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Fei Hu

Publications and source records attributed to Fei Hu.

At least 55 records · Page 3Linked to original sources
arXiv2020

Height Gap Conjectures, $D$-Finiteness, and Weak Dynamical Mordell-Lang

In previous work, the first author, Ghioca, and the third author introduced a broad dynamical framework giving rise to many classical sequences from number theory and algebraic combinatorics. Specifically, these are sequences of the form $f(Φ^n(x))$, where $Φ\colon X\to X$ and $f\colon X\to\mathbb{P}^1$ are rational maps defined over $\overline{\mathbb{Q}}$ and $x\in X(\overline{\mathbb{Q}})$ is a point whose forward orbit avoids the indeterminacy loci of $Φ$ and $f$. They conjectured that if the sequence is infinite, then $\limsup \frac{h(f(Φ^n(x)))}{\log n} > 0$. They also made a corresponding conjecture for $\liminf$ and showed that it implies the Dynamical Mordell-Lang Conjecture. In this paper, we prove the $\limsup$ conjecture as well as the $\liminf$ conjecture away from a set of density $0$. As applications, we prove results concerning the growth rate of coefficients of $D$-finite power series as well as the Dynamical Mordell-Lang Conjecture up to a set of density $0$.

math.NT↗
arXiv2019

Diversifying Topic-Coherent Response Generation for Natural Multi-turn Conversations

Although response generation (RG) diversification for single-turn dialogs has been well developed, it is less investigated for natural multi-turn conversations. Besides, past work focused on diversifying responses without considering topic coherence to the context, producing uninformative replies. In this paper, we propose the Topic-coherent Hierarchical Recurrent Encoder-Decoder model (THRED) to diversify the generated responses without deviating the contextual topics for multi-turn conversations. In overall, we build a sequence-to-sequence net (Seq2Seq) to model multi-turn conversations. And then we resort to the latent Variable Hierarchical Recurrent Encoder-Decoder model (VHRED) to learn global contextual distribution of dialogs. Besides, we construct a dense topic matrix which implies word-level correlations of the conversation corpora. The topic matrix is used to learn local topic distribution of the contextual utterances. By incorporating both the global contextual distribution and the local topic distribution, THRED produces both diversified and topic-coherent replies. In addition, we propose an explicit metric (\emph{TopicDiv}) to measure the topic divergence between the post and generated response, and we also propose an overall metric combining the diversification metric (\emph{Distinct}) and \emph{TopicDiv}. We evaluate our model comparing with three baselines (Seq2Seq, HRED and VHRED) on two real-world corpora, respectively, and demonstrate its outstanding performance in both diversification and topic coherence.

cs.CL↗
arXiv2019

An Improved Historical Embedding without Alignment

Many words have evolved in meaning as a result of cultural and social change. Understanding such changes is crucial for modelling language and cultural evolution. Low-dimensional embedding methods have shown promise in detecting words' meaning change by encoding them into dense vectors. However, when exploring semantic change of words over time, these methods require the alignment of word embeddings across different time periods. This process is computationally expensive, prohibitively time consuming and suffering from contextual variability. In this paper, we propose a new and scalable method for encoding words from different time periods into one dense vector space. This can greatly improve performance when it comes to identifying words that have changed in meaning over time. We evaluated our method on dataset from Google Books N-gram. Our method outperformed three other popular methods in terms of the number of words correctly identified to have changed in meaning. Additionally, we provide an intuitive visualization of the semantic evolution of some words extracted by our method

cs.CL↗
arXiv2019

Model Asset eXchange: Path to Ubiquitous Deep Learning Deployment

A recent trend observed in traditionally challenging fields such as computer vision and natural language processing has been the significant performance gains shown by deep learning (DL). In many different research fields, DL models have been evolving rapidly and become ubiquitous. Despite researchers' excitement, unfortunately, most software developers are not DL experts and oftentimes have a difficult time following the booming DL research outputs. As a result, it usually takes a significant amount of time for the latest superior DL models to prevail in industry. This issue is further exacerbated by the common use of sundry incompatible DL programming frameworks, such as Tensorflow, PyTorch, Theano, etc. To address this issue, we propose a system, called Model Asset Exchange (MAX), that avails developers of easy access to state-of-the-art DL models. Regardless of the underlying DL programming frameworks, it provides an open source Python library (called the MAX framework) that wraps DL models and unifies programming interfaces with our standardized RESTful APIs. These RESTful APIs enable developers to exploit the wrapped DL models for inference tasks without the need to fully understand different DL programming frameworks. Using MAX, we have wrapped and open-sourced more than 30 state-of-the-art DL models from various research fields, including computer vision, natural language processing and signal processing, etc. In the end, we selectively demonstrate two web applications that are built on top of MAX, as well as the process of adding a DL model to MAX.

