Related papers: The core model induction beyond $L(\mathbb{R})$: n…

We describe a corpus-based induction algorithm for probabilistic context-free grammars. The algorithm employs a greedy heuristic search within a Bayesian framework, and a post-pass using the Inside-Outside algorithm. We compare the…

Inferences that arise from loss functions determined by the prior are considered and it is shown that these lead to limiting Bayes rules that are closely connected with likelihood. The procedures obtained via these loss functions are…

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…

We present an extension of the large $N_f$ formalism that allows to study cases with multiple fermion representations. The pole structure in the beta function is traced back to the intrinsic non-abelian nature of the gauge group,…

Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal…

We study minimal idempotents $J^{\mathrm{min}}(X)$ in the Ellis semigroup $E(X)$ associated with a Floyd-Auslander system $(X,T)$. We show that $(X,T)$ is non-tame if and only if $|J^{\mathrm{min}}(X)| > 2^{\aleph_0}$, which happens exactly…

Here, we show that the InfoNCE objective is equivalent to the ELBO in a new class of probabilistic generative model, the recognition parameterised model (RPM). When we learn the optimal prior, the RPM ELBO becomes equal to the mutual…

In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor…

We construct non-isomorphic models M, N, e.g. of cardinality aleph_1 such that in the Ehrenfeucht-Fraisse game of length zeta < omega_1 the isomorphism player wins

We show that (i) the standard fine structural properties for premice follow from normal iterability (whereas the classical proof relies on iterability for stacks of normal trees), and (ii) every mouse which is finitely generated above its…

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function…

Let M be a closed manifold and f be a diffeomorphism on M. We show that if f has a nontrivial dominated splitting TM=E\oplus F, then f can not be minimal. The proof mainly use Mane's argument and Liao's selecting lemma.

We present a new explainable AI (XAI) framework aimed at increasing justified human trust and reliance in the AI machine through explanations. We pose explanation as an iterative communication process, i.e. dialog, between the machine and…

We present Bournemouth Forced Aligner (BFA), a system that combines a Contextless Universal Phoneme Encoder (CUPE) with a connectionist temporal classification (CTC)based decoder. BFA introduces explicit modelling of inter-phoneme gaps and…

We show that the universally axiomatized, induction-free theory PA^- is a sequential theory in the sense of Pudl\'ak [5], in contrast to the closely related Robinson's arithmetic.

We show that bounded-error affine finite automata recognize uncountably many (and so some non-Turing recognizable) languages when using real-valued transitions.

Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…

While interpretability is crucial for machine learning applications in safety-critical domains and for regulatory compliance, existing tabular foundation models like TabPFN lack transparency. Generalized Additive Models (GAMs) provide the…

We show that more head-driven parsing algorithms can be formulated than those occurring in the existing literature. These algorithms are inspired by a family of left-to-right parsing algorithms from a recent publication. We further…

There has been much interest on constructing models which are not isomorphic of cardinality lambda but are equivalent under the Ehrenfeucht-Fraisse game of length alpha even for every alpha<lambda. So under G.C.H. we know much. We deal here…