Executive Summary
Paper XV showed that INLP projections outperform full activations for domain classification, suggesting that lower-bandwidth transmission can sometimes beat higher-bandwidth. This paper systematically explores the bandwidth-fidelity tradeoff by comparing text-only, activation-only, and combined transmission at multiple PCA dimensionalities.
The central finding is that text and activations carry fundamentally different kinds of information. All text conditions — regardless of verbosity or structure — cluster at RSA similarity ~0.11, while BOS + full activations achieves RSA 0.47, a 4x improvement in geometric fidelity. Yet despite this massive geometric advantage, KL divergence remains similar across conditions (6.97-7.35 nats), meaning the activation-level similarity does not translate into more similar output distributions.
Perhaps most striking is the domain reversal pattern: text-based coordination preserves legal reasoning best (RSA 0.23 for legal vs 0.08-0.12 for other domains), while activation-based coordination preserves scientific reasoning best (RSA 0.64 for science vs 0.30-0.45 for other domains). This suggests that different domains are encoded at different levels of abstraction — legal reasoning lives more in the symbolic/linguistic layer, while scientific reasoning lives more in the geometric/activation layer. A bandwidth ceiling emerges at approximately 100 PCA dimensions, beyond which additional activation dimensions provide no benefit.
Key Findings
- Fundamental information type distinction: All text conditions cluster at RSA ~0.11; BOS + full activations achieves RSA 0.47 (4x higher geometric fidelity)
- Geometric fidelity does not transfer: Despite 4x RSA advantage, KL divergence remains similar (6.97-7.35 nats) across all conditions
- Domain reversal: Text preserves legal best (RSA 0.23), activations preserve science best (RSA 0.64) — different domains live at different abstraction layers
- Bandwidth ceiling: Returns diminish beyond ~100 PCA dimensions; additional activation bandwidth provides no benefit
Key References
- McEntire (2026) — INLP Projection Transmission: denoising effect in low-dimensional transfer (Paper XV)
- McEntire (2026) — Sender Continuation Perplexity: reasoning trajectory alignment (Paper XVII)
- McEntire (2026) — The Inter-Instance Compression Barrier: uniform lossy channel (Paper XIV)
- Kriegeskorte et al. (2008) — Representational similarity analysis