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.
Paper detects gradual changes in cluster structure using MC fusion.
Paper confirms MCS spaces are equivalent to CS sets.
Let be a non-compact geometrically finite hyperbolic 3-manifold without cusps of rank 1. The deformation space $\mc{H}$ of can be identified with the Teichmüller space $\mc{T}$ of the conformal boundary of as the graph of a section in $T^*\mc{T}$. We construct a Hermitian holomorphic line bundle $\mc{L}$ on…
New algebraic structures help categorify link invariants.
MC-CP combines adaptive MC dropout with conformal prediction for robust uncertainty quantification.
We determine the homogeneous Kähler diffeomorphism which expresses the Kähler two-form on the Siegel-Jacobi ball $\mc{D}^J_n=\C^n\times \mc{D}_n$ as the sum of the Kähler two-form on $\C^n$ and the one on the Siegel ball $\mc{D}_n$. The classical motion and quantum evolution on $\mc{D}^J_n$ determined by a hermiti…
We give a homological characterization of -manifolds whose universal covering $\Wi M$ has Gromov's macroscopic dimension $\dim_{mc}\Wi M<n$. As the result we distinguish from the macroscopic dimension defined by the author \cite{Dr}. We prove the inequality $\dim_{mc}\Wi M<\dim_{MC}\Wi M=n$ f…
A fast single-shot MC dropout method for neural networks.
Qualitative analysis of MC dropout for NN model uncertainty.
We study the structure of classical groups of equivalences for smooth multigerms , and extend several known results for monogerm equivalences to the case of mulitgerms. In particular, we study the group $\A$ of source- and target diffeomorphism germs, and its stabilizer $\A_f$. For monogerms $…
ADRL improves participant selection in MCS systems.
Proposes mCS for multivariate selection with FDR control.
Compressed Monte Carlo improves efficiency in Bayesian inference.
Let $π:\mc{X}\to \mc{T}$ be Teichmüller curve over Teichmüller space $\mc{T}$, such that the fiber $\mc{X}_z=π^{-1}(z)$ is exactly the Riemann surface given by the complex structure $z\in \mc{T}$. For a fixed Riemannian manifold and a continuous map $u_0: M\to \mc{X}_{z_0}$, let denote the energy function of…
CST-YOLO improves blood cell detection with YOLOv7 and CNN-Swin Transformer.
MC Dropout is re-evaluated as not Bayesian, affecting predictive posterior and multimodality.
MC-LSTM extends LSTM to conserve mass in neural networks.
Deep neural networks (DNNs) provide state-of-the-art results for a multitude of applications, but the approaches using DNNs for multimodal audiovisual applications do not consider predictive uncertainty associated with individual modalities. Bayesian deep learning methods provide principled confidence and quantify pred…
In this analytical study we derive the optimal unbiased value estimator (MVU) and compare its statistical risk to three well known value estimators: Temporal Difference learning (TD), Monte Carlo estimation (MC) and Least-Squares Temporal Difference Learning (LSTD). We demonstrate that LSTD is equivalent to the MVU if …
For a Legendrian knot L in R^3 with a chosen Morse complex sequence (MCS) we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MC…
This study compares MC and QMC methods for likelihood functions.
The sigma invariant is studied for torus, K3 surface, and 3d manifolds.
Let be a closed surface. By $\Homeo(M)$ we denote the group of orientation preserving homeomorphisms of and let $\MC(M)$ denote the Mapping class group. In this paper we complete the proof of the conjecture of Thurston that says that for any closed surface of genus $\g \ge 2$, there is no homomorphic sectio…
The complete part of the earthquake frequency-magnitude distribution (FMD), above completeness magnitude mc, is well described by the Gutenberg-Richter law. The parameter mc however varies in space due to the seismic network configuration, yielding a convoluted FMD shape below max(mc). This paper investigates the shape…
We prove that for 4-manifolds with residually finite fundamental group and non-spin universal covering $\Wi M$, the inequality $\dim_{mc}\Wi M\le 3$ implies the inequality $\dim_{mc}\Wi M\le 2$.
Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing "related" objects/phenomena. The first o…
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
Sensor fusion has wide applications in many domains including health care and autonomous systems. While the advent of deep learning has enabled promising multi-modal fusion of high-level features and end-to-end sensor fusion solutions, existing deep learning based sensor fusion techniques including deep gating architec…
Constructs Poisson structures on gauge orbits of Maurer-Cartan elements.
Proposes Fusion Recurrent Neural Network for sequence data.
MC-GMENN improves neural networks for clustered data using Monte Carlo methods.
Meta Fusion integrates various multimodal data fusion strategies into a unified framework.
Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…
Our understanding of reinforcement learning (RL) has been shaped by theoretical and empirical results that were obtained decades ago using tabular representations and linear function approximators. These results suggest that RL methods that use temporal differencing (TD) are superior to direct Monte Carlo estimation (M…
We propose a generalized class of multimodal fusion operators for the task of visual question answering (VQA). We identify generalizations of existing multimodal fusion operators based on the Hadamard product, and show that specific non-trivial instantiations of this generalized fusion operator exhibit superior perform…
For a fixed smooth map between two Riemann surfaces and with non-zero degree, we consider the energy function on Teichmüller space $\mc{T}$ of that assigns to a complex structure $t\in \mc{T}$ on the energy of the harmonic map homotopic to . We prove that the energy fun…
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional d…
Posterior refinement improves sample efficiency in Bayesian neural networks.
New insights into knot fusion numbers via cabling.
Existing Markov Chain Monte Carlo (MCMC) methods are either based on general-purpose and domain-agnostic schemes which can lead to slow convergence, or hand-crafting of problem-specific proposals by an expert. We propose A-NICE-MC, a novel method to train flexible parametric Markov chain kernels to produce samples with…
We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.
Bayesian Neural Networks improve uncertainty modeling in facial emotion recognition.
A new memory-based fusion layer improves multi-modal deep learning performance.
The excellent performance of representation learning of autoencoders have attracted considerable interest in various applications. However, the structure and multi-local collaborative relationships of unlabeled data are ignored in their encoding procedure that limits the capability of feature extraction. This paper pre…
Enhances uncertainty estimation in medical image segmentation.
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…
We show that for a sufficiently simple surface , a right-angled Artin group embeds into $\Mod(S)$ if and only if embeds into the curve graph $\mC(S)$ as an induced subgraph. When is sufficiently complicated, there exists an embedding $A(Γ)\to\Mod(S)$ for some not contained in $\mC(S)$.
Enhances uncertainty estimation in neural networks using Dirichlet-based MC Dropout.