Executive Summary
When two model instances communicate through natural language, a massive compression occurs — from thousands of activation dimensions to a sequence of discrete tokens. This paper asks whether that compression selectively targets domain-specific information, which would constitute a second barrier beyond the concentration barrier (Paper XI) to multi-agent domain coordination. Using Qwen 2.5-7B as both sender and receiver, it compares activations before and after three levels of compression (full reproduction, 3-sentence summary, 1-sentence abstract) and splits the difference into domain-specific (36 INLP directions) and domain-agnostic (top-20 PCA) components.
The hypothesis is not supported. The domain-specific fraction of the compression loss is stable at approximately 1.4% at layer 10 and 4.4% at layer 27 at every compression level, and the domain-specific to domain-agnostic ratio holds at 0.07 (layer 10) and 0.13 (layer 27). The NL interface drops approximately 80% of activation information at layer 10, but it does so proportionally — domain-specific and domain-agnostic information are lost at the same rate. The communication bottleneck is a uniform lossy channel, not a selective filter.
This is an important negative result. Because domain-specific information is only about 1.4% of the activation variance to begin with, any lossy channel destroys it — even a fair one. The concentration barrier identified in Paper XI is the binding constraint; the communication interface is innocent, and a better summary protocol cannot raise the domain-specific fraction.
Key Findings
- H1 not supported: The natural language interface does not selectively drop domain-specific information
- Stable domain fraction: Domain-specific fraction of compression loss holds at ~1.4% (layer 10) and ~4.4% (layer 27) across all three compression levels; DS/DA ratio stays at 0.07 and 0.13
- Uniform lossy channel: The NL interface drops ~80% of activation information at layer 10, proportionally across domain-specific and domain-agnostic components
- Concentration barrier is sole constraint: The communication interface is innocent; the concentration barrier (Paper XI) is the binding constraint on domain-specific information transfer
Key References
- McEntire (2026) — The Concentration Barrier: effective dimensionality bounds (Paper XI)
- McEntire (2026) — Causal Basis Discovery: classification-intervention dissociation (Paper XIV)
- McEntire (2026) — Spectral Geometry of the Forward Pass: the isotropic Jacobian (Paper X)
- McEntire (2026) — Layer-Resolved Response Tensor: selectivity peak at layer 10 (Paper IX)