arXiv subjects

Hantian Zhang

Publications and source records attributed to Hantian Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Two-Loop Rational Terms for Spontaneously Broken Theories

Rational counterterms are a key ingredient for the automation of loop calculations through numerical methods. Building on the recently established properties of rational terms of UV origin at two loops, in this paper we present a systematic method for the determination of rational counterterms within spontaneously broken theories. In particular we introduce a generalised vev-expansion approach that makes it possible to obtain the rational counterterms of UV origin for a spontaneously broken theory by means of calculations in the unbroken phase. The drastic simplifications that result from the underlying symmetry open the door to the efficient determination of rational counterterms for the full Standard Model at two loops. The renormalisation-scheme dependence is analysed in detail, and we show that rational counterterms need to be determined only once and for all in a generic renormalisation scheme for the symmetric phase and, a posteriori, they can be easily adapted to a wide range of physical renormalisation schemes for the spontaneously broken phase. As a first application we determine the full set of $\mathcal{O}(α_{\mathrm s}^2)$ rational counterterms of UV origin for the full Standard Model, i.e. for all superficially UV-divergent two-loop vertex functions involving combinations of gluons, quarks, electroweak vector bosons and scalar bosons.

hep-ph↗

arXiv2021

Study of similarity rules for electromagnetic process in partially ionized plasmas

As proved by previous study, the similarity of electromagnetic processes in plasmas will be violated by Coulomb collisions between electron and ions. Therefore, there is no similarity in highly ionized collisional plasma. But the situation will be completely different for collisional plasmas with low ionization degree. The main collision type will change from electron-ion Coulomb collision to electron-molecule collision, and a new variable (the number density of neutral molecules) will be introduced into the similarity constraint, which can increase the degree of freedom.Thus, in this condition, the similarity restriction caused by the collision process does not conflict with the other restrictions. Therefore, the similarity for electromagnetic process in collisional plasmas can be valid for partially ionized plasmas. In this paper, we propose the similarity in partially ionized plasmas, and prove it via particle in cell/Monte Carlo (PIC/MCC) simulation. Our research has a wide range of engineering applications.

physics.plasm-ph↗

arXiv2021

OmniFair: A Declarative System for Model-Agnostic Group Fairness in Machine Learning

Machine learning (ML) is increasingly being used to make decisions in our society. ML models, however, can be unfair to certain demographic groups (e.g., African Americans or females) according to various fairness metrics. Existing techniques for producing fair ML models either are limited to the type of fairness constraints they can handle (e.g., preprocessing) or require nontrivial modifications to downstream ML training algorithms (e.g., in-processing). We propose a declarative system OmniFair for supporting group fairness in ML. OmniFair features a declarative interface for users to specify desired group fairness constraints and supports all commonly used group fairness notions, including statistical parity, equalized odds, and predictive parity. OmniFair is also model-agnostic in the sense that it does not require modifications to a chosen ML algorithm. OmniFair also supports enforcing multiple user declared fairness constraints simultaneously while most previous techniques cannot. The algorithms in OmniFair maximize model accuracy while meeting the specified fairness constraints, and their efficiency is optimized based on the theoretically provable monotonicity property regarding the trade-off between accuracy and fairness that is unique to our system. We conduct experiments on commonly used datasets that exhibit bias against minority groups in the fairness literature. We show that OmniFair is more versatile than existing algorithmic fairness approaches in terms of both supported fairness constraints and downstream ML models. OmniFair reduces the accuracy loss by up to $94.8\%$ compared with the second best method. OmniFair also achieves similar running time to preprocessing methods, and is up to $270\times$ faster than in-processing methods.

cs.CY↗

arXiv2020

Two-Loop Rational Terms in Yang-Mills Theories

Scattering amplitudes in $D$ dimensions involve particular terms that originate from the interplay of UV poles with the $D-4$ dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the $D-4$ dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to $n_{f}$ fermions with arbitrary masses.

