SOPHIA XT

LOTU

Lattice-Optimized Training Unit

Explore how spatial diffusion processes language on a probability lattice. Visualize token routing, diffusion steps, and sequence confidence in real-time.

Input
464
0.12.0
Visualization
Enter text and press Analyze to visualize lattice processing.

How It Works

LOTU's lattice models token probability evolution via a spatial diffusion PDE:

∂P/∂t = D∇²P − λP + ΣSᵢ(z,t)

P = probability density, D = diffusion coefficient, λ = decay rate, Sᵢ = source terms (token anchors)

Token Anchoring

Each input token is mapped to a 3D lattice coordinate via its hash. These positions act as probability source terms S(z,t) in the diffusion equation, seeding the lattice with localized energy peaks.

Route Scoring

Sequential token pairs define directed routes through the lattice. Route confidence is computed as the geometric mean of adjacent token probabilities, weighted by their spatial proximity on the lattice.

Confidence Collapse

After diffusion steps converge, the probability field is collapsed to yield a final sequence confidence score. Temperature controls the sharpness of this collapse -- lower values produce sharper, more confident distributions.