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Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
When using language models (LMs) to solve complex problems, humans might struggle to understand the LM-generated solutions and repair the flawed ones. To assist humans in repairing them, we propose to automatically decompose complex…
Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…
Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial…
This paper addresses the limitations of a single agent in task decomposition and collaboration during complex task execution, and proposes a multi-agent architecture for modular task decomposition and dynamic collaboration based on large…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Recognising that real-world optimisation problems have multiple interdependent components can be quite easy. However, providing a generic and formal model for dependencies between components can be a tricky task. In fact, a PMIC can be…
Explainable AI is an important area of research within which Explainable Planning is an emerging topic. In this paper, we argue that Explainable Planning can be designed as a service -- that is, as a wrapper around an existing planning…
This paper investigates how learning can be used to ease the design of high-quality paths for the assembly of deformable objects. Object dynamics plays an important role when manipulating deformable objects; thus, detailed models are often…
This chapter presents methodological reflections on the necessity and utility of artificial intelligence in generative design. Specifically, the chapter discusses how generative design processes can be augmented by AI to deliver in terms of…
Automated management requires decomposing high-level user requests, such as intents, to an abstraction that the system can understand and execute. This is challenging because even a simple intent requires performing a number of ordered…
Generalized planning accelerates classical planning by finding an algorithm-like policy that solves multiple instances of a task. A generalized plan can be learned from a few training examples and applied to an entire domain of problems.…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
Cloud manufacturing system is a service-oriented and knowledge-based one, which can provide solutions for the large-scale customized production. The service resource allocation is the primary factor that restricts the production time and…
This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was…
The definition and representation of planning problems is at the heart of AI planning research. A key part is the representation of action models. Decades of advances improving declarative action model representations resulted in numerous…
We review the cumulant decomposition (a way of decomposing the expectation of a product of random variables (e.g. $\mathbb{E}[XYZ]$) into a sum of terms corresponding to partitions of these variables.) and the Wick decomposition (a way of…
We present a framework for deformable object manipulation that interleaves planning and control, enabling complex manipulation tasks without relying on high-fidelity modeling or simulation. The key question we address is when should we use…
Large Language Models (LLMs) suffer from reliability issues on complex tasks, as existing decomposition methods are heuristic and rely on agent or manual decomposition. This work introduces a novel, systematic decomposition framework that…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…