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arXiv research

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.

169,042 papers · 148 categories

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285785113 · Jun 202019922001200920172026
48 results for fixed-size encoding

A method to uniformly sample graph-encoded surfaces of fixed size.

problem Sampling uniformly from combinatorial isomorphism types of balanced triangulations of surfaces.
method Relies on connections between graph-encoded surfaces and permutations, and basic properties of the symmetric group.
result Empirical mean genus of the sample is very close to a specific formula as nn increases.

Deep neural networks can approximate complex functions through repeated compositions of a fixed-size ReLU network.

problem Understanding the expressive power of deep neural networks through function compositions.
method Demonstrated the surprising expressive power of repeated compositions of a single fixed-size ReLU network.
result Repeated compositions of a single fixed-size ReLU network can approximate 1-Lipschitz continuous functions on [0,1]d[0,1]^d with an error O(r1/d)\mathcal{O}(r^{-1/d}).

In Statistical Learning, the Vapnik-Chervonenkis (VC) dimension is an important combinatorial property of classifiers. To our knowledge, no theoretical results yet exist for the VC dimension of edited nearest-neighbour (1NN) classifiers with reference set of fixed size. Related theoretical results are scattered in the …

2019-02-07abs ↗pdf ↗

Unsupervised model learns word and context embeddings from character sequences.

problem Learning meaningful word and context embeddings from unlabeled data.
method Character-aware neural architecture that jointly learns word and context embeddings.
result Compact encoders achieve high performance in downstream tasks.

MeshfreeFlowNet generates high-resolution spatio-temporal solutions from low-resolution inputs.

problem Generating high-resolution spatio-temporal solutions from low-resolution inputs.
method Physics-constrained deep learning framework using fully convolutional encoders.
result Significantly outperforms existing baselines in super-resolution of turbulent flows.

New findings show modern neural networks have finite sample complexity in o-minimal structures.

problem Understanding the learnability of modern neural networks in a broad context.
method Analyzing feedforward neural networks definable in o-minimal structures.
result Modern neural networks, including MLPs, CNNs, GNNs, and transformers, have finite sample complexity in the agnostic PAC setting.

In this paper, we study the global geometry of complete, constant mean curvature hypersurfaces embedded in n-manifolds. More precisely, we give conditions that imply properness of such surfaces and prove the existence of fixed size one-sided regular neighborhoods for certain constant mean curvature hypersurfaces in cer…

2010-02-26abs ↗pdf ↗

New model generates realistic single-cell gene expression data.

problem Generating realistic single-cell gene expression profiles is challenging.
method scLDM, a latent diffusion model using Diffusion Transformers and linear interpolants.
result Superior performance in generating realistic single-cell gene expression data.

Introduces Spectral Attention for better long-range time series forecasting.

problem Challenges in capturing long-range dependencies in time series forecasting.
method Spectral Attention mechanism that preserves temporal correlations and long-range dependencies.
result Achieves state-of-the-art results on 11 real-world time series datasets.

MR-GNN predicts interactions between structured entities using multi-resolution and dual graph neural networks.

problem Predicting interactions between structured entities, especially considering features in substructures of different sizes and interactions between entities.
method MR-GNN uses a multi-resolution architecture and dual graph-state L-STMs to extract features from different neighborhoods and pairwise graphs, respectively.
result MR-GNN improves prediction accuracy compared to state-of-the-art methods.

Capsule Neural Networks classify graphs from categorical features and relationships.

problem Graph classification in scientific domains, especially with varying graph sizes and features.
method Explicit tensor representations, Capsule Network for classification.
result Capsule Network model performs competitively with state-of-the-art models.

The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-b…

1999-03-08abs ↗pdf ↗

OMD monitors stock market dynamics through matrix trajectories and reveals crisis patterns.

problem Understanding and predicting stock market crises and sector rotations.
method Applying OMD to S\&P 500 returns over three crises, analyzing distance matrices and their spectra.
result Market dynamics show coherent changes during crises, with distinct sector leadership.

OMD monitors stock market dynamics through matrix trajectories, revealing crisis patterns and sector rotations.

problem Understanding and predicting stock market dynamics during crises.
method Applying OMD to S&P 500 returns over three crises, analyzing distance matrices and their spectra.
result Market dynamics show coherent changes during crises, with sector-specific patterns and volatility clustering.

There are two important statements regarding the Trautman-Bondi mass [1,8,5] at null infinity: one is the positivity [7,6], and the other is the Bondi mass loss formula [1], which are both global in nature. The positivity of the quasi-local mass can potentially lead to a local description at null infinity. This is conf…

2016-08-22abs ↗pdf ↗

The ability to learn from a small number of examples has been a difficult problem in machine learning since its inception. While methods have succeeded with large amounts of training data, research has been underway in how to accomplish similar performance with fewer examples, known as one-shot or more generally few-sh…

2017-08-22abs ↗pdf ↗

GraphSW reduces training cost for GNN-based recommender models by selectively accessing graph features.

problem Training GNN-based recommender models on full KG is computationally expensive and impractical.
method GraphSW uses stage-wise training to access a subset of entities in the KG, gradually learning from higher-order features.
result GraphSW improves recommendation performance and helps models converge effectively in high-order features.

Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to rep…

2015-05-01abs ↗pdf ↗

Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provi…

2017-10-28abs ↗pdf ↗

Graph connection Laplacian (GCL) is a modern data analysis technique that is starting to be applied for the analysis of high dimensional and massive datasets. Motivated by this technique, we study matrices that are akin to the ones appearing in the null case of GCL, i.e the case where there is no structure in the datas…

2013-10-01abs ↗pdf ↗

SHMM models human mobility from GPS and text data, overcoming text sparsity.

problem Modeling human mobility from semantic trace data, especially addressing text sparsity.
method SHMM is a multi-modal spherical hidden Markov model that jointly models location, time, and text embeddings on a unit sphere using vMF distribution.
result SHMM outperforms state-of-the-art models in next location prediction and has lower training cost.

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine with typical machine learning workflows. In this paper we introduce persistence c…

2018-02-13abs ↗pdf ↗

Conformal prediction sets improve human decision making by quantifying model uncertainty.

problem Humans signal uncertainty and offer alternatives when unsure, but machine learning models often lack this feature.
method Conducted a randomized controlled trial with human subjects given conformal prediction sets.
result Human accuracy improves when given conformal prediction sets compared to fixed-size prediction sets.

The paper computes an approximation to the sample Frechet mean of graph sets using spectral information.

problem Characterizing the location of a set of graphs in a metric space.
method The Frechet mean is computed for sets of large graphs using the pseudometric defined by the norm between eigenvalues of adjacency matrices.
result An algorithm to approximate the sample Frechet mean of undirected unweighted graphs is described.

Graph convolutional network (GCN) is an emerging neural network approach. It learns new representation of a node by aggregating feature vectors of all neighbors in the aggregation process without considering whether the neighbors or features are useful or not. Recent methods have improved solutions by sampling a fixed …

2018-11-30abs ↗pdf ↗