arXiv subjects

William Chang

Publications and source records attributed to William Chang.

23 records · Page 2Linked to original sources

arXiv2022

Stochastic Couplings and Bijections from the Symmetric Group to Itself

Inspired by the Stochastic processes described by the Feller Coupling and Chinese Restaurant Processes, we create four different bijections from words in the set $[1]\times [2] \times\cdot \times[n]$ to $S_n$. We then compose these maps with their inverse to obtain a toal of six bijections $S_n \to S_n$. Following that, we investigate the fixed points ($1$-cycle) and higher $k$-cycles of these maps. We characterized some of their properties completely as well as empirically showing the complexity of the higher $k$-cycle structures for these maps.

math.CO↗

arXiv2022

Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations

Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously proposed morphological perceptrons use max-sum, in place of sum-product, node processing and have promising properties for circuit implementations. In this paper we show that these max-sum ANNs do not have universal approximation capabilities. Furthermore, we consider proposed signed-max-sum and max-star-sum generalizations of morphological ANNs and show that these variants also do not have universal approximation capabilities. We contrast these variations to log-number system (LNS) implementations which also avoid multiplications, but do exhibit universal approximation capabilities.

cs.LG↗

arXiv2022

Compatibility in Ozsvath-Szabo's bordered HFK via higher representations

We equip the basic local crossing bimodules in Ozsváth-Szabó's theory of bordered knot Floer homology with the structure of 1-morphisms of 2-representations, categorifying the $U_q(\mathfrak{gl}(1|1)^+)$-intertwining property of the corresponding maps between ordinary representations. Besides yielding a new connection between bordered knot Floer homology and higher representation theory in line with work of Rouquier and the second author, this structure gives an algebraic reformulation of a ``compatibility between summands'' property for Ozsváth-Szabó's bimodules that is important when building their theory up from local crossings to more global tangles and knots.

math.GT↗

arXiv2021

Online Learning for Cooperative Multi-Player Multi-Armed Bandits

We introduce a framework for decentralized online learning for multi-armed bandits (MAB) with multiple cooperative players. The reward obtained by the players in each round depends on the actions taken by all the players. It's a team setting, and the objective is common. Information asymmetry is what makes the problem interesting and challenging. We consider three types of information asymmetry: action information asymmetry when the actions of the players can't be observed but the rewards received are common; reward information asymmetry when the actions of the other players are observable but rewards received are IID from the same distribution; and when we have both action and reward information asymmetry. For the first setting, we propose a UCB-inspired algorithm that achieves $O(\log T)$ regret whether the rewards are IID or Markovian. For the second section, we offer an environment such that the algorithm given for the first setting gives linear regret. For the third setting, we show that a variation of the `explore then commit' algorithm achieves almost log regret.

cs.LG↗

arXiv2019

Toward Automatic Threat Recognition for Airport X-ray Baggage Screening with Deep Convolutional Object Detection

For the safety of the traveling public, the Transportation Security Administration (TSA) operates security checkpoints at airports in the United States, seeking to keep dangerous items off airplanes. At these checkpoints, the TSA employs a fleet of X-ray scanners, such as the Rapiscan 620DV, so Transportation Security Officers (TSOs) can inspect the contents of carry-on possessions. However, identifying and locating all potential threats can be a challenging task. As a result, the TSA has taken a recent interest in deep learning-based automated detection algorithms that can assist TSOs. In a collaboration funded by the TSA, we collected a sizable new dataset of X-ray scans with a diverse set of threats in a wide array of contexts, trained several deep convolutional object detection models, and integrated such models into the Rapiscan 620DV, resulting in functional prototypes capable of operating in real time. We show performance of our models on held-out evaluation sets, analyze several design parameters, and demonstrate the potential of such systems for automated detection of threats that can be found in airports.

cs.CV↗