arXiv subjects

Zheng Qu

Publications and source records attributed to Zheng Qu.

At least 19 recordsLinked to original sources

arXiv2026

PortraitCraft: A Benchmark for Portrait Composition Understanding and Generation

Portrait composition plays a central role in portrait aesthetics and visual communication, yet existing datasets and benchmarks mainly focus on coarse aesthetic scoring, generic image aesthetics, or unconstrained portrait generation. This limits systematic research on structured portrait composition analysis and controllable portrait generation under explicit composition requirements. In this paper, we introduce PortraitCraft, a unified benchmark for portrait composition understanding and generation. PortraitCraft is built on a dataset of approximately 50,000 curated real portrait images with structured multi-level supervision, including global composition scores, annotations over 13 composition attributes, attribute-level explanation texts, visual question answering pairs, and composition-oriented textual descriptions for generation. Based on this dataset, we establish two complementary benchmark tasks for composition understanding and composition-aware generation within a unified framework. The first evaluates portrait composition understanding through score prediction, fine-grained attribute reasoning, and image-grounded visual question answering, while the second evaluates portrait generation from structured composition descriptions under explicit composition constraints. We further define standardized evaluation protocols and provide reference baseline results with representative multimodal models. PortraitCraft provides a comprehensive benchmark for future research on fine-grained portrait understanding, interpretable aesthetic assessment, and controllable portrait generation.

cs.CV↗

arXiv2025

Progressive Bound Strengthening via Doubly Nonnegative Cutting Planes for Nonconvex Quadratic Programs

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate separating cuts, which are iteratively added to improve the relaxation. We establish that, at any Karush-Kuhn-Tucker (KKT) point satisfying a second-order sufficient condition, a valid cut can be obtained by solving a linear semidefinite program (SDP), and we devise a finite-termination local search procedure to identify such points. Extensive computational experiments on both benchmark and synthetic instances demonstrate that our approach yields tighter bounds and consistently outperforms leading commercial and academic solvers in terms of efficiency, robustness, and scalability. Notably, on a standard desktop, our algorithm reduces the relative optimality gap to 0.01% on 138 out of 140 instances of dimension 100 within one hour, without resorting to branch-and-bound.

math.OC↗

arXiv2025

Drop-Muon: Update Less, Converge Faster

Conventional wisdom in deep learning optimization dictates updating all layers at every step-a principle followed by all recent state-of-the-art optimizers such as Muon. In this work, we challenge this assumption, showing that full-network updates can be fundamentally suboptimal, both in theory and in practice. We introduce a non-Euclidean Randomized Progressive Training method-Drop-Muon-a simple yet powerful framework that updates only a subset of layers per step according to a randomized schedule, combining the efficiency of progressive training with layer-specific non-Euclidean updates for top-tier performance. We provide rigorous convergence guarantees under both layer-wise smoothness and layer-wise $(L^0, L^1)$-smoothness, covering deterministic and stochastic gradient settings, marking the first such results for progressive training in the stochastic and non-smooth regime. Our cost analysis further reveals that full-network updates are not optimal unless a very specific relationship between layer smoothness constants holds. Through controlled CNN experiments, we empirically demonstrate that Drop-Muon consistently outperforms full-network Muon, achieving the same accuracy up to $1.4\times$ faster in wall-clock time. Together, our results suggest a shift in how large-scale models can be efficiently trained, challenging the status quo and offering a highly efficient, theoretically grounded alternative to full-network updates.

cs.LG↗

arXiv2025

Delta: A Learned Mixed Cost-based Query Optimization Framework

Query optimizer is a crucial module for database management systems. Existing optimizers exhibit two flawed paradigms: (1) cost-based optimizers use dynamic programming with cost models but face search space explosion and heuristic pruning constraints; (2) value-based ones train value networks to enable efficient beam search, but incur higher training costs and lower accuracy. They also lack mechanisms to detect queries where they may perform poorly. To determine more efficient plans, we propose Delta, a mixed cost-based query optimization framework that consists of a compatible query detector and a two-stage planner. Delta first employs a Mahalanobis distancebased detector to preemptively filter out incompatible queries where the planner might perform poorly. For compatible queries, Delta activates its two-stage mixed cost-based planner. Stage I serves as a coarse-grained filter to generate high-quality candidate plans based on the value network via beam search, relaxing precision requirements and narrowing the search space. Stage II employs a fine-grained ranker to determine the best plan from the candidate plans based on a learned cost model. Moreover, to reduce training costs, we reuse and augment the training data from stage I to train the model in stage II. Experimental results on three workloads demonstrate that Delta identifies higher-quality plans, achieving an average 2.34x speedup over PostgreSQL and outperforming the state-of-the-art learned methods by 2.21x.

