Differential Hamiltonian Solvers in Continuous Phase Space

In standard discrete transformers, every subsequent token concatenates to a key-value manifold, producing memory scaling of O(N) and attention compute of O(N²). Hambaz replaces attention matrices with a continuous phase-space Hamiltonian field ℋ(q, p, t), evolving state vectors along a symplectic manifold where the memory footprint remains locked at 0.84 MiB regardless of token volume:

import torch
from hambaz.phase import ContinuousStateVector, HamiltonianEvolution

# O(1) state memory evolution in continuous phase space
psi_0 = ContinuousStateVector.initialize(dim=4096, dtype=torch.complex64)
H = HamiltonianEvolution(kinetic_term="p^2/2m", potential="V(q)")
psi_t = H.step_forward(psi_0, dt=0.005, resonance_mode="locked")

print(f"Memory footprint: {psi_t.memory_footprint_mib} MiB (Constant)")