| """Probes. |
| |
| All probes share a tiny interface so the pipeline is agnostic to type: |
| |
| probe = make_probe("logreg", num_labels=2, seed=0).fit(X_train, y_train) |
| y_hat = probe.predict(X_eval) |
| D = probe.direction # [C, H] concept-direction matrix, or None (MLP) |
| |
| `direction` is what claim C1/C2 measure rotation on. For LogReg it is the weight matrix; |
| for mass-mean it is (class_centroid - global_mean). MLP has no single linear direction, so |
| it returns None and the eval step skips rotation for it (still reports accuracy). |
| """ |
| from __future__ import annotations |
|
|
| import numpy as np |
| from sklearn.linear_model import LogisticRegression |
|
|
|
|
| class BaseProbe: |
| direction: np.ndarray | None = None |
|
|
| def fit(self, X: np.ndarray, y: np.ndarray) -> "BaseProbe": |
| raise NotImplementedError |
|
|
| def predict(self, X: np.ndarray) -> np.ndarray: |
| raise NotImplementedError |
|
|
|
|
| class LogRegProbe(BaseProbe): |
| """L2-regularised multinomial logistic regression (the default diagnostic probe).""" |
|
|
| def __init__(self, num_labels: int, l2: float = 1.0, seed: int = 0, max_iter: int = 500, **_): |
| self.num_labels = num_labels |
| self.C = 1.0 / max(l2, 1e-8) |
| self.seed = seed |
| self.max_iter = max_iter |
| self._clf: LogisticRegression | None = None |
|
|
| def fit(self, X, y): |
| self._clf = LogisticRegression( |
| C=self.C, max_iter=self.max_iter, random_state=self.seed, |
| ).fit(X, y) |
| coef = self._clf.coef_ |
| self.direction = coef.copy() |
| return self |
|
|
| def predict(self, X): |
| return self._clf.predict(X) |
|
|
|
|
| class MassMeanProbe(BaseProbe): |
| """Difference-of-means / mass-mean probe. Predicts by nearest class centroid. |
| |
| Often *more* OOD-robust than LogReg (a hypothesis under claim C3). |
| """ |
|
|
| def __init__(self, num_labels: int, **_): |
| self.num_labels = num_labels |
| self._centroids: np.ndarray | None = None |
| self._classes: np.ndarray | None = None |
|
|
| def fit(self, X, y): |
| y = np.asarray(y) |
| self._classes = np.unique(y) |
| centroids = np.stack([X[y == c].mean(0) for c in self._classes]) |
| self._centroids = centroids |
| self.direction = centroids - X.mean(0, keepdims=True) |
| return self |
|
|
| def predict(self, X): |
| |
| d = np.linalg.norm(X[:, None, :] - self._centroids[None, :, :], axis=2) |
| return self._classes[np.argmin(d, axis=1)] |
|
|
|
|
| class MLPProbe(BaseProbe): |
| """2-layer MLP probe (torch). No single linear direction -> direction stays None.""" |
|
|
| def __init__(self, num_labels: int, hidden: int = 128, epochs: int = 50, |
| lr: float = 1e-3, seed: int = 0, **_): |
| self.num_labels = num_labels |
| self.hidden = hidden |
| self.epochs = epochs |
| self.lr = lr |
| self.seed = seed |
| self._model = None |
| self._device = None |
|
|
| def fit(self, X, y): |
| import torch |
| import torch.nn as nn |
|
|
| torch.manual_seed(self.seed) |
| self._device = "cuda" if torch.cuda.is_available() else "cpu" |
| Xt = torch.tensor(np.asarray(X), dtype=torch.float32, device=self._device) |
| yt = torch.tensor(np.asarray(y), dtype=torch.long, device=self._device) |
| self._model = nn.Sequential( |
| nn.Linear(Xt.shape[1], self.hidden), nn.ReLU(), |
| nn.Linear(self.hidden, self.num_labels), |
| ).to(self._device) |
| opt = torch.optim.Adam(self._model.parameters(), lr=self.lr) |
| lossfn = nn.CrossEntropyLoss() |
| self._model.train() |
| for _ in range(self.epochs): |
| opt.zero_grad() |
| loss = lossfn(self._model(Xt), yt) |
| loss.backward() |
| opt.step() |
| return self |
|
|
| def predict(self, X): |
| import torch |
| self._model.eval() |
| with torch.no_grad(): |
| Xt = torch.tensor(np.asarray(X), dtype=torch.float32, device=self._device) |
| return self._model(Xt).argmax(1).cpu().numpy() |
|
|
|
|
| class ControlTaskProbe(LogRegProbe): |
| """Hewitt & Liang control-task probe: fit on RANDOM labels to measure selectivity. |
| |
| selectivity = real_task_acc - control_task_acc. A high-selectivity probe reflects the |
| representation, not probe memorisation. We report this to pre-empt the standard |
| "your probe is just memorising" reviewer attack. |
| """ |
|
|
| def fit(self, X, y): |
| rng = np.random.default_rng(self.seed) |
| y_rand = rng.permutation(np.asarray(y)) |
| return super().fit(X, y_rand) |
|
|
|
|
| _REGISTRY = { |
| "logreg": LogRegProbe, |
| "mass_mean": MassMeanProbe, |
| "mlp": MLPProbe, |
| "control": ControlTaskProbe, |
| } |
|
|
|
|
| def make_probe(kind: str, num_labels: int, **kwargs) -> BaseProbe: |
| if kind not in _REGISTRY: |
| raise KeyError(f"unknown probe '{kind}', choose from {list(_REGISTRY)}") |
| return _REGISTRY[kind](num_labels=num_labels, **kwargs) |
|
|