arXiv subjects

Xiang Yu

Publications and source records attributed to Xiang Yu.

At least 127 records · Page 7Linked to original sources

arXiv2022

Controllable Dynamic Multi-Task Architectures

Multi-task learning commonly encounters competition for resources among tasks, specifically when model capacity is limited. This challenge motivates models which allow control over the relative importance of tasks and total compute cost during inference time. In this work, we propose such a controllable multi-task network that dynamically adjusts its architecture and weights to match the desired task preference as well as the resource constraints. In contrast to the existing dynamic multi-task approaches that adjust only the weights within a fixed architecture, our approach affords the flexibility to dynamically control the total computational cost and match the user-preferred task importance better. We propose a disentangled training of two hypernetworks, by exploiting task affinity and a novel branching regularized loss, to take input preferences and accordingly predict tree-structured models with adapted weights. Experiments on three multi-task benchmarks, namely PASCAL-Context, NYU-v2, and CIFAR-100, show the efficacy of our approach. Project page is available at https://www.nec-labs.com/~mas/DYMU.

cs.CV↗

arXiv2022

Optimal Consumption with Reference to Past Spending Maximum

This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables. The Hamilton-Jacobi-Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account all constraints. By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that a classical solution to the HJB equation and the feedback optimal investment and consumption strategies can be obtained in closed form in each region. A complete proof of the verification theorem is provided, and numerical examples are presented to illustrate some financial implications.

q-fin.MF↗

arXiv2022

On Generalizing Beyond Domains in Cross-Domain Continual Learning

Humans have the ability to accumulate knowledge of new tasks in varying conditions, but deep neural networks often suffer from catastrophic forgetting of previously learned knowledge after learning a new task. Many recent methods focus on preventing catastrophic forgetting under the assumption of train and test data following similar distributions. In this work, we consider a more realistic scenario of continual learning under domain shifts where the model must generalize its inference to an unseen domain. To this end, we encourage learning semantically meaningful features by equipping the classifier with class similarity metrics as learning parameters which are obtained through Mahalanobis similarity computations. Learning of the backbone representation along with these extra parameters is done seamlessly in an end-to-end manner. In addition, we propose an approach based on the exponential moving average of the parameters for better knowledge distillation. We demonstrate that, to a great extent, existing continual learning algorithms fail to handle the forgetting issue under multiple distributions, while our proposed approach learns new tasks under domain shift with accuracy boosts up to 10% on challenging datasets such as DomainNet and OfficeHome.

cs.LG↗

arXiv2022

Bone tumor suppression in rabbits by hyperthermia below the clinical safety limit using aligned magnetic bone cement

Demonstrating highly efficient alternating current (AC) magnetic field heating of nanoparticles in physiological environments under clinically safe field parameters has remained a great challenge, hindering clinical applications of magnetic hyperthermia. In this work, we report exceptionally high loss power of magnetic bone cement under clinical safety limit of AC field parameters, incorporating DC field-aligned soft magnetic Zn0.3Fe2.7O4 nanoparticles with low concentration. Under an AC field of 4 kA/m at 430 kHz, the aligned bone cement with 0.2 wt% nanoparticles achieved a temperature increase of 30 C in 180 s. This amounts to a specific loss power value of 327 W/gmetal and an intrinsic loss power of 47 nHm^2/kg, which is enhanced by 50-fold compared to randomly oriented samples. The high-performance magnetic bone cement allows for the demonstration of effective hyperthermia suppression of tumor growth in the bone marrow cavity of New Zealand White Rabbits subjecting to rapid cooling due to blood circulation, and significant enhancement of survival rate.

physics.med-ph↗

arXiv2021

Finiteness of Stationary Configurations of the Planar Four-vortex Problem. II

In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar four-vortex problem. However, we only established finiteness of collapse configurations in the sense of prescribing a collapse constant. In this paper, by developing ideas of Albouy-Kaloshin and Hampton-Moeckel to do an analysis of the singularities, we further show that there really are finitely many collapse configurations in the four-vortex problem. This is an unexpectedly result, because the $N$-vortex problem has infinitely many collapse configurations for $N= 3$ and for $N= 5$. %to complete the work on finiteness of stationary configurations of the planar four-vortex problem. We also provide better upper bounds for collapse configurations than that in \cite{yu2021Finiteness}.

math-ph↗

arXiv2021

A new sieve for restricted multiset counting

The Li--Wan sieve is extended to multisets when the underlying set is symmetric. The main ingredient of the proof is the Mobius inversion formula on the poset of partitions of $\{1,2,\dots,k\}$ ordered by refinement. As illustrative applications, we investigate the problems of partitions over finite fields and zero-sum multisets over the additive group $\mathbb{Z}/n\mathbb{Z}$. .

