Related papers: Featured Weighted Automata
We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting…
Each LoRA checkpoint compactly stores task-specific updates in low-rank weight matrices, offering an efficient way to adapt large language models to new tasks and domains. In principle, these weights already encode what the adapter does and…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
In this paper we introduce a weighted LTL over product $\omega$-valuation monoids that satisfy specific properties. We also introduce weighted generalized B\"uchi automata with $\varepsilon$-transitions, as well as weighted B\"uchi automata…
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Forecasting is an indispensable element of operational research (OR) and an important aid to planning. The accurate estimation of the forecast uncertainty facilitates several operations management activities, predominantly in supporting…
Unsupervised feature extraction algorithms form one of the most important building blocks in machine learning systems. These algorithms are often adapted to the event-based domain to perform online learning in neuromorphic hardware.…
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages can converge much faster (sometimes superpolynomially, even…
Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
Both in the domains of Feature Selection and Interpretable AI, there exists a desire to `rank' features based on their importance. Such feature importance rankings can then be used to either: (1) reduce the dataset size or (2) interpret the…
Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper…
We consider weighted tree automata over strong bimonoids (for short: wta). A wta $\mathcal{A}$ has the finite-image property if its recognized weighted tree language $[\![\mathcal{A}]\!]$ has finite image; moreover, $\mathcal{A}$ has the…
Let $\{W_i\}_{i\in I}$ be a (redundant) sequence of subspaces each being endowed with a weight $v_i$, and let $\mathcal{H}$ be the closed linear span of the $W_i$'s, a composite Hilbert space. Provided that $\{(W_i,v_i)\}_{i \in I}$…
In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved…
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the…
Wheeler automata were introduced in 2017 as a tool to generalize existing indexing and compression techniques based on the Burrows-Wheeler transform. Intuitively, an automaton is said to be Wheeler if there exists a total order on its…
In this paper, we define weighted failure rate and their different means from the stand point of an application. We begin by emphasizing that the formation of n independent component series system having weighted failure rates with sum of…
Often the rows (cases, objects) of a dataset have weights. For instance, the weight of a case may reflect the number of times it has been observed, or its reliability. For analyzing such data many rowwise weighted techniques are available,…