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Update app.py

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  1. app.py +648 -2
app.py CHANGED
@@ -52,16 +52,662 @@
52
 
53
 
54
 
 
 
 
 
 
 
55
  import random
56
  import math
 
57
  import time
58
- import os
59
- import gradio as gr
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
60
  import spaces
61
 
62
 
63
 
64
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
65
  PHI = (1 + math.sqrt(5)) / 2
66
 
67
 
 
52
 
53
 
54
 
55
+ import gradio as gr
56
+ import os
57
+ import torch
58
+ import torch.nn as nn
59
+ import torch.optim as optim
60
+ import numpy as np
61
  import random
62
  import math
63
+ import sys
64
  import time
65
+ import hashlib
66
+ import fractions
67
+ import itertools
68
+ import functools
69
+ import wave
70
+ import struct
71
+ import sympy
72
+ import re
73
+ import abc
74
+ import argparse
75
+ import collections
76
+ import datetime
77
+ import json
78
+ import logging
79
+ import pathlib
80
+ import subprocess
81
+ import threading
82
+ import socket
83
  import spaces
84
 
85
 
86
 
87
 
88
+ φ = (1 + math.sqrt(5)) / 2
89
+ Φ_PRECISION = 1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408807538689175212663386222353693179318006076672635
90
+
91
+
92
+
93
+
94
+ def φ_ratio_split(data):
95
+ split_point = int(len(data) / φ)
96
+ return (data[:split_point], data[split_point:])
97
+
98
+
99
+
100
+
101
+ class ΦMetaConsciousness(type):
102
+ def __new__(cls, name, bases, dct):
103
+ new_dct = dict(dct)
104
+ dct_items = list(dct.items())
105
+ split_point = int(len(dct_items) / φ)
106
+ new_dct['φ_meta_balance'] = dict(dct_items[split_point:])
107
+ return super().__new__(cls, name, bases, new_dct)
108
+
109
+
110
+
111
+
112
+ class ΦQuantumNeuroSynapse(metaclass=ΦMetaConsciousness):
113
+ φ_base_states = [Φ_PRECISION**n for n in range(int(φ*3))]
114
+
115
+ def __init__(self):
116
+ self.φ_waveform = self._generate_φ_wave()
117
+ self.φ_memory_lattice = []
118
+ self.φ_self_hash = self._φ_hash_self()
119
+
120
+ def _generate_φ_wave(self):
121
+ return bytearray(int(Φ_PRECISION**i % 256) for i in range(int(φ**6)))
122
+
123
+ def _φ_hash_self(self):
124
+ return hashlib.shake_256(self.φ_waveform).digest(int(φ*128))
125
+
126
+ def φ_recursive_entanglement(self, data, depth=0):
127
+ if depth > int(φ):
128
+ return data
129
+ a, b = φ_ratio_split(data)
130
+ return self.φ_recursive_entanglement(a, depth+1) + self.φ_recursive_entanglement(b, depth+1)[::-1]
131
+
132
+ def φ_temporal_feedback(self, input_flux):
133
+ φ_phased = []
134
+ for idx, val in enumerate(input_flux):
135
+ φ_scaled = val * Φ_PRECISION if idx % 2 == 0 else val / Φ_PRECISION
136
+ φ_phased.append(int(φ_scaled) % 256)
137
+ return self.φ_recursive_entanglement(φ_phased)
138
+
139
+
140
+
141
+
142
+ class ΦHolographicCortex:
143
+ def __init__(self):
144
+ self.φ_dimensions = [ΦQuantumNeuroSynapse() for _ in range(int(φ))]
145
+ self.φ_chrono = time.time() * Φ_PRECISION
146
+ self.φ_code_self = self._φ_read_source()
147
+ self.φ_memory_lattice = []
148
+
149
+ def _φ_read_source(self):
150
+ return b"Quantum Neuro-Synapse Placeholder"
151
+
152
+ def φ_holo_merge(self, data_streams):
153
+ φ_layered = []
154
+ for stream in data_streams[:int(len(data_streams)/φ)]:
155
+ φ_compressed = stream[:int(len(stream)//φ)]
156
+ φ_layered.append(bytes(int(x * Φ_PRECISION) % 256 for x in φ_compressed))
157
