dimensionality reduction

A sheet of paper left on a wet table warps and lifts its edges. No one controls that motion, but it follows the same laws as plant growth: some areas of the sheet shrink more than others, and the flat form becomes three-dimensional. Engineers have long dreamed of taming this process so that a flat blank folds itself into a desired sculpture. In the new work, that trick succeeded with accuracy down to one percent.

A deck of cards in which each card is slightly rotated cannot lie flat: the backs and faces will never align. But if the cards are flexible, they will start to adjust, shifting by fractions of a millimeter to find the perfect match. Something similar happens inside crystals when two thick layers of MoS2 or MoS2 with WS2 are stacked with a twist of 1–2 degrees.

A protein engineer is like a chef trying to make a dish that is tasty, healthy, and cheap all at once. Change one ingredient, and you risk ruining another. In the past, computer assistants could only evaluate protein properties one at a time, missing how they are connected.

Two photographers shoot the same mountain. One takes a hundred shots from the summit and only a couple from the base; the other does the opposite. If you try to align their images, the algorithm might decide that the summit in one photo matches the summit in the other simply because there are many similar points there, not because it's the same spot. Sampling density throws it off.

Two photographers shoot the same mountain. One takes a hundred shots from the summit and only a couple from the base; the other does the opposite. If you try to align their images, the algorithm might decide that the summit in one photo matches the summit in the other simply because there are many similar points there, not because it's the same spot. Sampling density throws it off.

Two scans of the same brain taken at different times are like photographs of the same house before and after renovation. To see what changed, you overlay them and look at the differences. But an MRI scanner is not a perfect camera: it adds its own distortions, as if the photo were taken through slightly warped glass.

Holding in mind the exact position of a pen as it's slowly moved is a routine task for the brain. For artificial neural networks, it's nearly impossible. Standard recurrent networks like GRU and LSTM tend to break continuous motion into rigid steps: the pen doesn't glide smoothly but jumps from point to point.

In a noisy hall, an interpreter tries to catch every word, but rustles and echoes muddle the meaning. That's roughly how conventional computer methods handle complex quantum systems: the more particles and the stronger their correlations, the faster calculations drown in interference.

Predicting the yield of a chemical reaction is a bit like trying to guess the harvest knowing only the soil composition. Traditionally, chemists have relied on long columns of numbers, quantum descriptors, that describe electron energies but say nothing about molecular shape.

Two hundred forty-two thousand three hundred twenty-seven galaxies — like grains of sand on a beach. But astronomers turned this chaos into a map: the UMAP algorithm (a machine learning method) took from each galaxy eleven parameters — seven colors from optical to mid-infrared (that's photometry), magnitude…

To capture every detail of a statue's shape, you could break it into millions of tiny cubes and describe each one — slow, heavy, and your computer's memory would groan at the seams. That's how 3D medical scans are usually handled: a CT or MRI is a huge array of such cubes (voxels), and to create or improve an image, the machine has to plow through all of them.

In a three-dimensional scene, each point is like a candy whose color changes depending on the viewing angle. To describe this play of shades, dozens of numbers are stored for each point — a special mathematical function invented by Joseph Fourier. Memory fills up instantly.

Ordinary AI looks at medical images like puzzles made of unfamiliar pieces: it considers any two unmatched pictures completely different. It's like trying to tell twins apart without knowing they're related. In medicine, however, patients with the same condition look nearly identical on MRI, and the algorithm mistakes 'relatives'.

A single-pixel camera works like an artist creating a picture through a stencil with many holes. In each frame, only a portion of the light, modulated by a mask, a spatial light modulator, reaches the single sensor, and then the computer reconstructs the full image by assembling this mosaic with computational algorithms.

An ordinary road map with traffic is a heap of numbers. Sending them all as is takes too long. But you can reduce the volume without losing the gist. Researchers found a clever solution: first redraw the map so that streets become points, and intersections become bridges between these points.

The photo enhancement algorithm is like a navigator that step by step leads a blurry picture toward a sharp view. It removes noise and distortions, moving pixel by pixel along a familiar map. But if the image was taken in unfamiliar conditions (say, with unusual blur) the map doesn't match the terrain.

A regular radar is like a microphone in a buzzing crowd: individual sounds blend into mush. PiVoT works like a conductor who instantly recognizes each instrument in the tuning chaos. Instead of shuffling through hypotheses, the algorithm tightens a loop around the most likely targets — cars, cyclists, pedestrians.

The data from a single CT scan is comparable to several feature-length films. TCAM-Diff bypasses this bottleneck: the program compresses the 3D scene into three shadow projections — like a sculptor reconstructing a solid statue from silhouettes on three walls.

Data on gene activity usually looks like a long string of numbers, like a rainbow stripe (spectrum) with no visible connections. In the scVision model, these numbers are turned into a meaningful picture — not a list of ingredients, but a photo of a finished dish.

Usually a CT scanner takes many X-ray images from different angles and assembles a 3D picture. But sometimes doctors only scan a small area (say, one lung) and the data cuts off. It's like a chef given a single spoonful of soup and asked to name the exact recipe for the entire pot.

