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Symmetric Poincaré vs. Euclidean hierarchy embedding.
Design choice, stated explicitly (deviates from how the rest of this
codebase trains hyperbolic components, on purpose, for this experiment):
the hierarchical field-predictor (model.py) parameterizes points in the
tangent space and only ever calls expmap0 at the boundary, trained with
plain Euclidean Adam. That's a reasonable simplification for a predictor
whose main job is spatiotemporal forecasting. For THIS experiment — whose
entire point is to test whether hyperbolic geometry helps hierarchy
recovery — using genuine Riemannian optimization (geoopt.ManifoldParameter
+ geoopt.optim.RiemannianAdam, verified working in this session before
being used here) is more faithful to the original Nickel & Kiela / Sala
et al. methodology this whole test is trying to reproduce in miniature.
Using a weaker approximation here would bias the comparison against the
Poincaré model and undermine the point of running the experiment at all.
The Euclidean baseline is a plain nn.Embedding trained with ordinary
Adam — the natural, undiluted comparison point.
"""
from __future__ import annotations
from typing import Dict, Optional, Tuple
import torch
import torch.nn as nn
import geoopt
from .data_pbdb_taxonomy import TaxonomyEdgeDataset
class HierarchyEmbedding(nn.Module):
"""
Shared interface over the two geometries so training/eval code never
needs an if/else on `geometry` — everything goes through .points(),
.distance(), and .parameters()/.embed_optimizer().
"""
def __init__(
self,
num_nodes: int,
dim: int = 8,
geometry: str = "poincare",
c: float = 1.0,
learnable_c: bool = False,
init_scale: float = 1e-3,
):
super().__init__()
if geometry not in ("poincare", "euclidean"):
raise ValueError(f"geometry must be 'poincare' or 'euclidean', got {geometry!r}")
self.geometry = geometry
self.dim = dim
self.num_nodes = num_nodes
init = torch.randn(num_nodes, dim) * init_scale
if geometry == "poincare":
self.manifold = geoopt.PoincareBall(c=c, learnable=learnable_c)
self.emb = geoopt.ManifoldParameter(init, manifold=self.manifold)
else:
self.manifold = None
self.emb = nn.Parameter(init)
def points(self, idx: torch.Tensor) -> torch.Tensor:
return self.emb[idx]
def distance(self, a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
if self.geometry == "poincare":
return self.manifold.dist(a, b)
return (a - b).pow(2).sum(-1).clamp_min(1e-12).sqrt()
def make_optimizer(self, lr: float, curvature_lr_mult: float = 0.1, optimizer_type: str = "radam"):
if self.geometry == "poincare":
groups = [{"params": [self.emb], "lr": lr}]
if hasattr(self.manifold, "isp_c"):
groups.append({"params": [self.manifold.isp_c], "lr": lr * curvature_lr_mult})
if optimizer_type == "radam":
return geoopt.optim.RiemannianAdam(groups)
elif optimizer_type == "rsgd":
return geoopt.optim.RiemannianSGD(groups, lr=lr)
else:
raise ValueError(f"optimizer_type must be 'radam' or 'rsgd', got {optimizer_type!r}")
return torch.optim.Adam(self.parameters(), lr=lr) if optimizer_type == "radam" \
else torch.optim.SGD(self.parameters(), lr=lr)
@torch.no_grad()
def clip_to_ball(self, margin: float = 0.95):
if self.geometry != "poincare":
return
self.emb.data = self.manifold.projx(self.emb.data)
max_norm = (1.0 / self.manifold.c.clamp_min(1e-8).sqrt()) * margin
norms = self.emb.data.norm(dim=-1, keepdim=True).clamp_min(1e-12)
factor = torch.clamp(max_norm / norms, max=1.0)
self.emb.data = self.emb.data * factor
@torch.no_grad()
def clamp_curvature(self, c_min: float = 0.1, c_max: float = 3.0):
if self.geometry != "poincare" or not hasattr(self.manifold, "isp_c"):
return
lo = torch.log(torch.expm1(torch.tensor(c_min, dtype=self.manifold.isp_c.dtype)))
hi = torch.log(torch.expm1(torch.tensor(c_max, dtype=self.manifold.isp_c.dtype)))
self.manifold.isp_c.clamp_(lo.item(), hi.item())
def radii(self) -> torch.Tensor:
return self.emb.detach().norm(dim=-1)
def negative_sample(
child_idx: torch.Tensor,
true_parent_idx: torch.Tensor,
num_nodes: int,
k: int,
generator: Optional[torch.Generator] = None,
) -> torch.Tensor:
B = child_idx.shape[0]
neg = torch.randint(0, num_nodes, (B, k), generator=generator)
collision = neg.eq(true_parent_idx.unsqueeze(1)) | neg.eq(child_idx.unsqueeze(1))
