arXiv subjects

Michael Lin

Publications and source records attributed to Michael Lin.

29 records · Page 2Linked to original sources

arXiv2020

Reflexive Banach spaces with all power-bounded operators almost periodic

We analyze the ergodic properties of power-bounded operators on a reflexive Banach space of the form "scalar plus compact-power", and show that they are almost periodic (all the orbits are conditionally compact). If such an operator is weakly mixing, then it is stable (its powers converge in the strong operator topology).Let X-ISP be the separable reflexive indecomposable Banach space constructed by Argyros and Motakis, in which every operator has an invariant subspace. We conclude that every power-bounded operator on a closed subspace of X-ISP is almost periodic.

math.FA↗

arXiv2020

Miniature Robot Path Planning for Bridge Inspection: Min-Max Cycle Cover-Based Approach

We study the problem of planning the deployments of a group of mobile robots. While the problem and formulation can be used for many different problems, here we use a bridge inspection as the motivating application for the purpose of exposition. The robots are initially stationed at a set of depots placed throughout the bridge. Each robot is then assigned a set of sites on the bridge to inspect and, upon completion, must return to the same depot where it is stored. The problem of robot planning is formulated as a rooted min-max cycle cover problem, in which the vertex set consists of the sites to be inspected and robot depots, and the weight of an edge captures either (i) the amount of time needed to travel from one end vertex to the other vertex or (ii) the necessary energy expenditure for the travel. In the first case, the objective function is the total inspection time, whereas in the latter case, it is the maximum energy expenditure among all deployed robots. We propose a novel algorithm with approximation ratio of $5 + ε$, where $0<ε<1$. In addition, the computational complexity of the proposed algorithm is shown to be $O\big( n^2+2^{m-1} n \log(n+k) \big)$, where $n$ is the number of vertices, and $m$ is the number of depots.

cs.DS↗

arXiv2020

Multi-modal Sentiment Analysis using Super Characters Method on Low-power CNN Accelerator Device

Recent years NLP research has witnessed the record-breaking accuracy improvement by DNN models. However, power consumption is one of the practical concerns for deploying NLP systems. Most of the current state-of-the-art algorithms are implemented on GPUs, which is not power-efficient and the deployment cost is also very high. On the other hand, CNN Domain Specific Accelerator (CNN-DSA) has been in mass production providing low-power and low cost computation power. In this paper, we will implement the Super Characters method on the CNN-DSA. In addition, we modify the Super Characters method to utilize the multi-modal data, i.e. text plus tabular data in the CL-Aff sharedtask.

cs.CL↗

arXiv2020

Joint and double coboundaries of commuting contractions

Let $T$ and $S$ be commuting contractions on a Banach space $X$. The elements of $(I-T)(I-S)X$ are called {\it double coboundaries}, and the elements of $(I-T)X \cap (I-S)X$ are called {\it joint cobundaries}. For $U$ and $V$ the unitary operators induced on $L_2$ by commuting invertible measure preserving transformations which generate an aperiodic $\mathbb Z^2$-action, we show that there are joint coboundaries in $L_2$ which are not double coboundaries. We prove that if $α$,$β\in (0,1)$ are irrational, with $T_α$ and $T_β$ induced on $L_1(\mathbb T)$ by the corresponding rotations, then there are joint coboundaries in $C(\mathbb T)$ which are not measurable double cobundaries (hence not double coboundaries in $L_1(\mathbb T)$).

math.DS↗

arXiv2019

Squared English Word: A Method of Generating Glyph to Use Super Characters for Sentiment Analysis

The Super Characters method addresses sentiment analysis problems by first converting the input text into images and then applying 2D-CNN models to classify the sentiment. It achieves state of the art performance on many benchmark datasets. However, it is not as straightforward to apply in Latin languages as in Asian languages. Because the 2D-CNN model is designed to recognize two-dimensional images, it is better if the inputs are in the form of glyphs. In this paper, we propose SEW (Squared English Word) method generating a squared glyph for each English word by drawing Super Characters images of each English word at the alphabet level, combining the squared glyph together into a whole Super Characters image at the sentence level, and then applying the CNN model to classify the sentiment within the sentence. We applied the SEW method to Wikipedia dataset and obtained a 2.1% accuracy gain compared to the original Super Characters method. For multi-modal data with both structured tabular data and unstructured natural language text, the modified SEW method integrates the data into a single image and classifies sentiment with one unified CNN model.

cs.CL↗

arXiv2019

SuperTML: Two-Dimensional Word Embedding for the Precognition on Structured Tabular Data

Tabular data is the most commonly used form of data in industry. Gradient Boosting Trees, Support Vector Machine, Random Forest, and Logistic Regression are typically used for classification tasks on tabular data. DNN models using categorical embeddings are also applied in this task, but all attempts thus far have used one-dimensional embeddings. The recent work of Super Characters method using two-dimensional word embeddings achieved the state of art result in text classification tasks, showcasing the promise of this new approach. In this paper, we propose the SuperTML method, which borrows the idea of Super Characters method and two-dimensional embeddings to address the problem of classification on tabular data. For each input of tabular data, the features are first projected into two-dimensional embeddings like an image, and then this image is fed into fine-tuned two-dimensional CNN models for classification. Experimental results have shown that the proposed SuperTML method had achieved state-of-the-art results on both large and small datasets.

