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 reading what concepts a model represents by training linear classifiers on activations from contrasting stimuli. LAT answers the question: "Does this model represent concept X? Where? How strongly?"

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:

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

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

4. Extract the concept direction. The weight vector $\mathbf{w}$ of the trained classifier is the concept direction. It points in the direction that best separates the two classes.

The result is a concept direction -- a linear direction in activation space that distinguishes one behavior from another.

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.

In practice, the methods often produce similar directions. LAT has the advantage of providing a natural confidence measure (classifier accuracy) and can handle cases where the positive and negative sets have different sizes or distributions.LAT is closely related to probing classifiers discussed in earlier articles. The key difference is intent: probing asks whether information is decodable from representations, while LAT asks whether it is represented as a direction that can be read and controlled. In practice, the methods are nearly identical -- both train linear classifiers on activations.

Probing Safety-Relevant Properties

LAT can probe safety-relevant properties:

• Honesty. Does the model's representation encode whether it is generating truthful or false information? LAT can detect when a model "knows" it is lying.

• 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.

The ability to read safety-relevant representations is arguably as important as the ability to control them. If we can detect when a model is being dishonest from its internal representations, we have a monitoring tool that does not depend on the model's outputs.

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 for monitoring and auditing. You might want to know whether a model is being honest without intervening -- for instance, during evaluation or deployment monitoring. Controlling without reading first is risky: you might steer in a direction that does not correspond to the concept you intended. In practice, it's best to always read first (to verify the direction is meaningful) before using it for control.

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 strongly represented? Classifier accuracy peaks where the concept is most salient.
• Does it persist to the final layer? Some concepts are used internally but not directly reflected in outputs.

This layer-wise profile tells us how the model processes and represents concepts throughout its forward pass.

The Connection to Control

The direction that LAT uses to detect a concept is the same direction that addition steering adds to induce that concept. Reading and control are two sides of the same coin:

• 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 concept has a clean linear separation in activation space -- the model represents it as a clear direction. Low accuracy could mean several things: the concept is not linearly represented, the concept is distributed across multiple directions, or the contrast pairs do not cleanly isolate the concept. You can still have a meaningful direction with moderate accuracy if the direction is consistent and steers behavior effectively. The classifier accuracy is one signal among several.

Looking Forward

LAT provides a principled method for reading what concepts a model represents. Combined with CAA, it forms the probing half of representation engineering. The directions identified through probing can then be used for steering and ablation, completing the toolkit for understanding and controlling model representations.