◄ Circuits · geometry · capacity · hologram · the interference field

THE INTERFERENCE FIELD

superposition, rendered as a 2D / 4D hologram

A hologram is an interference pattern — many waves superposed. So is superposition. Each learned feature becomes a plane-wave grating (direction = its weight vector), and the whole feature set is superposed into one fringe field. In 4D the model's features live in four dimensions and the screen is a rotating 2D slice through the 4-dimensional wave field — you watch the 4D hologram tumble as a living cross-section. This is the smear, made of light, in four dimensions.

S=0.85
volume
4D
represented (norm>0.5)
waves in the slice
train step
0
How the 4D hologram is made. The model is the superposition autoencoder with m hidden dimensions; after training, each feature points in a direction in that m-space. We treat each feature f as a wave aᵥcos(k·(Wᵥ·r) + φ) and sum them — the superposition of wavefronts that records a hologram. In 2D the screen is the feature plane. In 4D the screen is a 2D plane spanned by two basis vectors that rotate through the 4-space (in the (x,w) and (y,z) planes), so the image you see is a moving cross-section of a 4-dimensional interference field — the fringes flow as the slice sweeps a dimension you can't directly see. Bright/dark = where features reinforce or cancel: the interference the network accepts to store more features than it has dimensions. A from-scratch JS reimplementation built on Anthropic's Toy Models of Superposition (Elhage…Olah 2022, MIT) — math re-derived, trained live; the phenomenon is theirs.