Many dimensionality reduction algorithms share a few central principles.... 1. Construct a graph that captures the data's local structure 2. Measure "geodesic" distances between points using the graph 3. Project the points to a lower dimension while preserving these distancesshow more

Laplacian eigenmaps perform non-linear dimensionality reduction ("manifold learning") by... embedding data points using the eigenvectors of a graph Laplacian as coordinates.show more

Oldies but goldies: M. Belkin, P. Niyogi, Laplacian Eigenmaps... for Dimensionality Reduction and Data Representation, 2003. Non-linear dimensionality reduction by embedding data points using the eigenvectors of a graph Laplacian as coordinates.show more

I wrote this fun interactive article explaining Isomap, a... classic non-linear dimensionality reduction technique. Isomap captures the local similarity structure of data through a graph and computes an embedding that preserves this structure. Check it out! Link below.show more

In the data manifold, the shortest path between two... points is a geodesic that pass through high density regions of data. Just like mass curves the space geometry, data also curves the space. In the example below we can see a geodesic being optimized between two points. 1/3show more

Without touching a single piece of land, it's possible... to sail from Alaska to India in a completely straight line. More precisely, along a geodesic, or a curve that constitutes the shortest path (arc) between two points on a surface, like a spheroid.show more

AN ENGINEER SOLVED A PROBLEM NOBODY IN THE COMPANY... COULD FULLY MAP ON THEIR OWN The problem wasn't a missing tool, it was that every process touched three other processes nobody had written down. He wired dozens of agents into one shared graph instead of documenting each department's workflow by hand. Each agent owned one process, reading its own logs while writing every dependency it found straight into the shared structure. Within days, the graph surfaced a connection between two departments that had been quietly blocking each other for over a year. The company adopted the graph as its live map of operations, and it hasn't stopped finding new connections since. See what the graph found in the first 48 hours below👇show more

A TEAM JUST DEPLOYED 15 AUTONOMOUS LOOP AGENTS FROM... A SINGLE PROMPT USING APPLIED GRAPH ENGINEERING Most developers still manually hardcode multi agent systems, writing separate logic for every individual task. Graph engineering changes this by using a central topological map to spin up all 15 nodes simultaneously. A single 200 word input generates the architecture, routing 120 unique pathways between agents instantly. Instead of failing under conflicting instructions, these loop agents self correct via continuous state sharing. Managing a 15 node mesh requires high token throughput, making this dependent on strict low-] latency API tiers. See exactly how this automated multi agent graph architecture actually operates in real time ↓show more

i don't f*cking understand why this isn't popular yet... someone has created a memory system that uses 90% fewer tokens while still finding all the expected symbols it builds a local graph of source symbols and their relationships. architecture, decisions and handoffs live as Git-tracked Markdown. a note can point to the code behind it, so a code change can flag that knowledge for review the loop: scan the repo → map the code → write the why → anchor notes to symbols → retrieve a task-sized slice → review drift → commit to Git → continue in the next session in the author's small, one-repo test, graph retrieval returned 10.74× less context than grep top-3 while finding every expected symbol across six tasks the useful part is the connection between memory and evidence. the repo carries what the agent learned, and the code gives you a way to check whether that knowledge still holds save this, then build a second brain for your company⭣show more

if you use claude code, this will save you... real money. the problem: every time you make an edit, your ai rereads the whole codebase to figure out what changed. tens of thousands of tokens, every turn, for context it already had. this repo fixes it. it’s called code review graph, and it just maps your entire codebase: every file, every function, every connection laid out so you can see the actual shape of your project how to set up (2 min): 1. pip install code-review-graph 2. code-review-graph install - auto-configures Claude Code, Cursor, Codex, Gemini CLI + more 3. code-review-graph build change one function, and it traces exactly what that touches... every caller, every dependent file, every test. your ai only reads what's affected, not the whole repo. and the savings are wild. a task that used to burn ~100,000 tokens (about a dollar) now runs closer to a penny.show more

Back in 2014, 17-year old Jalen Brunson already understood... the value of making the right play finding the balance between being a scorer and playmaker. 39 points, 12 assists, 1 turnover for the 2-time all-star in a crucial Game 5 to put the Knicks up 3-1 on Boston.show more

The Brava Race to a Thousand Galxe Quest is... now live! 1/2 Join the quest and be one of the winners to get a share of the 1,000 $USDC Prize Pool! Start collecting Brava points and get exclusive Discord roles that entitle you to future rewards within the Brava ecosystem.show more

(🧵1/3) The largest groups receiving British Citizenships are Sub-Saharan... Africans & South Asians (graph below). Who is granting these citizenships and why? Both denaturalisation & deportation are crucial to prevent the Native British becoming a minority in our own homeland.show more

The incident that led to Bolton Wanderers going 2-1... up vs Leyton Orient A corner comes into the box and it’s alleged that Azeem Abdulai handles the ball 😳 Referee points to the spot! Harsh or definitely a penalty?🤔 #bwfc #LOFC #OneOrientshow more

After EATING FROZEN RAW LIVER and bone marrow, I... was truly accepted by these local Buryats. Descendants from the Mongolian steppe nomads, they would eat this (and still do!) while travelling vast distances on horseback. It was a bit like tartar, nicer than the cooked stuff. I’m just glad they didn’t make me try any other local delicacies, that was enough for one day!show more

3 games to go. 3 cup finals. Win all... 3 and we win the league. Simple as that. First up … Wealdstone (H). We haven’t been convincing for a while now. But, now’s the time for us to step up with a huge performance and a big 3 points. Let’s do it together, Up The Dale!👊💙 #RAFCshow more

The Brava Galxe Quest is now live! 1/2 Join... the Quest to earn points and unlock the exclusive Initiator Badge on Discord, entitling you to future rewards within the Brava ecosystem. Also, 10 lucky participants will share a 250 $USDC prize pool.show more