Sparse Auto-Encoders and Holism about Large Language Models

Understanding whether large language models (LLMs) capture structured meaning requires examining how they represent concept relationships. In this work, we study three models of increasing scale: Pythia-70M, GPT-2, and Llama 3.1 8B, focusing on four semantic relations: synonymy, antonymy, hypernymy, and hyponymy. We combine linear probing with mechanistic interpretability techniques, including sparse autoencoders (SAE) and activation patching, to identify where these relations are encoded and how specific features contribute to their representation. Our results reveal a directional asymmetry in hierarchical relations: hypernymy is encoded redundantly and resists suppression, while hyponymy relies on compact features that are more easily disrupted by ablation. More broadly, relation signals are diffuse but exhibit stable profiles: they peak in the mid-layers and are stronger in post-residual/MLP pathways than in attention. Difficulty is consistent across models (antonymy easiest, synonymy hardest). Probe-level causality is capacity-dependent: on Llama 3.1, SAE-guided patching reliably shifts these signals, whereas on smaller models the shifts are weak or unstable. Our results clarify where and how reliably semantic relations are represented inside LLMs, and provide a reproducible framework for relating sparse features to probe-level causal evidence.

Recent work in Mechanistic Interpretability (MI) has enabled the identification and intervention of internal features in Large Language Models (LLMs). However, a persistent challenge lies in linking such internal features to the reliable control of complex, behavior-level semantic attributes in language generation. In this paper, we propose a Sparse Autoencoder-based framework for retrieving and steering semantically interpretable internal features associated with high-level linguistic behaviors. Our method employs a contrastive feature retrieval pipeline based on controlled semantic oppositions, combing statistical activation analysis and generation-based validation to distill monosemantic functional features from sparse activation spaces. Using the Big Five personality traits as a case study, we demonstrate that our method enables precise, bidirectional steering of model behavior while maintaining superior stability and performance compared to existing activation steering methods like Contrastive Activation Addition (CAA). We further identify an empirical effect, which we term Functional Faithfulness, whereby intervening on a specific internal feature induces coherent and predictable shifts across multiple linguistic dimensions aligned with the target semantic attribute. Our findings suggest that LLMs internalize deeply integrated representations of high-order concepts, and provide a novel, robust mechanistic path for the regulation of complex AI behaviors.

Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens -- a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that interprets LLM hidden states as points on a latent semantic manifold: a Riemannian submanifold equipped with the Fisher information metric, where tokens correspond to Voronoi regions partitioning the manifold. We define the expressibility gap, a geometric measure of the semantic distortion from vocabulary discretization, and prove two theorems: a rate-distortion lower bound on distortion for any finite vocabulary, and a linear volume scaling law for the expressibility gap via the coarea formula. We validate these predictions across six transformer architectures (124M-1.5B parameters), confirming universal hourglass intrinsic dimension profiles, smooth curvature structure, and linear gap scaling with slopes 0.87-1.12 (R^2 > 0.985). The margin distribution across models reveals a persistent hard core of boundary-proximal representations invariant to scale, providing a geometric decomposition of perplexity. We discuss implications for architecture design, model compression, decoding strategies, and scaling laws