Extent of linear dimensions in generative AI embeddings

Determine the extent to which generative AI systems, including large language models used for social simulation, possess meaningful linear dimensions in their embedding spaces as posited by the linear representation hypothesis, so that steering-vector interventions can be rigorously assessed for feasibility and precision in controlling model behavior or injecting humanlike variation.

Background

The paper proposes steering vectors as a method to directly inject variation into an LLM’s embedding space to improve diversity and potentially control behaviors like sycophancy. This approach assumes that model representations admit approximately linear semantic dimensions that can be manipulated with activation additions.

However, the authors caution that superposition and current interpretability limits create uncertainty about whether such linear dimensions robustly exist across models and contexts. Clarifying the linear representation hypothesis is essential to determine whether steering vectors can reliably match human diversity or control specific behaviors without harmful side effects.

References

Nevertheless, it could be intractable to identify vectors that precisely match real human diversity or specific model behaviors given issues such as superposition and open questions about the extent to which generative AI systems have meaningful linear dimensions in their embeddings (i.e., the “linear representation hypothesis”).

— LLM Social Simulations Are a Promising Research Method  (2504.02234 - Anthis et al., 3 Apr 2025) in Promising directions, Subsection "Steering vectors"

We describe the conditions where linear accessibility is possible, the extent LLMs utilize this remains unknown.

— High-probability guarantees for linear accessibility in feature superposition  (2609.09556 - Vompa, 9 Sep 2026) in Section 'Limitations'

This does not rule out the existence of a privileged direction; it shows that reaching one is not necessary. Establishing the stronger claim would require comparing vectors extracted from disjoint reference subsets of the same author against vectors from different authors, which we leave to future work.

— Predicting Steering Vectors and Adapter Weights for Few-Shot Author-Style Transfer  (2610.03163 - Popp et al., 2 Oct 2026) in Section 7, subsection “No Single Style Axis” (paragraph “Manual and learned steering vectors are near-orthogonal”)

They are linear-algebra properties; perceptual composition and timed acoustic realization remain empirical questions.

— ParaGeo: Decomposing Paralinguistic Variation into a Shared Latent Geometry  (2610.03125 - Liu et al., 2 Oct 2026) in Appendix, Section \ref{app:operators}, subsection “The shared projector is the operative object”

Although prior work has shown that CLIP text embeddings often exhibit approximate linear compositionality over semantic factors, it is non-trivial whether the same property holds at the $\langle$EOS$\rangle$ hidden state, which aggregates contextual information through causal attention rather than being a simple sum of word embeddings.

— Not Just a Subject: Capturing Adaptive Scene-Specific Variance for Visual Storytelling  (2610.22320 - Cha et al., 15 Oct 2026) in Appendix, Section "EOS Analysis" (Section \ref{sec:eos_linear}), subsection "Empirical Analysis of EOS Linearity"