arXiv research

LoD improves model safety by integrating unlabeled wild data, reducing OOD misclassification.

WILDS 2.0 expands benchmark datasets for unsupervised adaptation.

Study of wild mapping class groups and their cabled braids.

We study (i) asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor $D$-modules. As an application, we show the hard Lefschetz theorem for algebraic semis…

The Ooguri-Vafa space is linked to framed wild harmonic bundles via hyperkähler geometry.

Constructs infinitely many non-equivalent wild knots in Menger sponge.

New method uses mosaics to study wild knots.

This paper constructs wild knots from beaded necklaces using a Schottky group.

Injectivity proven for measure homology of certain wild spaces.

Study of wild mapping class groups on complex reflection groups.

The Gauss-Bonnet formula for classical translation surfaces relates the cone angle of the singularities (geometry) to the genus of the surface (topology). When considering more general translation surfaces, we observe so-called wild singularities for which the notion of cone angle is not applicable any more. We study w…

The paper revisits the investment simulation based on strategies exhibited by Generalized (m,2)-Zipf law to present an interesting characterization of the wildness in financial time series. The investigations of dominant strategies on each specific time series shows that longer words dominant in larger time scale exhib…

We will construct twisted versions of the wild character varieties.

Study detects synthetic tabular data across different tables.

Algorithm describes Fourier transform of Stokes data at infinity.

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on…

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $Λ$ also fibers over the circle. As a consequence, the universal covering of $\mathbb{S}^{3}-Λ$ is $\mathbb{R}^{3}$. We p…

Efficiently refits black box predictions with wild refitting method.

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered $λ$-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way t…

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge w…

Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.

Automatic understanding of human affect using visual signals is of great importance in everyday human-machine interactions. Appraising human emotional states, behaviors and reactions displayed in real-world settings, can be accomplished using latent continuous dimensions (e.g., the circumplex model of affect). Valence …

New method estimates model risk without knowing function class.

In this paper we prove that a wild knot $K$ which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points $p, q\in{K}$ there exists a homeomorphism $f$ of the sphere such that $f(K)=K$ and $f(p)=q$. We also show that if the wild knot is a …

We will give several descriptions of some basic examples of wild character varieties, including a discussion of links to work of Sibuya, Calabi and Euler, amongst others.

In the context of HCI, building an automatic system to recognize affect of human facial expression in real-world condition is very crucial to make machine interact naturallisticaly with a man. However, existing facial emotion databases usually contain expression in the limited scenario under well-controlled condition. …

Two-stream model recognizes affect from audio and video.

New method refines model-free evaluation of complex machine learning models.

Summary of main work 1999-2012

Paper presents a novel framework for OOD learning with human feedback.

In this paper we construct infinitely many wild knots, $\mathbb{S}^{n}\hookrightarrow\mathbb{S}^{n+2}$, for $n=2,3,4$ and 5, each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties

New embeddings show answer to Baker-Laidacker question can be yes or no.

Automatic understanding of human affect using visual signals is a problem that has attracted significant interest over the past 20 years. However, human emotional states are quite complex. To appraise such states displayed in real-world settings, we need expressive emotional descriptors that are capable of capturing an…

We consider flat surfaces and the points of their metric completions, particularly the singularities to which the flat structure of the surface does not extend. The local behavior near a singular point x can be partially described by a topological space L(x) which captures all the ways that x can be "approached linearl…

A novel procedure is presented in this paper, for training a deep convolutional and recurrent neural network, taking into account both the available training data set and some information extracted from similar networks trained with other relevant data sets. This information is included in an extended loss function use…

New method for estimating high-dimensional binary time series coefficients.

Many modern Artificial Intelligence (AI) systems make use of data embeddings, particularly in the domain of Natural Language Processing (NLP). These embeddings are learnt from data that has been gathered "from the wild" and have been found to contain unwanted biases. In this paper we make three contributions towards me…

Every countable compact subset of sphere is tame.

The purpose of this paper is to construct an example of a 2-knot wildly embedded in $\mathbb{S}^{4}$ as the limit set of a Kleinian group. We find that this type of wild 2-knots has very interesting topological properties.

Emotions recognition is the task of recognizing people's emotions. Usually it is achieved by analyzing expression of peoples faces. There are two ways for representing emotions: The categorical approach and the dimensional approach by using valence and arousal values. Valence shows how negative or positive an emotion i…

Let $C$ and $D$ be a pair of crumpled $n$-cubes and $h$ a homeomorphism of $\text{Bd }C$ to $\text{Bd }D$ for which there exists a map $f_h: C\to D$ such that $f_h|\text{Bd }C =h$ and $f_{h}^{-1}(\text{Bd }D)=\text{Bd }C$. In our view the presence of such a triple $(C,D,h)$ suggests that $C$ is "at least as wild as" $D…

The paper shows strong correlation between in-distribution and out-of-distribution performance in various machine learning models.

WILD-SCAV benchmarks AI in complex 3D FPS environments.

HHAR-net uses neural networks to recognize human activities at different levels of abstraction.

Supervised learning from training data with imbalanced class sizes, a commonly encountered scenario in real applications such as anomaly/fraud detection, has long been considered a significant challenge in machine learning. Motivated by recent progress in curriculum and self-paced learning, we propose to adopt a semi-s…

A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.

4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders horned sphere) which can be interpreted as quantum states. This relation can be co…

Lifelong learning with deep neural networks is well-known to suffer from catastrophic forgetting: the performance on previous tasks drastically degrades when learning a new task. To alleviate this effect, we propose to leverage a large stream of unlabeled data easily obtainable in the wild. In particular, we design a n…