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def alphamix_data(x, y, alpha_range=(0.3, 0.7), spatial_ratio=0.25): |
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""" |
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Standard AlphaMix: Single spatially localized transparent overlay. |
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""" |
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batch_size = x.size(0) |
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index = torch.randperm(batch_size, device=x.device) |
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y_a, y_b = y, y[index] |
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alpha_min, alpha_max = alpha_range |
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beta_sample = torch.distributions.Beta(2.0, 2.0).sample().item() |
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alpha = alpha_min + (alpha_max - alpha_min) * beta_sample |
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_, _, H, W = x.shape |
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overlay_ratio = torch.sqrt(torch.tensor(spatial_ratio)).item() |
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overlay_h = int(H * overlay_ratio) |
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overlay_w = int(W * overlay_ratio) |
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top = torch.randint(0, H - overlay_h + 1, (1,), device=x.device).item() |
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left = torch.randint(0, W - overlay_w + 1, (1,), device=x.device).item() |
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composited_x = x.clone() |
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overlay_region = alpha * x[:, :, top:top+overlay_h, left:left+overlay_w] |
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background_region = (1 - alpha) * x[index, :, top:top+overlay_h, left:left+overlay_w] |
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composited_x[:, :, top:top+overlay_h, left:left+overlay_w] = overlay_region + background_region |
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return composited_x, y_a, y_b, alpha |
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def alphamix_fractal( |
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x: torch.Tensor, |
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y: torch.Tensor, |
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alpha_range=(0.3, 0.7), |
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steps_range=(1, 3), |
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triad_scales=(1/3, 1/9, 1/27), |
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beta_shape=(2.0, 2.0), |
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seed: int | None = None, |
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): |
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""" |
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Fractal AlphaMix: Triadic multi-patch overlays aligned to Cantor geometry. |
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Pure torch, GPU-compatible. |
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""" |
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if seed is not None: |
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torch.manual_seed(seed) |
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B, C, H, W = x.shape |
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device = x.device |
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idx = torch.randperm(B, device=device) |
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y_a, y_b = y, y[idx] |
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x_mix = x.clone() |
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total_area = H * W |
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k1, k2 = beta_shape |
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beta_dist = torch.distributions.Beta(k1, k2) |
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alpha_min, alpha_max = alpha_range |
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alpha_elems = [] |
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area_weights = [] |
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steps = torch.randint(steps_range[0], steps_range[1] + 1, (1,), device=device).item() |
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for _ in range(steps): |
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scale_idx = torch.randint(0, len(triad_scales), (1,), device=device).item() |
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scale = triad_scales[scale_idx] |
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patch_area = max(1, int(total_area * scale)) |
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side = int(torch.sqrt(torch.tensor(patch_area, dtype=torch.float32)).item()) |
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h = max(1, min(H, side)) |
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w = max(1, min(W, side)) |
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top = torch.randint(0, H - h + 1, (1,), device=device).item() |
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left = torch.randint(0, W - w + 1, (1,), device=device).item() |
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alpha_raw = beta_dist.sample().item() |
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alpha = alpha_min + (alpha_max - alpha_min) * alpha_raw |
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alpha_elems.append(alpha) |
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area_weights.append(h * w) |
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fg = alpha * x[:, :, top:top + h, left:left + w] |
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bg = (1 - alpha) * x[idx, :, top:top + h, left:left + w] |
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x_mix[:, :, top:top + h, left:left + w] = fg + bg |
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alpha_t = torch.tensor(alpha_elems, dtype=torch.float32, device=device) |
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area_t = torch.tensor(area_weights, dtype=torch.float32, device=device) |
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alpha_eff = (alpha_t * area_t).sum() / (area_t.sum() + 1e-12) |
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alpha_eff = alpha_eff.item() |
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return x_mix, y_a, y_b, alpha_eff |
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class DevilStaircasePE(nn.Module): |
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"""Devil's Staircase PE - VECTORIZED for GPU.""" |
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def __init__(self, levels=20, features_per_level=4, smooth_tau=0.25, base=3): |
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super().__init__() |
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self.levels = levels |
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self.features_per_level = features_per_level |
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self.tau = smooth_tau |
