arXiv subjects

Ning Xie

Publications and source records attributed to Ning Xie.

72 records · Page 4Linked to original sources

arXiv2017

Relating Input Concepts to Convolutional Neural Network Decisions

Many current methods to interpret convolutional neural networks (CNNs) use visualization techniques and words to highlight concepts of the input seemingly relevant to a CNN's decision. The methods hypothesize that the recognition of these concepts are instrumental in the decision a CNN reaches, but the nature of this relationship has not been well explored. To address this gap, this paper examines the quality of a concept's recognition by a CNN and the degree to which the recognitions are associated with CNN decisions. The study considers a CNN trained for scene recognition over the ADE20k dataset. It uses a novel approach to find and score the strength of minimally distributed representations of input concepts (defined by objects in scene images) across late stage feature maps. Subsequent analysis finds evidence that concept recognition impacts decision making. Strong recognition of concepts frequently-occurring in few scenes are indicative of correct decisions, but recognizing concepts common to many scenes may mislead the network.

cs.LG↗

arXiv2017

Explaining Trained Neural Networks with Semantic Web Technologies: First Steps

The ever increasing prevalence of publicly available structured data on the World Wide Web enables new applications in a variety of domains. In this paper, we provide a conceptual approach that leverages such data in order to explain the input-output behavior of trained artificial neural networks. We apply existing Semantic Web technologies in order to provide an experimental proof of concept.

cs.AI↗

arXiv2016

Parallel Integer Polynomial Multiplication

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this new approach.

cs.SC↗

arXiv2015

Fourier Sparsity of GF(2) Polynomials

We study a conjecture called "linear rank conjecture" recently raised in (Tsang et al., FOCS'13), which asserts that if many linear constraints are required to lower the degree of a GF(2) polynomial, then the Fourier sparsity (i.e. number of non-zero Fourier coefficients) of the polynomial must be large. We notice that the conjecture implies a surprising phenomenon that if the highest degree monomials of a GF(2) polynomial satisfy a certain condition, then the Fourier sparsity of the polynomial is large regardless of the monomials of lower degrees -- whose number is generally much larger than that of the highest degree monomials. We develop a new technique for proving lower bound on the Fourier sparsity of GF(2) polynomials, and apply it to certain special classes of polynomials to showcase the above phenomenon.

cs.CC↗

arXiv2014

Sunflowers and Testing Triangle-Freeness of Functions

A function $f: \mathbb{F}_2^n \rightarrow \{0,1\}$ is triangle-free if there are no $x_1,x_2,x_3 \in \mathbb{F}_2^n$ satisfying $x_1+x_2+x_3=0$ and $f(x_1)=f(x_2)=f(x_3)=1$. In testing triangle-freeness, the goal is to distinguish with high probability triangle-free functions from those that are $\varepsilon$-far from being triangle-free. It was shown by Green that the query complexity of the canonical tester for the problem is upper bounded by a function that depends only on $\varepsilon$ (GAFA, 2005), however the best known upper bound is a tower type function of $1/\varepsilon$. The best known lower bound on the query complexity of the canonical tester is $1/\varepsilon^{13.239}$ (Fu and Kleinberg, RANDOM, 2014). In this work we introduce a new approach to proving lower bounds on the query complexity of triangle-freeness. We relate the problem to combinatorial questions on collections of vectors in $\mathbb{Z}_D^n$ and to sunflower conjectures studied by Alon, Shpilka, and Umans (Comput. Complex., 2013). The relations yield that a refutation of the Weak Sunflower Conjecture over $\mathbb{Z}_4$ implies a super-polynomial lower bound on the query complexity of the canonical tester for triangle-freeness. Our results are extended to testing $k$-cycle-freeness of functions with domain $\mathbb{F}_p^n$ for every $k \geq 3$ and a prime $p$. In addition, we generalize the lower bound of Fu and Kleinberg to $k$-cycle-freeness for $k \geq 4$ by generalizing the construction of uniquely solvable puzzles due to Coppersmith and Winograd (J. Symbolic Comput., 1990).

cs.DS↗

arXiv2014

Conditional Density Estimation with Dimensionality Reduction via Squared-Loss Conditional Entropy Minimization

Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challenging in high-dimensional space. A naive approach to coping with high-dimensionality is to first perform dimensionality reduction (DR) and then execute CDE. However, such a two-step process does not perform well in practice because the error incurred in the first DR step can be magnified in the second CDE step. In this paper, we propose a novel single-shot procedure that performs CDE and DR simultaneously in an integrated way. Our key idea is to formulate DR as the problem of minimizing a squared-loss variant of conditional entropy, and this is solved via CDE. Thus, an additional CDE step is not needed after DR. We demonstrate the usefulness of the proposed method through extensive experiments on various datasets including humanoid robot transition and computer art.

cs.LG↗

arXiv2014

A Many-core Machine Model for Designing Algorithms with Minimum Parallelism Overheads

