Paper analyzes biases in video QA datasets, showing models can answer 37-48% questions correctly without multimodal context.
problem Question answering biases in video QA datasets can lead to model overfitting and poor generalization.
method Analyzed popular video question answering datasets, conducted ablation studies on biases from annotators and question types.
result Pretrained language models can answer 37-48% questions correctly without multimodal context, far exceeding random guess baseline.
Study realizes symplectic algebras and homotopy types on manifolds.
problem Realizing symplectic algebras and homotopy types on manifolds.
method Addressing questions on realizability of symplectic algebras and rational homotopy types by closed symplectic manifolds.
result Realization of symplectic algebras and homotopy types in various dimensions.
Two results on end spaces of infinite type surfaces, answering questions about their topology and equivalence.
problem Topology and equivalence of end spaces of infinite type surfaces.
method Examples and Tsankov's argument to show equivalence relation.
result Examples of infinite type surfaces with end spaces that are not self-similar but have a unique maximal type.
We discuss a question by Felix, Oprea, and Tanre concerning nonnegative curvature and (rational) homotopy type.
Study on compact and finite-type support in mapping class group homology.
problem Understanding non-trivial classes supported on compact or finite-type subsurfaces.
method Use of shiftable subsurfaces and homological stability for finite-type surfaces.
result Almost-complete answer for surfaces with positive genus, partial answer for zero genus.
Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.
problem Characterizing domains with Kähler-Einstein Bergman metrics.
method Asymptotics of derivatives of the Bergman kernel along critically tangent paths.
result Two-dimensional pseudoconvex domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.
We construct a family of right-angled Coxeter groups which provide counter-examples to questions about the stable boundary of a group, one-endedness of quasi-geodesically stable subgroups, and the commensurability types of right-angled Coxeter groups.
We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivati…
FactTest assesses LLM factuality with Type I error control.
problem Lack of rigorous factuality verification for LLMs.
method Formulates factuality testing as hypothesis testing, ensuring Type I and II error control.
result Improves model accuracy by over 40% in abstaining from unknown questions.
Classifies metric lines in Engel-type groups, a step towards solving sub-Riemannian manifold problems.
problem Classifying metric lines in Engel-type groups.
method Sequence method to study metric lines in jet space.
result Classified metric lines of Engel-type groups $\Eng(n)$.
We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties--current--form technique to J−nef genus 0 classes, we give affirmative answers of these two questions for all tamed almost complex structu…
Question classification (QC) is the primary step of the Question Answering (QA) system. Question Classification (QC) system classifies the questions in particular classes so that Question Answering (QA) System can provide correct answers for the questions. Our system categorizes the factoid type questions asked in natu…
Researchers solve a question about embedding knots into Legendrian structures.
problem Whether every fixed knot type and Legendrian representative have surjective homomorphisms.
method Study of Legendrian embeddings and smooth embeddings in (S3,ξstd) from a homotopical viewpoint. result Positive answer for infinitely many knot types in three main families, showing rigidity at higher homotopy levels.
G-SHAP generates multiple types of explanations for machine learning models.
problem Understanding model predictions and their differences across groups.
method Generalization of SHAP method to produce additional types of explanations.
result G-SHAP produces explanations for classification, intergroup differences, and model failure.
This paper provides many examples of Sbrana-Cartan hypersurfaces.
problem Existence of Sbrana-Cartan hypersurfaces in discrete class.
method Construction of hypersurfaces of hyperbolic and elliptic types.
result Abundance of examples of Sbrana-Cartan hypersurfaces of both types.
We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full automorphism groups.
Paper explores conditions for constructing new quasi-alternating links.
problem Applying construction method to non-alternating and opposite type tangles.
method Substituting quasi-alternating crossings with rational tangles of same type.
result Identifies conditions and specific tangles for construction validity.
Study Swan modules and homotopy types, resolving Wall and Dyer questions.
problem Homotopy classification of CW-complexes and Swan modules.
method Analysis of Swan modules and their stably free properties.
result Existence of non-free stably free Swan modules and implications for homotopy equivalence.
We discuss the cobordism type of spin manifolds with nonnegative sectional curvature. We show that in each dimension 4k≥12, there are infinitely many cobordism types of simply connected and nonnegatively curved spin manifolds. Moreover, we raise and analyze a question about possible cobordism obstructions to non…
Abstract: Shows nonexistence of Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.
problem Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.
method Constructs a metric on a compact manifold to demonstrate the nonexistence of Courant-type bounds.
result Provides a negative answer to the existence of Courant-type nodal domain bounds.
We propose a cost-effective framework for preference elicitation and aggregation under the Plackett-Luce model with features. Given a budget, our framework iteratively computes the most cost-effective elicitation questions in order to help the agents make a better group decision. We illustrate the viability of the fram…
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].
We show that compact, locally symmetric spaces of non-compact type have positive simplicial volume. This gives a positive answer to a question that was first raised by Gromov in 1982. We provide a summary of results that are known to follow from positivity of the simplicial volume.
