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
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
|
"""Matched non-backprop adapters for the audited CIFAR ResNet topology.
These adapters reuse :class:`CIFARLocalResNet`'s forward tensors, BatchNorm,
option-A shortcuts, and local optimizer. They are kept separate from the
established SDIL/KP implementation so a crossover baseline cannot silently
change the already confirmed forward model.
"""
import torch
import torch.nn.functional as F
from .conv import CIFARLocalResNet
class CIFARPEPITAResNet(CIFARLocalResNet):
"""Two-presentation PEPITA on the matched residual forward topology."""
def __init__(self, *args, projection_scale=0.05,
projection_seed=1731, **kwargs):
super().__init__(*args, **kwargs)
if projection_scale <= 0:
raise ValueError("PEPITA projection scale must be positive")
generator = torch.Generator(device="cpu").manual_seed(projection_seed)
input_units = 3 * 32 * 32
limit = (6.0 / input_units) ** 0.5 * projection_scale
projection = (
2.0 * torch.rand(
self.n_classes, 3, 32, 32, generator=generator) - 1.0
) * limit
self.input_feedback = projection.to(
device=self.device, dtype=self.dtype)
@property
def n_fixed_feedback_parameters(self):
return self.input_feedback.numel()
@torch.no_grad()
def pepita_ascent_directions(self, clean, modulated, modulated_error):
"""Return the explicit first-minus-second PEPITA correlations.
The post-activation difference directly multiplies the modulated
presynaptic activity, as in PEPITA/ERIN; it is not differentiated
through the ReLU. BatchNorm's current-layer Jacobian and a residual
branch's fixed multiplier remain part of that local synaptic
eligibility. Convolutional correlations follow the reference code's
additional average over spatial positions.
"""
batch = modulated_error.shape[0]
directions = []
gamma_directions = []
beta_directions = []
for index, (clean_hidden, modulated_hidden, cache, weight, spec) in (
enumerate(zip(
clean["hiddens"], modulated["hiddens"],
modulated["caches"], self.W, self.layer_specs))):
field = clean_hidden - modulated_hidden
local_field = field * spec.branch_scale
local_field, gamma_direction, beta_direction = (
self._normalization_backward(
index, local_field, cache["normalization"]))
spatial = local_field.shape[2] * local_field.shape[3]
correlation = torch.nn.grad.conv2d_weight(
cache["pre"], weight.shape, local_field,
stride=spec.stride, padding=spec.padding)
directions.append(-correlation / (batch * spatial))
if gamma_direction is not None:
gamma_directions.append(
-gamma_direction / (batch * spatial))
beta_directions.append(
-beta_direction / (batch * spatial))
output_weight = -(
modulated_error.t() @ modulated["features"]) / batch
output_bias = -modulated_error.mean(dim=0)
return (
directions, gamma_directions, beta_directions,
output_weight, output_bias)
def pepita_step(self, image, labels, eta, eta_output=None,
momentum=0.0, weight_decay=0.0):
"""One architecture-compatible PEPITA/ERIN local update."""
one_hot = F.one_hot(labels, self.n_classes).to(image.dtype)
with torch.no_grad():
clean = self.forward(
image, return_cache=True, training=True, update_stats=True)
clean_error = torch.softmax(clean["logits"], dim=1) - one_hot
input_error = torch.einsum(
"bc,cijk->bijk", clean_error, self.input_feedback)
modulated = self.forward(
image + input_error, return_cache=True,
training=True, update_stats=False)
modulated_error = (
torch.softmax(modulated["logits"], dim=1) - one_hot)
(directions, gamma_directions, beta_directions,
output_weight, output_bias) = self.pepita_ascent_directions(
clean, modulated, modulated_error)
self.apply_ascent(
directions, output_weight, output_bias, eta,
eta_output=eta_output, momentum=momentum,
weight_decay=weight_decay,
gamma_directions=gamma_directions,
beta_directions=beta_directions)
loss = F.cross_entropy(clean["logits"], labels)
return float(loss)
class CIFARForwardForwardResNet(CIFARLocalResNet):
"""Greedy supervised Forward-Forward on the residual parameter topology."""
