Calibrating Interpretability Instruments Before Trusting Their Verdicts

A central goal of mechanistic interpretability is to identify which internal components causally drive a language model's behavior. Because these importance estimates serve as the evidence for identifying circuits, systematic errors can lead to the misidentification of the underlying mechanisms. While activation patching provides a gold-standard causal metric, its computational cost is prohibitive at scale. Practitioners instead rely on attribution patching, a gradient-based, first-order approximation whose reliability remains poorly understood. In this work, we characterize the source of this unreliability, demonstrating that the dominant error stems from the non-linearities in the downstream network rather than local curvature at the patched component. This insight yields three practical tools: (i) a reliability score to detect untrustworthy estimates, (ii) error bounds quantifying potential attribution mis-specifications, and (iii) a Hessian-vector-product (HVP) correction that eliminates the leading-order error with only one additional backward pass. In evaluations across five model families (124M-9B parameters) and both random-token and naturalistic (name-swap) perturbations, HVP is the only second-order correction feasible at larger scale, where standard baselines like Integrated Gradients become computationally prohibitive. In comparative experiments, a multi-step HVP variant matches or exceeds the accuracy of Integrated Gradients at significantly lower compute, outperforming prior second-order baselines. These improvements lead to higher-fidelity circuit recovery on standard benchmarks and support a Screen-Flag-Fix workflow that targets computational effort only toward the components flagged as unreliable.

Attributing language model outputs to their internal computations is an open problem in interpretability. Existing methods, which use causal interventions, gradients, or learnable masks, either are infeasibly expensive or struggle to identify actual causally-important internal computations. We propose framing attribution as the problem of identifying nested subsets of internal components which minimise a downstream loss. To learn this task, we introduce Matryoshka Attribution (MAttr), a mask learning method that parametrises the mask with a simple differentiable sigmoid top-$k$ operator. We supervise training over all sparsities simultaneously by randomising $k$ over training, resulting in a learned ordering of components by attribution score. MAttr achieves number 1 on the official leaderboard of the Mechanistic Interpretability Benchmark (Mueller et al., 2025); our method identifies sparse and task-transferrable circuits across varying circuit bases. As a practical application, we show that MAttr can be trained with reinforcement learning to identify weight changes responsible for downstream behaviours in LLM finetuning. We train MAttr on refusal judge scores and find that restoring $1\%$ of Llama 3.1 8B Instruct's weights to their base model state is sufficient to remove refusals while maintaining capabilities. We view MAttr as a successful formulation of interpretability into a learnable objective that we can tackle with gradient descent, and encourage future work along these lines.

Large language models are increasingly deployed as protocols: structured multi-call procedures that spend additional computation to transform a baseline answer into a final one. These protocols are evaluated only by end-to-end accuracy, giving limited insight into when they help, when they hurt, and whether their behavior transfers under distribution shift or composition. We propose a paired-outcome measurement interface for auditing a single protocol step on exact-match tasks. For each instance, the interface records a baseline correctness bit $E_0\in\{0,1\}$ and a post-step correctness bit $E_1\in\{0,1\}$, separating correction ($E_0=0\to E_1=1$) from corruption ($E_0=1\to E_1=0$) through two rates: $c=\Pr(E_1=1\mid E_0=0)$ and $γ=\Pr(E_1=0\mid E_0=1)$. These rates predict accuracy changes and define a reusable empirical interface testable across seeds, mixtures, and pipelines. We identify three failure mechanisms. Under mixture shift, pooled estimates of $(c,γ)$ become biased when calibration and deployment mixtures differ; conditioning on a difficulty proxy restores stability without additional model calls. Under presentation contamination, selection protocols alter the interface through stable presentation artifacts when candidate content is fixed. Under state insufficiency, the correctness bit may not carry enough history for multi-step pipelines to compose predictably; a Markov factorization test identifies when composition is valid and where additional state is needed. When a protocol step passes these diagnostics, it becomes an auditable module: gated by estimated gain, conditioned on a difficulty proxy to correct mixture bias, and composed into multi-step pipelines with predictable accuracy. We demonstrate these ideas on synthetic mathematical tasks and on GSM8K, where the calibrated interface correctly predicts when protocol steps should be activated or suppressed.