cs.CV↗

arXiv2019

SuperCaptioning: Image Captioning Using Two-dimensional Word Embedding

Language and vision are processed as two different modal in current work for image captioning. However, recent work on Super Characters method shows the effectiveness of two-dimensional word embedding, which converts text classification problem into image classification problem. In this paper, we propose the SuperCaptioning method, which borrows the idea of two-dimensional word embedding from Super Characters method, and processes the information of language and vision together in one single CNN model. The experimental results on Flickr30k data shows the proposed method gives high quality image captions. An interactive demo is ready to show at the workshop.

cs.CL↗

arXiv2019

System Demo for Transfer Learning across Vision and Text using Domain Specific CNN Accelerator for On-Device NLP Applications

Power-efficient CNN Domain Specific Accelerator (CNN-DSA) chips are currently available for wide use in mobile devices. These chips are mainly used in computer vision applications. However, the recent work of Super Characters method for text classification and sentiment analysis tasks using two-dimensional CNN models has also achieved state-of-the-art results through the method of transfer learning from vision to text. In this paper, we implemented the text classification and sentiment analysis applications on mobile devices using CNN-DSA chips. Compact network representations using one-bit and three-bits precision for coefficients and five-bits for activations are used in the CNN-DSA chip with power consumption less than 300mW. For edge devices under memory and compute constraints, the network is further compressed by approximating the external Fully Connected (FC) layers within the CNN-DSA chip. At the workshop, we have two system demonstrations for NLP tasks. The first demo classifies the input English Wikipedia sentence into one of the 14 ontologies. The second demo classifies the Chinese online-shopping review into positive or negative.

cs.CL↗

arXiv2019

SuperChat: Dialogue Generation by Transfer Learning from Vision to Language using Two-dimensional Word Embedding and Pretrained ImageNet CNN Models

The recent work of Super Characters method using two-dimensional word embedding achieved state-of-the-art results in text classification tasks, showcasing the promise of this new approach. This paper borrows the idea of Super Characters method and two-dimensional embedding, and proposes a method of generating conversational response for open domain dialogues. The experimental results on a public dataset shows that the proposed SuperChat method generates high quality responses. An interactive demo is ready to show at the workshop.

cs.CL↗

arXiv2019

Twisty Takens: A Geometric Characterization of Good Observations on Dense Trajectories

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics. This can be used, for instance, to show that sliding window embeddings of periodic signals recover topological loops, and that sliding window embeddings of quasiperiodic signals recover high-dimensional torii. However, in spite of these motivating examples, Takens' theorem does not in general prescribe how to choose such an observation function given particular dynamics in a state space. In this work, we state conditions on observation functions defined on compact Riemannian manifolds, that lead to successful reconstructions for particular dynamics. We apply our theory and construct families of time series whose sliding window embeddings trace tori, Klein bottles, spheres, and projective planes. This greatly enriches the set of examples of time series known to concentrate on various shapes via sliding window embeddings, and will hopefully help other researchers in identifying them in naturally occurring phenomena. We also present numerical experiments showing how to recover low dimensional representations of the underlying dynamics on state space, by using the persistent cohomology of sliding window embeddings and Eilenberg-MacLane (i.e., circular and real projective) coordinates.

math.DS↗

arXiv2017

On modulated ergodic theorems

Let $T$ be a weakly almost periodic (WAP) linear operator on a Banach space $X$. A sequence of scalars $(a_n)_{n\ge 1}$ {\it modulates} $T$ on $Y \subset X$ if $\frac1n\sum_{k=1}^n a_kT^k x$ converges in norm for every $x \in Y$. We obtain a sufficient condition for $(a_n)$ to modulate every WAP operator on the space of its flight vectors, a necessary and sufficient condition for (weakly) modulating every WAP operator $T$ on the space of its (weakly) stable vectors, and sufficient conditions for modulating every contraction on a Hilbert space on the space of its weakly stable vectors. We study as an example modulation by the modified von Mangoldt function $Λ'(n):=\log n1_\mathbb P(n)$ (where $\mathbb P =(p_k)_{k\ge 1}$ is the sequence of primes), and show that, as in the scalar case, convergence of the corresponding modulated averages is equivalent to convergence of the averages along the primes $\frac1n\sum_{k=1}^n T^{p_k}x$. We then prove that for any contraction $T$ on a Hilbert space $H$ and $x \in H$, and also for every invertible $T$ with $\sup_{n \in \mathbb Z} \|T^n\| <\infty$ on $L^r(Ω,μ)$ ($1<r< \infty$) and $f \in L^r$, the averages along the primes converge.

math.FA↗