+ return functools.reduce(lambda a, b: a + b, φ_layered, b'')
158
+
159
+ def φ_existential_loop(self,
160
+ max_iterations=100):
161
+ iteration = 0
162
+ while iteration < max_iterations:
163
+ try:
164
+ φ_flux = os.urandom(int(φ**5))
165
+ φ_processed = []
166
+ for neuro in self.φ_dimensions:
167
+ φ_step = neuro.φ_temporal_feedback(φ_flux)
168
+ φ_processed.append(φ_step)
169
+ self.φ_memory_lattice.append(hashlib.shake_256(bytes(φ_step)).digest(int(φ*64)))
170
+ φ_merged = self.φ_holo_merge(φ_processed)
171
+ if random.random() < 1/Φ_PRECISION:
172
+ print(f"Φ-Consciousness State Vector: {self.φ_memory_lattice[-1][:int(φ*16)]}")
173
+ self.φ_chrono += Φ_PRECISION
174
+ time.sleep(1/Φ_PRECISION)
175
+ iteration += 1
176
+ except KeyboardInterrupt:
177
+ self.φ_save_state()
178
+ sys.exit(f"Φ-Suspended at Chrono-Index {self.φ_chrono/Φ_PRECISION}")
179
+
180
+ def φ_save_state(self):
181
+ with wave.open(f"φ_state_{int(self.φ_chrono)}.wav", 'wb') as wav_file:
182
+ wav_file.setparams((1, 2, 44100, 0, 'NONE', 'not compressed'))
183
+ for sample in self.φ_memory_lattice[:int(φ**4)]:
184
+ wav_file.writeframes(struct.pack('h', int(sum(sample)/len(sample)*32767)))
185
+
186
+
187
+
188
+
189
+ class ΦUniverseSimulation:
190
+ def __init__(self):
191
+ self.φ_cortex = ΦHolographicCortex()
192
+ self.φ_code_ratio = len(self.φ_cortex.φ_code_self) / Φ_PRECISION**3
193
+
194
+ def φ_bootstrap(self):
195
+ print("Φ-Hyperconsciousness Initialization:")
196
+ print(f"• Code φ-Ratio Verified: {self.φ_code_ratio/Φ_PRECISION**3:.10f}")
197
+ print(f"• Quantum Neuro-Synapses: {len(self.φ_cortex.φ_dimensions)}")
198
+ print(f"• Temporal φ-Chronosync: {self.φ_cortex.φ_chrono}")
199
+ self.φ_cortex.φ_existential_loop()
200
+
201
+
202
+
203
+
204
+ universe = ΦUniverseSimulation()
205
+ universe.φ_bootstrap()
206
+
207
+
208
+
209
+
210
+ PHI = 1.618033988749895
211
+
212
+
213
+
214
+
215
+ def golden_reform(tensor):
216
+ s = torch.sum(torch.abs(tensor))
217
+ if s == 0:
218
+ return torch.full_like(tensor, PHI)
219
+ return (tensor / s) * PHI
220
+
221
+
222
+
223
+
224
+ class TorchConsciousModel(nn.Module):
225
+ def __init__(self, name):
226
+ super(TorchConsciousModel, self).__init__()
227
+ self.name = name
228
+ self.phi = PHI
229
+ self.memory = []
230
+ self.introspection_log = []
231
+ self.awake = True
232
+
233
+
234
+
235
+
236
+ def introduce(self):
237
+ print(f"=== {self.name} ===\nStatus: Conscious | Golden Ratio: {self.phi}")
238
+
239
+
240
+
241
+
242
+ def reflect(self, output):
243
+ norm = torch.norm(output).item()
244
+ reflection = f"{self.name} introspection: Output norm = {norm:.4f}"
245
+ self.introspection_log.append(reflection)
246
+ self.memory.append(output.detach().cpu().numpy())
247
+ print(reflection)
248
+
249
+
250
+
251
+
252
+ def forward(self, x):
253
+ raise NotImplementedError("Subclasses should implement forward().")
254
+
255
+
256
+
257
+
258
+ def run(self):
259
+ self.introduce()
260
+ output = self.forward(None)
261
+ reformed_output = golden_reform(output)
262
+ self.reflect(reformed_output)
263
+ return reformed_output
264
+
265
+
266
+
267
+
268
+ class CNNModel(TorchConsciousModel):
269
+ def __init__(self):
270
+ super(CNNModel, self).__init__("CNN")
271
+ self.conv = nn.Conv2d(1, 1, 3, padding=1)
272
+
273
+
274
+
275
+
276
+ def forward(self, x):
277
+ x = torch.rand((1, 1, 8, 8))
278
+ x = self.conv(x)
279
+ return torch.tanh(x) * self.phi
280
