SuperValid: Capability-Aligned OOD Validation for Generalizable Downstream Scaling

Scaling test-time compute has emerged as a powerful mechanism for enhancing Large Language Model (LLM) performance. However, standard post-training paradigms, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), optimize the likelihood of individual samples under a base policy, creating a misalignment with test time procedures that rely on aggregated or filtered outputs. In this work, we propose Compute Aligned Training, which aligns training objectives with test-time strategies. By conceptualizing inference strategies as operators on the base policy, we derive new loss functions that maximize performance when said strategies are applied. We instantiate such loss functions for SFT and RL across common test time strategies. Finally, we provide empirical evidence that this training method substantially improves test time scaling over standard training.

The scaling laws guiding modern model training were calibrated for a single regime: data-rich, single-epoch pretraining. The dominant such scaling law form, Chinchilla's $L = E + A/N^α+ B/D^β$, has three structural limitations outside that regime: it diverges as unique data shrinks instead of saturating at the uninformed baseline; it cannot represent overfitting when capacity exceeds the data; and it conflates total examples seen with unique examples available. We propose a closed-form extension, $L(N, D, T) = E + (L_0 - E)\,h/(1+h)$ with $h = a/N^α+ b/T^β+ c\,N^γ/D^δ$, that decomposes loss into undercapacity, undertraining, and overfitting terms. It saturates between the irreducible loss $E$ and an uninformed baseline $L_0$ fixed by the loss type, and reduces to Chinchilla in the data-rich, single-epoch limit. We validate it on four multi-epoch experiments spanning four architecture families (MLPs, ResNets, Fourier neural operators, and transformers) across vision, scientific ML, and language domains, and refit it to five published LLM scaling-law grids. Extrapolating to higher compute and larger unique data than seen at fit time, our form achieves state-of-the-art RMSE on every published LLM grid we evaluate and on most cells of our constructed experiments. Once calibrated, the form admits a cost-aware allocation that recovers Chinchilla's optimum when data is free and shifts toward smaller corpora and more epochs as data grows expensive.

Capability distillation applies knowledge distillation to selected model capabilities, aiming to compress a large language model (LLM) into a smaller one while preserving the abilities needed for a downstream task. However, most existing methods treat capabilities as independent training targets and overlook how improving one capability can reshape the student's broader capability profile, especially when multiple abilities jointly determine task success. We study capability distillation under a fixed token budget and identify two consistent patterns: distillation induces systematic, budget-dependent cross-capability transfer, and additional budget often brings limited task-relevant gains while sometimes degrading other useful abilities. Building on these insights, we propose ReAD, a Reinforcement-guided cApability Distillation framework that explicitly accounts for capability interdependence. ReAD first infers task-essential capabilities, then generates capability-targeted supervision on the fly, and finally uses an uncertainty-aware contextual bandit to adaptively allocate the distillation budget based on expected utility gains. Extensive experiments show that ReAD improves downstream utility under the same token budget while reducing harmful spillover and wasted distillation effort compared to strong baselines. Our code is publicly available at https://github.com/LabRAI/ReAD.