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.
Random walks on Fuchsian Schottky groups have harmonic measures with lower dimension.
The study examines mass drop and multiplicity in mean curvature flow.
Lower Ricci curvature bound prevents first Betti number from dropping more than dimension in collapsing manifolds.
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an old question of Almgren. We also prove convexity of minimisers when the volume co…
We construct aspherical closed orientable 5-manifolds with perfect fundamental group. This completes part of our study (with D.H.Kochloukova and I.Lima) of -groups with pro- completion a pro- Poincaré duality group of dimension . We also consider the question of whether there are any examples wit…
Round balls minimize liquid drop model volumes ≤ 1.
The infinitesimal symmetry algebra of any Cartan geometry has maximum dimension realized by the flat model, but often this dimension drops significantly when considering non-flat geometries, so a gap phenomenon arises. For general (regular, normal) parabolic geometries of type (G,P), we use Tanaka theory to derive a un…
Empirical study shows GANs overfit and drop modes when training is deterministic.
Overfitting frequently occurs in deep learning. In this paper, we propose a novel regularization method called Drop-Activation to reduce overfitting and improve generalization. The key idea is to drop nonlinear activation functions by setting them to be identity functions randomly during training time. During testing, …
The paper examines stable CMC hypersurfaces with boundaries on parallel hyperplanes.
This paper analyzes the configurations of shapes that shows a spacelike liquid drop in Minkowski space deposited over a spacelike plane . We assume the presence of a uniform gravity field directed toward and that the volume of the drop is prescribed. Our interest are the liquid drops that are critical points of …
Deep neural networks have dramatically achieved great success on a variety of challenging tasks. However, most successful DNNs have an extremely complex structure, leading to extensive research on model compression.As a significant area of progress in model compression, traditional gradual pruning approaches involve an…
A new method compresses NLP networks by using multiple subspaces instead of a single one.
Low-entropy surfaces can be flowed into spheres and cylinders.
Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that the difficulties of various input samples being correctly classified are different…
Paper resolves Huisken's conjecture without strict genus drop theorem.
Study on liquidation games with market drop-out, proving unique equilibria.
DreamPropeller accelerates text-to-3D generation by 4.7x with minimal loss in quality.
This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception…
RDIS fills missing values in time series data explicitly.
The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method …
Study on minimizing singular capillary cones with stability and instability results.
Study connects hyperbolic geometry to membrane shapes.
In this paper we compare market price fluctuations with the response to fundamental price drops within the Lux-Marchesi model which is able to reproduce the most important stylized facts of real market data. Major differences can be observed between the decay of spontaneous fluctuations and of changes due to external p…
Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems where two consecutive rigid pieces are connected by a hinge, that is, a codimension…
In this project we further investigate the idea of reducing the dimensionality of datasets using a Borel isomorphism with the purpose of subsequently applying supervised learning algorithms, as originally suggested by my supervisor V. Pestov (in 2011 Dagstuhl preprint). Any consistent learning algorithm, for example kN…
Enhances time-series modeling by dropping patches, improving efficiency and adaptability.
Study reveals statistical bias in dataset replication, reducing accuracy drop from 11-14% to 3.6%.
Out-of-distribution (OOD) detection approaches usually present special requirements (e.g., hyperparameter validation, collection of outlier data) and produce side effects (e.g., classification accuracy drop, slower energy-inefficient inferences). We argue that these issues are a consequence of the SoftMax loss anisotro…
The study of heavy-tailed distributions in economic and financial systems has been widely addressed since financial time series has become a research subject.After the eighties, several "highly improbable" market drops were observed (e.g. the 1987 stock market drop known as "Black Monday" and on even more recent ones, …
Study on stability of 3D sessile drops, identifying degenerate kernel.
We study the long time existence theory for a non local flow associated to a free boundary problem for a trapped non liquid drop. The drop has free boundary components on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially symmetric initial surfaces with sufficiently large volume…
MsIGN tackles high-dimensional Bayesian inference using multiscale structure.
In this paper we study the learnability of deep random networks from both theoretical and practical points of view. On the theoretical front, we show that the learnability of random deep networks with sign activation drops exponentially with its depth. On the practical front, we find that the learnability drops sharply…
Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$, we get an almost hermitian manifold $(M, \om, …
Dropping a tiny fraction of preferences can significantly alter the rankings of top LLMs.
Transformers exhibit abrupt learning in matrix completion tasks.
Dropout as a common regularizer to prevent overfitting in deep neural networks has been less effective in convolutional layers than in fully connected layers. This is because Dropout drops features randomly, without considering local structure. When features are spatially correlated, as in the case of convolutional lay…
New metrics reveal oversmoothing in GNNs more accurately than traditional methods.
Deep neural networks are vulnerable against adversarial examples. In this paper, we propose to train and test the networks with randomly subsampled images with high drop rates. We show that this approach significantly improves robustness against adversarial examples in all cases of bounded L0, L2 and L_inf perturbation…
Algorithm corrects bias in classification data.
Machine learning is currently dominated by largely experimental work focused on improvements in a few key tasks. However, the impressive accuracy numbers of the best performing models are questionable because the same test sets have been used to select these models for multiple years now. To understand the danger of ov…
Drop-Muon updates only some layers, speeding up training.
We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results…
Dropout has proven to be an effective technique for regularization and preventing the co-adaptation of neurons in deep neural networks (DNN). It randomly drops units with a probability during the training stage of DNN. Dropout also provides a way of approximately combining exponentially many different neural networ…
System predicts HIV patients at risk of dropping out of care.
This paper develops dimension-agnostic inference methods for high-dimensional data.
A possible evolution of a compact hypersurface in R^n by mean curvature past singularities is defined via the level set flow. In the case that the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. We obtain as a conse…