State Transfer Reveals Reuse in Controlled Routing

Abstract: Prompt-based interventions can change model behavior, but trained success alone does not identify where the behaviorally relevant state is represented. We study this question in controlled routing tasks using interfaces chosen on support data, held-out query evaluation, and matched necessity, sufficiency, and wrong-interface controls. On GPT-2 triop, an early interface supports exact transfer under these tests. On GPT-2 add/sub, zero-retrain compiled transfer at the fixed interface recovers most of donor routing accuracy, while trainable prompt slots can relearn the same behavior at several other positions only after additional support examples and optimization. These results distinguish fixed-interface reuse from prompt relocation in a setting where the two can be tested directly. Qwen routing provides a cross-architecture consistency check for the same matched-interface pattern at the operator token, although donor-specific identity on the local V-path remains unresolved. Generation and reasoning branches are used to map scope: they show broader transport or weaker controller identifiability once control depends on longer trajectories or harder selection. In controlled routing, fixed-interface transfer is therefore stronger evidence of reuse than trained prompt success alone.

• The paper demonstrates that fixed-interface state transfer nearly replicates donor performance in controlled routing tasks without retraining.
• The methodology employs necessity/sufficiency tests and control interventions to confirm that transfer at a specific internal locus is identity-dependent.
• The findings indicate that while routing benefits from localized state reuse, more distributed control in complex tasks requires broader interface mechanisms.

Fixed-Interface State Transfer as Evidence of Reuse in Controlled Routing

Problem Motivation and Evidential Framework

The paper "State Transfer Reveals Reuse in Controlled Routing" (2604.18158) critically analyzes how prompt-based methods, commonly utilized to steer LLM behavior, interact with the internal state representations responsible for routing control. It interrogates whether behavioral control induced by prompts reflects the reuse of existing internal states or the relocation/reconstruction of control signals via new learned interventions. This distinction is nontrivial—mechanistic understanding of LM control requires stronger experimental standards than end-task behavioral success, especially given the flexibility of large models and the malleability of prompt-based steering.

The central argument is that fixed-interface state transfer at a support-selected internal locus, verified by necessity/sufficiency and negative controls, constitutes much stronger evidence of endogenous state reuse than the mere success of any trained prompt. To substantiate this, the authors develop an evidential protocol: interface selection is locked using support data, and only interventions at the chosen internal interface are permitted on held-out queries without query-side retuning. Several critical controls (wrong-layer/site, randomized state injections, moment-matching) differentiate true reuse from accidental or aggregate-feature matching.

Experimental Results: Routing, Transfer, and Relocation

Single-Interface Transfer in Controlled Routing

In the mainline controlled routing experiments on GPT-2, specifically the triop (add/sub/copy) and add/sub tasks, the results are decisive. For triop, compiled state transfer at a precisely support-selected early interface ("layer-0 block@ctrl") nearly matches the donor prompt on held-out routing accuracy ($0.799\pm0.040$ vs $0.824\pm0.030$), while the untransformed receiver prompt remains at chance ($0.333$). Key variants demonstrate:

• Exact sufficiency at the matched interface: Compiled state injected into the centered baseline recapitulates donor performance.
• Necessity: Destruction of the interface state erases the behavior.
• Specificity: Permuted, random, or wrong-interface interventions do not recover behavior, confirming that transfer is identity-dependent, not a byproduct of statistical similarity.
• Efficiency: Compiled transfer achieves transfer instantly—without retraining—whereas baselines like LoRA/applied at the same locus or prompt-slot tuning reach comparable accuracy only after significant optimization and data usage.