def __init__(self, *args, threshold=2.0, learning_rate=0.03,
score_from_layer=1, **kwargs):
super().__init__(*args, **kwargs)
if learning_rate <= 0 or threshold <= 0:
raise ValueError("invalid Forward-Forward hyperparameters")
self.ff_threshold = float(threshold)
self.ff_score_from_layer = int(score_from_layer)
self.ff_num_layers = self.n_hidden + 1
if not 0 <= self.ff_score_from_layer < self.ff_num_layers:
raise ValueError("Forward-Forward score range excludes all layers")
self.ff_optimizers = []
for index, weight in enumerate(self.W):
parameters = [weight]
if self.normalization == "batchnorm":
parameters.extend([self.gamma[index], self.beta[index]])
for parameter in parameters:
parameter.requires_grad_(True)
self.ff_optimizers.append(
torch.optim.Adam(parameters, lr=learning_rate))
self.W_out.requires_grad_(True)
self.b_out.requires_grad_(True)
self.ff_optimizers.append(torch.optim.Adam(
[self.W_out, self.b_out], lr=learning_rate))
@staticmethod
def _ff_normalize(value):
axes = tuple(range(1, value.ndim))
norm = torch.sqrt(torch.sum(value.square(), dim=axes, keepdim=True))
return value / (norm + 1e-8)
def ff_overlay(self, image, labels):
flat = image.reshape(image.shape[0], -1).clone()
flat[:, :self.n_classes] = 0.0
flat[torch.arange(image.shape[0], device=image.device), labels] = (
torch.max(image).detach())
return flat.reshape_as(image)
def ff_forward(self, image, training=False, update_stats=False):
"""Forward candidate-labelled data through normalized residual edges."""
hiddens = []
caches = []
pre = self._ff_normalize(image)
convolution = F.conv2d(pre, self.W[0], stride=1, padding=1)
normalized, norm_cache = self._normalize(
0, convolution, training, update_stats)
hidden = F.relu(normalized)
hiddens.append(hidden)
caches.append({
"pre": pre, "normalization": norm_cache, "shortcut": None})
for block in self.blocks:
first = block["first"]
second = block["second"]
parent = hidden
pre = self._ff_normalize(parent)
convolution = F.conv2d(
pre, self.W[first], stride=block["stride"], padding=1)
normalized, norm_cache = self._normalize(
first, convolution, training, update_stats)
first_hidden = F.relu(normalized)
hiddens.append(first_hidden)
caches.append({
"pre": pre, "normalization": norm_cache, "shortcut": None})
pre = self._ff_normalize(first_hidden)
shortcut = self._option_a_shortcut(
parent, block["out_channels"], block["stride"])
convolution = F.conv2d(
pre, self.W[second], stride=1, padding=1)
normalized, norm_cache = self._normalize(
second, convolution, training, update_stats)
hidden = F.relu(
shortcut + self.residual_scale * normalized)
hiddens.append(hidden)
caches.append({
"pre": pre, "normalization": norm_cache,
"shortcut": shortcut})
features = self._ff_normalize(hidden.mean(dim=(2, 3)))
logits = features @ self.W_out.t() + self.b_out
return {
"hiddens": hiddens,
"caches": caches,
"features": features,
"logits": logits,
}
def _ff_local_outputs(self, layer_index, positive, negative):
"""Re-evaluate exactly one target layer on detached prefix states."""
if layer_index == self.n_hidden:
inputs = torch.cat(
[positive["features"], negative["features"]], dim=0).detach()
outputs = inputs @ self.W_out.t() + self.b_out
else:
positive_cache = positive["caches"][layer_index]
negative_cache = negative["caches"][layer_index]
inputs = torch.cat(
[positive_cache["pre"], negative_cache["pre"]],
dim=0).detach()
spec = self.layer_specs[layer_index]
convolution = F.conv2d(
inputs, self.W[layer_index],
stride=spec.stride, padding=spec.padding)
normalized, _ = self._normalize(
layer_index, convolution, training=True, update_stats=True)
if positive_cache["shortcut"] is None:
outputs = F.relu(normalized)
else:
shortcut = torch.cat([
positive_cache["shortcut"],
negative_cache["shortcut"],
], dim=0).detach()
outputs = F.relu(
shortcut + spec.branch_scale * normalized)
return outputs.chunk(2, dim=0)
def ff_train_layer(self, layer_index, image, labels,
learning_rate=0.03, negative_labels=None):
"""Update one greedy FF layer; every prefix and non-target is detached."""
