# Frac

The work introduces FRAC, a selective state space model architecture derived from fractional dynamics that approximates a heavy-tailed fractional kernel with a finite-state, log-spaced sum of exponential modes, replacing exponential forgetting with power-law long memory and improving long-context performance over SSM baselines such as Mamba2, GDN, and Mamba3 on synthetic long-tail and recall tasks, 1.3B-parameter language modeling, and DNA modeling, while staying competitive on short-context tasks.

The work introduces FRAC, a selective state space model architecture derived from fractional dynamics that approximates a heavy-tailed fractional kernel with a finite-state, log-spaced sum of exponential modes, replacing exponential forgetting with power-law long memory and improving long-context performance over SSM baselines such as Mamba2, GDN, and Mamba3 on synthetic long-tail and recall tasks, 1.3B-parameter language modeling, and DNA modeling, while staying competitive on short-context tasks.