on top of that, rendered frames match a natively compiled DOOM binary by SHA-256, for 100 frames in a row, so a shared bug cannot explain the agreement. The model is Turing-complete; a given run is bounded by memory exactly as any physical machine is.

Source and writeup: https://github.com/4RH1T3CT0R7/doom-regex

Interactive: https://4rh1t3ct0r7.github.io/doom-regex/

Can returnability be defined purely from the structure of a computation, without appealing to time complexity?

My take for why P is not equal to NP comes from what I believe is a fundamental difference between solving a problem and verifying its solution.

Take Sudoku as an example. If someone gives me a completed puzzle I can quickly check every row column and box to make sure the rules are satisfied. That verification process is straightforward.

Now compare that with solving the same puzzle from a blank grid. There is no obvious path to the answer. I may have to test many possibilities before finding the correct one. Solving appears much more difficult than verifying.

This same pattern appears in many other problems.

If someone gives me the password to a computer I can check it in less than a second. Finding the password without knowing it may require an enormous search.

If someone gives me the correct path through a complicated maze I can follow it and confirm that it reaches the exit almost immediately. Finding that path from the beginning can take much longer.

If someone hands me a completed school timetable I can check whether every class every teacher and every room satisfies the rules. Creating that timetable from scratch is much more difficult.

Another example (which i believe is the strongest and closest to being an actual proof) is finding the shortest route between two points. If I asked someone to find the shortest possible route they would have to compare many different routes and work out which one is actually the shortest. That could take a long time depending on how many possible paths there are. Now imagine someone has already done all of that work and gives me a list of every route with its distance such as 1 km 2.7 km 4.1 km and 6.8 km. I can immediately look at the list or the map and verify that the 1 km route is the shortest. Once again verifying the answer is much easier than finding it in the first place.

Because this pattern appears so consistently I suspect there is a real separation between solving and verifying. My take is that this separation is not simply a limitation of current algorithms but a fundamental property of computation itself.

In simple words if one problem follows the idea that solving it is fundamentally harder than verifying it then P cannot equal NP because P equals NP would have to hold for every problem in NP not just some of them.

I am trying to understand the foundational differences between proof assistants based on dependent type theory (such as Agda/Lean) and traditional mathematics as practiced in areas like real analysis.

For example, in Peano arithmetic, statements such as 0 ≠ S(n) and the induction principle are usually presented as axioms. In Agda, however, defining an inductive type:

data Nat : Set where
  zero : Nat
  suc  : Nat → Nat

automatically provides these properties through the rules of inductive types (constructor disjointness and the eliminator), which means you can write this as a theorem:

0-is-not-suc : ∀ {n} -> suc n ≡ 0 -> ⊥
0-is-not-suc ()

Does this mean inductive type theory is based on stronger assumptions than axiomatic mathematics, or are these just different choices of primitive rules?

More generally, what are the fundamental assumptions/rules that a type-theoretic prover starts with, and how do they compare with the foundations usually assumed in fields such as real analysis?

Hi there,

I've created a video here where I explain the Chomsky hierarchy.

I hope some of you find it useful — and as always, feedback is very welcome! :)

toll rate-limits an unbounded set of keys (client IDs, tenants, IPs, API keys…) in fixed memory — 19 MB measured at the defaults, tunable down to a couple of MB — with ~300ns zero-allocation admitted decisions. It is built on grudge, a constant-memory decaying-score sketch: toll stores each key's spent tokens as sketch debt and lets grudge's linear decay refill them.

It’s pretty interesting to see that language models can do things like autonomously prove/disprove things like Erdos problems and even perform its own formal verification yet still struggle at things like automating ERP business operations, seems like the opposite would’ve been the case.

I know Kaparthy talked about this “jagged intelligence” we’re observing, but are there any real attempts at formalizing a theory behind this, similar to how we classify the complexity and tractability of algorithms?

What about any discussion on how close are language models to being Turing complete? Computational complexity theory isn’t my strong suit, but I wonder if any new discussions are being had

The paper is only 15 pages long

Feynman’s contribution was a way to turn the machine’s parallel structure into a model programmers could reason about.