Parcae: Scaling Laws For Stable Looped Language Models
Traditional fixed-depth architectures scale quality by increasing training FLOPs, typically through increased parameterization, at the expense of a higher memory footprint, or data. A potential alternative is looped architectures, which instead increase FLOPs by sending activations through a block of layers in a loop. While promising, existing recipes for training looped architectures can be unstable, suffering from residual explosion and loss spikes. We address these challenges by recasting looping as a nonlinear time-variant dynamical system over the residual stream. Via a linear approximation to this system, we find that instability occurs in existing looped architectures as a result o...
| Authors | Hayden Prairie, Zachary Novack, Taylor Berg-Kirkpatrick et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 April 2026 |
| Last updated at source | 14 April 2026 |
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