arXiv research

System uses neural networks to prove program equivalence via rewrite rules.

Solves Merton's investment-consumption problem with certainty equivalent approach.

Deep learning solves dynamic programming with recursive utility.

CEFOL uses deep learning for dynamic programming with recursive utility.

MEC-IP uses IP to efficiently find MECs in BNs from observational data.

IReEn reveals functionality of black-box agents via iterative neural synthesis.

To save manual effort, developers often translate programs from one programming language to another, instead of implementing it from scratch. Translating application program interfaces (APIs) used in one language to functionally equivalent ones available in another language is an important aspect of program translation…

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recove…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …

New approach uses neural networks to learn program structure and parameters.

Supporting evidence for adaptive feature program across diverse models.

SOC-ICNN expands neural network representational capacity by using conic optimization.

The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the ana…

Develops exact convex optimization formulations for neural networks.

We construct examples of nonresolvable generalized $n$-manifolds, $n\geq 6$, with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed $n$-manifold. We further investigate the structure of generalized manifolds and present a program for understanding their topology.

TF-Coder simplifies tensor manipulation programming in TensorFlow.

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the …

Paper tackles robust optimization under uncertainty using nested distance.

This paper formalizes manifolds in positive characteristic varieties.

New algorithms improve submodular minimization via DC programming.

This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs). Specifically, we reformulate these combinatorial problems as equivalent MPECs by…

Enhances Bayesian learning with rule-based evolutionary techniques.

New method for natural policy gradients converges linearly.

We give examples illustrating the fact that the different space/time splittings of the tangent bundle of a semi-Riemannian spin manifold give rise to non-equivalent norms on the space of compactly supported sections of the spinor bundle, and as a result, to different completions. We give a necessary and sufficient cond…

Computer experiments reveal complex knots that don't simplify.

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…

New method for finding function correspondences in binary programs.

Investigates how rebalancing frequency and transaction costs affect log-optimal portfolios.

Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions …

Polynomial-time convex optimization for CNNs with ReLU activations.

Neural networks solve copositive programs, revealing insights into training problems.

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of…

This work addresses time inconsistency in risk measures and develops a dynamic programming principle for risk minimization problems.

New methods optimize sums of bivariate functions on finite domains.

We describe a calculus of moves for modifying a framed flow category without changing the associated stable homotopy type. We use this calculus to show that if two framed flow categories give rise to the same stable homotopy type of homological width at most three, then the flow categories are move equivalent. The proc…

Paper proves polynomial equivalence of quantum complexity metrics.

This work connects neural network training to convex optimization via the NTK.

We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then endogenously as full support martingale measures (instead of equivalent martingale…

In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied. In this paper, we introduce DSOS and SDSOS optimization as linear …

We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take …

Unified approach to DP problems using Gumbel distribution and variational Bayesian inference.

Unified framework for model- and value-optimistic reinforcement learning.

In this paper we study properties of the Markov trace ${\rm tr}_d$ and the specialized trace ${\rm tr}_{d,D}$ on the Yokonuma-Hecke algebras, such as behaviour under inversion of a word, connected sums and mirror imaging. We then define invariants for framed, classical and singular links through the trace ${\rm tr}_{d,…

Study the tradeoff between signal distortion and human perception over finite channels.

Mathematical study supports connection between 3D manifolds and modular tensor categories.

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…

Differentiable structure learning addresses DAGs with multiple global minimizers.

We extend Bar-Natan's cobordism based categorification of the Jones polynomial to virtual links. Our topological complex allows a direct extension of the classical Khovanov complex ($h=t=0$), the variant of Lee ($h=0,t=1$) and other classical link homologies. We show that our construction allows, over rings of characte…