arXiv research

In this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states exist. In the 2d case, we prove that the quantum layer over a convex surface whose…

We study the existence of monopole bound states saturating the BPS bound in N=2 supersymmetric Yang-Mills theories. We describe how the existence of such bound states relates to the topology of index bundles over the moduli space of BPS solutions. Using an $L^2$ index theorem, we prove the existence of certain BPS stat…

Improved bounds for eigenfunctions on hyperbolic surfaces found.

PAC-Bayesian bounds for stochastic LTI systems derived.

New method shows hidden state can significantly improve differential privacy in SGD.

We study the existence of D-brane bound states at threshold in Type II string theories. In a number of situations, we can reduce the question of existence to quadrature, and the study of a particular limit of the propagator for the system of D-branes. This involves a derivation of an index theorem for a family of non-F…

New method improves adversarial training robustness.

The paper analyzes variational autoencoders for state space models with risk bounds.

We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike robustness verification, which aims to verify that the prediction of a network is stabl…

New RL method handles large state-action spaces with complex models.

Algorithm learns diffusion processes with high-dimensional state spaces.

The problem of reinforcement learning in an unknown and discrete Markov Decision Process (MDP) under the average-reward criterion is considered, when the learner interacts with the system in a single stream of observations, starting from an initial state without any reset. We revisit the minimax lower bound for that pr…

The study bounds entanglement entropy for coherent states on Kähler manifolds.

New neural stack and Turing Machine architectures prove stability and computational power.

This paper improves reinforcement learning policies in a scalable way.

We present an algorithm based on the \emph{Optimism in the Face of Uncertainty} (OFU) principle which is able to learn Reinforcement Learning (RL) modeled by Markov decision process (MDP) with finite state-action space efficiently. By evaluating the state-pair difference of the optimal bias function $h^{*}$, the propos…

This work improves understanding of reinforcement learning state representations.

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…

Study non-asymptotic estimation bounds for LTI models with Gaussian noise.

Study shows depth improves generalization in deep learning models.

We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For any arbitrary structure, we derive problem-specific regret lower bounds satisfie…

Paper derives an error bound for stochastic LTI systems.

A new method for state estimation in state-space models using incomplete data.

New bounds show current methods overestimate system parameter errors.

We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then the mean curvature must be H=1. Moreover, in the 2-dimensional case we obtain th…

New empirical PAC-Bayes bound for Markov chains with finite state space.

The paper provides a theoretical justification for using stable SSM blocks in deep sequential models.

Study of bound states in quantum layers with confining potentials.

New framework for discrete-state diffusion models reduces sample complexity.

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.

This paper addresses the problem of online learning in a dynamic setting. We consider a social network in which each individual observes a private signal about the underlying state of the world and communicates with her neighbors at each time period. Unlike many existing approaches, the underlying state is dynamic, and…

Improved confidence bounds for linear logistic model with applications to bandits.

Kernel-UCBVI algorithm balances exploration and exploitation in metric state-action spaces.

Study shows sample complexity for learning optimal policies in SSP with generative model.

New algorithm for multi-player bandits without needing lower bounds or scaling inversely.

The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we d…

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, i…

Bounds on chemical reaction network relaxation rates using convex analysis.

Proves error bounds for state representation in RL using graph spectral features.

We tackle the problem of acting in an unknown finite and discrete Markov Decision Process (MDP) for which the expected shortest path from any state to any other state is bounded by a finite number $D$. An MDP consists of $S$ states and $A$ possible actions per state. Upon choosing an action $a_t$ at state $s_t$, one re…

We consider Markov Decision Processes (MDPs) where the rewards are unknown and may change in an adversarial manner. We provide an algorithm that achieves state-of-the-art regret bound of $O( \sqrt{τ(\ln|S|+\ln|A|)T}\ln(T))$, where $S$ is the state space, $A$ is the action space, $τ$ is the mixing time of the MDP, and $…

We determine when certain state cycles represent nontrivial Khovanov homology classes by analyzing features of the state graph. Using this method, we are able to produce hyperbolic knots with arbitrarily many diagonals containing nontrivial state cycle homology classes. This gives lower bounds on the Khovanov width of …

This paper optimizes MDP policies for efficient state aggregation.

New bounds for adaptive control in high dimensions without fixed state space.

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

The paper solves a consumption-investment problem with state-dependent lower bounds.

Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient…

New RL algorithm reduces regret in birth-death queueing problems.