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.
Gradient descent trains shallow neural networks to approximate functions in 1D.
problem Approximating functions in 1D with shallow neural networks trained by gradient descent.
method Gradient descent optimization of non-convex weight space for finite width networks in 1D.
result Gradient descent can approximate functions in 1D with a minimal number of weights, balancing practical performance and theoretical capabilities.
The paper studies a 1D diffusion equation with nonlinear Robin boundary conditions and finds conditions for global and finite time blow-up or blow-down.
problem Investigating the behavior of solutions to a specific diffusion equation with nonlinear Robin boundary conditions.
method Analyzing the Ricci flow on a cylinder and applying it to the diffusion equation.
result Conditions for global and finite time blow-up or blow-down of solutions.
REGS samples from unnormalized distributions using gradient flow and neural networks.
problem Sampling from unnormalized distributions with high accuracy and efficiency.
method REGS is a particle method that iteratively transforms samples from a reference distribution to match an unnormalized target distribution using Wasserstein gradient flow and neural networks.
result REGS outperforms state-of-the-art methods in sampling from challenging multimodal distributions and real datasets.
Soil texture is important for many environmental processes. In this paper, we study the classification of soil texture based on hyperspectral data. We develop and implement three 1-dimensional (1D) convolutional neural networks (CNN): the LucasCNN, the LucasResNet which contains an identity block as residual network, a…
Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in…
The Madelung transform is known to relate Schrödinger-type equations in quantum mechanics and the Euler equations for barotropic-type fluids. We prove that, more generally, the Madelung transform is a Kähler map (i.e. a symplectomorphism and an isometry) between the space of wave functions and the cotangent bundle to t…
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…
The Receptive Field (RF) size has been one of the most important factors for One Dimensional Convolutional Neural Networks (1D-CNNs) on time series classification tasks. Large efforts have been taken to choose the appropriate size because it has a huge influence on the performance and differs significantly for each dat…
Capsule networks excel in understanding spatial relationships in 2D data for vision related tasks. Even though they are not designed to capture 1D temporal relationships, with TimeCaps we demonstrate that given the ability, capsule networks excel in understanding temporal relationships. To this end, we generate capsule…
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulatio…
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present explicit solutions of the binormal equation in higher-dimensions that collapse in finite time. The local nature of this phenomenon suggests the appearance of singularity in nearb…
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is that when a nonparame…
In this paper, we introduce an inclined curves according to parallel transport frame. Also, we define a vector field called Darboux vector field of an inclined curve in and we give a new characterization such as: "α: I \subset R \rightarrow E^4 is an inclined curve \Leftrightarrow k_1 \int k_1ds + k_2 \int \k_2 +k_3ds …
Deep neural networks continue to show improved performance with increasing depth, an encouraging trend that implies an explosion in the possible permutations of network architectures and hyperparameters for which there is little intuitive guidance. To address this increasing complexity, we propose Evolutionary DEep Net…
This paper proposes a framework based on deep convolutional neural networks (CNNs) for automatic heart sound classification using short-segments of individual heart beats. We design a 1D-CNN that directly learns features from raw heart-sound signals, and a 2D-CNN that takes inputs of two- dimensional time-frequency fea…
This paper shows the susceptibility of spectrogram-based audio classifiers to adversarial attacks and the transferability of such attacks to audio waveforms. Some commonly used adversarial attacks to images have been applied to Mel-frequency and short-time Fourier transform spectrograms, and such perturbed spectrograms…
Self attention mechanisms have become a key building block in many state-of-the-art language understanding models. In this paper, we show that the self attention operator can be formulated in terms of 1x1 convolution operations. Following this observation, we propose several novel operators: First, we introduce a 2D ve…