The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3-braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect.
For a given free group F of arbitrary rank (possibly infinite), and its subgroup G, we address the question whether a lower central subgroup of G can contain a lower central subgroup of F. We show that the answer is no if G does not normally generate F. The question comes from a study of Hirzebruch-type inv…
Talked about the Veech group of a specific surface.
problem Identifying the Veech group of a translation surface of infinite type.
method Analyzing the golden ladder surface.
result Answered a question posed by Hooper and Treviño.
The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo (2006).
We prove a Davies type double integral estimate for the heat kernel H(y,t;x,l) under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow etc.. Moreover, we apply the Davies type estimate to provide a new proof of the Gaussian upper and lower bounds of H(y,t;x,l) which were firs…
Question-answering (QA) is certainly the best known and probably also one of the most complex problem within Natural Language Processing (NLP) and artificial intelligence (AI). Since the complete solution to the problem of finding a generic answer still seems far away, the wisest thing to do is to break down the proble…
In this article we construct a piecewise Euclidean, non-positively curved 2-complex for the 3-generator Artin groups of large type. As a consequence we show that these groups are biautomatic. A slight modification of the proof shows that many other Artin groups are also biautomatic. The general question (whether all Ar…
We study the homotopy types of complements of arrangements of n transverse planes in R^4, obtaining a complete classification for n <= 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R^4 is not determined by the cohomology ring, thereby …
We consider the question whether an orientable 5-manifold can be equipped with a rank two distribution of Cartan type and what 2-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle the topological part of this problem and present partial results concerning its ge…
We show that there is an one-to-one correspondence between resolutions (equivariant w.r.t. a Lie groupoid action) of a singular subset of a manifold, and substacks (of a certain type) of the differential stack associated to the Lie groupoid in question. In particular, we show how to build an equivariant resolution out …
In this note we compute low degree rational Pontryagin classes for every closed locally symmetric manifold of noncompact type. In particular, we answer the question: Which locally symmetric M have at least one nonzero Pontryagin class?
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces…
Question 2.6 of Bestvina's Questions in Geometric Group Theory asks whether every pair of boundaries of a given CAT(0) group G is cell-like equivalent. The question was posed by Bestvina shortly after the discovery, by Croke and Kleiner, of a CAT(0) group that admits multiple boundaries. Previously, it had been observe…
Study on faithfulness of Burau representation for Artin-Tits groups.
problem Determining faithfulness of Burau representation for Artin-Tits groups.
method Algorithmic approach based on categorical methods.
result Burau representation is not faithful in specific cases.
Study extends Nirenberg-Spencer's question to families of submanifolds.
problem Determine the germ of compact complex submanifolds in complex manifolds.
method Reformulate the question for families of submanifolds and their infinitesimal neighborhoods. Prove sufficient conditions for first-order neighborhoods and additional assumptions for submanifolds with nonzero vector fields.
result Affirmative answer to the reformulated question for certain submanifolds.
Question-answering (QA) data often encodes essential information in many facets. This paper studies a natural question: Can we get supervision from QA data for other tasks (typically, non-QA ones)? For example, {\em can we use QAMR (Michael et al., 2017) to improve named entity recognition?} We suggest that simply furt…
The term "interpretability" is oftenly used by machine learning researchers each with their own intuitive understanding of it. There is no universal well agreed upon definition of interpretability in machine learning. As any type of science discipline is mainly driven by the set of formulated questions rather than by d…
Minimal area of spun trefoil knot is found in 4D cubical space.
problem Finding the minimum area for a spun trefoil knot in 4D cubical space.
method Defined minimal area of cubical 2-knots, used isotopy to find minimum area for spun trefoil.
result Spun trefoil knot requires a specific minimal area in 4D cubical space.
Measures three types of noise in LLM evaluations.
problem Separating signal from noise in LLM experiments.
method Defined and measured three types of noise: prediction, data, and total noise. Proposed the all-pairs paired method for statistical power.
result Total noise level is characteristic and predictable across all model pairs.
We give an overview of how calculus of the embedding functor can be used for the study of long knots and summarize various results connecting the calculus approach to the rational homotopy type of spaces of long knots, collapse of the Vassiliev spectral sequence, Hochschild homology of the Poisson operad, finite type k…
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we reformulate the latter in multisymplectic terms. Furthermore, we investigate basic que…
Model improves BERT for answering multiple-choice questions in large texts.
problem Improving machine comprehension of large text corpora for question answering.
method Developed a model using BERT with a semantic similarity attention layer to extract key sentences.
result Outperforms leading models in MovieQA challenge with 87.79% test accuracy.
We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature.
When can one 3-manifold be transformed to another by a finite sequence of Dehn surgeries which are restricted to preserve the first homology of the manifolds ? What is the resulting equivalence relation on 3-manifolds ? What if the surgery circle is further restricted to lie more deeply in the lower central series of t…
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has a finite or infinite number of the discrete pectrum. In this paper, we will give a generalization of this lemma on Euclidean spaces to that…