A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
New equivalences found between subsampling and ridge regularization methods.
asp2vec learns dynamic node aspect distributions for better network embedding.
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in variational analysis for more than two decades while being largely underinvestigated. We …
Study optimal ridge regularization for out-of-distribution prediction.
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated separately. In this paper, we propose an approach to entangle these two aspects …
We study the order of tangency between two manifolds of same dimension and give that notion three quite different geometric interpretations. Related aspects of the order of tangency, e.g., regular separation exponents, are also discussed.
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls C1 boundary regularity. We examin…
We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the gen…
This paper studies several aspects of asymptotically hyperbolic Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness …
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…
Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a BN layer, and a nonlinear activation function. This basic network helps us unde…
We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler--Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calc…
Optimal ridge regularization computed iteratively from generative parameters.
Deep learning systems thrive on abundance of labeled training data but such data is not always available, calling for alternative methods of supervision. One such method is expectation regularization (XR) (Mann and McCallum, 2007), where models are trained based on expected label proportions. We propose a novel applica…
This report has several purposes. First, our report is written to investigate the reproducibility of the submitted paper On the regularization of Wasserstein GANs (2018). Second, among the experiments performed in the submitted paper, five aspects were emphasized and reproduced: learning speed, stability, robustness ag…
Aspect-Based Sentiment Analysis (ABSA) deals with the extraction of sentiments and their targets. Collecting labeled data for this task in order to help neural networks generalize better can be laborious and time-consuming. As an alternative, similar data to the real-world examples can be produced artificially through …
Dropout is a widely-used regularization technique, often required to obtain state-of-the-art for a number of architectures. This work demonstrates that dropout introduces two distinct but entangled regularization effects: an explicit effect (also studied in prior work) which occurs since dropout modifies the expected t…
Mixup improves model performance by interpolating random training examples.
KL regularization helps RL algorithms by implicitly averaging q-values.
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a no…
Study pentagon growth with laser-cut models.
This paper tackles the curse of dimensionality in semi-supervised learning using Laplacian regularization.
Paper shows regularization improves robustness in domain generalization.
Most of the work on interpretable machine learning has focused on designing either inherently interpretable models, which typically trade-off accuracy for interpretability, or post-hoc explanation systems, which lack guarantees about their explanation quality. We propose an alternative to these approaches by directly r…
For proper subsets U of {1,2,...,31} we define and construct U-regular isotopy invariants of the Carter-Rieger-Saito movies (representing knotted surfaces) and use these to show that there are ambient isotopic knotted surfaces represented by movies M1 and M2 for which movie-moves of type 31 are required to get from M1 …
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection on a line bundle and a section of another bundle constructed from and a spinor bundle on a given four-dimensional Riem…
We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any -dimensional complete non-compact boundary-free Riemannian manifold through the square Sobolev/Nash/logarithmic-Sobolev inequalities plus the rough and s…
Study shows SGD's generalization is not explained by implicit bias.
Unsupervised representation learning via generative modeling is a staple to many computer vision applications in the absence of labeled data. Variational Autoencoders (VAEs) are powerful generative models that learn representations useful for data generation. However, due to inherent challenges in the training objectiv…
Paper explores stability, regularization, and gradient flows for stochastic inverse problems.
A generative model with a disentangled representation allows for independent control over different aspects of the output. Learning disentangled representations has been a recent topic of great interest, but it remains poorly understood. We show that even for GANs that do not possess disentangled representations, one c…
New method smooths optimization for sparse regularization.
Evolutionary methods improve neural network loss functions, reducing overfitting.
Proposes tPARAFAC2 for tracking evolving patterns in time-evolving data.
Gradient descent dynamics in nonconvex models explained with universality.
In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function, which is specified based on prior domain-specific expertise to induce a desired st…
We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common theory, leading to novel methods for working with several important models of inter…
This paper tackles catastrophic forgetting in neural networks by providing a unified framework for regularization-based continual learning.
Enhances deep kernel learning with stochastic latent variables for better model regularization.
We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold …
A new method solves l1-regularized optimization problems efficiently and sparsely.
Proposes a method for ranking items across multiple aspects based on user feedback.
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and functional (smooth) aspects and may benefit from a regularization scheme that can captur…
Paper shows how to embed Möbius bands with many twists and small aspect ratios.
This paper categorizes and analyzes existing outlying aspect mining methods.