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#lattice

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Léo Ducas 🇺🇦 ∀,≡,⊂

Ok, here is my very first serious math post. I'm going to do this at least once a week.

#Math4Crypto #Lattice #Torus #LocalitySensitiveHashing #TrainOfMathematicalThought.
*Locality Sensitive Hashing over the Torus, or how I fooled myself twice.*

Locality Sensitive Hashing (LSH) over a metric space is the task of tiling the space such that two close points are likely to fall in the same tile. The tile need not be periodic, but they typically are for algorithmic convenience. One example application is the "Shazam app": quickly find a song from a noisy recording of it, maybe having preprocessed the database of songs. But if you know me, you can certainly imagine that I will use them to break cryptography.

It is somewhat similar to two other tasks: coding and quantizing. For coding we want the tiles to have a large inner radius: that is the amount of error tolerated (see my banner !). For quantization (aka: lossy compression from continuous to discrete data), we want minimize the average distance to the center of the tile.

For LSH, what we want is that if we add a small error to a random point in a tile, the probability that the error drags us outside the tile is low: that is the probability that you will miss out on detecting a pair of close points. For a small error of radius \(\epsilon\), a tile of volume \(V\) and surface \(S\), you can quickly convince yourself that the failure probability is roughly proportional to \(S \cdot \epsilon / V\). Minimizing \(S/V\) is a well known question: the isoperimetric inequality. The best shape for the tiles would be Eucilidean balls... if only they could tile Eucilidean spaces.

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FeralRobots

It's hard to know where to start with this.

First, there's no meaningful way in which an "#AI" agent is an 'employee', so it's immediately clear that this ploy by #Lattice is pure Frankfurtian #bullshit.

Primary question should be: what end does this serve?

The obvious one is to further reduce human employees to assets. 'We're making you peer to a product' by acting as though a "#DigitalWorker" has feelings that can be hurt.

[h/t @MLE_online | social.afront.org/@MLE_online/]
lattice.com/blog/leading-the-w

Today Lattice is making AI history. We will be the first to give digital workers official employee records in Lattice. Digital workers will be securely onboarded, trained, and assigned goals, performance metrics, appropriate systems access, and even a manager. Just as any person would be.
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Heron&Fox Photo

A #Macro #Photo of the surface of a piece of Smoky #Quartz.
Found in the Great Smoky Mounters of North Carolina and Tennessee, among many other places, is colored by having energetic particles displace atoms from the #crystal #lattice. The radiation source was likely natural, such as being close to deposits of granite, which contains uranium.

Get a print or other merchandise with this image at heronfox.pixels.com/featured/s

#SmokyQuartz, #MacroPhotography, #Crystal, #BrownCrystal, #RocksOfMastodon, #Mineral, #Photograph

A macro photograph of a clear crystal with a brown cast and inclusions. The crystal is triangle-shaped, with one side on the bottom of the frame, with light emanating from the surface.
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