Proof of Lemma 2. Let U be the data set associated to ν. Proof of Lemma 3. First, we prove that the property holds for the root node. We wish to prove the property for some unexplored leaf after the iteration. This is trivial if the leaf ν is not expanded in that iteration. Suppose the leaf ν is expanded. Proof of Lemma 5. From Lemma 2, we note that Q Consider any path from the root to a leaf whose length is mK for some integer K > 0. We note that for each node ν and any of its children ν (Lemma 5).

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.

Predictive modeling has the potential to enhance human decision-making. However, many predictive models fail in practice due to problematic problem formulation in cases where the prediction target is an abstract concept or construct and practitioners need to define an appropriate target variable as a proxy to operationalize the construct of interest. The choice of an appropriate proxy target variable is rarely self-evident in practice, requiring both domain knowledge and iterative data modeling. This process is inherently collaborative, involving both domain experts and data scientists. In this work, we explore how human-machine teaming can support this process by accelerating iterations while preserving human judgment. We study the impact of two human-machine teaming strategies on proxy construction: 1) relevance-first: humans leading the process by selecting relevant proxies, and 2) performance-first: machines leading the process by recommending proxies based on predictive performance. Based on a controlled user study of a proxy construction task (N = 20), we show that the performance-first strategy facilitated faster iterations and decision-making, but also biased users towards well-performing proxies that are misaligned with the application goal. Our study highlights the opportunities and risks of human-machine teaming in operationalizing machine learning target variables, yielding insights for future research to explore the opportunities and mitigate the risks.

Abstract--Chip placement is a vital stage in modern chip design as it has a substantial impact on the subsequent processes and the overall quality of the final chip. The use of black-box optimization (BBO) for chip placement has a history of several decades. However, early efforts were limited by immature problem formulations and inefficient algorithm designs, leading to suboptimal efficiency, quality, and scalability, compared to the more prevalent analytical methods. Recent progress in problem formulation and algorithm design has shown the effectiveness and efficiency of BBO for chip placement, proving its potential to achieve state-of-the-art results. Despite these advancements, the field lacks a unified, BBO-specific benchmark for thoroughly assessing various problem formulations and BBO algorithms. T o fill this gap, we propose BBOPlace-Bench, the first benchmark designed specifically for evaluating and developing BBO algorithms for chip placement tasks. It integrates three problem formulations (with permutation, continuous, and mixed search spaces, respectively) of BBO for chip placement, and offers a modular, decoupled, and flexible framework that enables users to seamlessly implement, test, and compare their own algorithms. BBOPlace-Bench aggregates modern chip cases from representative chip cases (ISPD 2005, ICCAD 2015) and standardizes their formats, providing uniform and comprehensive information to support BBO optimization. Moreover, it integrates a wide variety of existing BBO algorithms, including simulated annealing (SA), evolutionary algorithms (EAs), and Bayesian optimization (BO), and systematically evaluates their performance across different problem formulations using key metrics (e.g., macro placement wirelength and global placement wirelength) of chip. Experimental results show that the problem formulations of mask-guided optimization and hyperparameter optimization exhibit superior performance than the sequence pair problem formulation, while EAs demonstrate better overall performance than SA and BO, especially in high-dimensional search spaces, and also achieve state-of-the-art performance compared to the mainstream chip placement methods, i.e., analytical methods and reinforcement learning methods. BBOPlace-Bench not only facilitates the development of efficient BBO-driven solutions for chip placement but also broadens the practical application scenarios (which are urgently needed) for the BBO community. The code of BBOPlace-Bench is available at https://github.com/ The first three authors contributed equally.

There has been increasing research interest in AI/ML for social impact, and correspondingly more publication venues have refined review criteria for practice-driven AI/ML research. However, these review guidelines tend to most concretely recognize projects that simultaneously achieve deployment and novel ML methodological innovation. We argue that this introduces incentives for researchers that undermine the sustainability of a broader research ecosystem of social impact, which benefits from projects that make contributions on single front (applied or methodological) that may better meet project partner needs. Our position is that researchers and reviewers in machine learning for social impact must simultaneously adopt: 1) a more expansive conception of social impacts beyond deployment and 2) more rigorous evaluations of the impact of deployed systems.

In modern chip design, placement aims at placing millions of circuit modules, which is an essential step that significantly influences power, performance, and area (PP A) metrics.

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data, our formulation directly models each data sample as a matrix and clusters them according to their underlying subspaces. We establish conceptual links to Subspace Clustering and Generalized Canonical Correlation Analysis (GCCA), and clarify key differences that arise in this more general setting. Our approach is based on a Block Term Decomposition (BTD) of a third-order tensor constructed from the input matrices, enabling joint estimation of cluster memberships and partially shared subspaces. We provide the first identifiability results for this formulation and propose scalable optimization algorithms tailored to large datasets. Experiments on real-world hyperspectral imaging datasets demonstrate that our method achieves superior clustering accuracy and robustness, especially under high noise and interference, compared to existing subspace clustering techniques. These results highlight the potential of the proposed framework in challenging high-dimensional applications where structure exists beyond individual data vectors.

This article presents a practitioner's reflection on applying declarative, 5th generation, problem formulation language (5GL) to de novo imaging system design, informed by experiences across the interdisciplinary research in academia and cross-functional product development within the private sector. Using the 96-Eyes project: 96-camera parallel multi-modal imager for high-throughput drug discovery as a representative case, I illustrate how project requirements, ranging from hardware constraints to life sciences needs, can be formalized into machine-readable problem statements to preserve mission-critical input from diverse domain stakeholders. This declarative approach enhances transparency, ensures design traceability, and minimizes costly misalignment across optical, algorithmic, hardware-accelerated compute, and life sciences teams. Alongside the technical discussion of 5GL with real-world code examples, I reflect on the practical barriers to adopting 5GL in environments where imperative, 3rd-generation languages (3GL) remain the default medium for inter-team collaboration. Rather than offering an one-size-fits-all solution, these learned lessons highlight how programming paradigms implicitly shapes research workflows through existing domain hierarchies. The discussion aims to invite further explorations into how declarative problem formulations can facilitate innovation in settings where concurrent R\&{}D workflows are gaining traction, as opposed to environments where sequential, phase-driven workflows remain the norm.