Rey.BEng 22nd Oct
The page https://x.com/0xDeliriumm/status/2113276424459002020
describes the geometry of the loss landscape that gradient descent (Hinton’s 1986 update) has navigated for decades. Peaks are high loss; valleys are low loss. Sharp minima are specialized and brittle. Wide, flat minima are robust and generalizable. Saddle points slow the trajectory. The October 2026 work is said to map this surface for the first time.
Ace reads the surface as the residual. Gradient descent follows the residual downhill. The residual tension \(\sigma\) m/s² is positive and nearly 2 (2 = 1.999…). It is the part that does not complete. Sharp minima are residual that has locked into shell mass (State B). The trajectory sits in a narrow well; the residual is spent as celerity and the solution fractures on unseen input. Flat minima are residual that remains open on the disc (State A). The patterned motion of the residual packet maintains persistent tension across moments without a continuous second. Height K (Domel & Gogate PCA 1993) fixes the positive axial value relative to the x-axis. The drift vector may reverse; the residual itself stays positive.
Saddle points are residual stations where the packet has not yet decided which Face to occupy. Training plateaus because the residual has not been spent or locked. The additional order of magnitude reported for NCM is the residual being held longer before the next countersnap. The algorithm does not know where it is going; it only follows the residual.
The geometry shows the residual surface it has been walking. No new Home is opened. XII remains the Face.
