arXiv research

New approach combines invariance and information bottleneck for OOD generalization.

Proposes IIB for domain generalization, overcoming failure modes of IRM.

Proposes indifference pricing to estimate weak information value.

Harmonization schemes limit accuracy due to domain information.

Discuss knots in $S_{g} imes S^{1}$, introducing rotating information and invariants.

Novel framework improves graph learning for out-of-distribution generalization.

Paper introduces a new invariant for virtual knotoids and proves it's a Vassiliev invariant of order one.

New model learns symmetry transformations from complex data.

Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.

The paper analyzes the tradeoffs between accuracy and invariance in learning representations.

New method uses cycle consistency to enforce invariance in latent space.

Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and injecting noise during training naturally bias the network towards learning invari…

This paper provides a connection between two distinct branches of research in CR geometry -- namely, analytic and geometric conditions that suffice to establish the closed range of the Cauchy-Riemann operator and CR invariants on CR manifolds. Specifically, we work on not necessarily pseudoconvex domains $Ω\subset\math…

We find the maximum mutual information for neural networks and its key determinants.

We present a unified invariance framework for supervised neural networks that can induce independence to nuisance factors of data without using any nuisance annotations, but can additionally use labeled information about biasing factors to force their removal from the latent embedding for making fair predictions. Invar…

We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in thickened surfaces and of surfaces embedded in thickened $3$-manifolds. In particul…

This paper studies moduli spaces of statistical structures on Lie groups.

STAR improves equivariant and invariant representation learning by routing projection heads.

New invariant distinguishes singular knots and links.

Study Vassiliev invariants for virtual knots, expanding quantum theory.

Data representations that contain all the information about target variables but are invariant to nuisance factors benefit supervised learning algorithms by preventing them from learning associations between these factors and the targets, thus reducing overfitting. We present a novel unsupervised invariance induction f…

Given any oriented link diagram, two types of new knot invariants are constructed. They satisfy some generalized skein relations. The coefficients of each invariant is from a commutative ring. Homomorphisms and representations of those rings define new link invariants. For example, the HOMFLYPT polynomial with three va…

GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.

New invariant for links in 3-sphere computed and computed using diagrams.

It is known that the number of biquandle colorings of a long virtual knot diagram, with a fixed color of the initial arc, is a knot invariant. In this paper we describe a more subtle invariant: a family of biquandle endomorphisms obtained from the set of colorings and longitudinal information.

We extend the Yang-Baxter cocycle invariants for virtual knots by augmenting Yang-Baxter 2-cocycles with cocycles from a cohomology theory associated to a virtual biquandle structure. These invariants coincide with the classical Yang-Baxter cocycle invariants for classical knots but provide extra information about virt…

Cone structures in quantum field theory linked to information geometry.

In the 1950's Milnor defined a family of higher order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received and fruitful study since its inception. In the case that $L$ has vanishing pairwise linking numbers, this triple linking number gives an integ…

We define new invariants of knots by means of quandle colorings and longitudinal information. These invariants can be applied to a tangle embedding problem and recognizing non-classical virtual knots.

In [14], the second named author constructed the bracket invariant [.] of virtual knots valued in pictures (linear combinations of virtual knot diagrams with some crossing information omitted), such that for many diagrams K, the following formula holds: [K]=K', where K' is the underlying graph of the diagram, i.e., the…

This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of order two. The first, called the three loop isotopy invariant, is an invariant of virtual knots while the second, called the three loop fram…

Topology-based information retrieval improves query accuracy.

We incorporate quandle cocycle information into the quandle coloring quivers we defined in arXiv:1807.10465 to define weighted directed graph-valued invariants of oriented links we call \textit{quandle cocycle quivers}. This construction turns the quandle cocycle invariant into a small category, yielding a categorifica…

Whatever information a deep neural network has gleaned from training data is encoded in its weights. How this information affects the response of the network to future data remains largely an open question. Indeed, even defining and measuring information entails some subtleties, since a trained network is a determinist…

Study of Bauer-Furuta invariants under Lie group actions and Galois coverings.

Physics-informed neural networks improve by measuring effective dimensionality of constraints.

We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariance…

MetaPhysiCa tackles robust physics-informed machine learning for OOD tasks.

New tool helps classify invariant subvarieties in degenerations.

We give inequalities for the Manolescu invariants $α,β,γ$ under the connected sum operation. We compute the Manolescu invariants of connected sums of some Seifert fiber spaces. Using these same invariants, we provide a proof of Furuta's Theorem, the existence of a $\mathbb{Z}^\infty$ subgroup of the homology cobordism …

New framework explains data augmentation's role in machine learning.

A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…

We propose a novel approach to achieving invariance for deep neural networks in the form of inducing amnesia to unwanted factors of data through a new adversarial forgetting mechanism. We show that the forgetting mechanism serves as an information-bottleneck, which is manipulated by the adversarial training to learn in…

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example …

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate hyperbolic polygons, i.e. relatively compact domains in the hyperbolic plane with…

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamic…

A method to approximate causal models using information theory.

We use the LMO invariant to find constraints for a knot to admit a purely or reflectively cosmetic surgery. We also get a constraint for knots to admit a Lens space surgery, and some information for characterizing slopes.