math.CO↗

arXiv2021

On propagation of waves in pressurized fiber-reinforced hyperelastic tubes based on a reduced model

A refined dynamic finite-strain shell theory for incompressible hyperelastic materials was developed by the authors recently. In this paper, we first derive the associated linearized incremental theory, and then use it to investigate wave propagation in a fiber-reinforced hyperelastic tube that is subjected to an axial pre-stretch and internal pressure. We obtain the dispersion relations for both axisymmetric and non-axisymmetric waves and discuss their accuracy by comparing them with the exact dispersion relations. The bending effect is also examined by comparing the dispersion curves based on the present theory and membrane theory. It is shown that the present theory is more accurate than the membrane theory in studying wave propagation and the bending effect plays an important role in some wave modes for relatively large wavenumbers. The effects of the pressure, axial pre-stretch and fiber angle on the dispersion relations are displayed. These results provide the necessary validation for using the refined dynamic finite-strain shell theory and wave propagation to determine arterial properties.

physics.bio-ph↗

arXiv2021

Learning Cross-modal Contrastive Features for Video Domain Adaptation

Learning transferable and domain adaptive feature representations from videos is important for video-relevant tasks such as action recognition. Existing video domain adaptation methods mainly rely on adversarial feature alignment, which has been derived from the RGB image space. However, video data is usually associated with multi-modal information, e.g., RGB and optical flow, and thus it remains a challenge to design a better method that considers the cross-modal inputs under the cross-domain adaptation setting. To this end, we propose a unified framework for video domain adaptation, which simultaneously regularizes cross-modal and cross-domain feature representations. Specifically, we treat each modality in a domain as a view and leverage the contrastive learning technique with properly designed sampling strategies. As a result, our objectives regularize feature spaces, which originally lack the connection across modalities or have less alignment across domains. We conduct experiments on domain adaptive action recognition benchmark datasets, i.e., UCF, HMDB, and EPIC-Kitchens, and demonstrate the effectiveness of our components against state-of-the-art algorithms.

cs.CV↗

arXiv2021

Risk-Sensitive Credit Portfolio Optimization under Partial Information and Contagion Risk

This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we connect the control problem to a quadratic BSDE with jumps, in which the driver term is non-standard and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and proving a uniform a priori estimates, we obtain the existence of a solution to the BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

q-fin.PM↗

arXiv2021

Optimal Entry and Consumption under Habit Formation

This paper studies a composite problem involving the decision making of the optimal entry time and dynamic consumption afterwards. In stage-1, the investor has access to full market information subjecting to some information costs and needs to choose an optimal stopping time to initiate stage-2; in stage-2, the investor terminates the costly full information acquisition and starts dynamic investment and consumption under partial observations of free public stock prices. The habit formation preference is employed, in which the past consumption affects the investor's current decisions. By using the stochastic Perron's method, the value function of the composite problem is proved to be the unique viscosity solution of some variational inequalities.

math.OC↗

arXiv2021

On the Problem of Infinite Spin in Total Collisions of the Planar N-Body Problem

For the planar $N$-body problem, we first introduce a class of moving frame suitable for orbits near central configurations, especially for total collision orbits, which is the main new ingredient of this paper. The moving frame allows us to reduce the degeneracy of the problem according to intrinsic symmetrical characteristic of the $N$-Body problem. First, we give a full answer to the infinite spin or $Painlev\acute{e}$-$Wintner$ problem in the case corresponding to nondegenerate central configurations. Then following some original ideas of C.L. Siegel, especially the idea of normal forms, and applying the theory of central manifolds, we give a partial answer to the problem in the case corresponding to degenerate central configurations. We completely answer the problem in the case corresponding to central configurations with one degree of degeneracy. Combining some results on the planar nonhyperbolic equilibrium point, we give a criterion for the case corresponding to central configurations with two degrees of degeneracy. We further answer the problem in the case corresponding to all known degenerate central configurations of four-body. Therefore, we solve the problem for almost every choice of the masses of the four-body problem. Finally, we give a measure of the set of initial conditions leading to total collisions.

math.DS↗

arXiv2021

Teamwise Mean Field Competitions

This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson project process; across all teams, a mean field competition game is formulated on the rank of the completion time, namely the jump time of Poisson project process, and the reward to each team is paid based on its ranking. On the layer of teamwise competition game, three optimization problems are introduced when the team size is determined by: (i) the team manager; (ii) the central planner; (iii) the team members' voting as partnership. We propose a relative performance criteria for each team member to share the team's reward and formulate some special cases of mean field games of mean field games, which are new to the literature. In all problems with homogeneous parameters, the equilibrium control of each worker and the equilibrium or optimal team size can be computed in an explicit manner, allowing us to analytically examine the impacts of some model parameters and discuss their economic implications. Two numerical examples are also presented to illustrate the parameter dependence and comparison between different team size decision making.