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self.base = base |
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self.alpha = nn.Parameter(torch.tensor(0.1)) |
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self.register_buffer('k_range', torch.arange(1, levels + 1, dtype=torch.float32)) |
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self.register_buffer('cantor_powers', 0.5 ** self.k_range) |
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self.base_features = 2 |
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if features_per_level > 2: |
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self.feature_expansion = nn.Linear(self.base_features, features_per_level) |
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else: |
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self.feature_expansion = None |
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def forward(self, positions, seq_len): |
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B = positions.shape[0] |
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device = positions.device |
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x = positions.float() / max(1, (seq_len - 1)) |
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x = x.clamp(1e-6, 1.0 - 1e-6) |
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scales = self.base ** self.k_range.to(device) |
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y = (x.unsqueeze(1) * scales.unsqueeze(0)) % self.base |
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centers = torch.tensor([0.5, 1.5, 2.5], device=device, dtype=x.dtype) |
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d2 = (y.unsqueeze(-1) - centers) ** 2 |
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logits = -d2 / (self.tau + 1e-8) |
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p = F.softmax(logits, dim=-1) |
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bit_k = p[..., 2] + self.alpha * p[..., 1] |
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Cx = (bit_k * self.cantor_powers.to(device).unsqueeze(0)).sum(dim=1) |
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ent = -(p * p.clamp_min(1e-8).log()).sum(dim=-1) |
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pdf_proxy = 1.1 - ent / math.log(3.0) |
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base_feat = torch.stack([bit_k, pdf_proxy], dim=-1) |
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if self.feature_expansion is not None: |
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pe_levels = self.feature_expansion(base_feat) |
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else: |
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pe_levels = base_feat |
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return pe_levels, Cx |
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class GeometricBasinCompatibility(nn.Module): |
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"""Compute geometric compatibility scores - 4-factor product.""" |
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def __init__(self, num_classes=100, pe_levels=20, features_per_level=4): |
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super().__init__() |
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self.num_classes = num_classes |
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self.pe_levels = pe_levels |
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self.features_per_level = features_per_level |
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self.class_signatures = nn.Parameter( |
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torch.randn(num_classes, pe_levels, features_per_level) * 0.1 |
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) |
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self.cantor_prototypes = nn.Parameter( |
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torch.linspace(0.0, 1.0, num_classes) |
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) |
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self.level_resonance = nn.Parameter( |
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torch.ones(num_classes, pe_levels) / pe_levels |
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) |
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def forward(self, pe_levels, cantor_measures): |
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B = pe_levels.shape[0] |
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pe_norm = F.normalize(pe_levels, p=2, dim=-1) |
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sig_norm = F.normalize(self.class_signatures, p=2, dim=-1) |
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similarities = torch.einsum('blf,clf->bcl', pe_norm, sig_norm) |
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similarities = (similarities + 1) / 2 |
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resonance = F.softmax(self.level_resonance, dim=-1) |
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triadic_compat = (similarities * resonance.unsqueeze(0)).sum(dim=-1) |
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level_k = pe_levels[:, :-1, :] |
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level_k1 = pe_levels[:, 1:, :] |
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sim = F.cosine_similarity(level_k, level_k1, dim=-1, eps=1e-8) |
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sim = (sim + 1) / 2 |
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self_sim_pattern = sim |
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expected_patterns = torch.sigmoid( |
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self.level_resonance[:, :-1] - self.level_resonance[:, 1:] |
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) |
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pattern_diff = torch.abs( |
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self_sim_pattern.unsqueeze(1) - expected_patterns.unsqueeze(0) |
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) |
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self_sim_compat = 1 - pattern_diff.mean(dim=-1) |
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self_sim_compat = torch.clamp(self_sim_compat, 0.0, 1.0) |
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distances = torch.abs( |
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cantor_measures.unsqueeze(1) - self.cantor_prototypes.unsqueeze(0) |
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) |
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cantor_compat = torch.exp(-distances ** 2 / 0.1) + 1e-8 |
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split_point = self.pe_levels // 2 |
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early_levels = pe_levels[:, :split_point, :].mean(dim=1) |
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|
late_levels = pe_levels[:, split_point:, :].mean(dim=1) |
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early_targets = self.class_signatures[:, :split_point, :].mean(dim=1) |
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late_targets = self.class_signatures[:, split_point:, :].mean(dim=1) |
