Adam Scherlis

Thomas Marshall, Adam Scherlis, Nora Belrose

We propose affine concept editing (ACE) as an approach for steering language models' behavior by intervening directly in activations. We begin with an affine decomposition of model activation vectors and show that prior methods for steering model behavior correspond to subsets of terms of this decomposition. We then provide a derivation of ACE and use it to control refusal behavior on ten different models, including Llama 3 70B. ACE combines affine subspace projection and activation addition to reliably control the model's refusal responses across prompt types. We evaluate the results using LLM-based scoring on a collection of harmful and harmless prompts. Our experiments demonstrate that ACE consistently achieves more precise control over model behavior than existing methods and generalizes to models where directional ablation via affine subspace projection alone produces incoherent outputs. Code for reproducing our results is available at https://github.com/EleutherAI/steering-llama3 .

Nora Belrose, Adam Scherlis

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

Adam Scherlis, Nora Belrose

We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the "local volume" of the anchor. We adapt an existing basin-volume estimator, which is very fast but in many cases only provides a lower bound. We show that this lower bound can be improved with an importance-sampling method using gradient information that is already provided by popular optimizers. The negative logarithm of local volume can also be interpreted as a measure of the anchor network's information content. As expected for a measure of complexity, this quantity increases during language model training. We find that overfit, badly-generalizing neighborhoods are smaller, indicating a more complex learned behavior. This smaller volume can also be interpreted in an MDL sense as suboptimal compression. Our results are consistent with a picture of generalization we call the "volume hypothesis": that neural net training produces good generalization primarily because the architecture gives simple functions more volume in parameter space, and the optimizer samples from the low-loss manifold in a volume-sensitive way. We believe that fast local-volume estimators are a promising practical metric of network complexity and architectural inductive bias for interpretability purposes.