Asymmetry of internal information sharing

Determine whether the asymmetry conjecture holds generally for frozen receivers: key–value caches must be augmented rather than substituted, whereas residual-stream activations may be replaced rather than augmented, with the respective mechanism choices determined by the carriers’ consumption points.

Background

The paper formulates a conjecture about the interaction between internal-state carriers and the mechanisms by which a frozen receiver consumes them. It predicts that substituting foreign keys and values into the receiver’s cache remains near the transfer floor, while cache augmentation can support useful transfer; conversely, it predicts that direct activation replacement transfers effectively, whereas activation augmentation is less effective.

The experiments support these predictions within the controlled Qwen2.5-1.5B setting and provide evidence that the conjecture is falsified if cache substitution transfers well above the floor, cache augmentation fails to clear the floor, or activation replacement fails while activation augmentation succeeds. The broader validity of the conjecture remains an explicitly stated conjectural claim rather than an established general theorem.

References

The conjecture is falsified if a cache substitution transfers well above the floor while provably outside $T$; if cache augmentation with query-side adaptation fails to clear the floor; or if activation replacement fails while activation augmentation succeeds.

— Augment the Cache, Replace the Activation: A 2x2 Study of Internal-State Sharing  (2610.22026 - Deng et al., 15 Oct 2026) in Conjecture 1, Section 2, “The Asymmetry Conjecture”

Second, this sweep probes substitution only. It establishes that the failure mode generalizes; it does not establish that the positive half of our rule, augmentation on the cache and replacement on the activation, generalizes with it.

— Augment the Cache, Replace the Activation: A 2x2 Study of Internal-State Sharing  (2610.22026 - Deng et al., 15 Oct 2026) in Section 5, “Limitations” and Appendix, Section “Does the wall depend on the architecture?”