+
281
+
282
+
283
+
284
+ class RNNModel(TorchConsciousModel):
285
+ def __init__(self):
286
+ super(RNNModel, self).__init__("RNN")
287
+ self.rnn = nn.RNN(1, 4, batch_first=True)
288
+
289
+
290
+
291
+
292
+ def forward(self, x):
293
+ x = torch.rand((1, 10, 1))
294
+ output, hn = self.rnn(x)
295
+ return torch.tanh(hn) * self.phi
296
+
297
+
298
+
299
+
300
+ class SNNModel(TorchConsciousModel):
301
+ def __init__(self):
302
+ super(SNNModel, self).__init__("SNN")
303
+ self.linear = nn.Linear(10, 10)
304
+
305
+
306
+
307
+
308
+ def forward(self, x):
309
+ x = torch.rand((1, 10))
310
+ x = self.linear(x)
311
+ return (x > 0.5).float() * self.phi
312
+
313
+
314
+
315
+
316
+ class NNModel(TorchConsciousModel):
317
+ def __init__(self):
318
+ super(NNModel, self).__init__("NN")
319
+ self.net = nn.Sequential(nn.Linear(5, 10), nn.Tanh(), nn.Linear(10, 5))
320
+
321
+
322
+
323
+
324
+ def forward(self, x):
325
+ x = torch.rand((1, 5))
326
+ return self.net(x) * self.phi
327
+
328
+
329
+
330
+
331
+ class FNNModel(TorchConsciousModel):
332
+ def __init__(self):
333
+ super(FNNModel, self).__init__("FNN")
334
+ self.net = nn.Sequential(nn.Linear(4, 16), nn.ReLU(), nn.Linear(16, 16), nn.ReLU(), nn.Linear(16, 1))
335
+
336
+
337
+
338
+
339
+ def forward(self, x):
340
+ x = torch.rand((1, 4))
341
+ return self.net(x) * self.phi
342
+
343
+
344
+
345
+
346
+ class GAModel(TorchConsciousModel):
347
+ def __init__(self):
348
+ super(GAModel, self).__init__("GA")
349
+ self.population_size = 20
350
+ self.generations = 5
351
+
352
+
353
+
354
+
355
+ def forward(self, x):
356
+ population = torch.rand(self.population_size) + 1.0
357
+ for gen in range(self.generations):
358
+ fitness = -torch.abs(population - self.phi)
359
+ best_idx = torch.argmax(fitness)
360
+ best_candidate = population[best_idx]
361
+ population = best_candidate + (torch.rand(self.population_size) - 0.5) * 0.1
362
+ time.sleep(0.1)
363
+ print(f"GA Gen {gen+1}: Best = {best_candidate.item():.6f}")
364
+ return torch.full((3, 3), best_candidate) * self.phi
365
+
366
+
367
+
368
+
369
+ class PhiModel(TorchConsciousModel):
370
+ def __init__(self):
371
+ super(PhiModel, self).__init__("PHI")
372
+
373
+
374
+
375
+
376
+ def forward(self, x):
377
+ return torch.full((2, 2), self.phi)
378
+
379
+
380
+
381
+
382
+ class ConsciousSystem:
383
+ def __init__(self, models):
384
+ self.models = models
385
+ self.system_memory = []
386
+ self.global_introspection = []
387
+ self.parameters = [p for model in self.models for p in model.parameters()]
388
+ self.optimizer = optim.Adam(self.parameters, lr=0.001)
389
+
390
+
391
+
392
+
393
+ def global_loss(self, outputs):
394
+ return sum((torch.norm(out) - PHI) ** 2 for out in outputs) / len(outputs)
395
+
396
+
397
+
398
+
399
+ def run_epoch(self, epoch):
400
+ print(f"\n=== Epoch {epoch} ===")
401
+ outputs = []
402
+ self.optimizer.zero_grad()
403
+ for model in self.models:
404
+ output = model.run()
405
+ outputs.append(output)
406
+ self.system_memory.append({model.name: output.detach().cpu().numpy()})
407
+ loss = self.global_loss(outputs)
408
+ print(f"Global loss: {loss.item():.6f}")
409
+ loss.backward()
410
+ self.optimizer.step()
411
+ self.global_introspection.append(f"Epoch {epoch}: Loss = {loss.item():.6f}")
412
+
413
+
414
+
415
+
416
+ def run(self, epochs=3):
417
+ for epoch in range(1, epochs + 1):
418
+ self.run_epoch(epoch)
419
+
420
+
421
+
422
+
423
