| |
| """#9 Hyperbolic Poincaré Ball Embeddings for ABZ hierarchy. |
| |
| Reference: Nickel & Kiela 2017 (arXiv:1705.08039); |
| Hyperbolic Image Embeddings (Khrulkov 2020 CVPR). |
| |
| Poincaré ball doğal olarak hiyerarşik yapıları embed eder. |
| ABZ numaralandırması tree-like → hyperbolic space ideal. |
| """ |
| import torch |
| import torch.nn as nn |
|
|
| def exponential_map(v, c=1.0): |
| """Exp map at origin: Euclidean → Poincaré ball.""" |
| v_norm = v.norm(dim=-1, keepdim=True).clamp(min=1e-8) |
| return torch.tanh(v_norm * c**0.5) * v / (v_norm * c**0.5) |
|
|
| def poincare_distance(x, y, c=1.0): |
| """Poincaré ball distance (batched).""" |
| x = x.clamp(max=1-1e-5, min=-(1-1e-5)) |
| y = y.clamp(max=1-1e-5, min=-(1-1e-5)) |
| diff = x - y |
| num = 2 * (diff * diff).sum(-1) |
| denom = (1 - c * (x*x).sum(-1)) * (1 - c * (y*y).sum(-1)) + 1e-8 |
| return torch.acosh(torch.clamp(1 + num / denom, min=1+1e-7)) / c**0.5 |
|
|
| class HyperbolicClassifier(nn.Module): |
| """Maps features → Poincaré ball → distance to class prototypes.""" |
| |
| def __init__(self, in_dim=1024, n_classes=198, hyperbolic_dim=128, c=1.0): |
| super().__init__() |
| self.project = nn.Linear(in_dim, hyperbolic_dim) |
| |
| self.class_protos = nn.Parameter(torch.randn(n_classes, hyperbolic_dim) * 0.01) |
| self.c = c |
| |
| def forward(self, features): |
| euc = self.project(features) |
| hyp = exponential_map(euc, self.c) |
| |
| protos_hyp = exponential_map(self.class_protos, self.c) |
| |
| dists = poincare_distance( |
| hyp.unsqueeze(1), |
| protos_hyp.unsqueeze(0), |
| self.c |
| ) |
| return -dists |
|
|
| if __name__ == '__main__': |
| torch.manual_seed(0) |
| hc = HyperbolicClassifier(in_dim=1024, n_classes=198, hyperbolic_dim=128) |
| feats = torch.randn(8, 1024) |
| logits = hc(feats) |
| print(f"Hyperbolic logits: {logits.shape}, range: [{logits.min().item():.3f}, {logits.max().item():.3f}]") |
|
|
