相关论文: Tractability and Decompositions of Global Cost Fun…
It is well known that the reachability problem for simply-typed lambda calculus with recursive definitions and finite base-type values (finitary PCF) is decidable. A recent paper by Dal Lago and Ghyselen has shown that the same problem…
We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion…
Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…
Contracts and contract monitoring are a powerful mechanism for specifying properties and guaranteeing them at run time. However, run time monitoring of contracts imposes a significant overhead. The execution time is impacted by the…
In the absence of a theory of everything, modern physicists need to rely on other predictive tools and turned to Effective Field Theories (EFTs) in a number of fields, including but not limited to statistical mechanics, condensed matter,…
We call an Ising model tractable when it is possible to compute its partition function value (statistical inference) in polynomial time. The tractability also implies an ability to sample configurations of this model in polynomial time. The…
The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…
The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two cases for (TRS), the so-called ``easy case'' and ``hard case''. Even in the ``easy case'', the sequence…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data…
Optimal control is an essential tool for stabilizing complex nonlinear systems. However, despite the extensive impacts of methods such as receding horizon control, dynamic programming and reinforcement learning, the design of cost functions…
We focus on Optimal Transport PDE on the unit sphere $\mathbb{S}^2$ with a particular type of cost function $c(x,y) = F(x \cdot y, x \cdot \hat{e}, y \cdot \hat{e})$ which we call cost functions with preferential direction, where $\hat{e}…
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…
Prompt tuning (PT), where a small amount of trainable soft (continuous) prompt vectors is affixed to the input of language models (LM), has shown promising results across various tasks and models for parameter-efficient fine-tuning (PEFT).…
Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP…
This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…
Safety is critical in robotic tasks. Energy function based methods have been introduced to address the problem. To ensure safety in the presence of control limits, we need to design an energy function that results in persistently feasible…
Extremum Seeking Control (ESC) is a well-known set of continuous time algorithms for model-free optimization of a cost function. One issue for ESCs is the convergence rates of parameters to extrema of unknown cost functions. The local…