if not 0 <= layer_index < self.ff_num_layers:
raise ValueError("invalid Forward-Forward layer")
if negative_labels is None:
offsets = torch.randint(
1, self.n_classes, labels.shape, device=labels.device)
negative_labels = (labels + offsets) % self.n_classes
with torch.no_grad():
positive = self.ff_forward(
self.ff_overlay(image, labels),
training=True, update_stats=False)
negative = self.ff_forward(
self.ff_overlay(image, negative_labels),
training=True, update_stats=False)
all_parameters = (
self.W + self.gamma + self.beta + [self.W_out, self.b_out])
for parameter in all_parameters:
parameter.grad = None
optimizer = self.ff_optimizers[layer_index]
optimizer.param_groups[0]["lr"] = learning_rate
positive_output, negative_output = self._ff_local_outputs(
layer_index, positive, negative)
axes = tuple(range(1, positive_output.ndim))
positive_goodness = positive_output.square().mean(dim=axes)
negative_goodness = negative_output.square().mean(dim=axes)
loss = (
F.softplus(-positive_goodness + self.ff_threshold)
+ F.softplus(negative_goodness - self.ff_threshold)
).mean()
loss.backward()
optimizer.step()
return {
"loss": float(loss.detach()),
"positive_goodness": float(positive_goodness.mean().detach()),
"negative_goodness": float(negative_goodness.mean().detach()),
"pair_accuracy": float(
(positive_goodness > negative_goodness).float().mean()),
}
@torch.no_grad()
def ff_candidate_scores(self, image):
scores = []
for candidate in range(self.n_classes):
labels = torch.full(
(image.shape[0],), candidate, device=image.device,
dtype=torch.long)
forward = self.ff_forward(
self.ff_overlay(image, labels), training=False)
layer_goodness = [
value.square().mean(dim=tuple(range(1, value.ndim)))
for value in forward["hiddens"] + [forward["logits"]]]
scores.append(sum(
layer_goodness[self.ff_score_from_layer:]))
return torch.stack(scores, dim=1)
class CIFARDualPropResNet(CIFARLocalResNet):
"""Dual Propagation on the residual DAG with author DP-transpose updates.
``s_plus`` and ``s_minus`` are initialized to the ordinary forward states.
A ``fwK`` pass updates every residual-DAG node in topological order. The
feedforward drive uses the forward edge, while the difference of each
child state is transported through the exact transpose of that same edge.
This is intentional symmetric feedback in the Dual Propagation baseline,
not a claim of weight-transport-free learning.
"""
def __init__(self, *args, alpha=0.0, dp_beta=0.1,
inference_passes=16, **kwargs):
super().__init__(*args, **kwargs)
if not 0.0 <= alpha <= 1.0:
raise ValueError("Dual Propagation alpha must lie in [0, 1]")
if dp_beta <= 0 or inference_passes < 1:
raise ValueError("invalid Dual Propagation inference settings")
self.dp_alpha = float(alpha)
self.dp_beta = float(dp_beta)
self.dp_inference_passes = int(inference_passes)
self._node_kind = {0: ("stem",)}
self._outgoing = {index: [] for index in range(self.n_hidden)}
for block in self.blocks:
first = block["first"]
second = block["second"]
parent = first - 1
self._node_kind[first] = ("first", parent)
self._node_kind[second] = (
"second", first, parent, block["out_channels"],
block["stride"])
self._outgoing[parent].append((first, "conv"))
self._outgoing[first].append((second, "conv"))
self._outgoing[parent].append((second, "shortcut"))
@staticmethod
def _option_a_shortcut_transpose(value, input_shape, stride):
"""Adjoint of the parameter-free option-A shortcut."""
in_channels = input_shape[1]
out_channels = value.shape[1]
missing = out_channels - in_channels
if missing < 0:
raise ValueError("option-A transpose cannot increase input width")
before = missing // 2
selected = value[:, before:before + in_channels]
if stride == 1:
if tuple(selected.shape) != tuple(input_shape):
raise ValueError("option-A transpose shape mismatch")
return selected
result = value.new_zeros(input_shape)
result[:, :, ::2, ::2] = selected
return result
def _node_prediction(self, index, states, image):
"""Return the unrectified local prediction and its edge cache."""
kind = self._node_kind[index]
if kind[0] == "stem":
pre = image
shortcut = None
elif kind[0] == "first":
pre = states[kind[1]]
shortcut = None
else:
pre = states[kind[1]]
shortcut = self._option_a_shortcut(
states[kind[2]], kind[3], kind[4])
spec = self.layer_specs[index]
convolution = F.conv2d(
pre, self.W[index], stride=spec.stride, padding=spec.padding)
normalized, normalization = self._normalize(
index, convolution, training=True, update_stats=False)
prediction = (
shortcut + spec.branch_scale * normalized
if shortcut is not None else normalized)
return prediction, {
"pre": pre,
"normalization": normalization,
"shortcut": shortcut,
}
def _edge_transpose(self, child, edge_kind, field, states, image):
"""Apply one residual-DAG edge transpose to a child state field."""