hep-ph↗

arXiv2020

Rational terms in two-loop calculations

We present an extension of the renormalisation procedure based on the R-operation in $D$ dimensions at two-loop level, in which the numerators of all Feynman diagrams can be constructed in four dimensions, and the rational terms stemming from the interplay of $(D-4)$-dimensional numerator parts and UV poles are fully reconstructed from a finite set of universal local counterterms. This represents an extension of the concept of rational terms of type $R_2$ to two loops. We provide a general method to compute one and two-loop rational counterterms from massive one-scale tadpole integrals. Finally, we present the full set of rational counterterms of UV origin for QED up to two-loop order.

hep-ph↗

arXiv2020

Rational Terms of UV Origin at Two Loops

The advent of efficient numerical algorithms for the construction of one-loop amplitudes has played a crucial role in the automation of NLO calculations, and the development of similar algorithms at two loops is a natural strategy for NNLO automation. Within a numerical framework the numerator of loop integrals is usually constructed in four dimensions, and the missing rational terms, which arise from the interplay of the $(D-4)$-dimensional parts of the loop numerator with $1/(D-4)$ poles in $D$ dimensions, are reconstructed separately. At one loop, such rational terms arise only from UV divergences and can be restored through process-independent local counterterms. In this paper we investigate the behaviour of rational terms of UV origin at two loops. The main result is a general formula that combines the subtraction of UV poles with the reconstruction of the associated rational parts at two loops. This formula has the same structure as the R-operation, and all poles and rational parts are described through a finite set of process-independent local counterterms. We also present a general formula for the calculation of all relevant two-loop rational counterterms in any renormalisable theory based on one-scale tadpole integrals. As a first application, we derive the full set of two-loop rational counterterms for QED in the $R_ξ$-gauge.

hep-ph↗

arXiv2020

ALEX: An Updatable Adaptive Learned Index

Recent work on "learned indexes" has changed the way we look at the decades-old field of DBMS indexing. The key idea is that indexes can be thought of as "models" that predict the position of a key in a dataset. Indexes can, thus, be learned. The original work by Kraska et al. shows that a learned index beats a B+Tree by a factor of up to three in search time and by an order of magnitude in memory footprint. However, it is limited to static, read-only workloads. In this paper, we present a new learned index called ALEX which addresses practical issues that arise when implementing learned indexes for workloads that contain a mix of point lookups, short range queries, inserts, updates, and deletes. ALEX effectively combines the core insights from learned indexes with proven storage and indexing techniques to achieve high performance and low memory footprint. On read-only workloads, ALEX beats the learned index from Kraska et al. by up to 2.2X on performance with up to 15X smaller index size. Across the spectrum of read-write workloads, ALEX beats B+Trees by up to 4.1X while never performing worse, with up to 2000X smaller index size. We believe ALEX presents a key step towards making learned indexes practical for a broader class of database workloads with dynamic updates.

cs.DB↗

arXiv2019

OpenLoops 2

We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications.

hep-ph↗

arXiv2019

Proposal for the validation of Monte Carlo implementations of the standard model effective field theory

We propose a procedure to cross-validate Monte Carlo implementations of the standard model effective field theory. It is based on the numerical comparison of squared amplitudes computed at specific phase-space and parameter points in pairs of implementations. Interactions are fully linearised in the effective field theory expansion. The squares of linear effective field theory amplitudes and their interference with standard-model contributions are compared separately. Such pairwise comparisons are primarily performed at tree level and a possible extension to the one-loop level is also briefly considered. We list the current standard model effective field theory implementations and the comparisons performed to date.

hep-ph↗

arXiv2019

Accelerating Generalized Linear Models with MLWeaving: A One-Size-Fits-All System for Any-precision Learning (Technical Report)

