Related papers: Petz map and Python's lunch

In the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong…

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…

Tensor network machine learning models have shown remarkable versatility in tackling complex data-driven tasks, ranging from quantum many-body problems to classical pattern recognitions. Despite their promising performance, a comprehensive…

The increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important…

In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and…

The Petz map has been established as a quantum version of the Bayes' rule. It unifies the conceptual belief update rule of a quantum state observed after a forward quantum process, and the operational reverse process that recovers the final…

Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…

Large Transformer-based models were shown to be reducible to a smaller number of self-attention heads and layers. We consider this phenomenon from the perspective of the lottery ticket hypothesis, using both structured and magnitude…

We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a…

We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a $\beta$-transformation.

We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…

We study the complexity of the itineraries of injective piecewise contracting maps on the interval. We prove that for any such map the complexity function of any itinerary is eventually affine. We also prove that the growth rate of the…

Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…

In this paper, we view a policy or plan as a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. Regardless of whether…

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…

Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous…

In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network,…