while collision.any():
resample = torch.randint(0, num_nodes, (int(collision.sum().item()),), generator=generator)
neg[collision] = resample
collision = neg.eq(true_parent_idx.unsqueeze(1)) | neg.eq(child_idx.unsqueeze(1))
return neg
def ranking_loss(
model: HierarchyEmbedding,
child_idx: torch.Tensor,
parent_idx: torch.Tensor,
neg_idx: torch.Tensor,
margin: float = 1.0,
) -> torch.Tensor:
child_pts = model.points(child_idx) # (B, D)
parent_pts = model.points(parent_idx) # (B, D)
B, K = neg_idx.shape
neg_pts = model.points(neg_idx.reshape(-1)).reshape(B, K, -1)
d_pos = model.distance(child_pts, parent_pts) # (B,)
d_neg = model.distance(
child_pts.unsqueeze(1).expand(-1, K, -1).reshape(-1, model.dim),
neg_pts.reshape(-1, model.dim),
).reshape(B, K) # (B, K)
loss = torch.relu(margin + d_pos.unsqueeze(1) - d_neg)
return loss.mean()
def softmax_ranking_loss(
model: HierarchyEmbedding,
child_idx: torch.Tensor,
parent_idx: torch.Tensor,
neg_idx: torch.Tensor,
) -> torch.Tensor:
child_pts = model.points(child_idx) # (B, D)
parent_pts = model.points(parent_idx) # (B, D)
B, K = neg_idx.shape
neg_pts = model.points(neg_idx.reshape(-1)).reshape(B, K, -1)
d_pos = model.distance(child_pts, parent_pts) # (B,)
d_neg = model.distance(
child_pts.unsqueeze(1).expand(-1, K, -1).reshape(-1, model.dim),
neg_pts.reshape(-1, model.dim),
).reshape(B, K) # (B, K)
logits = torch.cat([(-d_pos).unsqueeze(1), -d_neg], dim=1) # (B, K+1); true parent at index 0
target = torch.zeros(B, dtype=torch.long, device=logits.device)
return torch.nn.functional.cross_entropy(logits, target)
def train_hierarchy_embedding(
dataset: TaxonomyEdgeDataset,
geometry: str = "poincare",
dim: int = 8,
epochs: int = 50,
batch_size: int = 256,
lr: float = 1e-3,
neg_samples: int = 10,
margin: float = 1.0,
c: float = 1.0,
learnable_c: bool = False,
loss_type: str = "margin",
burn_in_epochs: int = 0,
burn_in_lr_mult: float = 0.1,
curvature_lr_mult: float = 0.1,
c_min: float = 0.1,
c_max: float = 3.0,
optimizer_type: str = "radam",
device: str = "cpu",
seed: int = 0,
) -> Tuple[HierarchyEmbedding, Dict[str, float]]:
if loss_type not in ("margin", "softmax"):
raise ValueError(f"loss_type must be 'margin' or 'softmax', got {loss_type!r}")
torch.manual_seed(seed)
gen = torch.Generator().manual_seed(seed)
model = HierarchyEmbedding(
num_nodes=dataset.num_nodes, dim=dim, geometry=geometry,
c=c, learnable_c=learnable_c,
).to(device)
opt = model.make_optimizer(lr, curvature_lr_mult=curvature_lr_mult, optimizer_type=optimizer_type)
for group in opt.param_groups:
group["lr"] = lr * burn_in_lr_mult if burn_in_epochs > 0 else lr
edge_idx = torch.tensor(dataset.edge_idx, dtype=torch.long) # (E, 2) = (child, parent)
n_edges = edge_idx.shape[0]
loss_history = []
c_history = []
max_norm_history = []
for epoch in range(epochs):
if burn_in_epochs > 0 and epoch == burn_in_epochs:
for group in opt.param_groups:
group["lr"] = lr
perm = torch.randperm(n_edges, generator=gen)
epoch_loss, n_batches = 0.0, 0
for start in range(0, n_edges, batch_size):
batch_idx = perm[start : start + batch_size]
batch = edge_idx[batch_idx].to(device)
child_idx, parent_idx = batch[:, 0], batch[:, 1]
neg_idx = negative_sample(
child_idx, parent_idx, dataset.num_nodes, neg_samples, generator=gen
).to(device)
if loss_type == "margin":
loss = ranking_loss(model, child_idx, parent_idx, neg_idx, margin=margin)
else:
loss = softmax_ranking_loss(model, child_idx, parent_idx, neg_idx)
if not torch.isfinite(loss):
raise RuntimeError(
f"[NON_FINITE_LOSS] loss={loss.item()} at epoch {epoch+1}, "
f"geometry={geometry}, loss_type={loss_type} — stopping "
f"rather than continuing with a corrupted embedding."
)
opt.zero_grad()
loss.backward()
opt.step()
model.clamp_curvature(c_min=c_min, c_max=c_max)
model.clip_to_ball()
epoch_loss += loss.item()
n_batches += 1
mean_loss = epoch_loss / max(n_batches, 1)
loss_history.append(mean_loss)
if geometry == "poincare":
c_history.append(model.manifold.c.item())
max_norm_history.append(model.emb.detach().norm(dim=-1).max().item())
metrics = {"final_loss": loss_history[-1], "loss_history": loss_history}
if geometry == "poincare":
metrics["c_history"] = c_history
metrics["max_norm_history"] = max_norm_history
return model, metrics
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