Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, msking the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers.

The clustering-based placement framework has demonstrated promising potential in improving the efficiency and quality of very-large-scale integration (VLSI) placement. However, existing methods typically impose unified and rule-based constraints on different clusters, overlooking the unique intra-and inter-cluster connection properties that vary across clusters, which leads to suboptimal results. To address this challenge and promote effective PPA optimization, we introduce an innovative PPA-driven placement paradigm with mixed-grained Adaptive Cluster Constraints Optimization (ACCO), which applies constraints with customized constraint tightness to different clusters, balancing local and global interactions for improved placement performance. Specifically, we propose a novel eBound model with quantified constraint tightness, combined with a Bayesian optimizer to dynamically adjust the constraints for each cluster based on PPA outcomes, which are ultimately passed on to the final flat placement. Experimental results on benchmarks across various domains show that our methods can achieve up to 62%, 97% and 25% improvements in post-route WNS, TNS and power compared to existing methods.

While LLMs show promise in automating educational content creation, their ability to generate questions that stimulate higher-order thinking remains understudied. This work evaluates six widely used LLMs through a Bloom's Taxonomy lens, focusing on their capacity to transcend rote memorization and achieve cognitive leaps. Using a hybrid human-AI evaluation protocol, we generate and analyze 20,700 questions across computer science, K-12 math, and social-science domains. Key contributions include: (1) a fine-grained prompting strategy that reduces question repetitiveness by 24.45% for Qwen2.5-7B-Instruct, and increases the proportion of higher-order cognitive-level outputs by 11.53% for InternLM3-8B-Instruct; (2) quantitative metrics for cognitive shift intensity (CogShift) and category drift, revealing InternLM3's superior performance in multi-level transitions; (3) an interpretability analysis revealing metric-level correlations that enhance the transparency of Chain-of-Thought prompting. Our findings highlight the importance of cognitive-aware prompt design and provide benchmarks for deploying LLMs in personalized learning systems.

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap.

Machine learning techniques have shown great potential in enhancing macro placement, a critical stage in modern chip design. However, existing methods primarily focus on *online* optimization of *intermediate surrogate metrics* that are available at the current placement stage, rather than directly targeting the *cross-stage metrics*---such as the timing performance---that measure the final chip quality. This is mainly because of the high computational costs associated with performing post-placement stages for evaluating such metrics, making the *online* optimization impractical. Consequently, these optimizations struggle to align with actual performance improvements and can even lead to severe manufacturing issues. To bridge this gap, we propose **LaMPlace**, which **L**earns **a** **M**ask for optimizing cross-stage metrics in macro placement. Specifically, LaMPlace trains a predictor on *offline* data to estimate these *cross-stage metrics* and then leverages the predictor to quickly generate a mask, i.e., a pixel-level feature map that quantifies the impact of placing a macro in each chip grid location on the design metrics. This mask essentially acts as a fast evaluator, enabling placement decisions based on *cross-stage metrics* rather than *intermediate surrogate metrics*. Experiments on commonly used benchmarks demonstrate that LaMPlace significantly improves the chip quality across several key design metrics, achieving an average improvement of 9.6\%, notably 43.0\% and 30.4\% in terms of WNS and TNS, respectively, which are two crucial cross-stage metrics that reflect the final chip quality in terms of the timing performance.

Machine learning (ML) techniques have shown great potential in generating high-quality solutions for integer linear programs (ILPs). However, existing methods typically rely on a *supervised learning* paradigm, leading to (1) *expensive training cost* due to repeated invocations of traditional solvers to generate training labels, and (2) *plausible yet infeasible solutions* due to the misalignment between the training objective (minimizing prediction loss) and the inference objective (generating high-quality solutions). To tackle this challenge, we propose **DiffILO** (**Diff**erentiable **I**nteger **L**inear Programming **O**ptimization), an *unsupervised learning paradigm for learning to solve ILPs*. Specifically, through a novel probabilistic modeling, DiffILO reformulates ILPs---discrete and constrained optimization problems---into continuous, differentiable (almost everywhere), and unconstrained optimization problems. This reformulation enables DiffILO to simultaneously solve ILPs and train the model via straightforward gradient descent, providing two major advantages. First, it significantly reduces the training cost, as the training process does not need the aid of traditional solvers at all. Second, it facilitates the generation of feasible and high-quality solutions, as the model *learns to solve ILPs* in an end-to-end manner, thus aligning the training and inference objectives. Experiments on commonly used ILP datasets demonstrate that DiffILO not only achieves an average training speedup of $13.2$ times compared to supervised methods, but also outperforms them by generating heuristic solutions with significantly higher feasibility ratios and much better solution qualities.

