Related papers: When "Normalization Without Loss of Generality" Lo…

Canonicalization provides an architecture-agnostic method for enforcing equivariance, with generalizations such as frame-averaging recently gaining prominence as a lightweight and flexible alternative to equivariant architectures. Recent…

That shared features between train and test data are required for generalisation in artificial neural networks has been a common assumption of both proponents and critics of these models. Here, we show that convolutional architectures avoid…

Regularized models are often sensitive to the scales of the features in the data and it has therefore become standard practice to normalize (center and scale) the features before fitting the model. But there are many different ways to…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…

The normalizing layer has become one of the basic configurations of deep learning models, but it still suffers from computational inefficiency, interpretability difficulties, and low generality. After gaining a deeper understanding of the…

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving…

We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…

Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…

This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas…

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the…

In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…

Counterfactual examples have emerged as an effective approach to produce simple and understandable post-hoc explanations. In the context of graph classification, previous work has focused on generating counterfactual explanations by…

Overfitting is a well-known issue in machine learning that occurs when a model struggles to generalize its predictions to new, unseen data beyond the scope of its training set. Traditional techniques to mitigate overfitting include early…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

Recently, a rigorous yet concise formula has been derived to evaluate the information flow, and hence the causality in a quantitative sense, between time series. To assess the importance of a resulting causality, it needs to be normalized.…

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…