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ToroidalAtom: a single computational primitive with 8 properties.
Design choice: atoms are represented as *tensors* (not Python objects)
so that the entire collection can be batched and differentiable.
Each property is a torch.Tensor of shape [d_model] (or scalar where appropriate).
"""
from __future__ import annotations
import torch
import torch.nn as nn
class ToroidalAtom(nn.Module):
"""
A single toroidal atom.
Properties (all differentiable tensors):
r [d_model] — position / radius direction in latent space
phi [d_model] — phase (angle latent)
omega [d_model] — natural frequency (positive)
E [d_model] — energy / activation / importance (0..1)
kappa [d_model] — coupling strength (positive)
M [d_model] — local memory direction
tau [d_model] — temporal scale (positive)
rho [1] — hierarchical level (integer)
"""
def __init__(
self,
r: torch.Tensor,
phi: torch.Tensor,
omega: torch.Tensor,
E: torch.Tensor,
kappa: torch.Tensor,
M: torch.Tensor,
tau: torch.Tensor,
rho: torch.Tensor,
payload: bytes = b"",
) -> None:
super().__init__()
self.register_buffer("r", r)
self.register_buffer("phi", phi)
self.register_buffer("omega", omega)
self.register_buffer("E", E)
self.register_buffer("kappa", kappa)
self.register_buffer("M", M)
self.register_buffer("tau", tau)
self.register_buffer("rho", rho)
# Surface bytes carried by this living atom (not a buffer; episode memory).
self.payload = bytes(payload) if payload else b""
def energy(self) -> torch.Tensor:
"""Scalar energy of this atom."""
return self.E.sum()
def phase_distance(self, other: "ToroidalAtom") -> torch.Tensor:
"""Phase difference (wrapped) with another atom."""
return torch.remainder(self.phi - other.phi, 2 * torch.pi)
def coupling_to(self, other: "ToroidalAtom") -> torch.Tensor:
"""Pairwise coupling K_ij = kappa_ij * cos(phi_i - phi_j)."""
dphi = self.phase_distance(other)
return self.kappa * other.kappa * torch.cos(dphi)
def clone(self) -> "ToroidalAtom":
return ToroidalAtom(
r=self.r.clone(),
phi=self.phi.clone(),
omega=self.omega.clone(),
E=self.E.clone(),
kappa=self.kappa.clone(),
M=self.M.clone(),
tau=self.tau.clone(),
rho=self.rho.clone(),
payload=self.payload,
)
def to(self, device):
return ToroidalAtom(
r=self.r.to(device),
phi=self.phi.to(device),
omega=self.omega.to(device),
E=self.E.to(device),
kappa=self.kappa.to(device),
M=self.M.to(device),
tau=self.tau.to(device),
rho=self.rho.to(device),
payload=self.payload,
)
class ToroidalAtomCollection(nn.Module):
"""
A batch/collection of toroidal atoms.
Stores atoms as stacked tensors for vectorized operations.
"""
def __init__(self, atoms: list[ToroidalAtom] | None = None) -> None:
super().__init__()
self.atoms: list[ToroidalAtom] = atoms or []
self._buffers: dict[str, torch.Tensor] = {}
self._dirty = True
if atoms:
self._rebuild_buffers()
def _rebuild_buffers(self) -> None:
if not self.atoms:
self._buffers = {}
self._dirty = False
return
self._buffers = {
"r": torch.stack([a.r for a in self.atoms]),
"phi": torch.stack([a.phi for a in self.atoms]),
"omega": torch.stack([a.omega for a in self.atoms]),
"E": torch.stack([a.E for a in self.atoms]),
"kappa": torch.stack([a.kappa for a in self.atoms]),
"M": torch.stack([a.M for a in self.atoms]),
"tau": torch.stack([a.tau for a in self.atoms]),
"rho": torch.stack([a.rho for a in self.atoms]),
}
self._dirty = False
def _ensure_buffers(self) -> None:
if getattr(self, "_dirty", True):
self._rebuild_buffers()
@property
def r(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("r", torch.zeros(0))
@property
def phi(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("phi", torch.zeros(0))
@property
def omega(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("omega", torch.zeros(0))
@property
def E(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("E", torch.zeros(0))
@property
def kappa(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("kappa", torch.zeros(0))
@property
def M(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("M", torch.zeros(0))
@property
def tau(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("tau", torch.zeros(0))
@property
def rho(self) -> torch.Tensor:
self._ensure_buffers()
return self._buffers.get("rho", torch.zeros(0))
def __len__(self) -> int:
return len(self.atoms)
def add(self, atom: ToroidalAtom) -> None:
self.atoms.append(atom)
self._dirty = True
def extend(self, atoms: list[ToroidalAtom]) -> None:
if atoms:
self.atoms.extend(atoms)
self._dirty = True
def remove(self, indices: list[int]) -> None:
# Remove in reverse order to preserve indices
for i in sorted(indices, reverse=True):
self.atoms.pop(i)
self._dirty = True
def top_by_energy(self, k: int) -> list[ToroidalAtom]:
energies = self.E.sum(dim=-1) if self.E.numel() else torch.zeros(len(self.atoms))
top_k = energies.topk(min(k, len(self.atoms)), dim=0).indices
return [self.atoms[i.item()] for i in top_k]
def to(self, device):
new_atoms = [a.to(device) for a in self.atoms]
collection = ToroidalAtomCollection(new_atoms)
return collection
def state_dict(self):
return {
"atoms": [
{
"r": a.r.cpu(), "phi": a.phi.cpu(), "omega": a.omega.cpu(),
"E": a.E.cpu(), "kappa": a.kappa.cpu(), "M": a.M.cpu(),
"tau": a.tau.cpu(), "rho": a.rho.cpu(),
"payload": bytes(getattr(a, "payload", b"") or b""),
}
for a in self.atoms
]
}
def load_state_dict(self, state: dict) -> None:
self.atoms = []
for sd in state["atoms"]:
self.atoms.append(ToroidalAtom(
r=sd["r"], phi=sd["phi"], omega=sd["omega"],
E=sd["E"], kappa=sd["kappa"], M=sd["M"],
tau=sd["tau"], rho=sd["rho"],
payload=bytes(sd.get("payload", b"") or b""),
))
self._rebuild_buffers()
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