arXiv research

New approach to convex hulls for low-rank problems.

This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of algebraic geometry, to characterize the decision boundaries of a simple network of the form (Affine, Re…

Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.

The predominant paradigm for using machine learning models on a device is to train a model in the cloud and perform inference using the trained model on the device. However, with increasing number of smart devices and improved hardware, there is interest in performing model training on the device. Given this surge in i…

This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.

Fairness is becoming a rising concern w.r.t. machine learning model performance. Especially for sensitive fields such as criminal justice and loan decision, eliminating the prediction discrimination towards a certain group of population (characterized by sensitive features like race and gender) is important for enhanci…

A general graph-structured neural network architecture operates on graphs through two core components: (1) complex enough message functions; (2) a fixed information aggregation process. In this paper, we present the Policy Message Passing algorithm, which takes a probabilistic perspective and reformulates the whole inf…

New approach uses FBSDE to sample complex distributions.

Transformers reduce redundancy by focusing on invariant relational quantities.

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the ext…

A theory of sufficient dimension reduction (SDR) is developed from an optimizational perspective. In our formulation of the problem, instead of dealing with raw data, we assume that our ground truth includes a mapping ${\mathbf f}: {\mathbb R}^n\rightarrow {\mathbb R}^m$ and a probability distribution function $p$ over…

In this paper, by using the regulator map of Beilinson-Deligne on a curve, we show that the quantization condition posed by Gukov is true for the SL_2(C) character variety of the hyperbolic knot in S^3. Furthermore, we prove that the corresponding $\mathbb{C}^{*}$-valued closed 1-form is a secondary characteristic clas…

We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several e…

Recently, a unified model for image-to-image translation tasks within adversarial learning framework has aroused widespread research interests in computer vision practitioners. Their reported empirical success however lacks solid theoretical interpretations for its inherent mechanism. In this paper, we reformulate thei…

ProPublica's analysis of recidivism predictions produced by Correctional Offender Management Profiling for Alternative Sanctions (COMPAS) software tool for the task, has shown that the predictions were racially biased against African American defendants. We analyze the COMPAS data using a causal reformulation of the un…

Marchal's lemma is the basic tool for eliminating collisions when using the direct method of the calculus of variations to establish existence of "designer" solutions to the classical N-body problem. Our goal here is to understand why Marchal's lemma holds, by taking a metric geometry perspective and employing the Jaco…

The paper reformulates Legendrian contact homology using string topology.

Study of tractor bundles and spacelike immersions in Lorentzian manifolds.

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an l0-norm penalty. Exactly enforcing the l0-no…

Reformulated Markov's conjecture in combinatorial terms.

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper…

In this paper, we reformulate the forest representation learning approach as an additive model which boosts the augmented feature instead of the prediction. We substantially improve the upper bound of generalization gap from $\mathcal{O}(\sqrt\frac{\ln m}{m})$ to $\mathcal{O}(\frac{\ln m}{m})$, while $λ$ - the margin r…

After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample and similar counterexamples in the light of the reformulated conjecture.

We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce pri…

Understanding the flow of information in Deep Neural Networks (DNNs) is a challenging problem that has gain increasing attention over the last few years. While several methods have been proposed to explain network predictions, there have been only a few attempts to compare them from a theoretical perspective. What is m…

A new GAN framework teaches models to avoid undesirable data.

We reformulate LIPs as min-max problems for easier solution.

Overparameterized MLR fits hyper-curves, improving model robustness.

The paper bounds generalization error for iterative learning with bounded updates.

New framework for DNN training guarantees convergence to global minimum.

New method learns dynamics from sparse data using geometric constraints.

Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.

Virtual index cocycles reformulate virtual link invariants.

A new method solves complex financial problems using deep learning.

DNNs with $L_{2}$ regularization reveal feature learning dynamics and sparsity.

Generative flow networks use RL to learn probabilistic models efficiently.

Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.

We reformulate data-dependent constraints to ensure they are always met with high probability.

We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and the essential surfaces that realize the slopes .For alternating knots the refor…

Novel optimization method detects change points in Gaussian data.

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physi…

We propose a method to efficiently learn diverse strategies in reinforcement learning for query reformulation in the tasks of document retrieval and question answering. In the proposed framework an agent consists of multiple specialized sub-agents and a meta-agent that learns to aggregate the answers from sub-agents to…

A restricted Boltzmann machine (RBM) is a two-layer neural network with shared weights and has been extensively studied for dimensionality reduction, data representation and recommendation systems in the literature. The traditional RBM requires a probabilistic interpretation of the values on both layers and a Markov ch…

This paper analyzes the multi-armed bandit problem using frequency-domain methods.

New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.

Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. Reinforcement learning such as policy gradient addresses the issue but can have prohibitively poor exploration …

Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern-Simons form, as well as a new formula…

Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.