cs.GT↗

arXiv2021

Optimal Tracking Portfolio with A Ratcheting Capital Benchmark

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total capital dominates a non-decreasing benchmark floor process at each intermediate time. The tracking problem is formulated to minimize the cost of accumulated capital injection. We first transform the original problem with floor constraints into an unconstrained control problem, however, under a running maximum cost. By identifying a controlled state process with reflection, the problem is further shown to be equivalent to an auxiliary problem, which leads to a nonlinear Hamilton-Jacobi-Bellman (HJB) equation with a Neumann boundary condition. By employing the dual transform, the probabilistic representation and some stochastic flow analysis, the existence of the unique classical solution to the HJB equation is established. The verification theorem is carefully proved, which gives the complete characterization of the feedback optimal portfolio. The application to market index tracking is also discussed when the index process is modeled by a geometric Brownian motion.

q-fin.PM↗

arXiv2021

On sums of coefficients of Borwein type polynomials over arithmetic progressions

We obtain asymptotic formulas for sums over arithmetic progressions of coefficients of polynomials of the form $$\prod_{j=1}^n\prod_{k=1}^{p-1}(1-q^{pj-k})^s,$$ where $p$ is an odd prime and $n, s$ are positive integers. Let us denote by $a_i$ the coefficient of $q^i$ in the above polynomial and suppose that $b$ is an integer. We prove that $$\Big|\sum_{i\equiv b\ \text{mod}\ 2pn}a_i-\frac{v(b)p^{sn}}{2pn}\Big|\leq p^{sn/2},$$ where $v(b)=p-1$ if $b$ divisible by $p$ and $v(b)=-1$ otherwise. This improves a recent result of Goswami and Pantangi.

math.NT↗

arXiv2021

Optimal Stopping under Model Ambiguity: a Time-Consistent Equilibrium Approach

An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $α$-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. For a one-dimensional diffusion with drift and volatility uncertainty, we show that every equilibrium can be obtained through a fixed-point iteration. This allows us to capture much more diverse behavior, depending on an agent's ambiguity attitude, beyond the standard worst-case (or best-case) analysis. In a concrete example of real options valuation under volatility uncertainty, all equilibrium stopping policies, as well as the best one among them, are fully characterized. It demonstrates explicitly the effect of ambiguity attitude on decision making: the more ambiguity-averse, the more eager to stop -- so as to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established.

q-fin.MF↗

arXiv2021

Finiteness of Stationary Configurations of the Planar Four-vortex Problem

For the planar four-vortex problem, we show that there are finitely many stationary configurations consisting of equilibria, rigidly translating configurations, relative equilibria (uniformly rotating configurations) and collapse configurations. We also provide upper bounds for these classes of stationary configurations.

math-ph↗

arXiv2021

Cross-Domain Similarity Learning for Face Recognition in Unseen Domains

Face recognition models trained under the assumption of identical training and test distributions often suffer from poor generalization when faced with unknown variations, such as a novel ethnicity or unpredictable individual make-ups during test time. In this paper, we introduce a novel cross-domain metric learning loss, which we dub Cross-Domain Triplet (CDT) loss, to improve face recognition in unseen domains. The CDT loss encourages learning semantically meaningful features by enforcing compact feature clusters of identities from one domain, where the compactness is measured by underlying similarity metrics that belong to another training domain with different statistics. Intuitively, it discriminatively correlates explicit metrics derived from one domain, with triplet samples from another domain in a unified loss function to be minimized within a network, which leads to better alignment of the training domains. The network parameters are further enforced to learn generalized features under domain shift, in a model-agnostic learning pipeline. Unlike the recent work of Meta Face Recognition, our method does not require careful hard-pair sample mining and filtering strategy during training. Extensive experiments on various face recognition benchmarks show the superiority of our method in handling variations, compared to baseline and the state-of-the-art methods.

cs.CV↗

arXiv2021

Voting-based Approaches For Differentially Private Federated Learning

Differentially Private Federated Learning (DPFL) is an emerging field with many applications. Gradient averaging based DPFL methods require costly communication rounds and hardly work with large-capacity models, due to the explicit dimension dependence in its added noise. In this work, inspired by knowledge transfer non-federated privacy learning from Papernot et al.(2017; 2018), we design two new DPFL schemes, by voting among the data labels returned from each local model, instead of averaging the gradients, which avoids the dimension dependence and significantly reduces the communication cost. Theoretically, by applying secure multi-party computation, we could exponentially amplify the (data-dependent) privacy guarantees when the margin of the voting scores are large. Extensive experiments show that our approaches significantly improve the privacy-utility trade-off over the state-of-the-arts in DPFL.

cs.LG↗