New method uses mosaics to study wild knots.
problem Classifying wild knots with infinite knotting behavior.
method Extending knot mosaic theory to represent wild knots with isolated wild points.
result Developed a framework for mosaic tangles and mosaic rigid vertex spatial graphs.
WILDS 2.0 expands benchmark datasets for unsupervised adaptation.
problem Leveraging unlabeled data for distribution shifts in real-world applications.
method Curated unlabeled data across various applications, tasks, and modalities.
result State-of-the-art methods perform poorly on WILDS datasets.
Efficiently refits black box predictions with wild refitting method.
problem Computing high-probability upper bounds on prediction errors.
method Three-step procedure: residuals, symmetrization, and solving a modified prediction problem.
result Wild refitting provides an upper bound on prediction error with high probability.
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…
Using methods of descriptive theory it is shown that the classification problem for wild knots is strictly harder than that for countable structures.
LoD improves model safety by integrating unlabeled wild data, reducing OOD misclassification.
problem Improving model safety and reliability using unlabeled wild data containing both in-distribution and out-of-distribution samples.
method Intentionally label-noisifying unlabeled wild data to enable joint learning of labeled ID and OOD data, distinguishing losses between ID and OOD samples.
result LoD framework achieves superior OOD detection without requiring thresholds, improving model safety.
Constructs infinitely many non-equivalent wild knots in Menger sponge.
problem Embedding non-equivalent wild knots in the Menger sponge.
method Recursive constructions and geometric approach.
result Controlled set of wild points in a Cantor set within the Menger sponge.
New method estimates model risk without knowing function class.
problem Evaluating model risk for complex, opaque models.
method Wild refitting with Bregman losses and randomized symmetrization.
result Valid upper bound on excess risk for opaque models.
This paper constructs wild knots from beaded necklaces using a Schottky group.
problem Creating wild knots from beaded necklaces and studying their properties.
method Using a Schottky group generated by inversions on spheres to construct wild knots.
result The constructed wild knots are fibered if the original knot is fibered.
Injectivity proven for measure homology of certain wild spaces.
problem Injectivity of measure homology for mildly wild spaces.
method Proving injectivity of the canonical map from singular to measure homology.
result Injectivity of measure homology for certain mildly wild spaces.
Study of wild mapping class groups on complex reflection groups.
problem Understanding deformations of wild Riemann surfaces.
method Construction of configuration spaces and combinatorial fission forests.
result Sharp parameterisation of admissible deformation classes of wild Riemann surfaces.
Deep learning model predicts human emotions in real-world settings.
problem Automatic emotional state assessment in natural settings.
method End-to-end deep neural architecture (AffWildNet) combining convolutional and recurrent layers.
result AffWildNet achieved state-of-the-art results on Aff-Wild Challenge.
New method refines model-free evaluation of complex machine learning models.
problem Evaluating the excess risk of opaque machine learning predictors.
method Perturbing derivatives to create pseudo-outcomes and refitting the model twice.
result Upper bound on excess risk derived efficiently without prior function class knowledge.
Two new methods for variational inference without tractable densities.
problem Challenges in variational inference due to computationally intractable probability density functions.
method Introduces wild variational inference methods that do not require tractable density functions.
result Significant improvement in stochastic gradient Langevin dynamics (SGLD) step size adjustment.
Study of wild mapping class groups and their cabled braids.
problem Understanding the structure of wild mapping class groups and their cabled versions.
method Define and study generalizations of pure g-braid groups, establish product decompositions, and introduce fission trees. result Obtain cabled versions of braid groups, related to braid operads.
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…
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…
We will construct twisted versions of the wild character varieties.
Wild involutions found in 3D sphere's Sobolev space.
problem Finding wild involutions in Sobolev spaces.
method Investigated wild involutions in W1,p(S3,S3) for 1≤p<2. result Existence of wild involution in Sobolev class W1,p(S3,S3) for 1≤p<2. 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 S3−Λ is R3. We p…
New embeddings show answer to Baker-Laidacker question can be yes or no.
problem Answer to Baker-Laidacker question about disjoint compacta in R^N.
method Use of specific wild Cantor sets and Antoine's methods.
result Answer to Baker-Laidacker question can be twofold.
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…
Paper presents a CNN-RNN method for multi-dimensional emotion recognition in-the-wild.
problem Dimensional emotion recognition in real-world scenarios.
method Pre-training with Aff-Wild and Aff-Wild2, extracting low-, mid-, and high-level features, using RNN subnets in a multi-task framework, and fusion of networks.
result Our approach outperformed state-of-the-art methods using only visual information.
Proves correspondence between harmonic and Higgs bundles.
problem Connecting harmonic and Higgs bundles for study.
method Kobayashi-Hitchin correspondence for polystable bundles.
result Establishes correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles. A new method shrinks a complex structure without much change.
problem Understanding the geometry of Bing's wild involution.
method Producing a counterintuitive construction to shrink the Bing decomposition without much change.
result A method to shrink a complex structure (Bing's decomposition) without much change.