To find an epileptic seizure in brain activity recordings, scientists used an approach akin to picking out sharp sounds in a noisy room: instead of deciphering the entire chorus of brainwaves (EEG), they isolated only the strongest spikes.

Three-dimensional worlds are made of millions of semi-transparent specks, like a giant tapestry woven from glowing droplets. Transmitting such a canvas usually takes ages and a beefy data pipe. SpeedyGS squeezes it into a tiny file, and it unfurls in a flash, like yanking a drawstring from a pouch.

A cook who learns to cook from hand-drawn pictures risks ruining every dish. The same trap awaits computer vision: models need thousands of labeled images, but collecting them manually is expensive and tedious. Synthetic frames solve the problem, but only if they look real.

Medical scans are maps of tissue density. The brightness of each pixel reveals what’s there, much like photometry measures light intensity. But conventional algorithms analyze pixels in isolation, producing jagged organ boundaries. A new approach compels the program to prioritize smoothness.

A raw digital photo resembles a mosaic: each pixel holds only one base color — red, green, or blue. To compress such a file, it's split into brightness (a detailed black-and-white image) and color components.

Imagine photographing a statue in dim light. You face a dilemma: take one bright shot or a series of dim frames from different angles. In the first case, quality is limited by photon noise, the graininess that arises from a lack of photons, while in the second, details overlap, making it harder to reconstruct the 3D structure.

Modern machine vision systems are gaining autonomy: engineers have managed to implement an image recognition algorithm directly on a miniature chip, freeing the camera from having to send data to a bulky computer.

A family tree becomes a tangle if you account for adopted children and remarriages. Evolution often resembles such a tangle: although the Standard Model, the traditional view of divergent evolution where species branch like a tree, paints a neat tree of species, in reality genes travel not only by inheritance but also directly between unrelated organisms — a process…

Building a light chip is like a game where you have to guide a beam through a maze of tiny mirrors and beam splitters. Each element acts like a railroad switch: it either lets light pass straight through or directs it to an adjacent track. The goal is to produce a specific light pattern at the output while using as few 'switches' as possible. Usually, engineers spend years finding the shortest route for each task.

Light from distant galaxies passes through warped space before reaching our telescopes. Massive clumps of matter act like uneven glass: galaxy images get slightly stretched and rotated. This phenomenon is called weak gravitational lensing.

The Universe is a giant labyrinth of curved mirrors. The mass of galaxies and clusters distorts the light of distant quasars, as if toying with our perception of the cosmos. Hidden in this hall of mirrors is the key to the greatest mystery: dark energy, which is pushing space apart ever faster.

On a topographic map, raindrops choose their path: falling on one slope, they flow into River A; on the other, into River B. An observer sees only the winding rivers (the response variables Y) and knows which slope the water came from (the instrument Z), but cannot see the drops themselves (the unobserved factors ε).

On the screen is the result of a complex simulation: two planets collided, a shockwave ripples outward. A couple of clicks in an editor, and harsh shadows soften, noise smooths out, the background darkens. This kind of digital retouching (image editing to enhance appearance) has long been part of the scientist’s toolkit.

Imagine a philharmonic orchestra playing, but the microphone picks up only a blended roar — a tutti where double basses, flutes, and timpani all merge. Physicists have grappled with a similar task for decades, staring at fields of density, temperature, or magnetic induction.

A cosmological map is like a snapshot of ripples on water: from it you can reconstruct what stone was thrown. The stone is the properties of the universe — how much ordinary matter it contains, how much dark matter, how fast it is expanding. The ripples are the pattern of galaxies that telescopes measure.

Space is threaded with magnetic fields. They exist around galaxies, stars, and even in nearly empty voids — the vast empty spaces between galaxy clusters. It's usually thought that fields are amplified from weak 'seed' fields by turbulence, much like a dynamo. But the origin of the seed fields themselves has remained a puzzle.

Creating a material with desired properties is an art that long relied on intuition and luck. Nature gives no hints: dozens of elements in the periodic table, and the number of their combinations tends to infinity. Previously, materials scientists resembled alchemists, trying everything in a row, or relied on statistical models that lost power beyond the known.

A lab robot counts molecules, and gets it wrong. One tube shows 0, another 12, a third 3, though in reality they all hold roughly the same amount. Such 'raw' numbers are common in biology: DNA sequencing, counting species in a water sample, gene activity. There's plenty of data, but it's sparse and more scattered than simple randomness would predict.

Imagine an interpreter sitting in a meeting room, translating every word. But then they notice their translation could improve if they learned from their mistakes. They start noting which phrases caused confusion and adjust them. Within an hour, their translation is more accurate and the meeting runs smoother.

A chef doesn't waste ingredients cooking the whole dish to check the taste: they just taste a drop of sauce. The same logic underlies the "information matching" method for predicting metal strength. Instead of expensive calculations of every atom's behavior, scientists "taste" only simple indicators linked to plasticity — a metal's ability to bend without breaking.