Published March 8, 2026
| Version v1
Preprint
Open
Mechanics of Meaning: Sparse Feature Interventions and the Basis Structure of Contextual Control in Transformers
Authors/Creators
Description
Preprint. Completed manuscript.
The Appearance of Meaning (AoM) showed that contextualized token-in-context states causally control
meaning-like preference margins in transformer models. This paper asks whether that already-localized con-
textual control is better recovered in the raw residual stream or in a sparse learned feature basis. In Gemma
2 2B, we compare matched raw residual and sparse autoencoder (SAE) interventions at shared resid_post
sites under hard invariants and endpoint-native accounting. On lexical disambiguation (DISAMB), layer-4
SAE patching yields a larger mean donor-directed effect than raw patching and higher RMS-based effect-
efficiency under scored-position disturbance accounting, although the paired SAE-over-raw difference is only
directionally positive and its 95% confidence interval includes zero. FP64 decomposition shows that the
paired difference is captured by expected-set and other-set candidate log-probability terms; diagnostic Δ log𝑍
is zero in the primary single-token regime. Matched-rank PCA recovers an intermediate effect, random or-
thogonal projections recover little, and an SAE reconstruction/residual split shows that the early result is
not well explained by generic compression or by a simple monotonic reconstruction-fidelity account. This
early, task-conditional pattern weakens or reverses at later layers and does not generalize uniformly to
counterfactual preference (CF) and discourse coherence (COH) tasks, where raw residual patching is near
parity or stronger on effect magnitude. We therefore conclude that AoM-relevant control is basis-sensitive,
layer-dependent, and task-heterogeneous rather than uniformly sparse. The result extends AoM from causal
localization to representational basis without implying meaning proper or sparse semantic atoms.
The Appearance of Meaning (AoM) showed that contextualized token-in-context states causally control
meaning-like preference margins in transformer models. This paper asks whether that already-localized con-
textual control is better recovered in the raw residual stream or in a sparse learned feature basis. In Gemma
2 2B, we compare matched raw residual and sparse autoencoder (SAE) interventions at shared resid_post
sites under hard invariants and endpoint-native accounting. On lexical disambiguation (DISAMB), layer-4
SAE patching yields a larger mean donor-directed effect than raw patching and higher RMS-based effect-
efficiency under scored-position disturbance accounting, although the paired SAE-over-raw difference is only
directionally positive and its 95% confidence interval includes zero. FP64 decomposition shows that the
paired difference is captured by expected-set and other-set candidate log-probability terms; diagnostic Δ log𝑍
is zero in the primary single-token regime. Matched-rank PCA recovers an intermediate effect, random or-
thogonal projections recover little, and an SAE reconstruction/residual split shows that the early result is
not well explained by generic compression or by a simple monotonic reconstruction-fidelity account. This
early, task-conditional pattern weakens or reverses at later layers and does not generalize uniformly to
counterfactual preference (CF) and discourse coherence (COH) tasks, where raw residual patching is near
parity or stronger on effect magnitude. We therefore conclude that AoM-relevant control is basis-sensitive,
layer-dependent, and task-heterogeneous rather than uniformly sparse. The result extends AoM from causal
localization to representational basis without implying meaning proper or sparse semantic atoms.
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Additional details
Dates
- Issued
-
2026-03-08
Software
- Repository URL
- https://github.com/Satori-1618/AoM_mechanism
- Programming language
- Python
- Development Status
- Active