cs.DB↗

arXiv2024

Sparse Polynomial Optimization with Matrix Constraints

This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient and necessary condition for the sparse hierarchy to be tight. Second, we discuss how to detect the tightness and extract minimizers. Third, for the convex case, we show that the hierarchy of the sparse matrix Moment-SOS relaxations is tight, under some general assumptions. In particular, we show that the sparse matrix Moment-SOS relaxation is tight for every order when the problem is SOS-convex. Numerical experiments are provided to show the efficiency of the sparse relaxations.

math.OC↗

arXiv2024

A Characterization for Tightness of the Sparse Moment-SOS Hierarchy

This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets.

math.OC↗

arXiv2023

A Correlatively Sparse Lagrange Multiplier Expression Relaxation for Polynomial Optimization

In this paper, we consider polynomial optimization with correlative sparsity. We construct correlatively sparse Lagrange multiplier expressions (CS-LMEs) and propose CS-LME reformulations for polynomial optimization problems using the Karush-Kuhn-Tucker optimality conditions. Correlatively sparse sum-of-squares (CS-SOS) relaxations are applied to solve the CS-LME reformulation. We show that the CS-LME reformulation inherits the original correlative sparsity pattern, and the CS-SOS relaxation provides sharper lower bounds when applied to the CS-LME reformulation, compared with when it is applied to the original problem. Moreover, the convergence of our approach is guaranteed under mild conditions. In numerical experiments, our new approach usually finds the global optimal value (up to a negligible error) with a low relaxation order for cases where directly solving the problem fails to get an accurate approximation. Also, by properly exploiting the correlative sparsity, our CS-LME approach requires less computational time than the original LME approach to reach the same accuracy level.

math.OC↗

arXiv2023

Globally Solving Concave Quadratic Programs via Doubly Nonnegative Relaxation

We consider the problem of maximizing a convex quadratic function over a bounded polyhedral set. We design a new framework based on SDP relaxations and cutting plane methods for solving the associated reference value problem. The major novelty is a new way to generate valid cuts through the doubly nonnegative (DNN) relaxation. We establish various theoretical properties of the DNN relaxation, including its equivalence with the Shor relaxation of an equivalent quadratically constrained problem, the strong duality, and the generation of valid cuts from an approximate solution of the DNN relaxation returned by an arbitrary SDP solver. Computational results on both real and synthetic data demonstrate the efficiency of the proposed method and its ability to solve high-dimensional problems with dense data. In particular, our new algorithm successfully solves in 3 days the reference value problem arising from computational biology for a dataset containing more than 300,000 instances of dimension 78. In contrast, CPLEX or Gurobi is estimated to require years of computational time for the same dataset on the same computing platform.

math.OC↗

arXiv2022

Dynamic N:M Fine-grained Structured Sparse Attention Mechanism

Transformers are becoming the mainstream solutions for various tasks like NLP and Computer vision. Despite their success, the high complexity of the attention mechanism hinders them from being applied to latency-sensitive tasks. Tremendous efforts have been made to alleviate this problem, and many of them successfully reduce the asymptotic complexity to linear. Nevertheless, most of them fail to achieve practical speedup over the original full attention under moderate sequence lengths and are unfriendly to finetuning. In this paper, we present DFSS, an attention mechanism that dynamically prunes the full attention weight matrix to N:M fine-grained structured sparse pattern. We provide both theoretical and empirical evidence that demonstrates DFSS is a good approximation of the full attention mechanism. We propose a dedicated CUDA kernel design that completely eliminates the dynamic pruning overhead and achieves speedups under arbitrary sequence length. We evaluate the 1:2 and 2:4 sparsity under different configurations and achieve 1.27~ 1.89x speedups over the full-attention mechanism. It only takes a couple of finetuning epochs from the pretrained model to achieve on par accuracy with full attention mechanism on tasks from various domains under different sequence lengths from 384 to 4096.

cs.LG↗

arXiv2021

Exactness and Effective Degree Bound of Lasserre's Relaxation for Polynomial Optimization over Finite Variety

