Dictionary Learning

The learned dictionary contains more feature directions than the original activation space dimensions. This overcompleteness allows the model to represent more independent concepts than it has neurons, directly addressing the Superposition Hypothesis. By expanding into a higher-dimensional space, features that were compressed into overlapping, nearly orthogonal directions can be disentangled into distinct, interpretable atoms.

The core optimization objective enforces that only a small subset of dictionary features activates for any given input. This is typically achieved through an L1 penalty on the feature coefficients during training. The sparsity prior is essential because it forces the decomposition to be parsimonious, preventing the model from explaining activations with a dense, uninterpretable combination of all features and instead selecting only the most relevant, distinct concepts.

The primary goal is to transform polysemantic neurons—which fire for multiple unrelated concepts—into a set of monosemantic features that each activate for a single, human-interpretable pattern. For example, a single neuron responding to both academic citations and DNA sequences can be decomposed into two distinct dictionary features, each specializing in one concept. This provides a faithful, granular map of the model's internal knowledge.

The learned dictionary must accurately reconstruct the original model activations from the sparse feature coefficients. The loss function balances two competing terms:

• Reconstruction error: Minimizing the difference between the original activation vector and the linear combination of active dictionary features.
• Sparsity penalty: Maximizing the number of zero coefficients. A well-trained dictionary achieves high fidelity with very few active features, proving it has captured the essential structure of the data.

Dictionary features are not merely correlational; they can be used for causal intervention. By artificially activating a specific dictionary feature's direction in the residual stream during a forward pass, researchers can steer the model's behavior in predictable ways. For instance, clamping the feature for 'sycophancy' can measurably reduce the model's tendency to agree with the user, validating that the feature represents a causally relevant internal variable.

Unlike traditional dictionary learning on static data like images, this technique is applied directly to the internal activations of a frozen, pre-trained model. A large corpus of text is fed through the model, and the intermediate activation vectors at a specific layer are collected. The dictionary is then trained on this dataset of activations, learning the recurring patterns in the model's representational space rather than patterns in the raw input data.

An unsupervised neural network trained to reconstruct model activations while enforcing a sparsity penalty on the hidden layer. This forces the autoencoder to learn an overcomplete basis of features, decomposing polysemantic neurons into a set of monosemantic directions. The sparsity constraint is typically implemented via an L1 penalty on the hidden activations or a top-k activation function. Sparse autoencoders are the primary tool for applying dictionary learning to large language models, revealing interpretable features in the residual stream.

The theory that neural networks represent more independent features than they have dimensions by encoding them in overlapping, nearly orthogonal directions within a shared activation space. This explains why individual neurons often appear polysemantic—responding to multiple unrelated inputs. Dictionary learning directly addresses superposition by finding an overcomplete basis that disentangles these compressed representations into distinct, interpretable feature directions.

A diagnostic technique that trains a simple linear classifier on top of a frozen model's internal representations to test what information is encoded at a specific layer. If a linear probe can accurately predict a property—such as part-of-speech or factual correctness—then that information is linearly separable in the representation space. Linear probing validates that features identified through dictionary learning correspond to genuine, extractable concepts rather than artifacts of the decomposition method.

A causal intervention method that replaces a model's internal activation at a specific location with a cached activation from a different input. By observing how the output changes, researchers can localize where a computation occurs. This technique is used to validate that dictionary-learned features are causally implicated in model behavior, not merely correlated. Common variants include resample ablation, mean ablation, and zero ablation.

A direction in a model's activation space that, when added to the residual stream during inference, reliably modifies the model's high-level behavior. Steering vectors are often derived from dictionary-learned features: once a feature direction is identified (e.g., the 'refusal' feature), adding or subtracting that direction can control the model's output. This technique is central to representation engineering and activation addition methods.

A statistical framework for quantifying how much a model's output depends on a specific intermediate representation by measuring the effect of intervening on that representation. It decomposes the total effect into direct effects and indirect effects mediated through other pathways. This analysis is essential for validating that dictionary-learned features are not just descriptive but causally necessary for the model's computation.