Trung Nguyen

Yihan Zhou, Eric Price, Trung Nguyen

We address the problem of active logistic regression in the realizable setting. It is well known that active learning can require exponentially fewer label queries compared to passive learning, in some cases using $\log \frac{1}{\eps}$ rather than $\poly(1/\eps)$ labels to get error $\eps$ larger than the optimum. We present the first algorithm that is polynomially competitive with the optimal algorithm on every input instance, up to factors polylogarithmic in the error and domain size. In particular, if any algorithm achieves label complexity polylogarithmic in $\eps$, so does ours. Our algorithm is based on efficient sampling and can be extended to learn more general class of functions. We further support our theoretical results with experiments demonstrating performance gains for logistic regression compared to existing active learning algorithms.

Trung Nguyen, Yan Leng

Linear representation hypothesis posits that high-level concepts are encoded as linear directions in the representation spaces of LLMs. Park et al. (2024) formalize this notion by unifying multiple interpretations of linear representation, such as 1-dimensional subspace representation and interventions, using a causal inner product. However, their framework relies on single-token counterfactual pairs and cannot handle ambiguous contrasting pairs, limiting its applicability to complex or context-dependent concepts. We introduce a new notion of binary concepts as unit vectors in a canonical representation space, and utilize LLMs' (neural) activation differences along with maximum likelihood estimation (MLE) to compute concept directions (i.e., steering vectors). Our method, Sum of Activation-base Normalized Difference (SAND), formalizes the use of activation differences modeled as samples from a von Mises-Fisher (vMF) distribution, providing a principled approach to derive concept directions. We extend the applicability of Park et al. (2024) by eliminating the dependency on unembedding representations and single-token pairs. Through experiments with LLaMA models across diverse concepts and benchmarks, we demonstrate that our lightweight approach offers greater flexibility, superior performance in activation engineering tasks like monitoring and manipulation.