We present a model of multithreaded computation, combining fork-join and single-instruction-multiple-data parallelisms, with an emphasis on estimating parallelism overheads of programs written for modern many-core architectures. We establish a Graham-Brent theorem for this model so as to estimate execution time of programs running on a given number of streaming multiprocessors. We evaluate the benefits of our model with four fundamental algorithms from scientific computing. In each case, our model is used to minimize parallelism overheads by determining an appropriate value range for a given program parameter; moreover experimentation confirms the model's prediction.

cs.DC↗

arXiv2013

Fourier sparsity, spectral norm, and the Log-rank conjecture

We study Boolean functions with sparse Fourier coefficients or small spectral norm, and show their applications to the Log-rank Conjecture for XOR functions f(x\oplus y) --- a fairly large class of functions including well studied ones such as Equality and Hamming Distance. The rank of the communication matrix M_f for such functions is exactly the Fourier sparsity of f. Let d be the F2-degree of f and D^CC(f) stand for the deterministic communication complexity for f(x\oplus y). We show that 1. D^CC(f) = O(2^{d^2/2} log^{d-2} ||\hat f||_1). In particular, the Log-rank conjecture holds for XOR functions with constant F2-degree. 2. D^CC(f) = O(d ||\hat f||_1) = O(\sqrt{rank(M_f)}\logrank(M_f)). We obtain our results through a degree-reduction protocol based on a variant of polynomial rank, and actually conjecture that its communication cost is already \log^{O(1)}rank(M_f). The above bounds also hold for the parity decision tree complexity of f, a measure that is no less than the communication complexity (up to a factor of 2). Along the way we also show several structural results about Boolean functions with small F2-degree or small spectral norm, which could be of independent interest. For functions f with constant F2-degree: 1) f can be written as the summation of quasi-polynomially many indicator functions of subspaces with \pm-signs, improving the previous doubly exponential upper bound by Green and Sanders; 2) being sparse in Fourier domain is polynomially equivalent to having a small parity decision tree complexity; 3) f depends only on polylog||\hat f||_1 linear functions of input variables. For functions f with small spectral norm: 1) there is an affine subspace with co-dimension O(||\hat f||_1) on which f is a constant; 2) there is a parity decision tree with depth O(||\hat f||_1 log ||\hat f||_0).

cs.CC↗

arXiv2012

Artist Agent: A Reinforcement Learning Approach to Automatic Stroke Generation in Oriental Ink Painting

Oriental ink painting, called Sumi-e, is one of the most appealing painting styles that has attracted artists around the world. Major challenges in computer-based Sumi-e simulation are to abstract complex scene information and draw smooth and natural brush strokes. To automatically find such strokes, we propose to model the brush as a reinforcement learning agent, and learn desired brush-trajectories by maximizing the sum of rewards in the policy search framework. We also provide elaborate design of actions, states, and rewards tailored for a Sumi-e agent. The effectiveness of our proposed approach is demonstrated through simulated Sumi-e experiments.

cs.LG↗

arXiv2012

Converting online algorithms to local computation algorithms

We propose a general method for converting online algorithms to local computation algorithms by selecting a random permutation of the input, and simulating running the online algorithm. We bound the number of steps of the algorithm using a query tree, which models the dependencies between queries. We improve previous analyses of query trees on graphs of bounded degree, and extend the analysis to the cases where the degrees are distributed binomially, and to a special case of bipartite graphs. Using this method, we give a local computation algorithm for maximal matching in graphs of bounded degree, which runs in time and space O(log^3 n). We also show how to convert a large family of load balancing algorithms (related to balls and bins problems) to local computation algorithms. This gives several local load balancing algorithms which achieve the same approximation ratios as the online algorithms, but run in O(log n) time and space. Finally, we modify existing local computation algorithms for hypergraph 2-coloring and k-CNF and use our improved analysis to obtain better time and space bounds, of O(log^4 n), removing the dependency on the maximal degree of the graph from the exponent.

cs.DS↗

arXiv2011

Space-efficient Local Computation Algorithms

Recently Rubinfeld et al. (ICS 2011, pp. 223--238) proposed a new model of sublinear algorithms called \emph{local computation algorithms}. In this model, a computation problem $F$ may have more than one legal solution and each of them consists of many bits. The local computation algorithm for $F$ should answer in an online fashion, for any index $i$, the $i^{\mathrm{th}}$ bit of some legal solution of $F$. Further, all the answers given by the algorithm should be consistent with at least one solution of $F$. In this work, we continue the study of local computation algorithms. In particular, we develop a technique which under certain conditions can be applied to construct local computation algorithms that run not only in polylogarithmic time but also in polylogarithmic \emph{space}. Moreover, these local computation algorithms are easily parallelizable and can answer all parallel queries consistently. Our main technical tools are pseudorandom numbers with bounded independence and the theory of branching processes.