kind = self._node_kind[child]
if edge_kind == "shortcut":
if kind[0] != "second":
raise AssertionError("only a second convolution has a shortcut")
return self._option_a_shortcut_transpose(
field, states[kind[2]].shape, kind[4])
_, cache = self._node_prediction(child, states, image)
spec = self.layer_specs[child]
local_field = field * spec.branch_scale
local_field, _, _ = self._normalization_backward(
child, local_field, cache["normalization"])
return torch.nn.grad.conv2d_input(
cache["pre"].shape, self.W[child], local_field,
stride=spec.stride, padding=spec.padding)
def _outgoing_feedback(self, index, deltas, states, image):
result = torch.zeros_like(states[index])
for child, edge_kind in self._outgoing[index]:
result.add_(self._edge_transpose(
child, edge_kind, deltas[child], states, image))
if index == self.n_hidden - 1:
spatial = states[index].shape[2] * states[index].shape[3]
result.add_(
(deltas[-1] @ self.W_out)[:, :, None, None] / spatial)
return result
def infer_dual_states(self, image, one_hot, clean_forward=None):
"""Run the author ``fwK`` DP-transpose state updates on the DAG."""
if clean_forward is None:
clean_forward = self.forward(
image, return_cache=True, training=True, update_stats=False)
plus = [
value.detach().clone() for value in clean_forward["hiddens"]]
minus = [value.detach().clone() for value in plus]
plus.append(clean_forward["logits"].detach().clone())
minus.append(clean_forward["logits"].detach().clone())
fixed_prediction = clean_forward["logits"].detach()
alpha = self.dp_alpha
for _ in range(self.dp_inference_passes):
for index in range(self.n_hidden):
states = [
alpha * positive + (1.0 - alpha) * negative
for positive, negative in zip(plus[:-1], minus[:-1])]
prediction, _ = self._node_prediction(index, states, image)
deltas = [
positive - negative
for positive, negative in zip(plus, minus)]
feedback = self._outgoing_feedback(
index, deltas, states, image)
plus[index] = F.relu(
prediction + (1.0 - alpha) * feedback)
minus[index] = F.relu(prediction - alpha * feedback)
states = [
alpha * positive + (1.0 - alpha) * negative
for positive, negative in zip(plus[:-1], minus[:-1])]
features = states[-1].mean(dim=(2, 3))
prediction = features @ self.W_out.t() + self.b_out
output_field = self.dp_beta * (
torch.softmax(fixed_prediction, dim=1) - one_hot)
plus[-1] = prediction - (1.0 - alpha) * output_field
minus[-1] = prediction + alpha * output_field
return plus, minus
@torch.no_grad()
def dualprop_ascent_directions(self, image, plus, minus):
"""Evaluate the local DP contrastive correlations without autograd."""
alpha = self.dp_alpha
beta = self.dp_beta
states = [
alpha * positive + (1.0 - alpha) * negative
for positive, negative in zip(plus[:-1], minus[:-1])]
deltas = [
(positive - negative) / beta
for positive, negative in zip(plus, minus)]
directions = []
gamma_directions = []
beta_directions = []
batch = image.shape[0]
for index in range(self.n_hidden):
_, cache = self._node_prediction(index, states, image)
spec = self.layer_specs[index]
local_field = deltas[index] * spec.branch_scale
local_field, gamma_direction, beta_direction = (
self._normalization_backward(
index, local_field, cache["normalization"]))
direction = torch.nn.grad.conv2d_weight(
cache["pre"], self.W[index].shape, local_field,
stride=spec.stride, padding=spec.padding)
directions.append(direction / batch)
if gamma_direction is not None:
gamma_directions.append(gamma_direction / batch)
beta_directions.append(beta_direction / batch)
features = states[-1].mean(dim=(2, 3))
output_weight = deltas[-1].t() @ features / batch
output_bias = deltas[-1].mean(dim=0)
return (
directions, gamma_directions, beta_directions,
output_weight, output_bias)
def dualprop_step(self, image, labels, eta, eta_output=None,
momentum=0.0, weight_decay=0.0):
"""One fully local DP-transpose update on a matched ResNet batch."""
one_hot = F.one_hot(labels, self.n_classes).to(image.dtype)
with torch.no_grad():
clean = self.forward(
image, return_cache=True, training=True, update_stats=True)
loss = F.cross_entropy(clean["logits"], labels)
plus, minus = self.infer_dual_states(
image, one_hot, clean_forward=clean)
(directions, gamma_directions, beta_directions,
output_weight, output_bias) = self.dualprop_ascent_directions(
image, plus, minus)
self.apply_ascent(
directions, output_weight, output_bias, eta,
eta_output=eta_output, momentum=momentum,
weight_decay=weight_decay,
gamma_directions=gamma_directions,
beta_directions=beta_directions)
return float(loss)
|