File size: 17,437 Bytes
3d6538d
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
a718888
3d6538d
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# MIXING AUGMENTATIONS
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

def alphamix_data(x, y, alpha_range=(0.3, 0.7), spatial_ratio=0.25):
    """
    Standard AlphaMix: Single spatially localized transparent overlay.
    """
    batch_size = x.size(0)
    index = torch.randperm(batch_size, device=x.device)
    
    y_a, y_b = y, y[index]
    
    # Sample alpha from Beta distribution
    alpha_min, alpha_max = alpha_range
    beta_sample = torch.distributions.Beta(2.0, 2.0).sample().item()
    alpha = alpha_min + (alpha_max - alpha_min) * beta_sample
    
    # Compute overlay region
    _, _, H, W = x.shape
    overlay_ratio = torch.sqrt(torch.tensor(spatial_ratio)).item()
    overlay_h = int(H * overlay_ratio)
    overlay_w = int(W * overlay_ratio)
    
    top = torch.randint(0, H - overlay_h + 1, (1,), device=x.device).item()
    left = torch.randint(0, W - overlay_w + 1, (1,), device=x.device).item()
    
    # Blend
    composited_x = x.clone()
    overlay_region = alpha * x[:, :, top:top+overlay_h, left:left+overlay_w]
    background_region = (1 - alpha) * x[index, :, top:top+overlay_h, left:left+overlay_w]
    composited_x[:, :, top:top+overlay_h, left:left+overlay_w] = overlay_region + background_region
    
    return composited_x, y_a, y_b, alpha


def alphamix_fractal(
    x: torch.Tensor,
    y: torch.Tensor,
    alpha_range=(0.3, 0.7),
    steps_range=(1, 3),
    triad_scales=(1/3, 1/9, 1/27),
    beta_shape=(2.0, 2.0),
    seed: int | None = None,
):
    """
    Fractal AlphaMix: Triadic multi-patch overlays aligned to Cantor geometry.
    Pure torch, GPU-compatible.
    """
    if seed is not None:
        torch.manual_seed(seed)
    
    B, C, H, W = x.shape
    device = x.device
    
    # Permutation for mixing
    idx = torch.randperm(B, device=device)
    y_a, y_b = y, y[idx]
    
    x_mix = x.clone()
    total_area = H * W
    
    # Beta distribution for transparency sampling
    k1, k2 = beta_shape
    beta_dist = torch.distributions.Beta(k1, k2)
    alpha_min, alpha_max = alpha_range
    
    # Storage for effective alpha calculation
    alpha_elems = []
    area_weights = []
    
    # Sample number of patches (same for all images in batch)
    steps = torch.randint(steps_range[0], steps_range[1] + 1, (1,), device=device).item()
    
    for _ in range(steps):
        # Choose triadic scale
        scale_idx = torch.randint(0, len(triad_scales), (1,), device=device).item()
        scale = triad_scales[scale_idx]
        
        # Compute patch dimensions (triadic area)
        patch_area = max(1, int(total_area * scale))
        side = int(torch.sqrt(torch.tensor(patch_area, dtype=torch.float32)).item())
        h = max(1, min(H, side))
        w = max(1, min(W, side))
        
        # Random position
        top = torch.randint(0, H - h + 1, (1,), device=device).item()
        left = torch.randint(0, W - w + 1, (1,), device=device).item()
        
        # Sample transparency from Beta distribution
        alpha_raw = beta_dist.sample().item()
        alpha = alpha_min + (alpha_max - alpha_min) * alpha_raw
        
        # Track for effective alpha
        alpha_elems.append(alpha)
        area_weights.append(h * w)
        
        # Blend patches
        fg = alpha * x[:, :, top:top + h, left:left + w]
        bg = (1 - alpha) * x[idx, :, top:top + h, left:left + w]
        x_mix[:, :, top:top + h, left:left + w] = fg + bg
    
    # Compute area-weighted effective alpha
    alpha_t = torch.tensor(alpha_elems, dtype=torch.float32, device=device)
    area_t = torch.tensor(area_weights, dtype=torch.float32, device=device)
    alpha_eff = (alpha_t * area_t).sum() / (area_t.sum() + 1e-12)
    alpha_eff = alpha_eff.item()
    
    return x_mix, y_a, y_b, alpha_eff


# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# DEVIL'S STAIRCASE PE
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

class DevilStaircasePE(nn.Module):
    """Devil's Staircase PE - VECTORIZED for GPU."""
    
    def __init__(self, levels=20, features_per_level=4, smooth_tau=0.25, base=3):
        super().__init__()
        self.levels = levels
        self.features_per_level = features_per_level
        self.tau = smooth_tau
        self.base = base
        
        self.alpha = nn.Parameter(torch.tensor(0.1))
        
