arXiv research

Neural surrogate predicts SPN rates from token trajectories.

In complex processes, various events can happen in different sequences. The prediction of the next event given an a-priori process state is of importance in such processes. Recent methods have proposed deep learning techniques such as recurrent neural networks, developed on raw event logs, to predict the next event fro…

Synthetic Petri Dish predicts neural architecture performance faster.

The paper studies almost complex torus manifolds using graphs and Hirzebruch genera, proving properties of their fixed points and cohomology.

SDE-Net quantifies uncertainty in deep nets using stochastic dynamics.

fSDE-Net generates time series with long-term memory using neural networks.

Learning to Optimize is a recently proposed framework for learning optimization algorithms using reinforcement learning. In this paper, we explore learning an optimization algorithm for training shallow neural nets. Such high-dimensional stochastic optimization problems present interesting challenges for existing reinf…

Delay-SDE-net models time series with memory and uncertainty, outperforming other models.

Improves model accuracy for neural nets in stochastic dynamics with partial prior knowledge.

Proposes a new deep learning model for uncertainty quantification and propagation.

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new empirical observations and theoretical results on both the optimization dynamics and…

Paper assesses GMMB in VAs using FST for accurate net liability calculations.

Proposes a new method to learn operators for stochastic problems using DeepONet with autoencoder.

Let $M$ be a manifold homotopy equivalent to the complex projective space $\C P^m$. Petrie conjectured that $M$ has standard total Pontrjagin class if $M$ admits a non-trivial action by $S^1$. We prove the conjecture for $m<12$ under the assumption that the action extends to a nice $Pin(2)$-action with fixed point. The…

Study on length spectrum of random hyperbolic 3-manifolds.

The paper clarifies the approximation of SGD with Ito SDEs for finite learning rates.

Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP)of arbitrary sets of the systems in such a Bayes net. I also derive ``conditional'' fluctuation theorems, gover…

Directly proves logarithmic systolic growth for all hyperbolic surfaces.

Study shows systole behavior changes significantly for large genus hyperbolic surfaces.

For G an almost-connected Lie group, we study G-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of G-invariant Riemannian metrics of positive scalar curvature. We prove a rigidity result for almost-complex manifolds, generalising Hattori's result…

APAC-Net solves high-dimensional stochastic MFGs using neural networks.

Classifies circle actions on 6D manifolds with 4 fixed points.

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales up kernel methods using a novel concept called "doubly stochastic functional grad…

Study on systole of random hyperbolic 3-manifolds, proving limit exists and calculating it.

Model assesses loan profitability under changing credit conditions.

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with boundary) with nonzero Euler characteristic, integral homology spheres. We prove that $Diff(X)$ is Jordan. This means that there exists a const…

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to th…

Optimizes gradual reduction of excess carbon emissions to net-zero.

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power …

In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. This work considers the diffusion limit of suc…

Estimates matrix trace optimization with statistical learning theory.

Modeling climate change costs with stochastic interest rates shows inequality, but funding abatement can reduce this.

In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called \textit{sigmoid-ADMM pair}), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of …

BCD Nets use variational inference to estimate DAGs with uncertainty.

Algorithm of multicurrency trading at the market of Forex is realized on the basis of nonlinear stochastic wavelets. The distinctive feature of the algorithm is the possibility of weakly- and strongly connected horizontal self-assemblies, as well as use of nested structures. On-line trading with eight currency couples …

Study on geodesics and eigenvalues on random hyperbolic surfaces with cusps.

NANSDE-Net models time series with memory using neural ARMA-type noise.

Automatic debiasing for causal and policy effects using Neural Nets and Random Forests.

We develop a scalable method for Bayesian neural networks with stochastic differential equations.

Mack-Net model combines Mack's model with RNNs for better insurance liability estimation.

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracl…

Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by switching between centered and differentiable non-centered parameterizations of …

This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to construct a kind of geometric composition series of projective embeddings. The concept of "geometric composition series" is…

LGS-Net improves NCO performance on combinatorial optimization tasks.

Study on random hyperbolic surfaces with many cusps, focusing on tight geodesics.

The paper explores discrete isothermic nets using checkerboard patterns in quadrilateral nets.

We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, $Q^*$-nets and conical…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks have a long history, recent advances have greatly improved their performance in…