Learning from the data stored in a database is an important function increasingly available in relational engines. Methods using lower precision input data are of special interest given their overall higher efficiency but, in databases, these methods have a hidden cost: the quantization of the real value into a smaller number is an expensive step. To address the issue, in this paper we present MLWeaving, a data structure and hardware acceleration technique intended to speed up learning of generalized linear models in databases. ML-Weaving provides a compact, in-memory representation enabling the retrieval of data at any level of precision. MLWeaving also takes advantage of the increasing availability of FPGA-based accelerators to provide a highly efficient implementation of stochastic gradient descent. The solution adopted in MLWeaving is more efficient than existing designs in terms of space (since it can process any resolution on the same design) and resources (via the use of bit-serial multipliers). MLWeaving also enables the runtime tuning of precision, instead of a fixed precision level during the training. We illustrate this using a simple, dynamic precision schedule. Experimental results show MLWeaving achieves up to16 performance improvement over low-precision CPU implementations of first-order methods.

cs.DS↗

arXiv2018

On-the-fly reduction of open loops

We describe new developments in the OpenLoops framework based on the recently introduced on-the-fly method. The on-the-fly approach exploits the factorisation of one-loop diagrams into segments in order to perform various operations, such as helicity summation, diagram merging and the reduction of Feynman integrands in between the recursion steps for the amplitude construction. This method significantly reduces the complexity of scattering amplitude calculations for multi-particle processes, leading to a major increase in CPU efficiency and numerical stability. The unification of the reduction to scalar integrals with the amplitude construction in a single algorithm, allows to identify problematic kinematical configurations and cure numerical instabilities in single recursion steps. A simple permutation trick in combination with a one-parameter expansion for a single topology, which is now implemented to any order, eliminate rank-two Gram determinant instabilities altogether. Due to this any-order expansion, the numerical accuracy of the algorithm can be determined with a rescaling test. The on-the-fly algorithm is fully implemented for double and quadruple precision, which allows for true quadruple precision benchmarks with up to 32 correct digits as well as a powerful rescue system for unstable points. We present first speed and stability results for these new features. The on-the-fly algorithm is part of the forthcoming release of OpenLoops 2.

hep-ph↗

arXiv2018

PSFGAN: a generative adversarial network system for separating quasar point sources and host galaxy light

The study of unobscured active galactic nuclei (AGN) and quasars depends on the reliable decomposition of the light from the AGN point source and the extended host galaxy light. The problem is typically approached using parametric fitting routines using separate models for the host galaxy and the point spread function (PSF). We present a new approach using a Generative Adversarial Network (GAN) trained on galaxy images. We test the method using Sloan Digital Sky Survey (SDSS) r-band images with artificial AGN point sources added which are then removed using the GAN and with parametric methods using GALFIT. When the AGN point source PS is more than twice as bright as the host galaxy, we find that our method, PSFGAN, can recover PS and host galaxy magnitudes with smaller systematic error and a lower average scatter ($49\%$). PSFGAN is more tolerant to poor knowledge of the PSF than parametric methods. Our tests show that PSFGAN is robust against a broadening in the PSF width of $\pm 50\%$ if it is trained on multiple PSF's. We demonstrate that while a matched training set does improve performance, we can still subtract point sources using a PSFGAN trained on non-astronomical images. While initial training is computationally expensive, evaluating PSFGAN on data is more than $40$ times faster than GALFIT fitting two components. Finally, PSFGAN it is more robust and easy to use than parametric methods as it requires no input parameters.

astro-ph.GA↗

arXiv2017

MLBench: How Good Are Machine Learning Clouds for Binary Classification Tasks on Structured Data?

We conduct an empirical study of machine learning functionalities provided by major cloud service providers, which we call machine learning clouds. Machine learning clouds hold the promise of hiding all the sophistication of running large-scale machine learning: Instead of specifying how to run a machine learning task, users only specify what machine learning task to run and the cloud figures out the rest. Raising the level of abstraction, however, rarely comes free - a performance penalty is possible. How good, then, are current machine learning clouds on real-world machine learning workloads? We study this question with a focus on binary classication problems. We present mlbench, a novel benchmark constructed by harvesting datasets from Kaggle competitions. We then compare the performance of the top winning code available from Kaggle with that of running machine learning clouds from both Azure and Amazon on mlbench. Our comparative study reveals the strength and weakness of existing machine learning clouds and points out potential future directions for improvement.

