A linear probe is usually a logistic regression fit on frozen activations: collect hidden states from inputs where some property is known (language, truthfulness, board state), train the probe to predict the property, and if it generalizes, the information is linearly present. The learned weight vector doubles as a candidate direction for the concept.
Probes are cheap and quantitative but come with two standing caveats. They are correlational: showing information exists in an activation is not showing the model uses it, which requires causal interventions like patching or ablation. And they are supervised: a probe can only confirm or refute hypotheses you already thought to test, which is why unsupervised tools like sparse autoencoders complement them.