Add/Sub: Reuse vs. Relocation

GPT-2 add/sub experiments emphasize the separation between state reuse via transfer and the capacity of trainable prompts to relocate/reconstruct control elsewhere. Zero-retrain state transfer at the chosen interface achieves $0.9113\pm0.0010$ accuracy, while even strong PEFT baselines (plain LoRA, LoRA+trainable embeddings, prompt-slot tuning) require $3200$ to $25600$ support steps to match this performance. Thus, although the behavior can eventually be rebuilt via training at other slots or weights, the existence of a fixed-interface that supports transfer without retraining demonstrates reuse rather than mere reconstructibility.

Furthermore, scaling up support pairs strengthens relocation, but compiled transfer remains more data/optimization-efficient.

Cross-Architecture and Reasoning Generalization

Experiments with Qwen and Qwen2.5-3B verify that the routing result extends to non-GPT architectures, specifically at the operator token interface. Compiled $V$-only interventions suffice for routing, whereas $K$-only, prompt-last, or random-$KV$ baselines fail. However, these experiments reveal that donor-specific content identity on local $V$-path remains unresolved; random $0.824\pm0.030$0 perturbations can sometimes rise above null baselines in some settings. Thus, the result supports cross-architecture consistency in localized control but cannot claim strict identity-level reuse.

When the selection/control objective becomes more complex (e.g., multi-step generation, deep reasoning), control becomes distributed and necessitates broader interfaces. For copy-generation tasks, wider prompt-conditioned interfaces (covering $0.824\pm0.030$1) significantly outperformed narrow ones, confirming that the transportability of state is present but less localized. In Qwen "verify" and "solve" tasks, proposal/commit separation emerges—proposals can be reproduced by state transfer, but robust selection/reranking evades concise mechanistic capture.

Theoretical and Practical Implications

The methodological contribution is the rigorous separation of reuse (transfer at a single support-locked internal site) from retrained relocation (prompt form success after optimization at arbitrary locations). The appendix details the search burden, confirming that support-query locks guarantee experimental rigor, but do not imply the existence of a uniquely privileged site; interface selection is nontrivial and familial rather than singleton.

The main practical implication is mechanistic: routing-style control in LMs can be traced to support-selectable, interface-localized internal states that are reusable across instances without retraining. This strengthens causal claims about the internal loci of control, which is fundamental for interpretability, robust model editing, and safety-focused interventions.

However, the existence of transferable internal state does not guarantee universal control or transferability across tasks. For long-horizon generation and harder selection/reasoning, control becomes more distributed and less locally transferable. Thus, claims of interpretable control through prompt engineering alone are overconfident unless interface-localized, necessity/sufficiency-verified transfer is established.

Limitations and Avenues for Future Research

Several limitations are highlighted. First, interface-family selection on support data still implies search multiplicity, not uniqueness. Second, the strongest claims pertain to controlled/routing tasks rather than unconstrained generative tasks or frontier-scale models. Third, the evidence for donor-specific identity (especially on $0.824\pm0.030$2-path content in Qwen) is incomplete. Finally, baseline coverage focuses on mechanistically relevant alternatives, not exhaustive benchmarking of all PEFT or adapter strategies.

Future research should:

• Explore the existence and nature of reusable fixed-interface loci in larger or instruction-tuned models.
• Investigate whether similar transfer mechanisms arise in multi-modal or cross-lingual architectures.
• Develop stricter diagnostics for donor-specific content identity, possibly integrating causal tracing, ablation, and information-theoretic profiling at scale.
• Examine the implications for robust model editing, e.g., by leveraging interface-localized transfer for safety or factual updates.

Conclusion

This study establishes that fixed-interface state transfer, verified by strong experimental controls, provides unambiguous evidence for endogenous state reuse in controlled routing tasks. While prompt training can reconstruct behaviors broadly, only interventions at support-selected internal loci achieve immediate, retraining-free transfer—a mechanistic criterion that moves beyond prompt form success. The scope of this approach is defined: strong for routing-style control, weaker as control becomes distributed or trajectories grow. The methodological lesson is that careful interface targeting, proper baselining, and locked evaluation protocols are necessary to progress in the causal understanding of LM behavior.