In this paper, we address the effective degree bound problem for Lasserre's hierarchy of moment-sum-of-squares (SOS) relaxations in polynomial optimization involving $n$ variables. We assume that the first $n$ equality constraint polynomials $g_1,\ldots,g_n$ do not share any nontrivial common complex zero locus at infinity and that the optimal solutions are nonsingular. Under these conditions, we derive an effective degree bound for the exactness of Lasserre's hierarchy. Importantly, the assumption of no solutions at infinity holds on a Zariski open set within the space of polynomials of fixed degrees. As a direct consequence, we provide the first explicit degree bound for gradient-type SOS relaxation under a generic condition.

math.OC↗

arXiv2021

Transformer Acceleration with Dynamic Sparse Attention

Transformers are the mainstream of NLP applications and are becoming increasingly popular in other domains such as Computer Vision. Despite the improvements in model quality, the enormous computation costs make Transformers difficult at deployment, especially when the sequence length is large in emerging applications. Processing attention mechanism as the essential component of Transformer is the bottleneck of execution due to the quadratic complexity. Prior art explores sparse patterns in attention to support long sequence modeling, but those pieces of work are on static or fixed patterns. We demonstrate that the sparse patterns are dynamic, depending on input sequences. Thus, we propose the Dynamic Sparse Attention (DSA) that can efficiently exploit the dynamic sparsity in the attention of Transformers. Compared with other methods, our approach can achieve better trade-offs between accuracy and model complexity. Moving forward, we identify challenges and provide solutions to implement DSA on existing hardware (GPUs) and specialized hardware in order to achieve practical speedup and efficiency improvements for Transformer execution.

cs.LG↗

arXiv2021

H2Learn: High-Efficiency Learning Accelerator for High-Accuracy Spiking Neural Networks

Although spiking neural networks (SNNs) take benefits from the bio-plausible neural modeling, the low accuracy under the common local synaptic plasticity learning rules limits their application in many practical tasks. Recently, an emerging SNN supervised learning algorithm inspired by backpropagation through time (BPTT) from the domain of artificial neural networks (ANNs) has successfully boosted the accuracy of SNNs and helped improve the practicability of SNNs. However, current general-purpose processors suffer from low efficiency when performing BPTT for SNNs due to the ANN-tailored optimization. On the other hand, current neuromorphic chips cannot support BPTT because they mainly adopt local synaptic plasticity rules for simplified implementation. In this work, we propose H2Learn, a novel architecture that can achieve high efficiency for BPTT-based SNN learning which ensures high accuracy of SNNs. At the beginning, we characterized the behaviors of BPTT-based SNN learning. Benefited from the binary spike-based computation in the forward pass and the weight update, we first design lookup table (LUT) based processing elements in Forward Engine and Weight Update Engine to make accumulations implicit and to fuse the computations of multiple input points. Second, benefited from the rich sparsity in the backward pass, we design a dual-sparsity-aware Backward Engine which exploits both input and output sparsity. Finally, we apply a pipeline optimization between different engines to build an end-to-end solution for the BPTT-based SNN learning. Compared with the modern NVIDIA V100 GPU, H2Learn achieves 7.38x area saving, 5.74-10.20x speedup, and 5.25-7.12x energy saving on several benchmark datasets.

cs.NE↗

arXiv2021

Entropic Regularization of the Nested Distance

In 2012, Pflug and Pichler proved, under regularity assumptions, that the value function in Multistage Stochastic Programming (MSP) is Lipschitz continuous w.r.t. the Nested Distance, which is a distance between scenario trees (or discrete time stochastic processes with finite support). The Nested Distance is a refinement of the Wasserstein distance to account for proximity of the filtrations of discrete time stochastic processes. The computation of the Nested Distance between two scenario trees amounts to the computation of an exponential (in the horizon $T$) number of optimal transport problems between smaller conditional probabilities of size $n$, where $n$ is less than maximal number of children of each node. Such optimal transport problems can be solved by the auction algorithm with complexity $O(n^3\log(n))$. In 2013, Cuturi introduced Sinkhorn's algorithm, an alternating projection scheme which solves an entropic regularized optimal transport problem. Sinkhorn's algorithm converges linearly and each iteration has a complexity of $O(n^2)$. In this article, we present and test numerically an entropic regularization of the Nested Distance.

