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"""
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]
context = h[-2]
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": [], "traffic_norm": [],
"traffic_residual_norm": [], "traffic_r2": [], "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, context)
Ac = net.vectorizer(l, c, h[l + 1], context) # pure vectorizer output
traffic = net.apical_traffic(l, h[l + 1], context)
unexplained = traffic - net.baseline(l, h[l + 1])
# 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())
out["traffic_norm"].append(traffic.norm(dim=1).mean().item())
out["traffic_residual_norm"].append(unexplained.norm(dim=1).mean().item())
traffic_power = traffic.pow(2).mean()
if traffic_power > 0:
out["traffic_r2"].append(
(1.0 - unexplained.pow(2).mean() / traffic_power).item())
else:
out["traffic_r2"].append(float("nan"))
return out
@torch.no_grad()
def fa_alignment_report(net, x, y, y_onehot):
"""Alignment of sequential-FA local update signals with exact descent.
``FANet.fa_hidden_gradients`` performs the same fixed-feedback transport
used during learning. Autograd appears only here to obtain the reference
hidden-state gradients for measurement.
"""
grads, loss = true_hidden_grads(net, x, y)
fwd = net.forward(x)
estimated = net.fa_hidden_gradients(fwd, y_onehot)
cosines = []
for l, (estimate, true_grad) in enumerate(zip(estimated, grads)):
gain = net.act_prime(fwd["u"][l])
cosines.append(_row_cos(-estimate * gain, -true_grad * gain))
return {"cos_fa_negg": cosines, "loss": loss}
@torch.no_grad()
def nodepert_alignment_report(net, x, y, cfg):
"""Alignment of the unamortized perturbation signal actually used."""
grads, loss = true_hidden_grads(net, x, y)
estimator = (core.simultaneous_node_perturbation_targets
if cfg.pert_mode == "simultaneous"
else core.node_perturbation_targets)
targets = estimator(net, x, y, sigma=cfg.pert_sigma, n_dirs=cfg.pert_ndirs)
fwd = net.forward(x)
cosines = []
q_norm = []
g_norm = []
for layer, (target, grad) in enumerate(zip(targets, grads)):
gain = net.act_prime(fwd["u"][layer])
cosines.append(_row_cos(target * gain, -grad * gain))
q_norm.append(target.norm(dim=1).mean().item())
g_norm.append(grad.norm(dim=1).mean().item())
return {"cos_q_negg": cosines, "q_norm": q_norm, "g_norm": g_norm, "loss": loss}
@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.A_gate = ([a.clone() for a in net.A_gate]
if getattr(net, "A_gate", None) is not None else None)
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.Bcontext = [b.clone() for b in net.Bcontext]
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)
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