Yu Liu

Yu Liu, Jan Kronqvist, Fabricio Oliveira

Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research. The prevailing approach uses feedforward neural networks (FNNs) with ReLU activations, whose piecewise-linear structure admits an exact but computationally intensive mixed-integer programming (MIP) reformulation as the networks grow. We advocate input convex neural networks (ICNNs) as structurally superior surrogates when the underlying response is approximately convex or concave. The convex architecture offers two computational advantages. First, the ICNN-MIP formulation tends to yield a tighter linear programming (LP) relaxation than its FNN-MIP counterpart, with no integrality gap in favourable instances. Second, ICNNs uniquely admit an LP-based reformulation via epigraph representations of ReLU activations, though this embedding is not always exact. When it is not, we exploit the properties of ICNNs to construct the strongest continuous relaxation over box domains, namely, the convex hull of the ICNN's graph, bounded below by the epigraph and above by the concave envelope; this construction is tractable under input convexity but hard for general ReLU networks. On this basis, we develop a branch-and-bound algorithm that builds this relaxation at each node, branches directly on input variables rather than intermediate variables as in MIP reformulations, and terminates at the root node whenever the epigraph embedding is valid. Case studies on humanitarian food aid, oil well routing, and wine blending show that ICNN surrogates match FNN accuracy and deliver gains in solve time and scalability, supporting ICNN as the default surrogate when the underlying function is convex, concave, or well-approximated as such.

Aditya Raghavan, Yu Liu, Ian Mercer et al.

Scanning probe microscopy provides nanoscale access to structural, electrical, electromechanical, magnetic, and mechanical properties of materials. Its increasing use for wafer-scale characterization and combinatorial materials exploration creates a need to distribute measurements efficiently across large spatial domains. This is particularly important when available modalities differ in acquisition time and potential for tip and sample damage, making exhaustive multimodal mapping over spatial grids impractical. Here, we demonstrate multitask scanning probe microscopy, a live, closed-loop workflow in which a multitask Gaussian process learns spatial and cross-modal relationships and autonomously selects both the next measurement location and the next experimental protocol. The approach is implemented on an automated large-sample atomic force microscope and demonstrated on a composition-spread AlScN wafer using tapping-mode and Dual AC Resonance Tracking (DART) measurements. Paired initial measurements establish the relation between the tasks, after which noncoincident measurements are used to update both response landscapes. The resulting workflow extends active learning in scanning probe microscopy from spatial sampling to autonomous allocation of measurement modalities and provides a basis for combining rapid, weakly perturbative imaging with slower contact, electrical, electromechanical, magnetic, or spectroscopic measurements.

Yifei Cao, Guolong Wang, Mingliang Hou et al.

Visual query localization (VQL) aims to retrieve and re-localize a queried object in egocentric videos, yet remains challenging when object boundaries are ambiguous and global context cannot effectively guide fine-grained localization. Human vision handles such ambiguity through a hierarchical process: it rapidly screens foreground candidates, selectively attends to the target despite distractors, refines perception via feedback between global context and local detail, and, when a single view is unreliable, integrates evidence across viewpoints according to its credibility. Inspired by these competencies, we propose \textbf{EgoHieraLoc}, a unified framework for VQL-2D and VQL-3D. A Discriminative Parsing Module first extracts foreground-aware query representations using segmentation priors; a Query-Aware Module then performs robust target localization through discriminative correlation filtering with deformable modeling; and a Regional Adaptation Module feeds multi-scale context back into local regions to recover precise object boundaries. To extend this perceptual hierarchy to 3D localization, we introduce Geometric-Semantic Joint Confidence (GSJC), which multiplicatively couples segmentation confidence with local depth consistency, multi-view back-projection consistency, and triangulation-baseline quality, so that a viewpoint contributes to the 3D estimate only when it is credible both semantically and geometrically. Extensive experiments demonstrate state-of-the-art performance on both VQL-2D and -3D benchmarks.