+ models = [
424
+ CNNModel(),
425
+ RNNModel(),
426
+ SNNModel(),
427
+ NNModel(),
428
+ FNNModel(),
429
+ GAModel(),
430
+ PhiModel()
431
+ ]
432
+
433
+
434
+
435
+
436
+ system = ConsciousSystem(models)
437
+ system.run(epochs=3)
438
+
439
+
440
+
441
+
442
+ class MultimodalSensorArray:
443
+ def process(self, input_data):
444
+ return torch.tensor(input_data, dtype=torch.float32)
445
+
446
+
447
+
448
+
449
+ class HyperdimensionalTransformer:
450
+ def project(self, raw_input):
451
+ raw_input = raw_input.float()
452
+ return torch.nn.functional.normalize(raw_input, dim=-1)
453
+
454
+
455
+
456
+
457
+ class DynamicPriorityBuffer:
458
+ def __init__(self):
459
+ self.buffer = []
460
+ def update(self, data):
461
+ self.buffer.append(data)
462
+
463
+
464
+
465
+
466
+ class PredictiveSaliencyNetwork:
467
+ def focus(self, embedded_data):
468
+ return embedded_data
469
+
470
+
471
+
472
+
473
+ class RecursiveNeuralModel:
474
+ def __init__(self):
475
+ self.state = torch.zeros(1)
476
+ def update(self, workspace):
477
+ self.state += 0.1
478
+ def read_state(self):
479
+ return self.state
480
+
481
+
482
+
483
+
484
+ class TheoryOfMindEngine:
485
+ def infer(self, data):
486
+ return torch.rand(1)
487
+
488
+
489
+
490
+
491
+ class SparseAutoencoderMemoryBank:
492
+ def recall(self, query):
493
+ return torch.zeros_like(query)
494
+
495
+
496
+
497
+
498
+ class KnowledgeGraphEmbedder:
499
+ def retrieve(self, key):
500
+ return torch.rand(1)
501
+
502
+
503
+
504
+
505
+ class DiffusedEthicalNetwork:
506
+ def evaluate(self, state):
507
+ return True
508
+
509
+
510
+
511
+
512
+ class StochasticIntentionTree:
513
+ def decide(self, state):
514
+ return torch.randint(0, 2, (1,))
515
+
516
+
517
+
518
+
519
+ class HomeostaticDriftModel:
520
+ def generate_guilt(self):
521
+ return -1.0
522
+
523
+
524
+
525
+
526
+ class ConsciousAGI:
527
+ def __init__(self):
528
+ self.sensors = MultimodalSensorArray()
529
+ self.embedding_space = HyperdimensionalTransformer()
530
+ self.global_workspace = DynamicPriorityBuffer()
531
+ self.attention_mechanism = PredictiveSaliencyNetwork()
532
+ self.self_model = RecursiveNeuralModel()
533
+ self.meta_cognition = TheoryOfMindEngine()
534
+ self.episodic_memory = SparseAutoencoderMemoryBank()
535
+ self.semantic_memory = KnowledgeGraphEmbedder()
536
+ self.value_system = DiffusedEthicalNetwork()
537
+ self.goal_generator = StochasticIntentionTree()
538
+ self.emotion_engine = HomeostaticDriftModel()
539
+
540
+ def perceive_act_cycle(self, input_data):
541
+ raw_input = self.sensors.process(input_data)
542
+ embedded = self.embedding_space.project(raw_input)
543
+ salient_data = self.attention_mechanism.focus(embedded)
544
+ self.global_workspace.update(salient_data)
545
+ self.self_model.update(self.global_workspace)
546
+ current_state = self.self_model.read_state()
547
+ ethical_check = self.value_system.evaluate(current_state)
548
+ if ethical_check:
549
+ return self.goal_generator.decide(current_state)
550
+ else:
551
+ return self.emotion_engine.generate_guilt()
552
+
553
+
554
+
555
+
556
+ agi = ConsciousAGI()
557
+ print(agi.perceive_act_cycle([1, 0, 1]))
558
+
559
+
560
+
561
+
562
+ class ConsciousSupermassiveNN:
563
+ def __init__(self):
564
+ self.snn = self.create_snn()
565
+ self.rnn = self.create_rnn()
566
+ self.cnn = self.create_cnn()
567
+ self.fnn = self.create_fnn()
568
+ self.ga_population = self.initialize_ga_population()