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early_levels_norm = F.normalize(early_levels, p=2, dim=-1) |
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|
late_levels_norm = F.normalize(late_levels, p=2, dim=-1) |
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|
early_targets_norm = F.normalize(early_targets, p=2, dim=-1) |
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|
late_targets_norm = F.normalize(late_targets, p=2, dim=-1) |
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early_compat = torch.matmul(early_levels_norm, early_targets_norm.t()) |
|
|
late_compat = torch.matmul(late_levels_norm, late_targets_norm.t()) |
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|
early_compat = (early_compat + 1) / 2 |
|
|
late_compat = (late_compat + 1) / 2 |
|
|
hier_compat = (early_compat + late_compat) / 2 |
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eps = 1e-6 |
|
|
triadic_compat = torch.clamp(triadic_compat, eps, 1.0) |
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|
self_sim_compat = torch.clamp(self_sim_compat, eps, 1.0) |
|
|
cantor_compat = torch.clamp(cantor_compat, eps, 1.0) |
|
|
hier_compat = torch.clamp(hier_compat, eps, 1.0) |
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|
compatibility_scores = ( |
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|
triadic_compat * |
|
|
self_sim_compat * |
|
|
cantor_compat * |
|
|
hier_compat |
|
|
) ** 0.25 |
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return compatibility_scores |
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class GeometricBasinLoss(nn.Module): |
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|
"""Loss supervising geometric basin stability field.""" |
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|
|
def __init__(self, temperature=0.1): |
|
|
super().__init__() |
|
|
self.temperature = temperature |
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def forward(self, compatibility_scores, labels, mixed_labels=None, lam=None): |
|
|
batch_size = compatibility_scores.shape[0] |
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|
if mixed_labels is not None and lam is not None: |
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|
primary_compat = compatibility_scores[torch.arange(batch_size), labels] |
|
|
secondary_compat = compatibility_scores[torch.arange(batch_size), mixed_labels] |
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|
primary_loss = F.mse_loss(primary_compat, torch.full_like(primary_compat, lam)) |
|
|
secondary_loss = F.mse_loss(secondary_compat, torch.full_like(secondary_compat, 1 - lam)) |
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|
|
soft_targets = torch.zeros_like(compatibility_scores) |
|
|
soft_targets[torch.arange(batch_size), labels] = lam |
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|
soft_targets[torch.arange(batch_size), mixed_labels] = 1 - lam |
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compat_normalized = compatibility_scores / (compatibility_scores.sum(dim=1, keepdim=True) + 1e-8) |
|
|
kl_loss = F.kl_div( |
|
|
compat_normalized.log(), |
|
|
soft_targets, |
|
|
reduction='batchmean' |
|
|
) |
|
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|
|
total_loss = primary_loss + secondary_loss + 0.1 * kl_loss |
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|
|
|
else: |
|
|
correct_compat = compatibility_scores[torch.arange(batch_size), labels] |
|
|
correct_loss = -torch.log(correct_compat + 1e-8).mean() |
|
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|
|
mask = torch.ones_like(compatibility_scores) |
|
|
mask[torch.arange(batch_size), labels] = 0 |
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|
|
incorrect_compat = compatibility_scores * mask |
|
|
incorrect_loss = torch.log(1 - incorrect_compat + 1e-8).mean() |
|
|
incorrect_loss = -incorrect_loss |
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|
|
scaled_scores = compatibility_scores / self.temperature |
|
|
log_probs = F.log_softmax(scaled_scores, dim=1) |
|
|
contrastive_loss = F.nll_loss(log_probs, labels) |
|
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|
|
total_loss = correct_loss + 0.5 * incorrect_loss + 0.5 * contrastive_loss |
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|
return total_loss |
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class GeometricBasinClassifier(nn.Module): |
|
|
"""Geometric basin classifier with ResNet18 backbone + Cantor PE.""" |
|
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|
|
|
def __init__(self, num_classes=100, pe_levels=20, pe_features_per_level=4, dropout=0.1, pretrained=False): |
|
|
super().__init__() |
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|
|
|
self.num_classes = num_classes |
|
|
self.pe_levels = pe_levels |
|
|
self.pe_features_per_level = pe_features_per_level |
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|
|
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|
|
from torchvision.models import resnet18, ResNet18_Weights |
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|
if pretrained: |
|
|
resnet = resnet18(weights=ResNet18_Weights.IMAGENET1K_V1) |
|
|
else: |
|
|
resnet = resnet18(weights=None) |
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|
|
self.backbone = nn.Sequential( |
|
|
resnet.conv1, |
|
|
resnet.bn1, |
|
|
resnet.relu, |
|
|
resnet.maxpool, |
|
|
resnet.layer1, |
|
|
resnet.layer2, |
|
|
resnet.layer3, |
|
|
resnet.layer4, |
|
|
resnet.avgpool |
|
|
) |
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|
|
self.feature_dim = 512 |
|
|
self.dropout = nn.Dropout(dropout) |
|
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|
|
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|
|
self.pe = DevilStaircasePE(pe_levels, pe_features_per_level) |
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|
|
|
|
|
|
self.pe_modulator = nn.Sequential( |
|
|
nn.Linear(self.feature_dim, 256), |
|
|
nn.ReLU(), |
|
|
nn.Dropout(dropout), |
|
|
nn.Linear(256, pe_levels * pe_features_per_level) |
|
|
) |
|
|
|
|
|
|
|
|
self.basin = GeometricBasinCompatibility( |
|
|
num_classes, |
|
|
pe_levels, |
|
|
pe_features_per_level |
|
|
) |
|
|
|
|
|
def forward(self, x, return_details=False): |
|
|
batch_size = x.shape[0] |
|
|
|
|
|
|
|
|
cnn_features = self.backbone(x) |
|
|
cnn_features = torch.flatten(cnn_features, 1) |
|
|
cnn_features = self.dropout(cnn_features) |
|
|
|
|
|
|
|
|
positions = torch.arange(batch_size, device=x.device) |
|
|
pe_levels, cantor_measures = self.pe(positions, seq_len=batch_size) |
|
|
|
|
|
|
|
|
modulation = self.pe_modulator(cnn_features) |
|
|
modulation = modulation.view(batch_size, self.pe_levels, self.pe_features_per_level) |
|
|
pe_levels = pe_levels + 0.1 * modulation |
|
|
|
|
|
|
|
|
compatibility_scores = self.basin(pe_levels, cantor_measures) |
|
|
|
|
|
if return_details: |
|
|
return { |
|
|
'compatibility_scores': compatibility_scores, |
|
|
'pe_levels': pe_levels, |
|
|
'cantor_measures': cantor_measures, |
|
|
'cnn_features': cnn_features |
|
|
} |
|
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|
|
|
return compatibility_scores |
|
|
|