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∈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.
The Ooguri-Vafa space is linked to framed wild harmonic bundles via hyperkähler geometry.
problem Relating the Ooguri-Vafa space to Hitchin moduli spaces.
method Interpreting the Ooguri-Vafa space as framed wild harmonic bundles over CP1.
result The Ooguri-Vafa space is a moduli space of framed wild harmonic bundles.
Improves deep pose estimation for extreme motions using pre-trained models.
problem Accuracy and training time issues for extreme/wild motions.
method Post-data augmentation to improve pre-trained models.
result Enhanced accuracy in pose estimation for extreme motions.
Two-stream model recognizes affect from audio and video.
problem Human affect recognition in real-world settings.
method Two-stream aural-visual analysis model with separate audio and visual processing.
result Model achieves promising results on Aff-Wild2 database.
Aff-Wild database expands facial expression recognition to real-world conditions.
problem Lack of spontaneous facial expression databases in real-world conditions.
method Collects spontaneous facial expressions from YouTube, annotates with valence and arousal, uses deep learning techniques.
result Developed an end-to-end DNN model achieving 0.555 CCC for valence and 0.499 CCC for arousal.
Quantum states in 4-manifolds linked to hyperbolic geometry.
problem Understanding quantum states and their geometric representations.
method Turaev-Drinfeld quantization and hyperbolic geometry.
result Deep connection between quantum mechanics and hyperbolic geometry.
Paper tackles biases in AI embeddings from wild data.
problem Biases in AI embeddings from uncontrolled data.
method Measures biases using social psychology word lists, observes gender bias in occupations, demonstrates simple projection to reduce bias.
result Simple projection significantly reduces embedding biases.
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…
In this paper we construct infinitely many wild knots, Sn↪Sn+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 method for estimating high-dimensional binary time series coefficients.
problem Statistical inference for high-dimensional binary time series.
method Post-selection estimator and second-order wild bootstrap algorithm.
result Good finite-sample performance of the proposed method.
Paper tackles multi-task learning for emotion recognition and generation using Aff-Wild dataset.
problem Developing a multi-task learning approach for emotion recognition and generation using Aff-Wild dataset.
method Deep neural network with shared hidden layers and GAN for multi-task learning and image generation.
result Good performance of the proposed approach on Aff-Wild dataset.
Gradient matching method improves domain generalization across various datasets.
problem Machine learning's inability to generalize to unseen domains.
method Inter-domain gradient matching objective and first-order algorithm Fish.
result Fish method produces competitive results and surpasses baselines on 4 datasets.
Project creates new dataset for 'in the wild' emotions recognition.
problem Recognition of emotions in real-life unpredictable situations.
method Design and implement a new dataset and deep learning model.
result Demonstrates effectiveness of the new deep learning model for real-life emotions recognition.
Every countable compact subset of sphere is tame.
problem Characterizing compact subsets of spheres.
method Proving homeomorphic complements imply homeomorphic subsets.
result Wild subspaces like Antoine contain Cantor sets.
The purpose of this paper is to construct an example of a 2-knot wildly embedded in S4 as the limit set of a Kleinian group. We find that this type of wild 2-knots has very interesting topological properties.
Let C and D be a pair of crumpled n-cubes and h a homeomorphism of Bd C to Bd D for which there exists a map fh:C→D such that fh∣Bd C=h and fh−1(Bd D)=Bd C. In our view the presence of such a triple (C,D,h) suggests that C is "at least as wild as" $D…
WILD-SCAV benchmarks AI in complex 3D FPS environments.
problem Lack of complexity and diversity in RL environments.
method Developed a 3D open-world FPS game environment.
result Demonstrates effectiveness in benchmarking RL algorithms.
Extends Aff-Wild database for affect recognition in real-world settings.
problem Complex human emotional states in real-world settings.
method Developed deep neural architectures with attention mechanism for emotion recognition.
result Improved performance in emotion recognition using Aff-Wild2.
We apply a wild bootstrap method to the Lancaster three-variable interaction measure in order to detect factorisation of the joint distribution on three variables forming a stationary random process, for which the existing permutation bootstrap method fails. As in the i.i.d. case, the Lancaster test is found to outperf…
The paper constructs wild Cantor sets in high dimensions.
problem Embedding Cantor sets in high-dimensional spaces.
method Constructing embeddings of Cantor sets in \(\mathbb{R}^n\).
result Embeddings create pairwise wild Cantor sets that are ambiently incomparable.
HHAR-net uses neural networks to recognize human activities at different levels of abstraction.
problem Recognizing different layers of human activities concealed in behavior.
method Hierarchical classification with Neural Networks.
result 95.8% accuracy for low-level activities and 92.8% overall accuracy.
Algorithm describes Fourier transform of Stokes data at infinity.
problem Understanding the Fourier transform of Stokes data at infinity.
method Topological description and algorithmic approach using recent results and language of Stokes local systems.
result Explicit isomorphisms between wild character varieties are induced.