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
|
"""
Measurement probes. These use autograd to compute the TRUE gradient purely for
diagnostics -- the learning rules in core.py never call these. The central
quantity is the alignment cos(r_l, -grad_{h_l}L): SDIL claims the innovation
r_l points along the causal descent direction without weight transport.
"""
import copy
import torch
import torch.nn.functional as F
from . import core
def true_hidden_grads(net, x, y):
"""Return (list of g_l = dL/dh_l over hidden layers, scalar loss).
Uses autograd; temporarily flags W to build the graph, then restores."""
with torch.enable_grad():
for W in net.W:
W.requires_grad_(True)
x = x.detach()
h = x
hs = []
for l in range(net.L):
pre = h @ net.W[l].t() + net.b[l]
if l < net.L - 1:
act = net.act(pre)
h = (h + net.res_alpha * act) if (getattr(net, "residual", False) and l >= 1) else act
hs.append(h)
else:
logits = pre
loss = F.cross_entropy(logits, y)
grads = torch.autograd.grad(loss, hs, retain_graph=False)
for W in net.W:
W.requires_grad_(False)
return [g.detach() for g in grads], loss.item()
def _row_cos(u, v):
"""Mean per-sample cosine, excluding rows with an exact zero vector.
Adding an absolute epsilon to the denominator makes cosine spuriously
depend on signal magnitude near convergence. In particular, a positive
per-sample rescaling can then appear to change direction. Exact zero rows
have no defined direction and are omitted instead.
"""
num = (u * v).sum(1)
den = u.norm(dim=1) * v.norm(dim=1)
valid = den > 0
if not valid.any():
return float("nan")
return (num[valid] / den[valid]).mean().item()
@torch.no_grad()
def alignment_report(net, x, y, y_onehot, cfg):
"""Per-hidden-layer alignments of the teaching signals with -grad.
Returns dict of lists (index = hidden layer)."""
grads, loss = true_hidden_grads(net, x, y) # g_l
fwd = net.forward(x)
h = fwd["h"]
u = fwd["u"]
logits = h[-1]
e = net.output_error(logits, y_onehot)
c = e
out = {"cos_r_negg": [], "cos_innovation_negg": [],
"cos_apical_negg": [], "cos_Ac_negg": [],
"r_norm": [], "g_norm": [], "loss": loss}
for l in range(net.L - 1):
g = grads[l]
negg = -g
teaching, a, innovation = core.teaching_signal(net, l, c, h[l + 1], cfg)
Ac = c @ net.A[l].t() # pure vectorizer output
# include the phi' gain that the plasticity rule actually applies,
# so the reported alignment is what the weight update "sees"
gain = net.act_prime(u[l])
out["cos_r_negg"].append(_row_cos(teaching * gain, negg * gain))
out["cos_innovation_negg"].append(_row_cos(innovation * gain, negg * gain))
out["cos_apical_negg"].append(_row_cos(a * gain, negg * gain))
out["cos_Ac_negg"].append(_row_cos(Ac * gain, negg * gain))
out["r_norm"].append(teaching.norm(dim=1).mean().item())
out["g_norm"].append(g.norm(dim=1).mean().item())
return out
@torch.no_grad()
def loss_decrease_ratio(net, x, y, y_onehot, cfg, step):
"""Single-step descent quality: apply one SDIL update to a scratch copy and
measure the actual loss drop on the same batch, compared to one plain-SGD
(true-gradient) step at the same learning rate. Ratio in (0,1] means SDIL
descends but less steeply than exact GD; <=0 means it went uphill."""
y_ = y
L0 = core.loss_ce(net.logits(x), y_).mean().item()
# SDIL step on a copy
net_sdil = _clone(net)
core.sdil_step(net_sdil, x, y_, y_onehot, cfg, step)
L_sdil = core.loss_ce(net_sdil.logits(x), y_).mean().item()
# exact-gradient SGD step on a copy at the same eta
net_bp = _clone(net)
_sgd_step(net_bp, x, y_, cfg.eta)
L_bp = core.loss_ce(net_bp.logits(x), y_).mean().item()
d_sdil = L_sdil - L0
d_bp = L_bp - L0
ratio = d_sdil / d_bp if abs(d_bp) > 1e-9 else float("nan")
return {"dL_sdil": d_sdil, "dL_bp": d_bp, "ratio": ratio}
def _clone(net):
n = copy.copy(net)
n.W = [w.clone() for w in net.W]
n.b = [b.clone() for b in net.b]
n.A = [a.clone() for a in net.A]
n.P = [p.clone() for p in net.P]
n.P_bias = ([p.clone() for p in net.P_bias]
if getattr(net, "P_bias", None) is not None else None)
n.Bnuis = [b.clone() for b in net.Bnuis]
n.mW = [torch.zeros_like(w) for w in net.W]
n.mb = [torch.zeros_like(b) for b in net.b]
return n
def _sgd_step(net, x, y, eta):
with torch.enable_grad():
for W in net.W:
W.requires_grad_(True)
for b in net.b:
b.requires_grad_(True)
logits = net.logits(x)
loss = F.cross_entropy(logits, y)
grads = torch.autograd.grad(loss, net.W + net.b)
nW = len(net.W)
with torch.no_grad():
for i in range(nW):
net.W[i] -= eta * grads[i]
net.b[i] -= eta * grads[nW + i]
for W in net.W:
W.requires_grad_(False)
for b in net.b:
b.requires_grad_(False)
|
