Related papers: Open class determinacy is preserved by forcing
In many daily tasks we make multiple decisions before reaching a goal. In order to learn such sequences of decisions, a mechanism to link earlier actions to later reward is necessary. Reinforcement learning theory suggests two classes of…
In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that…
We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…
In general class-incremental learning, researchers typically use sample sets as a tool to avoid catastrophic forgetting during continuous learning. At the same time, researchers have also noted the differences between class-incremental…
Through well-motivated models in particle physics, we demonstrate the power of a general class of selection rules arising from non-invertible fusion algebras that are only exact at low orders in perturbation theory. Surprisingly, these…
We add to the theory of preservation of topological properties under forcing. In particular, we answer a question of Gilton and Holshouser in a strong sense, showing that if player II has a winning strategy in the strong countable fan…
It is widely agreed that exams must be fair; yet what this exactly means is not made clear. One may mean fairness of treatment, but this merely propagates the fairness or unfairness of pre-existing rules. Fairness of opportunity on the…
We look at equivalence relations on the set of models of a theory -- MERs, for short -- such that the class of equivalent pairs is itself an elementary class, in a language appropriate for pairs of models. We provide many examples of…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness…
In \cite{MV} we defined and proved the consistency of the principle ${\rm GM}^+(\omega_3,\omega_1)$ which implies that many consequences of strong forcing axioms hold simultaneously at $\omega_2$ and $\omega_3$. In this paper we formulate a…
We investigate a generalization of the {\L}o\'s-Tarski preservation theorem via the semantic notion of \emph{preservation under substructures modulo $k$-sized cores}. It was shown earlier that over arbitrary structures, this semantic notion…
In class-incremental learning, a learning agent faces a stream of data with the goal of learning new classes while not forgetting previous ones. Neural networks are known to suffer under this setting, as they forget previously acquired…
We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several…
The forward-forward algorithm presents a new method of training neural networks by updating weights during an inference, performing parameter updates for each layer individually. This immediately reduces memory requirements during training…
The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of…
We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a…
Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping,…