Related papers: Revisiting virtual difference ideals
Transformer-based tabular foundation models have recently demonstrated promising in-context learning (ICL) performance on structured data, emerging as competitive alternatives to gradient-boosted trees. However, the fairness implications of…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
The main focus of this paper is on the problem of relating an ideal $I$ in the polynomial ring $\mathbb Q[x_1, \dots, x_n]$ to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]$ where $p$ is a prime number; in other words, the…
The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…
Considering the concept of time-dilation, there exist some major issues with recurrent neural Architectures. Any variation in time spans between input data points causes performance attenuation in recurrent neural network architectures.…
Inference is the task of drawing conclusions about unobserved variables given observations of related variables. Applications range from identifying diseases from symptoms to classifying economic regimes from price movements. Unfortunately,…
Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal…
We use minimal tilting complexes to construct an explicit bijection between the set of thick tensor ideals with the two-out-of-three property in the category of finite-dimensional modules over a quantum group at a root of unity and the set…
In the theory of commutative semirings, the lack of additive inverses creates a structural divergence between ideals and congruences that does not exist in ring theory. The aim of this article is to restore critical ideal-theoretic…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…
Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…
Selective rationalization improves neural network interpretability by identifying a small subset of input features -- the rationale -- that best explains or supports the prediction. A typical rationalization criterion, i.e. maximum mutual…
Neural ideals, originally defined in arXiv:1212.4201, give a way of translating information about the firing pattern of a set of neurons into a pseudomonomial ideal in a polynomial ring. We give a simple criterion for determining whether a…
Standard imitation learning can fail when the expert demonstrators have different sensory inputs than the imitating agent. This is because partial observability gives rise to hidden confounders in the causal graph. In previous work, to work…
Using the concept of principal stratification from the causal inference literature, we introduce a new notion of fairness, called principal fairness, for human and algorithmic decision-making. The key idea is that one should not…
Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser…
A knowledge system S describing a part of real world does in general not contain complete information. Reasoning with incomplete information is prone to errors since any belief derived from S may be false in the present state of the world.…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
Utopian images in XR-games are often ambiguous. How can ambiguity be consciously designed in virtual worlds? What are the design principles for game designers? Ambiguity arises from discontinuity and decontextualization, from the deliberate…