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from __future__ import annotations
import torch
import torch.nn.functional as F
def off_diagonal_mask(size: int, device: torch.device | str) -> torch.Tensor:
return ~torch.eye(size, dtype=torch.bool, device=device)
def standardized_relation(
features: torch.Tensor, mask: torch.Tensor | None = None
) -> tuple[torch.Tensor, torch.Tensor]:
"""Cosine relation field and its standardized off-diagonal values."""
features = F.normalize(features.float(), dim=-1)
relation = features @ features.T
if mask is None:
mask = off_diagonal_mask(len(features), features.device)
values = relation[mask]
standardized = (values - values.mean()) / values.std().clamp_min(1e-6)
return relation, standardized
def relation_field_energy(
visual_relation: torch.Tensor,
visual_standardized: torch.Tensor,
language_particles: torch.Tensor,
temperatures: tuple[float, ...] = (0.03, 0.07, 0.15),
) -> tuple[torch.Tensor, torch.Tensor]:
"""Second-order and multiscale conditional relation energies."""
language_relation, language_standardized = standardized_relation(
language_particles
)
mse = F.mse_loss(language_standardized, visual_standardized)
diagonal = torch.eye(
len(language_particles),
dtype=torch.bool,
device=language_particles.device,
)
conditional_kl = language_particles.new_zeros(())
for temperature in temperatures:
visual_logits = (visual_relation / temperature).masked_fill(
diagonal, -1e4
)
language_logits = (language_relation / temperature).masked_fill(
diagonal, -1e4
)
visual_probability = F.softmax(visual_logits, dim=-1)
conditional_kl = conditional_kl + (
visual_probability
* (
F.log_softmax(visual_logits, dim=-1)
- F.log_softmax(language_logits, dim=-1)
)
).sum(-1).mean()
return mse, conditional_kl
def projection_quantile_target(
text_features: torch.Tensor,
particles: int,
projections: int,
generator: torch.Generator,
) -> tuple[torch.Tensor, torch.Tensor]:
"""Fixed sliced-distribution target from an unpaired text population."""
directions = F.normalize(
torch.randn(
text_features.shape[-1],
projections,
generator=generator,
device=text_features.device,
),
dim=0,
)
projected = (text_features @ directions).sort(dim=0).values
quantile_indices = (
torch.linspace(
0,
len(projected) - 1,
particles,
device=text_features.device,
)
.round()
.long()
)
return directions, projected[quantile_indices]
def sliced_distribution_energy(
particles: torch.Tensor,
directions: torch.Tensor,
target_quantiles: torch.Tensor,
) -> torch.Tensor:
projected = (F.normalize(particles, dim=-1) @ directions).sort(
dim=0
).values
return F.mse_loss(projected, target_quantiles)
def prototype_manifold_energy(
particles: torch.Tensor, prototypes: torch.Tensor
) -> torch.Tensor:
particles = F.normalize(particles, dim=-1)
prototypes = F.normalize(prototypes, dim=-1)
return (1 - (particles @ prototypes.T).max(dim=-1).values).mean()
def log_sinkhorn(
logits: torch.Tensor, temperature: float, iterations: int = 12
) -> torch.Tensor:
"""Doubly stochastic coupling with differentiable log-domain updates."""
log_coupling = logits / temperature
for _ in range(iterations):
log_coupling = log_coupling - torch.logsumexp(
log_coupling, dim=1, keepdim=True
)
log_coupling = log_coupling - torch.logsumexp(
log_coupling, dim=0, keepdim=True
)
return log_coupling.exp()
def retrieval_metrics(
particles: torch.Tensor, paired_text: torch.Tensor
) -> dict[str, float]:
particles = F.normalize(particles.float(), dim=-1)
paired_text = F.normalize(paired_text.float(), dim=-1)
similarity = particles @ paired_text.T
target = similarity.diagonal()
ranks = (similarity > target[:, None]).sum(-1) + 1
return {
"r@1": float((ranks <= 1).float().mean()),
"r@5": float((ranks <= 5).float().mean()),
"r@10": float((ranks <= 10).float().mean()),
"median_rank": float(ranks.float().median()),
"paired_cosine": float(target.mean()),
}
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