Quantifying Feature Space Universality Across Large Language Models via Sparse Autoencoders

TL;DR

The paper investigates whether large language models share universal semantic structure in their latent representations by introducing Analogous Feature Universality. It pairs sparse autoencoder (SAE) features across models via activation correlations and assesses cross-model similarity of the resulting feature spaces using rotation-invariant measures such as SVCCA and RSA. Across multiple model pairs and semantic subspaces, the study finds high similarity in SAE feature spaces, particularly in middle layers and for semantically coherent subspaces, supporting a form of weak universality. These results imply potential transferability of latent-space interpretability techniques across models, while also highlighting limitations tied to SAE quality and tokenizer dependencies. The work advances mechanistic interpretability by shifting focus from exact features to analogous, transformable feature spaces.

Abstract

The Universality Hypothesis in large language models (LLMs) claims that different models converge towards similar concept representations in their latent spaces. Providing evidence for this hypothesis would enable researchers to exploit universal properties, facilitating the generalization of mechanistic interpretability techniques across models. Previous works studied if LLMs learned the same features, which are internal representations that activate on specific concepts. Since comparing features across LLMs is challenging due to polysemanticity, in which LLM neurons often correspond to multiple unrelated features rather than to distinct concepts, sparse autoencoders (SAEs) have been employed to disentangle LLM neurons into SAE features corresponding to distinct concepts. In this paper, we introduce a new variation of the universality hypothesis called Analogous Feature Universality: we hypothesize that even if SAEs across different models learn different feature representations, the spaces spanned by SAE features are similar, such that one SAE space is similar to another SAE space under rotation-invariant transformations. Evidence for this hypothesis would imply that interpretability techniques related to latent spaces, such as steering vectors, may be transferred across models via certain transformations. To investigate this hypothesis, we first pair SAE features across different models via activation correlation, and then measure spatial relation similarities between paired features via representational similarity measures, which transform spaces into representations that reveal hidden relational similarities. Our experiments demonstrate high similarities for SAE feature spaces across various LLMs, providing evidence for feature space universality.

Figures (37)

• Figure 1: We train SAEs on LLMs, and then compare their SAE feature space similarity using measures such as Singular Value Canonical Correlation Analysis (SVCCA).
• Figure 2: (a) SVCCA and (b) RSA 1-1 paired scores of SAEs for layers in Pythia-70m vs layers in Pythia-160m. We find that middle layers have the most similarity with one another (as shown by the high-similarity block spanned by layers 1 to 3 in Pythia-70m and Layers 4 to 7 in Pythia-160m). We exclude layers 0, as we observe they always have non-statistically significant similarity. The 1-1 scores are slightly higher for most of the Many-to-1 scores shown in Figure \ref{['fig:pythia70m_160m_heatmap_both']}, and the SVCCA score at L2 vs L3 for 70m vs 160m is much higher.
• Figure 3: (a) SVCCA and (b) RSA 1-1 paired scores of SAEs for layers in Gemma-1-2B vs layers in Gemma-2-2B. Middle layers have the best performance. The later layer 17 in Gemma-1 is more similar to later layers in Gemma-2. Early layers like Layer 2 in Gemma-2 have very low similarity. We exclude layers 0, as we observe they always have non-statistically significant similarity. The 1-1 scores are slightly higher for most of the Many-to-1 scores shown in Figure \ref{['fig:gemma1_gemma2_heatmap_both']}.
• Figure 4: (a) SVCCA and (b) RSA 1-1 paired scores of SAEs for layers in Gemma-2-2B vs layers in Gemma-2-9B. Middle layers have the best performance. We exclude layers 0, as we observe they always have non-statistically significant similarity.
• Figure 5: Gemma-2-9B vs Gemma-2-9B-Instruct 1-1 paired SAE scores for (a) SVCCA and (b) RSA.