How Fast Should a Model Commit to Supervision? Training Reasoning Models on the Tsallis Loss Continuum

arXiv:2604.25907v1 Announce Type: cross
Abstract: Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability $p_0$ is small. Using the Tsallis $q$-logarithm, we define a loss family $J_Q$ that interpolates between RLVR (at $q=0$, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at $q=1$, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification $P_theta^-q$ that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires $Omega(frac1p_0)$ time to escape cold start, while the density-estimation pole escapes in $Thetabig(log(frac1p_0)big)$; intermediate $q$ trades escape speed against noise memorization. Because $P_theta$ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias $Obig(fracqM P_theta^q+1big)$; GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at $q=0.75$ substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low $q$ dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at $q=0.75$ provides stable gradients (best overall on HotPotQA at 47.9 maj@16, $+14.4$ over GRPO).