arXiv:2512.22420v2 Announce Type: replace-cross Abstract: Speculative decoding (SD) accelerates LLM inference by verifying draft tokens in parallel. However, this method presents a critical trade-off: it improves throughput in low-load, memory-bound systems but degrades performance in high-load, compute-bound environments due to verification overhead. Current SD implementations use a fixed speculative length, failing to adapt to dynamic request rates and creating a significant performance bottleneck in real-world serving scenarios. To overcome this, we propose Nightjar, a novel learning-based algorithm for adaptive speculative inference that adjusts to request load by dynamically selecting the optimal speculative length for different batch sizes and even disabling speculative decoding when it provides no benefit. Experiments show that Nightjar achieves up to 14.8% higher throughput and 20.2% lower latency compared to standard speculative decoding, demonstrating robust efficiency for real-time serving.

arXiv:2602.13021v2 Announce Type: replace-cross Abstract: Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity.