Combinatorial problems on graphs have attracted extensive efforts from the machine learning community over the past decade. Despite notable progress in this area under the umbrella of ML4CO, a comprehensive categorization, unified reproducibility, and transparent evaluation protocols are still lacking for the emerging and immense pool of neural CO solvers. In this paper, we establish a modular and streamlined framework benchmarking prevalent neural CO methods, dissecting their design choices via a tri-leveled "paradigm-model-learning" taxonomy to better characterize different approaches. Further, we integrate their shared features and respective strengths to form 3 unified solvers representing global prediction (GP), local construction (LC), and adaptive expansion (AE) mannered neural solvers. We also collate a total of 65 datasets for 7 mainstream CO problems (including both edge-oriented tasks: TSP, ATSP, CVRP, as well as node-oriented: MIS, MCl, MVC, MCut) across scales to facilitate more comparable results among literature. Extensive experiments upon our benchmark reveal a fair and exact performance exhibition indicative of the raw contribution of the learning components in each method, rethinking and insisting that pre-and post-inference heuristic tricks are not supposed to compensate for sub-par capability of the data-driven counterparts. Under this unified benchmark, an up-to-date replication of typical ML4CO methods is maintained, hoping to provide convenient reference and insightful guidelines for both engineering development and academic exploration of the ML4CO community in the future.

Training-free guided generation is a widely used and powerful technique that allows the end user to exert further control over the generative process of flow/diffusion models. Generally speaking, two families of techniques have emerged for solving this problem for gradient-based guidance: namely, posterior guidance (i.e., guidance by projecting the current sample to the target distribution via the target prediction model) and end-to-end guidance (i.e., guidance by performing backpropagation throughout the entire ODE solve). In this work, we show that these two seemingly separate families can actually be unified by looking at the posterior guidance as a greedy strategy of end-to-end guidance. We explore the theoretical connections between these two families and provide an in-depth theoretical understanding of these two techniques relative to the continuous ideal gradients. Motivated by this analysis, we then show a method for interpolating between these two families enabling a trade-off between compute and accuracy of the guidance gradients.

Autoregressive language models accumulate errors due to their fixed, irrevocable left-to-right token generation. To address this, we propose a new sampling method called Resample-Previous-Tokens (RPT). RPT mitigates error accumulation by iteratively revisiting and potentially replacing tokens in a window of previously generated text. Fine-tuning a pretrained 8B parameter model with RPT for only 100B resulted in 10% relative improvements on reasoning and coding benchmarks compared to the standard sampling.

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.

We proceed to show the sparsistency510 of the estimated parameters. First, suppose that Θ t;ij 6= 0 for some time tand index (i,j). Due to 0 < γ < 1, the above inequality implies that bΘt;ij = 0521 for every t and (i,j) 6 St, and bΘt;ij bΘt 1;ij = 0 for every t > 0 and (i,j) 6 Dt. The proof is inspired527 by Corollary 1 in [47]. First, we present the following key lemmas.528

Wegiveasmoothed analysis, showing that evenwhen contexts may be chosen by an adversary, small perturbations of the adversary's choices suffice for the algorithm to achieve "no regret", perhaps (depending on the specifics of the setting) with a constant amount of initial training data.

These methods, while effective, often involve manually intensive prompt engineering.