Linear Artificial Tomography (LAT)

Reading Representations

CAA computes concept directions by averaging activation differences. But there is another way to find these directions: train a classifier to predict which concept is active, then examine what direction the classifier uses.

Zou et al. (2023) proposed Linear Artificial Tomography (LAT) as part of the Representation Engineering (RepE) framework [1]Representation Engineering: A Top-Down Approach to AI Transparency
Zou, A., Phan, L., Chen, S., et al.
arXiv, 2023. The key analogy comes from cognitive neuroscience: neuroscientists do not study individual neurons in isolation. They study population-level activity patterns, the collective behavior of neural populations that corresponds to cognition, perception, and decision-making.

LAT applies the same philosophy to neural networks. Instead of dissecting individual circuits or features, LAT works at the level of representations, the collective activation patterns that encode high-level concepts.The population-level perspective represents a genuine philosophical shift. Most mechanistic interpretability work focuses on individual components: specific attention heads, individual neurons, or sparse autoencoder features. LAT argues that the most important unit of analysis is the representation, a direction in the high-dimensional activation space that corresponds to a behavioral concept.

Linear Artificial Tomography (LAT): A method for training linear classifiers on activations from contrasting stimuli. It tests where a labeled distinction is linearly decodable and extracts the classifier's separating direction.

The LAT Procedure

The procedure mirrors contrastive methods from neuroscience:

1. Stimulate the model with contrasting inputs. Present pairs of prompts that differ in a target concept, for example, honest versus dishonest completions, or harmful versus harmless responses.

2. Collect activations. Run both sets through the model and collect residual stream activations at intermediate layers.

3. Train a linear classifier. Fit a logistic regression or linear probe on the activations to predict which behavior is active:

$$p(\text{concept} | \mathbf{h}) = \sigma(\mathbf{w} \cdot \mathbf{h} + b)$$

where $\mathbf{w}$ is the learned weight vector, $\mathbf{h}$ is the activation, and $\sigma$ is the sigmoid function.

4. Extract a candidate direction. The classifier weight $\mathbf{w}$ defines the separating direction learned from these examples.

The classifier weights define a candidate concept direction: a direction that separates the two labeled sets. Transfer and counterexample tests are needed to determine whether the direction tracks the intended concept rather than a correlated difference.

LAT vs. CAA

LAT and CAA are closely related but approach the problem differently:

Method	Approach	Output
CAA	Mean difference of activations	Concept direction (difference vector)
LAT	Train linear classifier	Concept direction (classifier weights)

Both produce a direction in activation space. The difference is methodology:

• CAA computes the direction directly from activation differences.
• LAT learns the direction by training a classifier to distinguish the concepts.

The methods can produce similar directions when the class covariances are well behaved. LAT directly optimizes classification and supplies held-out accuracy as an accessibility measure; CAA estimates a mean shift without fitting a decision boundary. Neither metric alone measures causal use or semantic purity.LAT is closely related to the probing classifiers discussed earlier. The mathematical procedure is probing; the Representation Engineering framing emphasizes reusing the learned direction for analysis and possible intervention.

Probing Safety-Relevant Properties

LAT can probe safety-relevant properties:

• Honesty labels. Can a classifier distinguish activations from examples labeled truthful and deceptive, including on new topics and prompt formats?

• Harmlessness. Do harmful and harmless response trajectories separate in activation space? LAT can track this separation across layers.

• Power-seeking. Can we identify representations associated with power-seeking behavior? LAT provides a way to measure this.

A direction that generalizes across suitable held-out conditions could become one signal in an internal monitor. It would still require calibration against false positives, distribution shift, and strategic evasion before “dishonesty detector” is an appropriate label.

Pause and think: Reading versus controlling

LAT reads what concepts a model represents. Addition steering controls behavior by adding directions. These use the same concept direction for different purposes. In what situations would you want to read a model's representations without controlling them? When would you want to control without reading first?

Reading without controlling is useful when the goal is diagnosis or monitoring. Control without a prior probe is possible, for example through direct optimization of a behavioral metric, but then the mechanism and off-target effects may be harder to characterize. In either order, readout and intervention provide different evidence and should be evaluated separately.

Layer-by-Layer Analysis

LAT naturally supports layer-by-layer analysis. By training classifiers at each layer, you can track:

• Where does the concept first become detectable? Early layers may not yet encode high-level concepts.
• Where is it most linearly accessible? Classifier accuracy can peak where the labeled distinction is easiest to separate.
• Does it persist to the final layer? Some concepts are used internally but not directly reflected in outputs.

This layer-wise profile maps linear decodability through the forward pass. It does not, by itself, reveal when the information was computed or where it is causally used.

The Connection to Control

The direction that LAT uses to separate labels can also be tried as an addition-steering vector. Good classification does not guarantee good steering, so the two uses form a useful comparison:

• Read: What does the model represent? (LAT, CAA)
• Control: How can we steer it? (Addition, Ablation)

A concept direction that reads well but steers poorly suggests the representation is correlated with but not causal for the behavior. A direction that steers well but reads poorly suggests the intervention works through a mechanism we do not yet understand.

Pause and think: Classifier accuracy as a metric

LAT produces a classifier accuracy: how well can the linear probe distinguish the two concepts? What does high accuracy tell us? What does low accuracy tell us? Can you have a meaningful concept direction with low classifier accuracy?

High accuracy means the labeled examples are linearly separable in the sampled activations. The separating direction may encode the target property, a correlated cue in the dataset, or both. Low accuracy could reflect nonlinear encoding, weak labels, a poor layer choice, or a concept the model does not represent. Accuracy is therefore one piece of evidence, to be paired with transfer tests and interventions.

Looking Forward

LAT provides a standard linear-probing route to candidate representation directions. Combined with CAA, it supplies hypotheses that can be tested with steering, ablation, transfer sets, and off-target evaluations.