cs.LG↗
arXiv2019

A variant of the Mordell-Lang conjecture

The Mordell-Lang conjecture (proven by Faltings, Vojta and McQuillan) states that the intersection of a subvariety $V$ of a semiabelian variety $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$ with a finite rank subgroup $Γ\le G(\mathbb{k})$ is a finite union of cosets of subgroups of $Γ$. We explore a variant of this conjecture when $G$ is a product of an abelian variety $A$ defined over $\mathbb{k}$ with the additive group $\mathbb{G}_a$.

math.NT↗
arXiv2019

Higher arithmetic degrees of dominant rational self-maps

Suppose that $f \colon X \dashrightarrow X$ is a dominant rational self-map of a smooth projective variety defined over ${\overline{\mathbf Q}}$. Kawaguchi and Silverman conjectured that if $P \in X({\overline{\mathbf Q}})$ is a point with well-defined forward orbit, then the growth rate of the height along the orbit exists, and coincides with the first dynamical degree $λ_1(f)$ of $f$ if the orbit of $P$ is Zariski dense in $X$. In this note, we extend the Kawaguchi-Silverman conjecture to the setting of orbits of higher-dimensional subvarieties of $X$. We begin by defining a set of arithmetic degrees of $f$, independent of the choice of cycle, and we then develop the theory of arithmetic degrees in parallel to existing results for dynamical degrees. We formulate several conjectures governing these higher arithmetic degrees, relating them to dynamical degrees.

math.NT↗
arXiv2018

A Resource Pooling Switch Architecture with High Performance Scheduler

With the rapid development of network-based services and applications, current data plane solutions of network node, which focus on packets forwarding traditionally, are not optimally addressing new requirements such as function flexibility, performance expansibility and resource utilization, etc. In this paper, we propose a novel data plane structure called Resource Pooling Switch Architecture (RPSA), which utilizes global shared resource pool to provide different processing functionalities and capacities to different packets/flows. As all network functions are instantiated by the resources connected to the switching fabric and constructed in the form of Service Function Chains (SFC), the traffic patterns changed a lot. We design Balanced Service Capacity based FIRM algorithm (BSC-FIRM) to overcome the deficiencies of classical scheduler in RPSA. Simulation results show that our algorithm outperforms on the aspect of packet switching delay and loss rate compared with FIRM and iSLIP algorithm.

cs.NI↗
arXiv2018

Optimized Deployment of Network Function for Resource Pooling Switch

The disadvantages of the combination of traditional switches and middleboxes have being exposed under the condition of increasingly various network function demands,such as function flexibility, performance scalability and resource utilization. To solve this problem, we design Resource Pooling Switch Architecture (RPSA), which separates some non-essential functions from line card and allocate them in Network Function Pool (NFP) to provide flexible services for data plane in the form of Service Function Chains (SFC). As the performance of the whole system could be decided by whether function deployment is reasonable or not, we purpose heuristic algorithm called Modified Fiduccia-Mattheyses based Two Phase Algorithm (MFMTP) to optimize the deployment of functions. The simulation results show that this algorithm performs well in throughput and convergence.

cs.NI↗
arXiv2018

Density of orbits of endomorphisms of commutative linear algebraic groups

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $Φ\colon G\longrightarrow G$ is a dominant endomorphism, we prove that one of the following holds: either there exists a non-constant rational function $f\in \mathbb{k}(G)$ preserved by $Φ$ (i.e., $f\circ Φ= f$), or there exists a point $x\in G(\mathbb{k})$ whose $Φ$-orbit is Zariski dense in $G$.

