An ordinary neural network for quantum chemistry is like a student who learns from mistakes but keeps tripping over the same spot. It crawls toward the right answer, is sensitive to settings, and often loses stability.
Scientists proposed a different path: instead of picking the step size at random, they turn the training problem into finding the steepest descent on the error surface. The implicitly restarted Lanczos method solves a small but well-conditioned eigenvalue problem, as if finding the principal axis along which the error drops fastest. This automatically chooses both the direction and magnitude of the step, without manual tuning.
The result is impressive: even a simple neural network with few parameters achieves 10⁻¹² kcal/mol accuracy (that's like measuring the distance from Earth to the Moon to within a hair's width) in just 3–5 steps. This approach opens the door to accurate and fast calculations in quantum physics and chemistry.
An accuracy of 10⁻¹² kcal/mol is equivalent to measuring the distance from Earth to the Moon with an error smaller than the diameter of a human hair.