arXiv research

Rule induction explains neural network predictions globally.

We propose a method for finding alternate features missing in the Lasso optimal solution. In ordinary Lasso problem, one global optimum is obtained and the resulting features are interpreted as task-relevant features. However, this can overlook possibly relevant features not selected by the Lasso. With the proposed met…

Neural NMF discovers hierarchical topics in multilayer data.

LIME explanations can be uncertain, even for accurate models.

Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response var…

Proposes a new deep topic model using MBN and Lasso.

New method uses hypergraphs to improve semi-supervised learning accuracy.

Training a source model optimally for its own task is suboptimal for downstream transfer.

New algorithms speed up EMD computation by four orders of magnitude.

This paper proposes the continuous semantic topic embedding model (CSTEM) which finds latent topic variables in documents using continuous semantic distance function between the topics and the words by means of the variational autoencoder(VAE). The semantic distance could be represented by any symmetric bell-shaped geo…

Paper defends LSTM-based text classification models from backdoor attacks.

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed …

Tsetlin Machine improves text categorization accuracy and interpretability.

New attacks exploit transfer learning to misclassify text models.

The 20/60/20 rule improves risk management and portfolio optimization in finance.

For any positive integer r, we exhibit a knot Kr with (20 $\times$ 2 r--1 + 1) crossings whose Jones polynomial V (Kr) is equal to 1 mod-ulo 2 r. Our construction rests on a certain 20-crossing tangle T 20 which is undetectable by the Kauffman bracket polynomial pair mod 2.

Pareto's 80/20 rule follows a Gaussian distribution with twice the mean standard deviation.

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomp…

Proves Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings.

Enhances relational reasoning with multi-layer architecture.

Neural nets solve braid untangling up to length 20.

Deep Learning can significantly benefit cancer proteomics and genomics. In this study, we attempt to determine a set of critical proteins that are associated with the FLT3-ITD mutation in newly-diagnosed acute myeloid leukemia patients. A Deep Learning network consisting of autoencoders forming a hierarchical model fro…

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…

In Peña (2007), MCMC sampling is applied to approximately calculate the ratio of essential graphs (EGs) to directed acyclic graphs (DAGs) for up to 20 nodes. In the present paper, we extend that work from 20 to 31 nodes. We also extend that work by computing the approximate ratio of connected EGs to connected DAGs, of …

This paper is not ready for public consumption, as the last step (Figure 20) is incorrect.

For any discrete, torsion-free subgroup $Γ$ of $\mathrm{Sp}(n,1)$ (resp.\ $\mathrm{F}_4^{-20}$) with no parabolic elements, we prove that $H_{4n-1}(Γ;V)=0$ (resp.\ $H_i(Γ;V)=0$ for $i=13,14,15$) for any $Γ$--module $V$. The main technical advance is a new bound on the $p$--Jacobian of the barycenter map of Besson--Cour…

The early layers of a deep neural net have the fewest parameters, but take up the most computation. In this extended abstract, we propose to only train the hidden layers for a set portion of the training run, freezing them out one-by-one and excluding them from the backward pass. Through experiments on CIFAR, we empiri…

A graph is 2-apex if it is planar after the deletion of at most two vertices. Such graphs are not intrinsically knotted, IK. We investigate the converse, does not IK imply 2-apex? We determine the simplest possible counterexample, a graph on nine vertices and 21 edges that is neither IK nor 2-apex. In the process, we s…

This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20 (resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the number of essentially distinc…

DNM learns efficient representations of input data using deep neural maps.

The number of closed billiard trajectories in a rational-angled polygon grows quadratically in the length. This paper gives an analogue on K3 surfaces, by considering special Lagrangian tori. The analogue of the angle of a billiard trajectory is a point on a twistor sphere, and the number of directions admitting a spec…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $u_t=Δ_φ(u^p)$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the $m$-dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain gradient estimates which…

Study estimates risks of nuclear waste storage projects.

Germany's tax admin costs likely exceed 20% of total revenue, requiring system improvement.

The study classifies complex parallelisable nilmanifolds with unobstructed deformations.

We address the question of the growth of firm size. To this end, we analyze the Compustat data base comprising all publicly-traded United States manufacturing firms within the years 1974-1993. We find that the distribution of firm sizes remains stable for the 20 years we study, i.e., the mean value and standard deviati…

Maximal knotless graphs have at least 74% of their vertices' edges.

We study 3-valent maps $M_n(p,q)$ consisting of a ring of $n$ $q$-gons whose the inner and outer domains are filled by $p$-gons, for $p,q \ge 3$. We describe a domain in the space of parameters $p$, $q$, and $n$, for which such a map may exist. With four infinite sequences of maps - prisms $M_p(p \ge 3,4)$, $M_4(4,q \g…

The definition of deposit substitutes in Philippine tax law fails to consider the maturity of a debt instrument. This makes it possible for long-term bonds to be considered as deposit substitutes if they meet the 20-lender rule, taxable at 20% final tax. However, long-term debt instruments cannot realistically function…

The paper classifies natural almost Hermitian structures on Lie groups with minimal conformal leaves.

Paper introduces Arte-Blue Chip Index for diversifying portfolios with art investments.

Mirzakhani studied Riemann surfaces and their spaces.

Extended LSTMs improve volatility prediction by 20%.

DPM-Solver speeds up DPM sampling to 10-20 function evaluations.

Solves C^3 null gluing problem for Einstein vacuum equations.

Improved clustering speed for 20 clusters on CIFAR-100 dataset.

Hybrid framework predicts Arctic permafrost decline, risks infrastructure, and provides tools.