Investigating Sensitive Directions in GPT-2: An Improved Baseline and Comparative Analysis of SAEs

Sensitive directions experiments attempt to understand the computational features of Language Models (LMs) by measuring how much the next token prediction probabilities change by perturbing activations along specific directions. We extend the sensitive directions work by introducing an improved baseline for perturbation directions. We demonstrate that KL divergence for Sparse Autoencoder (SAE) reconstruction errors are no longer pathologically high compared to the improved baseline. We also show that feature directions uncovered by SAEs have varying impacts on model outputs depending on the SAE's sparsity, with lower L0 SAE feature directions exerting a greater influence. Additionally, we find that end-to-end SAE features do not exhibit stronger effects on model outputs compared to traditional SAEs.

Evolution of SAE Features Across Layers in LLMs

Sparse Autoencoders for transformer-based language models are typically defined independently per layer. In this work we analyze statistical relationships between features in adjacent layers to understand how features evolve through a forward pass. We provide a graph visualization interface for features and their most similar next-layer neighbors, and build communities of related features across layers. We find that a considerable amount of features are passed through from a previous layer, some features can be expressed as quasi-boolean combinations of previous features, and some features become more specialized in later layers.

Characterizing stable regions in the residual stream of LLMs

We identify "stable regions" in the residual stream of Transformers, where the model's output remains insensitive to small activation changes, but exhibits high sensitivity at region boundaries. These regions emerge during training and become more defined as training progresses or model size increases. The regions appear to be much larger than previously studied polytopes. Our analysis suggests that these stable regions align with semantic distinctions, where similar prompts cluster within regions, and activations from the same region lead to similar next token predictions. This work provides a promising research direction for understanding the complexity of neural networks, shedding light on training dynamics, and advancing interpretability.

Using Degeneracy in the Loss Landscape for Mechanistic Interpretability

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

How to use and interpret activation patching

Activation patching is a popular mechanistic interpretability technique, but has many subtleties regarding how it is applied and how one may interpret the results. We provide a summary of advice and best practices, based on our experience using this technique in practice. We include an overview of the different ways to apply activation patching and a discussion on how to interpret the results. We focus on what evidence patching experiments provide about circuits, and on the choice of metric and associated pitfalls.

Towards Automated Circuit Discovery for Mechanistic Interpretability

Recent work in mechanistic interpretability has reverse-engineered nontrivial behaviors of transformer models. These contributions required considerable effort and researcher intuition, which makes it difficult to apply the same methods to understand the complex behavior that current models display. At their core however, the workflow for these discoveries is surprisingly similar. Researchers create a data set and metric that elicit the desired model behavior, subdivide the network into appropriate abstract units, replace activations of those units to identify which are involved in the behavior, and then interpret the functions that these units implement. By varying the data set, metric, and units under investigation, researchers can understand the functionality of each neural network region and the circuits they compose. This work proposes a novel algorithm, Automatic Circuit DisCovery (ACDC), to automate the identification of the important units in the network. Given a model's computational graph, ACDC finds subgraphs that explain a behavior of the model. ACDC was able to reproduce a previously identified circuit for Python docstrings in a small transformer, identifying 6/7 important attention heads that compose up to 3 layers deep, while including 91% fewer the connections.