arXiv research

The paper analyzes Laplacian pyramids for extending and denoising discrete functions.

A novel approach for augmenting histopathological images by blending Gaussian-Laplacian pyramids.

Non-linear dimensionality reduction techniques such as manifold learning algorithms have become a common way for processing and analyzing high-dimensional patterns that often have attached a target that corresponds to the value of an unknown function. Their application to new points consists in two steps: first, embedd…

In recent years there has been a growing interest in image generation through deep learning. While an important part of the evaluation of the generated images usually involves visual inspection, the inclusion of human perception as a factor in the training process is often overlooked. In this paper we propose an altern…

Low level features like edges and textures play an important role in accurately localizing instances in neural networks. In this paper, we propose an architecture which improves feature pyramid networks commonly used instance segmentation networks by incorporating low level features in all layers of the pyramid in an o…

Pyramid Attention Networks improve image restoration by leveraging self-similarities across scales.

Simulation reveals relationships in stock market pyramid schemes.

A new pyramidal diffusion model speeds up image generation.

Single wide layer followed by a pyramidal structure ensures global convergence in deep networks.

We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition proper…

By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…

TP-AIS improves sampling efficiency over existing methods.

In this paper, we construct a pyramid Ricci flow starting with a complete Riemannian manifold $(M^n,g_0)$ that is PIC1, or more generally satisfies a lower curvature bound $K_{IC_1}\geq -α_0$. That is, instead of constructing a flow on $M\times [0,T]$, we construct it on a subset of space-time that is a union of parabo…

Study smoothings of ellipsoid intersections with singularities.

Improves speaker verification for variable-duration utterances using a feature pyramid module.

We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of $U_q(sl_2)$. We apply the same method to define Yokota's invariants, and we call these invariants Yokota type invariants. Then we propose a volume conjecture of t…

PyFi uses adversarial agents to train VLMs on financial image understanding.

SPF uses a hierarchical approach to efficiently emulate climate changes.

Enhances neural networks' robustness against adversarial samples without sacrificing clean sample generalization.

Pyramidal GNN combines RC and pooling for efficient graph embeddings.

We introduce a wavelet-domain functional analysis of variance (fANOVA) method based on a Bayesian hierarchical model. The factor effects are modeled through a spike-and-slab mixture at each location-scale combination along with a normal-inverse-Gamma (NIG) conjugate setup for the coefficients and errors. A graphical mo…

This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of age pyramid which evolves according to immigration and births. The virtue if t…

Biological neural network mimics CCA for multi-channel data.

PC-RNN reconstructs MRI images from undersampled data with more details.

The challenge of object categorization in images is largely due to arbitrary translations and scales of the foreground objects. To attack this difficulty, we propose a new approach called collaborative receptive field learning to extract specific receptive fields (RF's) or regions from multiple images, and the selected…

Many real-world time series, such as in health, have changepoints where the system's structure or parameters change. Since changepoints can indicate critical events such as onset of illness, it is highly important to detect them. However, existing methods for changepoint detection (CPD) often require user-specified mod…

GSANet improves semantic segmentation accuracy with selective and global attention.

In this paper, we propose a new pooling method called spatial pyramid encoding (SPE) to generate speaker embeddings for text-independent speaker verification. We first partition the output feature maps from a deep residual network (ResNet) into increasingly fine sub-regions and extract speaker embeddings from each sub-…

We construct a global homeomorphism from any 3D Ricci limit space to a smooth manifold, that is locally bi-Holder. This extends the recent work of Miles Simon and the second author, and we build upon their techniques. A key step in our proof is the construction of local "pyramid Ricci flows", existing on uniform region…

Hyperbolic links in thickened torus decompose into angled tetrahedra.

Remote Sensing Images from satellites have been used in various domains for detecting and understanding structures on the ground surface. In this work, satellite images were used for localizing parking spaces and vehicles in parking lots for a given parcel using an RCNN based Neural Network Architectures. Parcel shapef…

The predictions of the S&P 500 returns made in 2007 have been tested and the underlying models amended. The period between 2003 and 2008 should be described by the dependence of the S&P 500 stock market index on real GDP because the population pyramid was highly inaccurate. The 2008 trough and 2009 rally are well predi…

A family of algorithms for time series classification (TSC) involve running a sliding window across each series, discretising the window to form a word, forming a histogram of word counts over the dictionary, then constructing a classifier on the histograms. A recent evaluation of two of this type of algorithm, Bag of …

Study on convergence of transformed metric spaces as dimensions grow.

ADAVI tackles variational inference for large HBM models in neuroimaging.

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is the case as all local minima are close to being globally optimal. We show that thi…

MRCNet tackles crowd counting and density mapping in aerial imagery.

Defines vector Laplacian on statistical manifolds.

BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.

Paper introduces magnetic Hodge Laplacian for differential forms.

The paper extends Laplacian spectra approximations to vector bundles.

Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.

We present a machine learning-based approach to lossy image compression which outperforms all existing codecs, while running in real-time. Our algorithm typically produces files 2.5 times smaller than JPEG and JPEG 2000, 2 times smaller than WebP, and 1.7 times smaller than BPG on datasets of generic images across all …

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph $p$-Laplacian. Unlike the …

In the recent literature the important role of depth in deep learning has been emphasized. In this paper we argue that sufficient width of a feedforward network is equally important by answering the simple question under which conditions the decision regions of a neural network are connected. It turns out that for a cl…

The paper sets up eigenvalue comparison theorems for specific Laplacians on manifolds.

Extended bounds on small eigenvalues for pseudo-Laplacians on hyperbolic surfaces.