cs.DC↗

arXiv2017

Electroweak Higgs production with HiggsPO at NLO QCD

We present the HiggsPO UFO model for Monte Carlo event generation of electroweak $VH$ and VBF Higgs production processes at NLO in QCD in the formalism of Higgs pseudo-observables (PO). We illustrate the use of this tool by studying the QCD corrections, matched to a parton shower, for several benchmark points in the Higgs PO parameter space. We find that, while being sizable and thus important to be considered in realistic experimental analyses, the QCD higher-order corrections largely factorize. As an additional finding, based on the NLO results, we advocate to consider 2D distributions of the two-jet azimuthal-angle difference and the leading jet $p_T$ for new physics searches in VBF Higgs production. The HiggsPO UFO model is publicly available.

hep-ph↗

arXiv2017

NNLO QCD corrections to event orientation in e+e- annihilation

We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.

hep-ph↗

arXiv2017

The ZipML Framework for Training Models with End-to-End Low Precision: The Cans, the Cannots, and a Little Bit of Deep Learning

Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train models at end-to-end low precision with provable guarantees? Can this lead to consistent order-of-magnitude speedups? We present a framework called ZipML to answer these questions. For linear models, the answer is yes. We develop a simple framework based on one simple but novel strategy called double sampling. Our framework is able to execute training at low precision with no bias, guaranteeing convergence, whereas naive quantization would introduce significant bias. We validate our framework across a range of applications, and show that it enables an FPGA prototype that is up to 6.5x faster than an implementation using full 32-bit precision. We further develop a variance-optimal stochastic quantization strategy and show that it can make a significant difference in a variety of settings. When applied to linear models together with double sampling, we save up to another 1.7x in data movement compared with uniform quantization. When training deep networks with quantized models, we achieve higher accuracy than the state-of-the-art XNOR-Net. Finally, we extend our framework through approximation to non-linear models, such as SVM. We show that, although using low-precision data induces bias, we can appropriately bound and control the bias. We find in practice 8-bit precision is often sufficient to converge to the correct solution. Interestingly, however, in practice we notice that our framework does not always outperform the naive rounding approach. We discuss this negative result in detail.

cs.LG↗

arXiv2017

Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit

Observations of astrophysical objects such as galaxies are limited by various sources of random and systematic noise from the sky background, the optical system of the telescope and the detector used to record the data. Conventional deconvolution techniques are limited in their ability to recover features in imaging data by the Shannon-Nyquist sampling theorem. Here we train a generative adversarial network (GAN) on a sample of $4,550$ images of nearby galaxies at $0.01<z<0.02$ from the Sloan Digital Sky Survey and conduct $10\times$ cross validation to evaluate the results. We present a method using a GAN trained on galaxy images that can recover features from artificially degraded images with worse seeing and higher noise than the original with a performance which far exceeds simple deconvolution. The ability to better recover detailed features such as galaxy morphology from low-signal-to-noise and low angular resolution imaging data significantly increases our ability to study existing data sets of astrophysical objects as well as future observations with observatories such as the Large Synoptic Sky Telescope (LSST) and the Hubble and James Webb space telescopes.

astro-ph.IM↗

arXiv2015

Non-smooth Approach for Contact Dynamics and Impulse-based Control of Frictional Furuta Pendulum

In this thesis, a non-penetrated and physically consistent non-smooth numerical approach has been proposed, by employing the Prox formulation and Moreau's mid-point time-stepping rule, for the contact dynamics with coupled and decoupled constraints. Under this circumstance, the robust impulse-based control has been successfully implemented and validated on the motion system of controlled frictional oscillator. Further improvement has been achieved by utilizing shooting method in the impulse estimating process instead of robust estimation. This non-smooth numerical technique has been applied to the under-actuated friction-coupled mulit-body system, by means of an implementation on the controlled frictional Furuta pendulum. The specifically designed impulse-based controller has successfully solved the problem of stabilization of the inverted frictional Furuta pendulum, which is suffered from the stiction effect of friction.

eess.SY↗