math.OC↗

arXiv2021

Multiply Accelerated Value Iteration for Non-Symmetric Affine Fixed Point Problems and application to Markov Decision Processes

We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or mean payoff criteria. We characterize the spectra of matrices for which this algorithm does converge with an accelerated asymptotic rate. We also introduce a $d$th-order algorithm, and show that it yields a multiply accelerated rate under more demanding conditions on the spectrum. We subsequently apply these methods to develop accelerated schemes for non-linear fixed point problems arising from Markov decision processes. This is illustrated by numerical experiments.

math.OC↗

arXiv2021

An adaptive proximal point algorithm framework and application to large-scale optimization

We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition parameter. We propose an adaptive generalized proximal point algorithm (AGPPA), which adaptively updates the proximal regularization parameters based on some implementable criteria. We show that AGPPA achieves linear convergence without any knowledge of the error bound condition parameter, and the rate only differs from the optimal one by a logarithm term. We apply AGPPA on convex minimization problem and analyze the iteration complexity bound of the resulting algorithm. Our framework and the complexity results apply to arbitrary linearly convergent inner solver and allows a hybrid with any locally fast convergent method. We illustrate the performance of AGPPA by applying it to solve large-scale linear programming (LP) problem. The resulting complexity bound has a weaker dependence on the Hoffman constant and scales with the dimension better than linearized ADMM. In numerical experiments, our algorithm demonstrates improved performance in obtaining solution of medium accuracy on large-scale LP problem.

math.OC↗

arXiv2019

An inexact proximal augmented Lagrangian framework with arbitrary linearly convergent inner solver for composite convex optimization

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic algorithms, making the resulting framework more scalable facing the ever-increasing problem dimension. Each subproblem is solved inexactly with an explicit and self-adaptive stopping criterion, without requiring to set an a priori target accuracy. When the primal and dual domain are bounded, our method achieves $O(1/\sqrtε)$ and $O(1/ε)$ complexity bound in terms of number of inner solver iterations, respectively for the strongly convex and non-strongly convex case. Without the boundedness assumption, only logarithm terms need to be added and the above two complexity bounds increase respectively to $\tilde O(1/\sqrtε)$ and $\tilde O(1/ε)$, which hold both for obtaining $ε$-optimal and $ε$-KKT solution. Within the general framework that we propose, we also obtain $\tilde O(1/ε)$ and $\tilde O(1/{ε^2})$ complexity bounds under relative smoothness assumption on the differentiable component of the objective function. We show through theoretical analysis as well as numerical experiments the computational speedup possibly achieved by the use of randomized inner solvers for large-scale problems.

math.OC↗

arXiv2019

Solving Ergodic Markov Decision Processes and Perfect Information Zero-sum Stochastic Games by Variance Reduced Deflated Value Iteration

Recently, Sidford, Wang, Wu and Ye (2018) developed an algorithm combining variance reduction techniques with value iteration to solve discounted Markov decision processes. This algorithm has a sublinear complexity when the discount factor is fixed. Here, we extend this approach to mean-payoff problems, including both Markov decision processes and perfect information zero-sum stochastic games. We obtain sublinear complexity bounds, assuming there is a distinguished state which is accessible from all initial states and for all policies. Our method is based on a reduction from the mean payoff problem to the discounted problem by a Doob h-transform, combined with a deflation technique. The complexity analysis of this algorithm uses at the same time the techniques developed by Sidford et al. in the discounted case and non-linear spectral theory techniques (Collatz-Wielandt characterization of the eigenvalue).

math.OC↗

arXiv2019

L-SVRG and L-Katyusha with Arbitrary Sampling

We develop and analyze a new family of {\em nonaccelerated and accelerated loopless variance-reduced methods} for finite sum optimization problems. Our convergence analysis relies on a novel expected smoothness condition which upper bounds the variance of the stochastic gradient estimation by a constant times a distance-like function. This allows us to handle with ease {\em arbitrary sampling schemes} as well as the nonconvex case. We perform an in-depth estimation of these expected smoothness parameters and propose new importance samplings which allow {\em linear speedup} when the expected minibatch size is in a certain range. Furthermore, a connection between these expected smoothness parameters and expected separable overapproximation (ESO) is established, which allows us to exploit data sparsity as well. Our results recover as special cases the recently proposed loopless SVRG and loopless Katyusha.

math.OC↗