Circuit Fingerprints: How Answer Tokens Encode Their Geometrical Path

TL;DR

This work proposes the Circuit Fingerprint Hypothesis: transformer circuits are geometric structures encoded in activation space, and answer tokens reveal the directions that would produce them. By reading these directions, the authors perform gradient-free circuit discovery that matches gradient-based baselines in identifying influential components, and they show that the same directions can be used to steer model outputs, achieving higher emotion-control accuracy than instruction prompting while maintaining factual grounding. The approach relies on reading by aligning target directions from answer tokens with component outputs, and on writing via steering interventions in a subspace constructed from prompt-derived directions, using Shapley-valued channel attribution to allocate credit across Q, K, and V. Experiments across IOI, SVA, and MCQA on four model families demonstrate comparable circuit discovery performance to gradient-based methods and effective steering toward affective outputs, supporting a read-write duality where interpretability and controllability are two facets of the same geometric structure. The practical implications include gradient-free circuit identification and more precise feature steering, with persona and instruction-prompt based prompt engineering offering a pathway to flexible, dataset-free circuit discovery and manipulation, albeit with limitations in zero-shot robustness and potential factual degradation under certain steering conditions.

Abstract

Circuit discovery and activation steering in transformers have developed as separate research threads, yet both operate on the same representational space. Are they two views of the same underlying structure? We show they follow a single geometric principle: answer tokens, processed in isolation, encode the directions that would produce them. This Circuit Fingerprint hypothesis enables circuit discovery without gradients or causal intervention -- recovering comparable structure to gradient-based methods through geometric alignment alone. We validate this on standard benchmarks (IOI, SVA, MCQA) across four model families, achieving circuit discovery performance comparable to gradient-based methods. The same directions that identify circuit components also enable controlled steering -- achieving 69.8\% emotion classification accuracy versus 53.1\% for instruction prompting while preserving factual accuracy. Beyond method development, this read-write duality reveals that transformer circuits are fundamentally geometric structures: interpretability and controllability are two facets of the same object.

Figures (11)

• Figure 1: Circuit Fingerprints unifies circuit discovery and activation steering as dual operations—reading and writing—on the same geometric structure encoded in answer token representations.
• Figure 2: Comparison of attention head importance on the IOI task. Top: Per-token identity scores computed with respect to answer token's attention head outputs (our method). Bottom: Head importance from EAP-IG-inputs (gradient-based). Both methods identify the same critical heads in layers 9--11, with strongest signal at the final token position.
• Figure 3: Edge-level circuit discovery on IOI. (Left) GPT2-Small. (Center) Qwen2.5-0.5B. (Right) Llama3.2-1B.
• Figure 4: Circuit function predicts QKV decomposition. Shapley values decompose each head's contribution into Query, Key, and Value components. Heads with similar circuit roles cluster together: output-focused heads (Name Movers) are Q-dominated, while routing heads (S-Inhibition) are K-dominated.
• Figure 5: Steering validation on IOI (n=100). Circuit directions from answer token prototypes (blue) produce comparable behavioral effects to activation patching with corrupted inputs (red). Left: P(correct) vs. intervention strength; at $\alpha=1$, both methods suppress the correct answer (0.014 vs 0.0). Right: IO--S logit difference ($-4.07$ vs $-7.34$). Shaded: $\pm 1$ SD. Similar patterns hold for SVA and MCQA and the other models. (Appendix \ref{['app:act_patch_comp']}).