Alexander Boesgaard Lorup

arXiv2026

Stage-Replay Divergence Follows the KV Cache: Fixed-Prefix Precision Controls and Bidirectional Cache Transplantation

Stage-replay diagnostics reconstruct intermediate token prefixes and treat fresh-prefill continuation as continuation from the decoder state that originally reached the prefix. We audit that assumption at a whole reasoning-stage boundary in a Qwen2.5-derived system. A matched 200-item experiment compares retained live cache with one-shot prefill of identical integer tokens and places an exact replica on both sides. In BF16, replicas remain exact while the constructions differ on 166 suffixes and 20 correctness labels; the accuracy difference is only one point (paired 95% CI [-3.5, +5.5]). A fixed-prefix 2x2 holds all 200 token states constant while crossing construction and precision. The BF16 disagreements recur, whereas FP32 produces no decoded disagreement (95% Wilson upper bound 1.88%). A prospective bridge makes token-by-token incremental and retained live caches bit-exact on 12/12 rows; an all-200 saved-ledger audit reproduces every retained trajectory and comparison fingerprint. Bidirectional transplantation of all 48 key/value layers makes every tested divergent continuation follow its cache donor, both on a selected set at the primary checkpoint (24/24) and an outcome-blind replication at a later checkpoint (43/43). Exact-token replay can therefore be repeatable without preserving live-state fidelity. On the tested states, boundary K/V cache is a causally sufficient carrier of the divergent trajectory, while numerical precision moderates its behavioral expression.

cs.LG↗

arXiv2026

Counterfactual Likelihood Tests for Indirect Influence in Private Reasoning Channels

Reasoning systems increasingly separate intermediate computation into private and public channels, creating evaluation cases that look similar in transcripts: independent co-derivation, direct access to private content, and indirect influence through public communication. This paper presents a counterfactual likelihood test for measuring influence between private reasoning channels. The method replaces an upstream private block with a length-matched donor block, holds the public token sequence and downstream target fixed, and measures the downstream target's negative-log-likelihood shift. On a 7B role-channel reasoning model used for validation, textual probes are unreliable: raw n-gram overlap overstates leakage, corrected overlap remains noisy, and canary reproduction reports no discrimination. Counterfactual likelihood separates unmasked and masked conditions, while length matching controls a RoPE positional confound. In the hardened masked validation, reverse B-to-A influence is near zero, while A-to-B influence persists through public-speech hidden states. A multi-checkpoint validation across three checkpoints, five seeds, and 13,734 valid directional contrasts replicates this asymmetry. A graph-separation control that blocks private-to-public carrier edges produces bit-identical natural and counterfactual scores across all 13,734 control evaluations, identifying the tested public-channel pathway as the complete carrier of the measured counterfactual signal under the implemented role-visibility mask. The results show that private-channel evaluation should report direct and indirect influence separately, and that counterfactual likelihood probes provide a practical default for measuring these boundaries.

cs.LG↗