A Geometric Notion of Causal Probing

Large language models rely on real-valued representations of text to make their predictions. These representations contain information learned from the data that the model has trained on, including knowledge of linguistic properties and forms of demographic bias, e.g., based on gender. A growing body of work has considered removing information about concepts such as these using orthogonal projections onto subspaces of the representation space. We contribute to this body of work by proposing a formal definition of $\textit{intrinsic}$ information in a subspace of a language model's representation space. We propose a counterfactual approach that avoids the failure mode of spurious correlations (Kumar et al., 2022) by treating components in the subspace and its orthogonal complement independently. We show that our counterfactual notion of information in a subspace is optimized by a $\textit{causal}$ concept subspace. Furthermore, this intervention allows us to attempt concept controlled generation by manipulating the value of the conceptual component of a representation. Empirically, we find that R-LACE (Ravfogel et al., 2022) returns a one-dimensional subspace containing roughly half of total concept information under our framework. Our causal controlled intervention shows that, for at least one model, the subspace returned by R-LACE can be used to manipulate the concept value of the generated word with precision.

Generalizing Backpropagation for Gradient-Based Interpretability

Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model's output with respect to its inputs. While these methods can indicate which input features may be important for the model's prediction, they reveal little about the inner workings of the model itself. In this paper, we observe that the gradient computation of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics about the gradient graph of a neural network, such as the highest-weighted path and entropy. We implement this generalized algorithm, evaluate it on synthetic datasets to better understand the statistics it computes, and apply it to study BERT's behavior on the subject-verb number agreement task (SVA). With this method, we (a) validate that the amount of gradient flow through a component of a model reflects its importance to a prediction and (b) for SVA, identify which pathways of the self-attention mechanism are most important.