        # Precompute level scales and powers
        self.register_buffer('k_range', torch.arange(1, levels + 1, dtype=torch.float32))
        self.register_buffer('cantor_powers', 0.5 ** self.k_range)
        
        self.base_features = 2
        if features_per_level > 2:
            self.feature_expansion = nn.Linear(self.base_features, features_per_level)
        else:
            self.feature_expansion = None
        
    def forward(self, positions, seq_len):
        B = positions.shape[0]
        device = positions.device
        
        x = positions.float() / max(1, (seq_len - 1))
        x = x.clamp(1e-6, 1.0 - 1e-6)  # [B]
        
        # VECTORIZED: Compute all levels at once
        scales = self.base ** self.k_range.to(device)  # [levels]
        y = (x.unsqueeze(1) * scales.unsqueeze(0)) % self.base  # [B, levels]
        
        # VECTORIZED: Triadic softmax for all levels
        centers = torch.tensor([0.5, 1.5, 2.5], device=device, dtype=x.dtype)
        d2 = (y.unsqueeze(-1) - centers) ** 2  # [B, levels, 3]
        logits = -d2 / (self.tau + 1e-8)
        p = F.softmax(logits, dim=-1)  # [B, levels, 3]
        
        # VECTORIZED: Cantor bits
        bit_k = p[..., 2] + self.alpha * p[..., 1]  # [B, levels]
        
        # VECTORIZED: Cantor sum (single matmul instead of loop)
        Cx = (bit_k * self.cantor_powers.to(device).unsqueeze(0)).sum(dim=1)  # [B]
        
        # VECTORIZED: Entropy and PDF
        ent = -(p * p.clamp_min(1e-8).log()).sum(dim=-1)  # [B, levels]
        pdf_proxy = 1.1 - ent / math.log(3.0)  # [B, levels]
        
        # Stack features
        base_feat = torch.stack([bit_k, pdf_proxy], dim=-1)  # [B, levels, 2]
        
        if self.feature_expansion is not None:
            # [B, levels, 2] -> [B, levels, features_per_level]
            pe_levels = self.feature_expansion(base_feat)
        else:
            pe_levels = base_feat
        
        return pe_levels, Cx


# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# GEOMETRIC BASIN COMPATIBILITY
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

class GeometricBasinCompatibility(nn.Module):
    """Compute geometric compatibility scores - 4-factor product."""
    
    def __init__(self, num_classes=100, pe_levels=20, features_per_level=4):
        super().__init__()
        
        self.num_classes = num_classes
        self.pe_levels = pe_levels
        self.features_per_level = features_per_level
        
        self.class_signatures = nn.Parameter(
            torch.randn(num_classes, pe_levels, features_per_level) * 0.1
        )
        
        self.cantor_prototypes = nn.Parameter(
            torch.linspace(0.0, 1.0, num_classes)
        )
        
        self.level_resonance = nn.Parameter(
            torch.ones(num_classes, pe_levels) / pe_levels
        )
    
    def forward(self, pe_levels, cantor_measures):
        B = pe_levels.shape[0]
        
        # 1. TRIADIC COMPATIBILITY
        pe_norm = F.normalize(pe_levels, p=2, dim=-1)
        sig_norm = F.normalize(self.class_signatures, p=2, dim=-1)
        
        similarities = torch.einsum('blf,clf->bcl', pe_norm, sig_norm)
        similarities = (similarities + 1) / 2
        
        resonance = F.softmax(self.level_resonance, dim=-1)
        triadic_compat = (similarities * resonance.unsqueeze(0)).sum(dim=-1)
        
        # 2. SELF-SIMILARITY - VECTORIZED
        level_k = pe_levels[:, :-1, :]   # [B, 19, features] - all levels except last
        level_k1 = pe_levels[:, 1:, :]    # [B, 19, features] - all levels except first

        # Compute all pairwise similarities at once
        sim = F.cosine_similarity(level_k, level_k1, dim=-1, eps=1e-8)  # [B, 19]
        sim = (sim + 1) / 2
        self_sim_pattern = sim  # No stack needed, already [B, levels-1]
        
        expected_patterns = torch.sigmoid(
            self.level_resonance[:, :-1] - self.level_resonance[:, 1:]
        )
        
        pattern_diff = torch.abs(
            self_sim_pattern.unsqueeze(1) - expected_patterns.unsqueeze(0)
        )
        self_sim_compat = 1 - pattern_diff.mean(dim=-1)
        self_sim_compat = torch.clamp(self_sim_compat, 0.0, 1.0)
        
        # 3. CANTOR COHERENCE
        distances = torch.abs(
            cantor_measures.unsqueeze(1) - self.cantor_prototypes.unsqueeze(0)
        )
        cantor_compat = torch.exp(-distances ** 2 / 0.1) + 1e-8
        
