Methods · Learning Dynamics and Mechanistic Interpretability
Loss-Curve Derivatives
Survey sections: §10.3.1 Loss-Curve Derivatives
Summary Loss-curve derivatives detect transitions during training by looking for local peaks in the derivative of the aggregate loss curve.
The crudest instrument is the aggregate loss curve itself: a transition large enough to affect overall performance appears as a bump, visible as a local peak in the loss derivative (Olsson et al., 2022).
Limitations
However, most transitions are too small to detect this way. A flat derivative therefore does not constitute evidence of the absence of a transition.
A key challenge in detecting transitions is that aggregate loss can hide abrupt changes in individual capabilities.
Related methods
Key papers
Cited in §10.3.1.
Other methods in Learning Dynamics and Mechanistic Interpretability
Trajectory-Based Attribution · Per-Token Learning Curves · Refined Local Learning Coefficients (Localising Change to Components) · Forked-Run Experiments and Linear Mode Connectivity · Capability-Specific Metrics · Per-Example Decomposition (POLCA) · Latent State Models · Progress Measures · Local Learning Coefficient (LLC) · Forecasting from Smaller and Partial Runs · Forecasting Safety-Relevant Behaviours · Internal Precursors as Early Warning · Pretraining Data Filtering (Deep Ignorance) · Gradient Routing · Monitoring and Steering During Fine-Tuning (Persona Vectors) · Train-Time Intervention Loop