Large language models exhibit a modular internal organization that mirrors well-studied functional networks of the human brain, but how this organization forms during training is unknown: prior work has characterized finished models, not the formation process. We track formation step by step: we train a Pythia-410M model from scratch (two trajectories, bf16 and fp32) and run attribution patching at every step, alongside probes for gradient norms, effective updates, weight norms, and first-order loss decomposition across 14 tasks in four cognitive domains. Three findings. First, the modular map is pre-carved: before any learning, the dominant task pair already overlaps at ~3.6x the attribution substrate (a task-independent baseline), and its layer-0 concentration is an architecture-level constant on this model family. Second, the partition locks in through two sharp jumps whose amplitudes do not track the learning-rate schedule (the second reaching 20.4 sigma quiet-window / 6.2 sigma global), accompanied by gradient-level relative deprivation--winners receive 2.25->2.73x the loser's gradient supply, 9.5-11.5 standard deviations below a random control--that does not propagate to updates or weights. Third, deviation from the substrate appears only in the domain being learned, consistent with the hypothesis that modularity tracks learning. We close by separating the feature-level account we can defend from the mechanistic questions we cannot, and we pre-register the scale-threshold hypothesis behind our ongoing 2.8B experiments.
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.