        # 4. HIERARCHICAL CHECK
        split_point = self.pe_levels // 2
        early_levels = pe_levels[:, :split_point, :].mean(dim=1)
        late_levels = pe_levels[:, split_point:, :].mean(dim=1)
        
        early_targets = self.class_signatures[:, :split_point, :].mean(dim=1)
        late_targets = self.class_signatures[:, split_point:, :].mean(dim=1)
        
        early_levels_norm = F.normalize(early_levels, p=2, dim=-1)
        late_levels_norm = F.normalize(late_levels, p=2, dim=-1)
        early_targets_norm = F.normalize(early_targets, p=2, dim=-1)
        late_targets_norm = F.normalize(late_targets, p=2, dim=-1)
        
        early_compat = torch.matmul(early_levels_norm, early_targets_norm.t())
        late_compat = torch.matmul(late_levels_norm, late_targets_norm.t())
        
        early_compat = (early_compat + 1) / 2
        late_compat = (late_compat + 1) / 2
        hier_compat = (early_compat + late_compat) / 2
        
        # 5. COMBINE (geometric mean)
        eps = 1e-6
        triadic_compat = torch.clamp(triadic_compat, eps, 1.0)
        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)
        
        compatibility_scores = (
            triadic_compat * 
            self_sim_compat * 
            cantor_compat * 
            hier_compat
        ) ** 0.25
        
        return compatibility_scores


# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# GEOMETRIC BASIN LOSS
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

class GeometricBasinLoss(nn.Module):
    """Loss supervising geometric basin stability field."""
    
    def __init__(self, temperature=0.1):
        super().__init__()
        self.temperature = temperature
        
    def forward(self, compatibility_scores, labels, mixed_labels=None, lam=None):
        batch_size = compatibility_scores.shape[0]
        
        if mixed_labels is not None and lam is not None:
            primary_compat = compatibility_scores[torch.arange(batch_size), labels]
            secondary_compat = compatibility_scores[torch.arange(batch_size), mixed_labels]
            
            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))
            
            soft_targets = torch.zeros_like(compatibility_scores)
            soft_targets[torch.arange(batch_size), labels] = lam
            soft_targets[torch.arange(batch_size), mixed_labels] = 1 - lam
            
            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'
            )
            
            total_loss = primary_loss + secondary_loss + 0.1 * kl_loss
            
        else:
            correct_compat = compatibility_scores[torch.arange(batch_size), labels]
            correct_loss = -torch.log(correct_compat + 1e-8).mean()
            
            mask = torch.ones_like(compatibility_scores)
            mask[torch.arange(batch_size), labels] = 0
            
            incorrect_compat = compatibility_scores * mask
            incorrect_loss = torch.log(1 - incorrect_compat + 1e-8).mean()
            incorrect_loss = -incorrect_loss
            
            scaled_scores = compatibility_scores / self.temperature
            log_probs = F.log_softmax(scaled_scores, dim=1)
            contrastive_loss = F.nll_loss(log_probs, labels)
            
            total_loss = correct_loss + 0.5 * incorrect_loss + 0.5 * contrastive_loss
        
        return total_loss


# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# GEOMETRIC BASIN CLASSIFIER
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

class GeometricBasinClassifier(nn.Module):
    """Geometric basin classifier with ResNet18 backbone + Cantor PE."""
    
    def __init__(self, num_classes=100, pe_levels=20, pe_features_per_level=4, dropout=0.1, pretrained=False):
        super().__init__()
        
        self.num_classes = num_classes
        self.pe_levels = pe_levels
        self.pe_features_per_level = pe_features_per_level
        
        # ResNet18 backbone from torchvision
        from torchvision.models import resnet18, ResNet18_Weights
        if pretrained:
            resnet = resnet18(weights=ResNet18_Weights.IMAGENET1K_V1)
        else:
            resnet = resnet18(weights=None) # will be running both types of train labeled
        
        # Extract feature extractor (everything except fc layer)
        self.backbone = nn.Sequential(
            resnet.conv1,
            resnet.bn1,
            resnet.relu,
            resnet.maxpool,
            resnet.layer1,
            resnet.layer2,
            resnet.layer3,
            resnet.layer4,
            resnet.avgpool
        )
        
        # ResNet18 outputs 512 features
        self.feature_dim = 512
        self.dropout = nn.Dropout(dropout)
        
        # Devil's Staircase PE
        self.pe = DevilStaircasePE(pe_levels, pe_features_per_level)
        
        # PE modulator (adjusted for ResNet18's 512 features)
        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)
        )
        
        # Geometric basin
        self.basin = GeometricBasinCompatibility(
            num_classes, 
            pe_levels, 
            pe_features_per_level
        )
        
    def forward(self, x, return_details=False):
        batch_size = x.shape[0]
        
        # ResNet18 backbone
        cnn_features = self.backbone(x)
        cnn_features = torch.flatten(cnn_features, 1)
        cnn_features = self.dropout(cnn_features)
        
        # Generate PE
        positions = torch.arange(batch_size, device=x.device)
        pe_levels, cantor_measures = self.pe(positions, seq_len=batch_size)
        
        # Modulate PE with CNN features
        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
        
        # Geometric basin compatibility
        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
            }
        
        return compatibility_scores