File size: 6,105 Bytes
45eaa9d | 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 | """Learnable spectral modulation model.
This implements the paper's learnable spectral nonlinearity idea using Haar
coefficients, coefficient-wise shrinkage, gain/phase-like scaling, and a final
linear task operator.
"""
from __future__ import annotations
from dataclasses import dataclass
import numpy as np
import torch
from torch import nn
from torch.utils.data import DataLoader, TensorDataset
from .transforms import torch_wavelet_features
from .metrics import nll_from_proba
class LearnableSpectralOperator(nn.Module):
"""Haar coefficients + learnable soft-threshold/gain + task operator."""
def __init__(self, input_shape=(1, 8, 8), n_classes: int = 10, levels: int = 3):
super().__init__()
self.levels = levels
n_coeff = int(np.prod(input_shape))
self.log_theta = nn.Parameter(torch.full((n_coeff,), -2.0))
self.gain = nn.Parameter(torch.ones(n_coeff))
self.operator = nn.Linear(n_coeff, n_classes)
def forward(self, x: torch.Tensor) -> torch.Tensor:
coeff = torch_wavelet_features(x, levels=self.levels)
theta = torch.nn.functional.softplus(self.log_theta) + 1e-6
shrink = coeff.abs() / (coeff.abs() + theta)
modulated = self.gain * shrink * coeff
return self.operator(modulated)
@property
def param_count(self) -> int:
return sum(p.numel() for p in self.parameters())
@dataclass
class TorchModelWrapper:
model: LearnableSpectralOperator
device: str = "cpu"
@property
def param_count_(self) -> int:
return self.model.param_count
def _tensor(self, X):
X = np.asarray(X, dtype=np.float32)
if X.ndim == 3:
X = X[:, None, :, :]
if X.max() > 1.0:
X = X / 16.0
return torch.from_numpy(X).to(self.device)
def decision_function(self, X):
self.model.eval()
with torch.no_grad():
logits = self.model(self._tensor(X)).cpu().numpy()
return logits
def predict_proba(self, X):
logits = self.decision_function(X)
logits = logits - logits.max(axis=1, keepdims=True)
e = np.exp(logits)
return e / e.sum(axis=1, keepdims=True)
def predict(self, X):
return self.decision_function(X).argmax(axis=1)
def _torch_metrics(wrapper: TorchModelWrapper, X, y, prefix: str) -> dict:
pred = wrapper.predict(X)
proba = wrapper.predict_proba(X)
return {
f"{prefix}_accuracy": float((pred == y).mean()),
f"{prefix}_macro_f1": float(__import__("sklearn.metrics").metrics.f1_score(y, pred, average="macro")),
f"{prefix}_nll": nll_from_proba(proba, y),
}
def train_learnable_spectral(
X_train,
y_train,
X_val,
y_val,
epochs: int = 30,
lr: float = 3e-2,
weight_decay: float = 1e-4,
seed: int = 7,
batch_size: int = 128,
device: str = "cpu",
):
torch.manual_seed(seed)
model = LearnableSpectralOperator().to(device)
opt = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=weight_decay)
loss_fn = nn.CrossEntropyLoss()
Xtr = np.asarray(X_train, dtype=np.float32)
Xva = np.asarray(X_val, dtype=np.float32)
if Xtr.ndim == 3:
Xtr = Xtr[:, None, :, :]
if Xva.ndim == 3:
Xva = Xva[:, None, :, :]
ytr = np.asarray(y_train, dtype=np.int64)
ds = TensorDataset(torch.from_numpy(Xtr), torch.from_numpy(ytr))
loader = DataLoader(ds, batch_size=batch_size, shuffle=True)
history = []
for epoch in range(1, epochs + 1):
model.train()
total = 0.0
seen = 0
for xb, yb in loader:
xb = xb.to(device)
yb = yb.to(device)
opt.zero_grad(set_to_none=True)
logits = model(xb)
# mild sparsity prior on spectral gains/shrinkage, matching the paper's regularized spectral learning theme
loss = loss_fn(logits, yb) + 1e-4 * model.gain.abs().mean()
loss.backward()
opt.step()
total += float(loss.item()) * len(xb)
seen += len(xb)
wrapper = TorchModelWrapper(model, device=device)
val_metrics = _torch_metrics(wrapper, X_val, y_val, "val")
history.append({"epoch": epoch, "train_loss": total / seen, **val_metrics})
return TorchModelWrapper(model, device=device), history
def fit_learnable_threshold_operator(X_train, y_train, X_val, y_val, lam: float = 1e-3, thresholds=None):
"""Fast validation-learned spectral soft-threshold operator.
This dependency-light variant learns a global spectral threshold by validation
search, then estimates the task operator with Hilbert-Schmidt ridge. It is
used in the default benchmark so the repo runs quickly on CPU.
"""
from .transforms import haar2d_batch
from .operators import HilbertSchmidtOperatorClassifier
if thresholds is None:
thresholds = [0.0, 0.005, 0.01, 0.025, 0.05, 0.10, 0.20]
Ctr = haar2d_batch(X_train)
Cva = haar2d_batch(X_val)
def shrink(C, theta):
return C * (np.abs(C) / (np.abs(C) + theta + 1e-8))
best = None
for theta in thresholds:
Ztr = shrink(Ctr, theta)
Zva = shrink(Cva, theta)
clf = HilbertSchmidtOperatorClassifier(ridge_lambda=lam).fit(Ztr, y_train)
val_acc = float((clf.predict(Zva) == y_val).mean())
if best is None or val_acc > best[0]:
best = (val_acc, theta, clf)
class ThresholdSpectralWrapper:
theta_ = best[1]
clf_ = best[2]
param_count_ = int(best[2].param_count_ + 1)
def _features(self, X):
C = haar2d_batch(X)
return shrink(C, self.theta_)
def decision_function(self, X):
return self.clf_.decision_function(self._features(X))
def predict_proba(self, X):
return self.clf_.predict_proba(self._features(X))
def predict(self, X):
return self.clf_.predict(self._features(X))
return ThresholdSpectralWrapper(), {"selected_threshold": float(best[1]), "val_accuracy": float(best[0])}
|