Dictionary Learning

The learned dictionary contains more basis vectors than the activation space's dimensionality, creating an overcomplete representation. A sparsity penalty (L1 regularization) forces each input to be reconstructed using only a small subset of available dictionary elements. This mirrors the hypothesized strategy biological neurons use for efficient coding and directly addresses the superposition hypothesis in artificial networks.

The primary objective is to find basis vectors that are monosemantic—each corresponding to exactly one human-interpretable concept. This contrasts with natural neurons which are often polysemantic, firing for multiple unrelated inputs. A successfully trained dictionary decomposes a neuron that fires for both 'DNA sequences' and 'academic citations' into two separate, independently activating feature directions.

The standard implementation uses a sparse autoencoder with a single hidden layer:

• Encoder: Maps activations to a sparse latent representation via a learned weight matrix and ReLU activation
• Decoder: Reconstructs the original activation from the sparse code
• Bias terms: Include both encoder and decoder biases, with the decoder bias often initialized to the geometric median of the data
• The L1 penalty on latent activations enforces sparsity, typically with a coefficient (λ) tuned per layer.

In transformer models, dictionary learning is applied to the residual stream at specific layers. The residual stream accumulates information from attention heads and MLP layers, making it a natural bottleneck for feature analysis. By decomposing mid-layer residual stream activations, researchers can identify the precise point where abstract concepts like sentiment, syntax, or factual knowledge are represented before being read by downstream components.

Once a dictionary is trained, the learned feature directions enable activation engineering. By clamping a specific dictionary feature to a high value during the forward pass, the model's behavior can be causally steered. For example, amplifying the 'romantic love' feature in a language model causes it to generate text about relationships regardless of the original prompt, providing direct evidence that the feature is causally implicated in that concept.

Cross-coders extend standard dictionary learning by training on activations from two different models simultaneously. The learned dictionary contains:

• Shared features: Basis vectors that activate for both models, representing universal concepts
• Model-specific features: Vectors unique to one model, highlighting representational differences This technique is critical for comparing how different architectures or checkpoints encode the same underlying concepts.

Dictionary learning is the primary tool for testing the Superposition Hypothesis. By training a sparse autoencoder to reconstruct activations from a higher-dimensional, sparse feature basis, researchers can recover more independent features than the model's native dimensionality. This provides empirical evidence that models compress representations and offers a method to extract them.

A single neuron often fires for multiple unrelated concepts (polysemanticity). Dictionary learning provides a systematic solution:

• Decomposition: A sparse autoencoder maps the neuron's activation context to a set of distinct dictionary elements.
• Result: A neuron that fires for both 'DNA sequences' and 'academic citations' can be separated into two independent, monosemantic feature vectors, each with a single, clear meaning.

Instead of manually inspecting individual neurons, researchers use dictionary features as the atomic units for automated circuit discovery. Algorithms search for sparse subgraphs of dictionary features that causally mediate a specific behavior. This replaces manual hypothesis generation with a scalable, bottom-up decomposition of the computational graph into interpretable components.

A Cross-Coder is a dictionary learning variant trained on the activations of two different models simultaneously. Its learned dictionary captures both model-specific and shared features. This enables direct comparison of how two distinct models—or a base model and its fine-tuned variant—internally represent the same concept, revealing the precise impact of training interventions.

A Transcoder is a dictionary learning model trained to replace a specific MLP layer or attention block. It decomposes the component's output into a sparse, interpretable feature basis. By analyzing the transcoder's dictionary, researchers can precisely define the function of a single layer in isolation, turning an opaque non-linear transformation into a transparent, feature-level operation.

Dictionary features provide a precise interface for activation engineering. Instead of adding a hand-crafted steering vector to control behavior, a practitioner can identify the specific dictionary element for a target concept (e.g., 'sycophancy') and directly modulate its coefficient during the forward pass. This enables surgical, causal control over model outputs with minimal side effects.

An unsupervised architecture trained to decompose a model's dense, polysemantic activations into a sparse set of interpretable, monosemantic features. It learns an overcomplete basis of feature directions by enforcing an L1 sparsity penalty on the latent representation.

• Encoder: Maps dense activations to a higher-dimensional sparse latent space
• Decoder: Reconstructs the original activation from the sparse code
• Loss: Reconstruction error + sparsity regularization term

Sparse autoencoders are the primary tool for implementing dictionary learning on transformer residual streams, MLP outputs, and attention head outputs.

The hypothesized phenomenon where a neural network represents more independent features than it has dimensions in a given layer. Features are compressed into a lower-dimensional space by exploiting their sparsity—most features are zero for any given input.

• Enables models to store vast quantities of knowledge in limited representational capacity
• Explains why individual neurons exhibit polysemanticity
• Dictionary learning aims to disentangle these compressed representations

Superposition is the central challenge that dictionary learning addresses, providing the theoretical motivation for sparse decomposition techniques.

The property of a single neuron or feature direction corresponding to exactly one natural, human-interpretable concept. A monosemantic feature activates consistently for a specific concept regardless of context.

• Ideal state: One feature = one concept (e.g., 'French text', 'DNA sequences')
• Contrast: Polysemantic neurons respond to multiple unrelated concepts
• Dictionary learning aims to recover monosemantic features from polysemantic activations

Achieving monosemanticity through learned dictionaries enables direct inspection of what a model 'thinks' at each layer.

An optimization-based technique that synthesizes input examples that maximally activate a specific feature direction or neuron. When combined with dictionary learning, it visualizes what each learned dictionary element represents.

• Optimization: Gradient ascent on the input to maximize feature activation
• Regularization: Frequency penalization and transformation robustness to produce natural outputs
• Application: Validating that learned dictionary features correspond to coherent, interpretable concepts

Feature visualization provides the qualitative evidence that dictionary learning has successfully decomposed a model's representations into meaningful components.

A systematic evaluation methodology that tests a hypothesized circuit or set of features by replacing all activations outside the target set with corrupted values from a different input. If the model's performance is preserved, the identified components are causally sufficient.

• Hypothesis testing: Validates that discovered features are causally responsible for behavior
• Corruption: Activations from unrelated inputs serve as the baseline
• Integration: Used to verify that dictionary-learned features form complete circuits

Causal scrubbing bridges the gap between correlational feature discovery and mechanistic proof of function.

The conjecture that high-level concepts are encoded as linear directions in a neural network's activation space. Under this hypothesis, features are vectors, and a model's representation of an input is a linear combination of active feature directions.

• Implication: Dictionary learning can recover features via linear decomposition
• Evidence: Concept vectors for sentiment, language, and truthfulness are linearly separable
• Mechanism: The residual stream accumulates feature vectors additively across layers

This hypothesis provides the mathematical foundation justifying why sparse linear dictionary learning can recover interpretable features from deep networks.