Profile-guided optimization (PGO) advances the frontiers of compiler optimization by leveraging dynamic runtime information to generate highly optimized binaries. Traditional instrumentation-based profiling collects accurate profile data but often suffers from heavy runtime overhead. In contrast, sampling-based profiling is more efficient and scalable when collecting profile data while avoiding intrusive source code modifications. However, accurately collecting execution profiles via sampling remains challenging, especially when applied to fully optimized binaries. Such inaccurate profile data can restrict the benefits of PGO. This paper presents PROFIX, a machine learning-guided approach based on hybrid GNN architecture that addresses the problem of profile inference, aiming to correct inaccuracies in the profiles collected by sampling. Experiments on the SPEC 2017 benchmarks demonstrate that PROFIX achieves up to a 9.15% performance improvement compared to the state-of-the-art traditional algorithm and an average 6.26% improvement over the baseline machine learning models.

Existing approaches usually assume shared generic knowledge (e.g., prototypes, spectral features) via aggregating local structures statistically to alleviate structural heterogeneity. However, imposing overly strict assumptions about the presumed correlation between structural features and the global objective often fails in generalizing to local tasks, leading to suboptimal performance. To tackle this issue, we propose a Federated Invariant Graph Learning (FedIGL) framework based on invariant learning, which effectively disrupts spurious correlations and further mines the invariant factors across different distributions. Specifically, a server-side global model is trained to capture client-agnostic subgraph patterns shared across clients, whereas client-side models specialize in client-specific subgraph patterns. Subsequently, without compromising privacy, we propose a novel Bi-Gradient Regularization strategy that introduces gradient constraints to guide the model in identifying client-agnostic and client-specific subgraph patterns for better graph representations. Extensive experiments on graph-level clustering and classification tasks demonstrate the superiority of FedIGL against its competitors.

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.

Interpretable reinforcement learning policies are essential for high-stakes decisionmaking, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing decision tree policies, which formulates the optimization problem as a mixedinteger linear program (MILP). To enhance efficiency, we employ a reduced-space branch-and-bound approach that decouples the MDP dynamics from tree-structure constraints, enabling efficient parallel search. This significantly improves runtime and scalability compared to previous methods. Our approach ensures that each iteration yields the optimal decision tree. Experimental results on standard benchmarks demonstrate that SPOT achieves substantial speedup and scales to larger MDPs with a significantly higher number of states. The resulting decision tree policies are interpretable and compact, maintaining transparency without compromising performance. These results demonstrate that our approach simultaneously achieves interpretability and scalability, delivering high-quality policies an order of magnitude faster than existing approaches.

Recent advances in large reasoning models (LRMs) demonstrate that sophisticated behaviors such as multi-step reasoning and self-reflection can emerge via reinforcement learning with verifiable rewards (RLVR). However, existing RLVR approaches are inherently "on-policy", limiting learning to a model's own outputs and failing to acquire reasoning abilities beyond its initial capabilities. To address this issue, we introduce LUFFY (Learning to reason Under oFF-policY guidance), a framework that augments RLVR with off-policy reasoning traces. LUFFY dynamically balances imitation and exploration by combining off-policy demonstrations with on-policy rollouts during training. Specifically, LUFFY combines the MixedPolicy GRPO framework, which has a theoretically guaranteed convergence rate, alongside policy shaping via regularized importance sampling to avoid superficial and rigid imitation during mixed-policy training. Compared with previous RLVR methods, LUFFY achieves an over +6.4 average gain across six math benchmarks and an advantage of over +6.2 points in out-of-distribution tasks. Most significantly, we show that LUFFY successfully trains weak models in scenarios where on-policy RLVR completely fails. These results provide compelling evidence that LUFFY transcends the fundamental limitations of on-policy RLVR and demonstrates the great potential of utilizing off-policy guidance in RLVR.

Top-kdecoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after renormalizing them to sum to unity. Top-kand other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We introduce Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ℓ0-regularization; in particular, these decoders are adaptive in the sense that the sparsity parameter k is chosen depending on the underlying token distribution. Despite the combinatorial nature of the sparse Bregman objective, we show how to optimize it efficiently for a large class of divergences. We prove that (i) the optimal decoding strategies are greedy, and further that (ii) the objective is discretely convex in k, such that the optimal k can be identified in logarithmic time. We note that standard top-k decoding arises as a special case for the KL divergence, and construct new decoding strategies with substantially different behaviors (e.g., non-linearly up-weighting larger probabilities after renormalization).

We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed reference measure, as well as the corresponding problem of solving entropy-regularized non-convex-non-concave min-max problems. We utilize the Best Response flow (also known in the literature as the fictitious play flow) and study how its convergence is influenced by the relation between the degree of non-convexity of the functional under consideration, the regularization parameter and the tail behaviour of the reference measure. In particular, we demonstrate how to choose the regularizer, given the non-convex functional, so that the Best Response operator becomes a contraction with respect to the L1Wasserstein distance, which ensures the existence of its unique fixed point that is then shown to be the unique global minimizer for our optimization problem. This extends recent results where the Best Response flow was applied to solve convex optimization problems regularized by the relative entropy with respect to arbitrary reference measures, and with arbitrary values of the regularization parameter. Our results explain precisely how the assumption of convexity can be relaxed, at the expense of making a specific choice of the regularizer. Additionally, we demonstrate how these results can be applied in reinforcement learning in the context of policy optimization for Markov Decision Processes and Markov games with softmax parametrized policies in the mean-field regime.

Sparse variable selection improves interpretability and generalization in highdimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale nonprivate sparse regression--known as Best Subset Selection (BSS)--with millions of variables in minutes. However, extending these algorithmic advances to the setting of Differential Privacy (DP) has remained largely unexplored. In this paper, we introduce two new pure differentially private estimators for sparse variable selection, levering modern MIP techniques. Our framework is general and applies broadly to problems like sparse regression or classification, and we provide theoretical support recovery guarantees in the case of BSS. Inspired by the exponential mechanism, we develop structured sampling procedures that efficiently explore the non-convex objective landscape, avoiding the exhaustive combinatorial search in the exponential mechanism. We complement our theoretical findings with extensive numerical experiments, using both least squares and hinge loss for our objective function, and demonstrate that our methods achieve state-of-the-art empirical support recovery, outperforming competing algorithms in settings with up to p = 104.

Recent advancements in foundation models for 2D vision have substantially improved the analysis of dynamic scenes from monocular videos. However, despite their strong generalization capabilities, these models often lack 3D consistency, a fundamental requirement for understanding scene geometry and motion, thereby causing severe spatial misalignment and temporal flickering in complex 3D environments.

Traditional curriculum learning proceeds from easy to hard samples, yet defining a reliable notion of difficulty remains elusive. Prior work has used submodular functions to induce difficulty scores in curriculum learning. We reinterpret adaptive subset selection and formulate it as a multi-armed bandit problem, where each arm corresponds to a submodular function guiding sample selection. We introduce ONLINESUBMOD, a novel online greedy policy that optimizes a utility-driven reward and provably achieves no-regret performance under various sampling regimes. Empirically, ONLINESUBMOD outperforms both traditional curriculum learning and bi-level optimization approaches across vision and language datasets, showing superior accuracy-efficiency tradeoffs. More broadly, we show that validationdriven reward metrics offer a principled way to guide the curriculum schedule. Our code is publicly available at GitHub 2.