Research

Four thrusts that define the Lane Vector program.

Thrust 1 — Stiff-PINN Architecture for Multi-Scale Behavioral Dynamics

Behavioral and temporal systems operate across temporal scales separated by six orders of magnitude. Fast events resolve in milliseconds; slow processes evolve over months. Lane Vector adapts Stiff-PINN architectures using implicit-explicit (IMEX) training schemes that partition the loss function into fast and slow components, stabilizing gradient flow across disparate timescales. This is a structural solution to a structural problem—one that standard neural networks cannot resolve through scale alone.

Thrust 2 — Equation Discovery via Kolmogorov-Arnold Networks

The objective is not to fit curves but to discover the equations that generate the data. KANs—architectures grounded in the Kolmogorov-Arnold representation theorem—perform symbolic regression on behavioral datasets, extracting closed-form expressions for “Market Pressure.” The result is not a black-box prediction but a publishable governing law subject to the same scrutiny as any equation in the physical sciences.

Thrust 3 — Digital Mass Action and Constrained Intent Neural Networks

The CINN architecture embeds “synthetic physics” constraints into the loss function: predicted velocity must be proportional to the product of signal density and alignment. This prevents scalar-bias hallucinations endemic to unconstrained models and enforces the fundamental coupling between magnitude and directionality.

Thrust 4 — Geodesic Intent Mapping

The optimal trajectory of a state through semantic space—whether intent, demand, or risk—is a geodesic, computable via boundary value problems. This formulation treats evolution as a global optimization over the entire trajectory. The equation sees the entire timeline as a constraint.