Cross-Layer Transcoders are incentivized to learn Unfaithful Circuits

Cross-layer transcoders (CLTs) enable circuit tracing that can extract high-level mechanistic explanations for arbitrary prompts and are emerging as general-purpose infrastructure for mechanistic interpretability. Because these tools operate at a relatively low level, their outputs are often treated as reliable descriptions of what a model is doing, not just predictive approximations. We therefore ask: when are CLT-derived circuits faithful to the model’s true internal computation? In a Boolean toy model with known ground truth, we show a specific unfaithfulness mode: CLTs can rewrite deep multi-hop circuits into sums of shallow single-hop circuits, yielding explanations that match behavior while obscuring the actual computational pathway. Moreover, we find that widely used sparsity penalties can incentivize this rewrite, pushing CLTs toward unfaithful decompositions. We then provide preliminary evidence that similar discrepancies arise in real language models, where per-layer transcoders and cross-layer transcoders sometimes imply sharply different circuit-level interpretations for the same behavior. Our results clarify a limitation of CLT-based circuit tracing and motivate care in how sparsity and interpretability objectives are chosen.