Hybrid models combining Transformers and State Space Models (SSMs) are promising for balancing performance and efficiency. However, optimizing these hybrid models, particularly by addressing the potential redundancy inherent within the Transformer components, remains a significant challenge. In this paper, we propose RAD (Redundancy-Aware Distillation), a novel framework that uses self-speculative decoding as a diagnostic tool to identify redundant attention layers within the model. These identified layers are then selectively replaced with SSM components, followed by targeted (self-)distillation. Specifically, RAD focuses knowledge transfer on the components identified as redundant, considering architectural changes and specific weight initialization strategies. We experimentally demonstrate that self-distillation using RAD significantly surpasses the performance of the original base model on mathematical and coding tasks. Furthermore, RAD is also effective in standard knowledge distillation settings, achieving up to approximately 2x faster convergence compared to baseline methods. Notably, while a baseline model distilled from a Llama-3.1 70B teacher achieves scores of 46.17 on GSM8K and 22.75 on CRUX, RAD achieves significantly higher scores of 71.27 on GSM8K and 28.25 on CRUX, even when using a much smaller Llama-3.1 8B teacher. RAD offers a new pathway for efficient optimization and performance enhancement in the distillation of hybrid models.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Finetuning foundation models for specific tasks is an emerging paradigm in modern machine learning. The efficacy of task-specific finetuning largely depends on the selection of appropriate training data. We present TSDS (Task-Specific Data Selection), a framework to select data for task-specific model finetuning, guided by a small but representative set of examples from the target task. To do so, we formulate data selection for task-specific finetuning as an optimization problem with a distribution alignment loss based on optimal transport to capture the discrepancy between the selected data and the target distribution. In addition, we add a regularizer to encourage the diversity of the selected data and incorporate kernel density estimation into the regularizer to reduce the negative effects of near-duplicates among the candidate data.We connect our optimization problem to nearest neighbor search and design efficient algorithms to compute the optimal solution based on approximate nearest neighbor search techniques.We evaluate our method on data selection for both continued pretraining and instruction tuning of language models.We show that instruction tuning using data selected by our method with a 1\% selection ratio often outperforms using the full dataset and beats the baseline selection methods by 1.5 points in F1 score on average.

We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures, utilizing an optimal transport map as its key component. Estimating the optimal transport map from samples finds several applications, such as simulating dynamics between probability measures and functional data analysis. However, some transport maps on infinite-dimensional spaces require exponential-order data for estimation, which undermines their applicability. In this paper, we investigate the estimation of an optimal transport map between infinite-dimensional spaces, focusing on optimal transport maps characterized by the notion of $γ$-smoothness. Consequently, we show that the order of the minimax risk is polynomial rate in the sample size even in the infinite-dimensional setup. We also develop an estimator whose estimation error matches the minimax optimal rate. With these results, we obtain a class of reasonably estimable optimal transport maps on infinite-dimensional spaces and a method for their estimation. Our experiments validate the theory and practical utility of our approach with application to functional data analysis.

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN (Binary Integer Programming Neural Network), an unsupervised learning framework to solve nonlinear BIP problems via hypergraph neural networks (HyperGNN). Specifically, BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions. The reformulation stems from the observation of a precise one-to-one mapping between polynomial BIP objectives and hypergraph structures, enabling the unsupervised training of HyperGNN to optimize BIP problems in an end-to-end manner. On this basis, we propose a GPU-accelerated and continuous-annealing-enhanced training pipeline for BIPNN. The pipeline enables BIPNN to optimize large-scale nonlinear terms in BIPs fully in parallel via straightforward gradient descent, thus significantly reducing the training cost while ensuring the generation of discrete, high-quality solutions. Extensive experiments on synthetic and real-world datasets highlight the superiority of our approach.