Key-Value (KV) cache eviction---which retains the KV pairs of the most important tokens while discarding less important ones---is a critical technique for optimizing both memory usage and inference latency in large language models (LLMs). However, existing approaches often rely on simple heuristics---such as attention weights---to measure token importance, overlooking the spatial relationships between token value states in the vector space. This often leads to suboptimal token selections and thus performance degradation. To tackle this problem, we propose a novel method, namely **AnDPro** (**An**chor **D**irection **Pro**jection), which introduces a projection-based scoring function to more accurately measure token importance. Specifically, AnDPro operates in the space of value vectors and leverages the projections of these vectors onto an *``Anchor Direction''*---the direction of the pre-eviction output---to measure token importance and guide more accurate token selection. Experiments on $16$ datasets from the LongBench benchmark demonstrate that AnDPro can maintain $96.07\\%$ of the full cache accuracy using only $3.44\\%$ KV cache budget, reducing KV cache budget size by $46.0\\%$ without compromising quality compared to previous state-of-the-arts.

Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains. Recently, learning-based methods have shown great promise in accelerating MILP solvers by predicting high-quality solutions. However, most existing approaches are developed and evaluated in single-domain settings, limiting their ability to generalize to unseen problem distributions. This limitation poses a major obstacle to building scalable and general-purpose learning-augmented solvers. To address this challenge, we introduce RoME, a domain-Robust Mixture-of-Experts (MoE) framework for predicting MILP solutions across domains. RoME dynamically routes problem instances to specialized experts based on learned task embeddings. The model is trained using a two-level distributionally robust optimization strategy: inter-domain to mitigate global shifts across domains, and intra-domain to enhance local robustness by introducing perturbations on task embeddings. We reveal that cross-domain training not only enhances the model's generalization capability to unseen domains but also improves performancewithin each individual domain by encouraging the model to capture more general intrinsic combinatorial patterns. Specifically, a single RoME model trained on three domains achieves an average improvement of $67.7\%$ then evaluated on five diverse domains. We further test the pretrained model on MIPLIB in a zero-shot setting, demonstrating its ability to deliver measurable performance gains on challenging real-world instances where existing learning-based approaches often struggle to generalize.

Chip placement is a critical step in the Electronic Design Automation (EDA) workflow, which aims to arrange chip modules on the canvas to optimize the performance, power, and area (PPA) metrics of final designs.Recent advances show great potential of AI-based algorithms in chip placement.However, due to the lengthy EDA workflow, evaluations of these algorithms often focus on intermediate surrogate metrics, which are computationally efficient but often misalign with the final end-to-end performance (i.e., the final design PPA).To address this challenge, we propose to build ChiPBench, a comprehensive benchmark specifically designed to evaluate the effectiveness of AI-based algorithms in final design PPA metrics.Specifically, we generate a diverse evaluation dataset from $20$ circuits across various domains, such as CPUs, GPUs, and NPUs.We then evaluate six state-of-the-art AI-based chip placement algorithms on the dataset and conduct a thorough analysis of their placement behavior.Extensive experiments show that AI-based chip placement algorithms produce unsatisfactory final PPA results, highlighting the significant influence of often-overlooked factors like regularity and dataflow.We believe ChiPBench will effectively bridge the gap between academia and industry.

Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in extremely redundant computations. To tackle this problem, we propose a novel method, namely **S**orting **K**rylov **R**ecycling (**SKR**), to boost the efficiency of solving these systems, thus significantly accelerating data generation for neural operators training. To the best of our knowledge, SKR is the first attempt to address the time-consuming nature of data generation for learning neural operators. The working horse of SKR is Krylov subspace recycling, a powerful technique for solving a series of interrelated systems by leveraging their inherent similarities. Specifically, SKR employs a sorting algorithm to arrange these systems in a sequence, where adjacent systems exhibit high similarities. Then it equips a solver with Krylov subspace recycling to solve the systems sequentially instead of independently, thus effectively enhancing the solving efficiency. Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times.

Macro placement is a crucial step in modern chip design, and reinforcement learning (RL) has recently emerged as a promising technique for improving the placement quality. However, existing RL-based techniques are hindered by their low sample efficiency, requiring numerous online rollouts or substantial offline expert data to achieve bootstrap, which are often impractical in industrial scenarios. To address this challenge, we propose a novel sample-efficient framework, namely **EfficientPlace**, for fast macro placement. EfficientPlace integrates a global tree search algorithm to strategically direct the optimization process, as well as a RL agent for local policy learning to advance the tree search. Experiments on commonly used benchmarks demonstrate that EfficientPlace achieves remarkable placement quality within a short timeframe, outperforming recent state-of-the-art approaches.

Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures—which are closely related to the problem formulations—in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations. To address this challenge, we propose a novel MILP generation framework, called Block Structure Decomposition (MILP-StuDio), to generate high-quality instances by preserving the block structures. Specifically, MILP-StuDio begins by identifying the blocks in CCMs and decomposing the instances into block units, which serve as the building blocks of MILP instances. We then design three operators to construct new instances by removing, substituting, and appending block units in the original instances, enabling us to generate instances with flexible sizes. An appealing feature of MILP-StuDio is its strong ability to preserve the feasibility and computational hardness of the generated instances. Experiments on the commonly-used benchmarks demonstrate that using instances generated by MILP-StuDio is able to significantly reduce over 10% of the solving time for learning-based solvers.

Solving large-scale sparse linear systems is essential in fields like mathematics, science, and engineering. Traditional numerical solvers, mainly based on the Krylov subspace iteration algorithm, suffer from the low-efficiency problem, which primarily arises from the less-than-ideal iteration. To tackle this problem, we propose a novel method, namely **Neur**al **K**rylov **It**era**t**ion (**NeurKItt**), for accelerating linear system solving. Specifically, NeurKItt employs a neural operator to predict the invariant subspace of the linear system and then leverages the predicted subspace to accelerate linear system solving. To enhance the subspace prediction accuracy, we utilize QR decomposition for the neural operator outputs and introduce a novel projection loss function for training. NeurKItt benefits the solving by using the predicted subspace to guide the iteration process, significantly reducing the number of iterations. We provide extensive experiments and comprehensive theoretical analyses to demonstrate the feasibility and efficiency of NeurKItt. In our main experiments, NeurKItt accelerates the solving of linear systems across various settings and datasets, achieving up to a 5.5× speedup in computation time and a 16.1× speedup in the number of iterations.

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, *the first* deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at [https://miralab-ustc.github.io/L2O-G2MILP](https://miralab-ustc.github.io/L2O-G2MILP).

Generalization across different environments with the same tasks is critical for successful applications of visual reinforcement learning (RL) in real scenarios. However, visual distractions---which are common in real scenes---from high-dimensional observations can be hurtful to the learned representations in visual RL, thus degrading the performance of generalization. To tackle this problem, we propose a novel approach, namely Characteristic Reward Sequence Prediction (CRESP), to extract the task-relevant information by learning reward sequence distributions (RSDs), as the reward signals are task-relevant in RL and invariant to visual distractions. Specifically, to effectively capture the task-relevant information via RSDs, CRESP introduces an auxiliary task---that is, predicting the characteristic functions of RSDs---to learn task-relevant representations, because we can well approximate the high-dimensional distributions by leveraging the corresponding characteristic functions. Experiments demonstrate that CRESP significantly improves the performance of generalization on unseen environments, outperforming several state-of-the-arts on DeepMind Control tasks with different visual distractions.