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

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

Structural models that admit multiple reduced forms, such as game-theoretic models with multiple equilibria, pose challenges in practice, especially when parameters are set-identified and the identified set is large. In such cases,…

In this paper we argue that, to its detriment, transparency research overlooks many foundational concepts of artificial intelligence. As an illustrating example we focus on uncertainty quantification in the context of counterfactual…

The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign…

Generalizing knowledge to unseen domains, where data and labels are unavailable, is crucial for machine learning models. We tackle the domain generalization problem to learn from multiple source domains and generalize to a target domain…

We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…

Softmax and related normalized response functions are widely used in choice theory, machine learning, and cognitive science. In non-Boolean event structures with overlapping contexts, however, local normalization does not automatically…

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…

Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…

Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more…

We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…

Let ${\cal F}$ be a family of meromorphic functions on a domain $D$. We present a quite general sufficient condition for ${\cal F}$ to be a normal family. This criterion contains many known results as special cases. The overall idea is that…

We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…

I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…

Despite their outstanding performance, large language models (LLMs) suffer notorious flaws related to their preference for simple, surface-level textual relations over full semantic complexity of the problem. This proposal investigates a…

This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…

We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…