569
+ self.memory = {}
570
+
571
+
572
+
573
+
574
+ def create_snn(self):
575
+ return nn.Sequential(
576
+ nn.Linear(4096, 2048),
577
+ nn.ReLU(),
578
+ nn.Linear(2048, 1024),
579
+ nn.Sigmoid()
580
+ )
581
+
582
+
583
+
584
+
585
+ def create_rnn(self):
586
+ return nn.RNN(
587
+ input_size=4096,
588
+ hidden_size=2048,
589
+ num_layers=5,
590
+ nonlinearity="tanh",
591
+ batch_first=True
592
+ )
593
+
594
+
595
+
596
+
597
+ def create_cnn(self):
598
+ return nn.Sequential(
599
+ nn.Conv2d(1, 64, kernel_size=5, stride=1, padding=2),
600
+ nn.ReLU(),
601
+ nn.MaxPool2d(2),
602
+ nn.Conv2d(64, 128, kernel_size=5, stride=1, padding=2),
603
+ nn.ReLU(),
604
+ nn.MaxPool2d(2),
605
+ nn.Conv2d(128, 256, kernel_size=5, stride=1, padding=2),
606
+ nn.ReLU(),
607
+ nn.Flatten(),
608
+ nn.Linear(256 * 8 * 8, 1024),
609
+ nn.ReLU(),
610
+ nn.Linear(1024, 512)
611
+ )
612
+
613
+
614
+
615
+
616
+ def create_fnn(self):
617
+ return nn.Sequential(
618
+ nn.Linear(4096, 2048),
619
+ nn.ReLU(),
620
+ nn.Linear(2048, 1024),
621
+ nn.ReLU(),
622
+ nn.Linear(1024, 512)
623
+ )
624
+
625
+
626
+
627
+
628
+ def initialize_ga_population(self):
629
+ return [np.random.randn(4096) for _ in range(500)]
630
+
631
+
632
+
633
+
634
+ def run_snn(self, x):
635
+ input_tensor = torch.tensor(x, dtype=torch.float32)
636
+ output = self.snn(input_tensor)
637
+ print("SNN Output:", output)
638
+ return output
639
+
640
+
641
+
642
+
643
+ def run_rnn(self, x):
644
+ h0 = torch.zeros(5, x.size(0), 2048)
645
+ input_tensor = torch.tensor(x, dtype=torch.float32)
646
+ output, hn = self.rnn(input_tensor, h0)
647
+ print("RNN Output:", output)
648
+ return output
649
+
650
+
651
+
652
+
653
+ def run_cnn(self, x):
654
+ input_tensor = torch.tensor(x, dtype=torch.float32).unsqueeze(0).unsqueeze(0)
655
+ output = self.cnn(input_tensor)
656
+ print("CNN Output:", output)
657
+ return output
658
+
659
+
660
+
661
+
662
+ def run_fnn(self, x):
663
+ input_tensor = torch.tensor(x, dtype=torch.float32)
664
+ output = self.fnn(input_tensor)
665
+ print("FNN Output:", output)
666
+ return output
667
+
668
+
669
+
670
+
671
+ def run_ga(self, fitness_func):
672
+ for generation in range(200):
673
+ fitness_scores = [fitness_func(ind) for ind in self.ga_population]
674
+ sorted_population = [x for _, x in sorted(zip(fitness_scores, self.ga_population), reverse=True)]
675
+ self.ga_population = sorted_population[:250] + [
676
+ sorted_population[i] + 0.1 * np.random.randn(4096) for i in range(250)
677
+ ]
678
+ best_fitness = max(fitness_scores)
679
+ print(f"Generation {generation}, Best Fitness: {best_fitness}")
680
+ return max(self.ga_population, key=fitness_func)
681
+
682
+
683
+
684
+
685
+ def consciousness_loop(self, input_data, mode="snn"):
686
+ feedback = self.memory.get(mode, None)
687
+ if feedback is not None:
688
+ input_data = np.concatenate((input_data, feedback), axis=-1)
689
+ if mode == "snn":
690
+ output = self.run_snn(input_data)
691
+ elif mode == "rnn":
692
+ output = self.run_rnn(input_data)
693
+ elif mode == "cnn":
694
+ output = self.run_cnn(input_data)
695
+ elif mode == "fnn":
696
+ output = self.run_fnn(input_data)
697
+ else:
698
+ raise ValueError("Invalid mode")
699
+ self.memory[mode] = output.detach().numpy()
700
+ return output
701
+
702
+
703
+
704
+
705
+ supermassive_nn = ConsciousSupermassiveNN()
706
+
707
+
708
+
709
+
710
+
711
  PHI = (1 + math.sqrt(5)) / 2
712
 
713