arXiv research

LESS combines local predictors for subsets to learn from heterogeneous input-output pairs.

Constructs diffeological moduli stacks for Higgs and flat bundles on Kähler manifolds

We use Morse theory to prove that the Lefschetz Hyperplane Theorem holds for compact smooth Deligne-Mumford stacks over the site of complex manifolds. For $Z \subset X$ a hyperplane section, $X$ can be obtained from $Z$ by a sequence of deformation retracts and attachments of high-dimensional finite disc quotients. We …

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 …

The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression problems. We propose two extensions to the standard stacking approach. In the fir…

This paper demonstrates how to apply machine learning algorithms to distinguish good stocks from the bad stocks. To this end, we construct 244 technical and fundamental features to characterize each stock, and label stocks according to their ranking with respect to the return-to-volatility ratio. Algorithms ranging fro…

Study on Čech-de Rham obstruction in diffeological spaces.

Develops connections and Chern-Weil theory for Lie groupoids.

Classifies singular foliations of a specific type and studies their extensions.

The paper evaluates company investment value using machine learning models.

Stacking is a general approach for combining multiple models toward greater predictive accuracy. It has found various application across different domains, ensuing from its meta-learning nature. Our understanding, nevertheless, on how and why stacking works remains intuitive and lacking in theoretical insight. In this …

We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which are algebraic objects) and large stacks (which are generalized spaces).

In this article, we derive many properties of étale stacks in various contexts, and prove that étale stacks may be characterized categorically as those stacks that arise as prolongations of stacks on a site of spaces and local homeomorphisms. Moreover, we show that the bicategory of étale differentiable stacks and loca…

The paper explores MMPR to select diverse models for scientific insight.

In biomedical research, many different types of patient data can be collected, such as various types of omics data and medical imaging modalities. Applying multi-view learning to these different sources of information can increase the accuracy of medical classification models compared with single-view procedures. Howev…

Proves properties of complex algebraic varieties and local systems.

Constructs cohomology decompositions for symmetric stacks.

New neural stack and Turing Machine architectures prove stability and computational power.

Bayesian stacking improves model performance with varying model weights.

Paper combines machine learning and model averaging for robust parameter estimation.

We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an étale topological or differentiable stack. We then provide a construction analogous to the étalé space construction in this context, establishing an equivalence of 2-categori…

MSB framework improves survival prediction in immunotherapy patients with missing data.

This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks $[M/G]$, where $M$ is a smooth manifold equipped with a smooth proper action by a Lie group $G$. The characterization is described in terms of the action of the connected componen…

The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.

Stacked conformal prediction simplifies model validation.

Constructs moduli stacks for quiver connections and extends non-Abelian Hodge theory.

Study connections on Lie groupoids and stacks using Atiyah sequences.

In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, as well as the "underlying" diffeological space of any stack. More precisely, we consider diffeological spaces as so-called concrete sheaves and show that the Grothendieck construction sending these sheaves to stacks has a left…

Constructs moduli stacks of quiver bundles and applies to Higgs bundles.

New potentials found for sheaves on Calabi-Yau 4-folds.

We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory Units (Tree-SMU) to enable strong compositional generalization. Tree-SMU is a recurs…

This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between the bicategory of internal groupoids and the bicategory of geometric stacks. The s…

Stacked LSTM networks improve traffic volume forecasting.

Studies geometric structures on Lie groupoids and differentiable stacks.

Stacking improves deep neural network training efficiency.

A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toen and Vezzosi, on the site of dg algebras whose cohomologies have finitely many generators in each degree. Stacks represented b…

Study moduli spaces of elliptic PDEs using derived $C^{\infty}$-geometry.

Stacking methods improve the prediction performance of regression models. A simple way to stack base regressions estimators is by combining them linearly, as done by \citet{breiman1996stacked}. Even though this approach is useful from an interpretative perspective, it often does not lead to high predictive power. We pr…

We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choo…

For a compact manifold M and a differentiable stack \cX presented by a Lie groupoid X, we show the Hom-stack Hom(M,\cX) is presented by a Fréchet-Lie groupoid Map(M,X) and so is an infinite-dimensional differentiable stack. We further show that if \cX is an orbifold, presented by a proper étale Lie groupoid, then Map(M…

We propose a novel stacked generalization (stacking) method as a dynamic ensemble technique using a pool of heterogeneous classifiers for node label classification on networks. The proposed method assigns component models a set of functional coefficients, which can vary smoothly with certain topological features of a n…

Paper proves stacking ensembling is effective and proposes a new family of stacked generalizations.

The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.

Researchers compute differential K-theory for moduli stacks.

In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold encodes the dynamics up to conjugation and inversion. We also prove a generaliz…

We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie algebroids. Cofoliations on stacks arise from flat connections on groupoids. Connecti…

Let $\mathcal{G}$ be a Lie groupoid. The category $B\mathcal{G}$ of principal $\mathcal{G}$-bundles defines a differentiable stack. On the other hand, given a differentiable stack $\mathcal{D}$, there exists a Lie groupoid $\mathcal{H}$ such that $B\mathcal{H}$ is isomorphic to $\mathcal{D}$. Define a gerbe over a stac…

Proves a stack of G-bundles with logarithmic connections is finite type.