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The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that poses difficulties for pure machine learning methods due to its requirement for fluid intelligence with a focus on reasoning and abstraction. In…
Training a deep neural network to maximize a target objective has become the standard recipe for successful machine learning over the last decade. These networks can be optimized with supervised learning, if the target objective is…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…
The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently…
As rapidly growing AI computational demands accelerate the need for new hardware installation and maintenance, this work explores optimal data center resource management by balancing operational efficiency with fault tolerance through…
In spite of the recent improvements in the performance of the solvers based on the DPLL procedure, it is still possible for the search algorithm to focus on the wrong areas of the search space, preventing the solver from returning a…
A large number of problems in optimization, machine learning, signal processing can be effectively addressed by suitable semidefinite programming (SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond instances with a few…
We present ReAct!, an interactive tool for high-level reasoning for cognitive robotic applications. ReAct! enables robotic researchers to describe robots' actions and change in dynamic domains, without having to know about the syntactic and…
In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnegative vector as variables. We develop a rank-support-adaptive…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio (SINR), incorporating a positive semidefinite constraint…
Safety is critical when applying reinforcement learning (RL) to real-world problems. As a result, safe RL has emerged as a fundamental and powerful paradigm for optimizing an agent's policy while incorporating notions of safety. A prevalent…
Humans intuitively solve complex problems by flexibly shifting among reasoning modes: they plan, execute, revise intermediate goals, resolve ambiguity through associative judgment, and apply formal procedures to well-specified subproblems.…
Deep reinforcement learning (DRL) has gained great success by learning directly from high-dimensional sensory inputs, yet is notorious for the lack of interpretability. Interpretability of the subtasks is critical in hierarchical…
Traditional machine learning depends on high-precision arithmetic and near-ideal hardware assumptions, which is increasingly challenged by variability in aggressively scaled semiconductor devices. Compute-in-memory (CIM) architectures…
We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…
Large language models (LLMs) are remarked by their substantial computational requirements. To mitigate the cost, researchers develop specialized CUDA kernels, which often fuse several tensor operations to maximize the utilization of GPUs as…