-- Counterfactual explanations (CFEs) are a popular approach for interpreting machine learning predictions by identifying minimal feature changes that alter model outputs. However, in real-world settings, users often refine feasibility constraints over time, requiring counterfactual generation to adapt dynamically. Existing methods fail to support such iterative updates, instead recomputing explanations from scratch with each change, an inefficient and rigid approach. We propose User-Guided Incremental Counterfactual Exploration (UGCE), a genetic algorithm-based framework that incrementally updates counterfactuals in response to evolving user constraints. Experimental results across five benchmark datasets demonstrate that UGCE significantly improves computational efficiency while maintaining high-quality solutions compared to a static, non-incremental approach. Our evaluation further shows that UGCE supports stable performance under varying constraint sequences, benefits from an efficient warm-start strategy, and reveals how different constraint types may affect search behavior . I NTRODUCTION Machine learning (ML) models are increasingly deployed in high-stakes decision-making domains, including lending, college admissions, and hiring, where their predictions influence critical life outcomes [1]-[3]. However, these models often function as black boxes, making it difficult for stakeholders to understand the rationale behind predictions, particularly when an unfavorable decision is made. This lack of transparency has driven the need for explanation techniques that help users interpret and contest automated decisions [4], [5]. As a result, research on explainability has gained significant traction, leading to a wide array of methodologies aimed at making ML models more transparent and interpretable [5]-[13].

We present Bencher, a modular benchmarking framework for black-box optimization that fundamentally decouples benchmark execution from optimization logic. Unlike prior suites that focus on combining many benchmarks in a single project, Bencher introduces a clean abstraction boundary: each benchmark is isolated in its own virtual Python environment and accessed via a unified, version-agnostic remote procedure call (RPC) interface. This design eliminates dependency conflicts and simplifies the integration of diverse, real-world benchmarks, which often have complex and conflicting software requirements. Bencher can be deployed locally or remotely via Docker or on high-performance computing (HPC) clusters via Singularity, providing a containerized, reproducible runtime for any benchmark. Its lightweight client requires minimal setup and supports drop-in evaluation of 80 benchmarks across continuous, categorical, and binary domains.

In cross-silo Federated Learning (FL), client selection is critical to ensure high model performance, yet it remains challenging due to data quality decompensa-tion, budget constraints, and incentive compatibility. As training progresses, these factors exacerbate client heterogeneity and degrade global performance. Most existing approaches treat these challenges in isolation, making jointly optimizing multiple factors difficult. To address this, we propose Shapley-Bid Reputation Optimized Federated Learning (SBRO-FL), a unified framework integrating dynamic bidding, reputation modeling, and cost-aware selection. Clients submit bids based on their perceived data quality, and their contributions are evaluated using Shapley values to quantify their marginal impact on the global model. A reputation system, inspired by prospect theory, captures historical performance while penalizing inconsistency. The client selection problem is formulated as a 0-1 integer program that maximizes reputation-weighted utility under budget constraints. Experiments on FashionMNIST, EMNIST, CIFAR-10, and SVHN datasets show that SBRO-FL improves accuracy, convergence speed, and robustness, even in adversarial and low-bid interference scenarios. Our results highlight the importance of balancing data reliability, incentive compatibility, and cost efficiency to enable scalable and trustworthy FL deployments.

Bayesian optimization (BO) is a powerful class of algorithms for optimizing expensive black-box functions, but designing effective BO algorithms remains a manual, expertise-driven task. Recent advancements in Large Language Models (LLMs) have opened new avenues for automating scientific discovery, including the automatic design of optimization algorithms. While prior work has used LLMs within optimization loops or to generate non-BO algorithms, we tackle a new challenge: Using LLMs to automatically generate full BO algorithm code. Our framework uses an evolution strategy to guide an LLM in generating Python code that preserves the key components of BO algorithms: An initial design, a surrogate model, and an acquisition function. The LLM is prompted to produce multiple candidate algorithms, which are evaluated on the established Black-Box Optimization Benchmarking (BBOB) test suite from the COmparing Continuous Optimizers (COCO) platform. Based on their performance, top candidates are selected, combined, and mutated via controlled prompt variations, enabling iterative refinement. Despite no additional fine-tuning, the LLM-generated algorithms outperform state-of-the-art BO baselines in 19 (out of 24) BBOB functions in dimension 5 and generalize well to higher dimensions, and different tasks (from the Bayesmark framework). This work demonstrates that LLMs can serve as algorithmic co-designers, offering a new paradigm for automating BO development and accelerating the discovery of novel algorithmic combinations. The source code is provided at https://github.com/Ewendawi/LLaMEA-BO.

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.