cs.DS↗

arXiv2011

Fast Local Computation Algorithms

For input $x$, let $F(x)$ denote the set of outputs that are the "legal" answers for a computational problem $F$. Suppose $x$ and members of $F(x)$ are so large that there is not time to read them in their entirety. We propose a model of {\em local computation algorithms} which for a given input $x$, support queries by a user to values of specified locations $y_i$ in a legal output $y \in F(x)$. When more than one legal output $y$ exists for a given $x$, the local computation algorithm should output in a way that is consistent with at least one such $y$. Local computation algorithms are intended to distill the common features of several concepts that have appeared in various algorithmic subfields, including local distributed computation, local algorithms, locally decodable codes, and local reconstruction. We develop a technique, based on known constructions of small sample spaces of $k$-wise independent random variables and Beck's analysis in his algorithmic approach to the Lov{á}sz Local Lemma, which under certain conditions can be applied to construct local computation algorithms that run in {\em polylogarithmic} time and space. We apply this technique to maximal independent set computations, scheduling radio network broadcasts, hypergraph coloring and satisfying $k$-SAT formulas.

cs.DS↗

arXiv2010

Property Testing via Set-Theoretic Operations

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference of these two properties also testable? We initiate a systematic study of these basic set-theoretic operations in the context of property testing. As an application, we give a conceptually different proof that linearity is testable, albeit with much worse query complexity. Furthermore, for the problem of testing disjunction of linear functions, which was previously known to be one-sided testable with a super-polynomial query complexity, we give an improved analysis and show it has query complexity $O(1/\eps^2)$, where $\eps$ is the distance parameter.

cs.DS↗

arXiv2010

Separations of Matroid Freeness Properties

Properties of Boolean functions on the hypercube invariant with respect to linear transformations of the domain are among the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of linear-invariant properties called matroid freeness properties. These properties have been conjectured to essentially coincide with all testable linear-invariant properties, and a recent sequence of works has established testability for increasingly larger subclasses. One question left open, however, is whether the infinitely many syntactically different properties recently shown testable in fact correspond to new, semantically distinct ones. This is a crucial issue since it has also been shown that there exist subclasses of these properties for which an infinite set of syntactically different representations collapse into one of a small, finite set of properties, all previously known to be testable. An important question is therefore to understand the semantics of matroid freeness properties, and in particular when two syntactically different properties are truly distinct. We shed light on this problem by developing a method for determining the relation between two matroid freeness properties P and Q. Furthermore, we show that there is a natural subclass of matroid freeness properties such that for any two properties P and Q from this subclass, a strong dichotomy must hold: either P is contained in Q or the two properties are "well separated." As an application of this method, we exhibit new, infinite hierarchies of testable matroid freeness properties such that at each level of the hierarchy, there are functions that are far from all functions lying in lower levels of the hierarchy. Our key technical tool is an apparently new notion of maps between linear matroids, called matroid homomorphisms, that might be of independent interest.

cs.CC↗

arXiv2009

Testing Linear-Invariant Non-Linear Properties

We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for "triangle freeness": a function $f:\cube^{n}\to\cube$ satisfies this property if $f(x),f(y),f(x+y)$ do not all equal 1, for any pair $x,y\in\cube^{n}$. Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points $v_{1},...,v_{k}\in\cube^{k}$ and $f:\cube^{n}\to\cube$ satisfies the property that if for all linear maps $L:\cube^{k}\to\cube^{n}$ it is the case that $f(L(v_{1})),...,f(L(v_{k}))$ do not all equal 1. We show that this property is testable if the underlying matroid specified by $v_{1},...,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties. Our techniques extend those of Green and in particular we establish a link between the notion of "1-complexity linear systems" of Green and Tao, and graphic matroids, to derive the results.

math.CO↗

arXiv1996

An extension of the characteristic angle method to the easy-plane spin-3/2 ferromagnet

The Characteristic Angle (CA) method [Lei Zhou and Ruibao Tao, J. Phys. A, {\bf 27} 5599] developed previously for the easy-plane spin-1 magnetic systems has been successfully extended to the spin-3/2 case. A compact form of the CA spin-3/2 operator transformation is given, then the ground state energy, the magnon dispersion relation and the spontaneous magnetization are discussed for an easy-plane spin-3/2 ferromagnet by using the CA method. Comparisons with the old theoretical methods are made in the end.

cond-mat↗

arXiv1996

A quantum model for the magnetic multi-valued recording

We have proposed a quantum model for the magnetic multi-valued recording in this paper. The hysteresis loops of the two-dimensional systems with randomly distributed magnetic atoms have been studied by the quantum theory developed previously. The method has been proved to be exact in this case. We find that the single-ion anisotropies and the densities of the magnetic atoms are mainly responsible for the hysterisis loops. Only if the magnetic atoms contained by the systems are of different (not uniform) anistropies and their density is low, there may be more sharp steps in the hysteresis loops. Such materials can be used as the recording media for the so-called magnetic multi-valued recording. Our result explained the experimental results qualitativly.

cond-mat↗

arXiv1996

Quantum model for magnetic multivalued recording in coupled multilayers

In this paper, we discuss the possibilities of realizing the magnetic multi-valued (MMV) recording in a magnetic coupled multilayer. The hysteresis loop of a double-layer system is studied analytically, and the conditions for achieving the MMV recording are given. The conditions are studied from different respects, and the phase diagrams for the anisotropic parameters are given in the end.

cond-mat↗