Related papers: A generic absoluteness principle consistent with l…

Based on the work of Shelah, Kellner, and T\u{a}nasie (Fund. Math., 166(1-2):109-136, 2000 and Comment. Math. Univ. Carolin., 60(1):61-95, 2019), and the recent developments in the third author's master's thesis, we develop a general theory…

We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that…

The stability-plasticity dilemma is a major challenge in continual learning, as it involves balancing the conflicting objectives of maintaining performance on previous tasks while learning new tasks. In this paper, we propose the…

This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…

Humans excel at continually learning from an ever-changing environment whereas it remains a challenge for deep neural networks which exhibit catastrophic forgetting. The complementary learning system (CLS) theory suggests that the interplay…

We consider discrete $\beta$-ensembles, as introduced by Borodin, Gorin and Guionnet in (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017). Under general assumptions, we establish a large deviation principle for the empirical…

The Recurrence Axiom for a class $\mathcal{P}$ of \pos\ and a set $A$ of parameters is an axiom scheme in the language of ZFC asserting that if a statement with parameters from $A$ is forced by a poset in $\mathcal{P}$, then there is a…

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

This paper presents a simple generalization of the basic atomic read/write register object, whose genericity parameter spans the whole set of integers and is such that its k-parameterized instance has exactly consensus number k. This…

In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $\omega_1$ or $\omega_2$ has small consistency strength, but that of a…

We show that for $\Pi_2$-properties of second or third order arithmetic as formalized in appropriate natural signatures the apparently weaker notion of forcibility overlaps with the standard notion of consistency (assuming large cardinal…

Nourdin et al. [9] established the following universality result: if a sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal random variables converges in distribution to a normal, then the convergence also holds…

Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…

The paper is an introduction into General Ether Theory (GET). We start with few assumptions about an universal ``ether'' in a Newtonian space-time which fulfils \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) +…

We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of…

We develop a general theory for class-sized symmetric systems as a natural extension of symmetric systems with respect to class forcing. In particular, adapting the usual notions of pretameness and tameness for class forcing, we present…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

Continual learning (CL) has emerged as a dominant paradigm for acquiring knowledge from sequential tasks while avoiding catastrophic forgetting. Although many CL methods have been proposed to show impressive empirical performance, the…

We show that in contrast with the Cohen version of Solovay's model, it is consistent for the continuum to be Cohen-measurable and for every function to be continuous on a non-meagre set.

Set-theoretic axioms formulated in terms of existence of a Laver-generic large cardinal were introduced in [16] and studied further in [17], [18], [20]. These axioms, let us call them Laver-genericity axioms, claim the existence of a…