Methods · Learning Dynamics and Mechanistic Interpretability
Forked-Run Experiments and Linear Mode Connectivity
Survey sections: §10.2.2 Causal Interventions on Mechanism Formation
A forked-run experiment spawns two or more training continuations from the same checkpoint, varying a single factor such as SGD noise, data order, or random seed, and compares the models the continuations produce. Linear mode connectivity is a standard instrument for the comparison. Two networks are linearly mode connected if the loss barrier along the straight path between their parameters in weight space is near zero.
Intended applications
Specifically, Frankle et al. (2020) examined the sensitivity of the model’s training results to SGD noise by restarting training from different checkpoints, each time using different SGD noise. Early in training, these runs may converge to different loss basins. Later, they tend to converge to linearly mode-connected solutions, indicating that the training outcome has become stable to SGD noise.
For example, degrading the data early in training causes permanent deficits that the same degradation applied later does not, establishing critical learning periods (Achille et al., 2019), and forking a run across many random seeds distinguishes properties of the training setup from accidents of a single run (van der Wal et al., 2025).
Limitations
Under this interpretation, a loss barrier between two checkpoints suggests that their mechanisms differ. However, the absence of a loss barrier does not guarantee that their mechanisms are the same.
Key papers
Cited in §10.2.2.
- Jonathan Frankle, Gintare Karolina Dziugaite, Daniel M. Roy, and Michael Carbin. Linear mode connectivity and the lottery ticket hypothesis. In International Conference on Machine Learning, pp. 3259–3269, 2020.
- Alessandro Achille, Matteo Rovere, and Stefano Soatto. Critical learning periods in deep networks. In International Conference on Learning Representations, 2019.
- Oskar van der Wal, Pietro Lesci, Max Müller-Eberstein, Naomi Saphra, Hailey Schoelkopf, Willem Zuidema, and Stella Biderman. PolyPythias: Stability and outliers across fifty language model pre-training runs. In The Thirteenth International Conference on Learning Representations, 2025.
- Ekdeep Singh Lubana, Eric J. Bigelow, Robert P. Dick, David Krueger, and Hidenori Tanaka. Mechanistic mode connectivity. In International Conference on Machine Learning, pp. 22965–23004, 2023.
Also discussed in: §10.2.2 Causal Interventions on Mechanism Formation · §10.3.5 Case Study: Induction Heads
Other methods in Learning Dynamics and Mechanistic Interpretability
Trajectory-Based Attribution · Per-Token Learning Curves · Refined Local Learning Coefficients (Localising Change to Components) · Loss-Curve Derivatives · 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