Related papers: Localising Stochasticity in Weighted Automata
In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree…
Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They…
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata…
We show how well known rules of back propagation arise from a weighted combination of finite automata. By redefining a finite automata as a predictor we combine the set of all $k$-state finite automata using a weighted majority algorithm.…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
We realize constant-space quantum computation by measure-many two-way quantum finite automata and evaluate their language recognition power by analyzing patterns of their exotic behaviors and by exploring their structural properties. In…
We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for…
Weighted automata are a generalization of nondeterministic automata that associate a weight drawn from a semiring $K$ with every transition and every state. Their behaviours can be formalized either as weighted language equivalence or…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…
The aim of this note is to state a couple of general results about the properties of the penalized maximum likelihood estimators (pMLE) and of the posterior distribution for parametric models in a non-asymptotic setup and for possibly large…
Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and…
We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple…
Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive…
A definition of a probabilistic automaton is formulated in which its prime decomposition follows as a direct consequence of Krohn-Rhodes theorem. We first characterize the local structure of probabilistic automata. The prime decomposition…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…