math.NT↗
arXiv2017

Periodic subvarieties of a projective variety under the action of a maximal rank abelian group of positive entropy

We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy. The motivation of the paper is to understand the obstruction for X to be G-equivariant birational to the quotient variety of an abelian variety modulo the action of a finite group.

math.AG↗
arXiv2017

An silicon nanocrystal laser

Silicon lasers have been the most challenging element for the monolithic integrated Si photonics. Here we report the first successful all-Si laser at room temperature based on silicon nanocrystals (Si NCs) with high optical gains. The active Si NC layer was made from hydrogen silsesquioxane (HSQ) that had undergone a phase separation annealing, followed by high-pressure hydrogen passivation. Using the nanoimprint technique, a second-order Bragg grating was made on the active layer as the distributed feedback (DFB) laser cavity. This Si NC DFB laser device was optically pumped with femtosecond pulses. Criteria for lasing action, i.e., the threshold effect, the polarization dependence and the significant spectral narrowing of stimulated emission were evidently fulfilled, which indicated the realization of an all-Si laser.

physics.optics↗
arXiv2017

The dimension of automorphism groups of algebraic varieties with pseudo-effective log canonical divisors

Let $(X,D)$ be a log smooth pair of dimension $n$, where $D$ is a reduced effective divisor such that the log canonical divisor $K_X + D$ is pseudo-effective. Let $G$ be a connected algebraic subgroup of $\mathrm{Aut}(X,D)$. We show that $G$ is a semi-abelian variety of dimension $\le \min\{n-\barκ(V), n\}$ with $V := X\setminus D$. In the dimension two, Shigeru Iitaka claimed in his 1979 Osaka J. Math. paper that $\dim G\le \bar{q}(V)$ for a log smooth surface pair with $\barκ(V) = 0$ and $\bar{p}_g(V) = 1$. We (re)prove and generalize this classical result for all surfaces with $\barκ=0$ without assuming Iitaka's classification of logarithmic Iitaka surfaces or logarithmic $K3$ surfaces.

math.AG↗
arXiv2016

An image compression and encryption scheme based on deep learning

Stacked Auto-Encoder (SAE) is a kind of deep learning algorithm for unsupervised learning. Which has multi layers that project the vector representation of input data into a lower vector space. These projection vectors are dense representations of the input data. As a result, SAE can be used for image compression. Using chaotic logistic map, the compression ones can further be encrypted. In this study, an application of image compression and encryption is suggested using SAE and chaotic logistic map. Experiments show that this application is feasible and effective. It can be used for image transmission and image protection on internet simultaneously.

cs.CV↗
arXiv2016

A Fast Pseudo-Stochastic Sequential Cipher Generator Based on RBMs

Based on Restricted Boltzmann Machines (RBMs), an improved pseudo-stochastic sequential cipher generator is proposed. It is effective and efficient because of the two advantages: this generator includes a stochastic neural network that can perform the calculation in parallel, that is to say, all elements are calculated simultaneously; unlimited number of sequential ciphers can be generated simultaneously for multiple encryption schemas. The periodicity and the correlation of the output sequential ciphers meet the requirements for the design of encrypting sequential data. In the experiment, the generated sequential cipher is used to encrypt the image, and better performance is achieved in terms of the key space analysis, the correlation analysis, the sensitivity analysis and the differential attack. The experimental result is promising that could promote the development of image protection in computer security.

cs.CR↗
arXiv2015

Compact Kähler manifolds admitting large solvable groups of automorphisms

Let G be a group of automorphisms of a compact Kähler manifold X of dimension n and N(G) the subset of null-entropy elements. Suppose G admits no non-abelian free subgroup. Improving the known Tits alternative, we obtain that, up to replace G by a finite-index subgroup, either G/N(G) is a free abelian group of rank < n-1, or G/N(G) is a free abelian group of rank n-1 and X is a complex torus, or G is a free abelian group of rank n-1. If the last case occurs, X is G-equivariant birational to the quotient of an abelian variety provided that X is a projective manifold of dimension n > 2 and is not rationally connected. We also prove and use a generalization of a theorem by Fujiki and Lieberman on the structure of Aut(X).

math.AG↗