arXiv subjects

Ling Liang

Publications and source records attributed to Ling Liang.

At least 55 records · Page 3Linked to original sources

arXiv2025

An Inexact Halpern Iteration with Application to Distributionally Robust Optimization

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in both deterministic and stochastic settings. We conduct extensive convergence analysis and show that by choosing the inexactness tolerances appropriately, the inexact schemes admit an $O(k^{-1})$ convergence rate in terms of the (expected) residue norm. Our results relax the state-of-the-art inexactness conditions employed in the literature while sharing the same competitive convergence properties. We then demonstrate how the proposed methods can be applied for solving two classes of data-driven Wasserstein distributionally robust optimization problems that admit convex-concave min-max optimization reformulations. We highlight its capability of performing inexact computations for distributionally robust learning with stochastic first-order methods and for general nonlinear convex-concave loss functions, which are competitive in the literature.

math.OC↗

arXiv2025

HybriMoE: Hybrid CPU-GPU Scheduling and Cache Management for Efficient MoE Inference

The Mixture of Experts (MoE) architecture has demonstrated significant advantages as it enables to increase the model capacity without a proportional increase in computation. However, the large MoE model size still introduces substantial memory demands, which usually requires expert offloading on resource-constrained platforms and incurs significant overhead. Hybrid CPU-GPU inference has been proposed to leverage CPU computation to reduce expert loading overhead but faces major challenges: on one hand, the expert activation patterns of MoE models are highly unstable, rendering the fixed mapping strategies in existing works inefficient; on the other hand, the hybrid CPU-GPU schedule for MoE is inherently complex due to the diverse expert sizes, structures, uneven workload distribution, etc. To address these challenges, in this paper, we propose HybriMoE, a hybrid CPU-GPU inference framework that improves resource utilization through a novel CPU-GPU scheduling and cache management system. HybriMoE introduces (i) a dynamic intra-layer scheduling strategy to balance workloads across CPU and GPU, (ii) an impact-driven inter-layer prefetching algorithm, and (iii) a score-based caching algorithm to mitigate expert activation instability. We implement HybriMoE on top of the kTransformers framework and evaluate it on three widely used MoE-based LLMs. Experimental results demonstrate that HybriMoE achieves an average speedup of 1.33$\times$ in the prefill stage and 1.70$\times$ in the decode stage compared to state-of-the-art hybrid MoE inference framework. Our code is available at: https://github.com/PKU-SEC-Lab/HybriMoE.

cs.LG↗

arXiv2025

FlexMem: High-Parallel Near-Memory Architecture for Flexible Dataflow in Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) imposes substantial memory bandwidth demands, presenting significant challenges for efficient hardware acceleration. Near-memory Processing (NMP) has emerged as a promising architectural solution to alleviate the memory bottleneck. However, the irregular memory access patterns and flexible dataflows inherent to FHE limit the effectiveness of existing NMP accelerators, which fail to fully utilize the available near-memory bandwidth. In this work, we propose FlexMem, a near-memory accelerator featuring high-parallel computational units with varying memory access strides and interconnect topologies to effectively handle irregular memory access patterns. Furthermore, we design polynomial and ciphertext-level dataflows to efficiently utilize near-memory bandwidth under varying degrees of polynomial parallelism and enhance parallel performance. Experimental results demonstrate that FlexMem achieves 1.12 times of performance improvement over state-of-the-art near-memory architectures, with 95.7% of near-memory bandwidth utilization.

cs.AR↗

arXiv2025

Towards Effective and Sparse Adversarial Attack on Spiking Neural Networks via Breaking Invisible Surrogate Gradients

Spiking neural networks (SNNs) have shown their competence in handling spatial-temporal event-based data with low energy consumption. Similar to conventional artificial neural networks (ANNs), SNNs are also vulnerable to gradient-based adversarial attacks, wherein gradients are calculated by spatial-temporal back-propagation (STBP) and surrogate gradients (SGs). However, the SGs may be invisible for an inference-only model as they do not influence the inference results, and current gradient-based attacks are ineffective for binary dynamic images captured by the dynamic vision sensor (DVS). While some approaches addressed the issue of invisible SGs through universal SGs, their SGs lack a correlation with the victim model, resulting in sub-optimal performance. Moreover, the imperceptibility of existing SNN-based binary attacks is still insufficient. In this paper, we introduce an innovative potential-dependent surrogate gradient (PDSG) method to establish a robust connection between the SG and the model, thereby enhancing the adaptability of adversarial attacks across various models with invisible SGs. Additionally, we propose the sparse dynamic attack (SDA) to effectively attack binary dynamic images. Utilizing a generation-reduction paradigm, SDA can fully optimize the sparsity of adversarial perturbations. Experimental results demonstrate that our PDSG and SDA outperform state-of-the-art SNN-based attacks across various models and datasets. Specifically, our PDSG achieves 100% attack success rate on ImageNet, and our SDA obtains 82% attack success rate by modifying only 0.24% of the pixels on CIFAR10DVS. The code is available at https://github.com/ryime/PDSG-SDA .

cs.CV↗

arXiv2024

A squared smoothing Newton method for semidefinite programming

This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber function. Using these results and existing ones in the literature, we then conduct rigorous convergence analysis and establish convergence properties for the proposed algorithm. In particular, we show that the proposed method is well-defined and admits global convergence. Moreover, under suitable regularity conditions, i.e., the primal and dual constraint nondegenerate conditions, the proposed method is shown to have a superlinear convergence rate. To evaluate the practical performance of the algorithm, we conduct extensive numerical experiments for solving various classes of SDPs. Comparison with the state-of-the-art SDP solvers demonstrates that our method is also efficient for computing accurate solutions of SDPs.

math.OC↗

arXiv2024

PNOD: An Efficient Projected Newton Framework for Exact Optimal Experimental Designs

Computing the exact optimal experimental design has been a longstanding challenge in various scientific fields. This problem, when formulated using a specific information function, becomes a mixed-integer nonlinear programming (MINLP) problem, which is typically NP-hard, thus making the computation of a globally optimal solution extremely difficult. The branch and bound (BnB) method is a widely used approach for solving such MINLPs, but its practical efficiency heavily relies on the ability to solve continuous relaxations effectively within the BnB search tree. In this paper, we propose a novel projected Newton framework, combining with a vertex exchange method for efficiently solving the associated subproblems, designed to enhance the BnB method. This framework offers strong convergence guarantees by utilizing recent advances in solving self-concordant optimization and convex quadratic programming problems. Extensive numerical experiments on A-optimal and D-optimal design problems, two of the most commonly used models, demonstrate the framework's promising numerical performance. Specifically, our framework significantly improves the efficiency of node evaluation within the BnB search tree and enhances the accuracy of solutions compared to state-of-the-art methods. The proposed framework is implemented in an open source Julia package called \texttt{PNOD.jl}, which opens up possibilities for its application in a wide range of real-world scenarios.

stat.ME↗

arXiv2024

Accelerating Multi-Block Constrained Optimization Through Learning to Optimize

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of Multipliers (ADMM) and its variants. However, the natural extension of L2O to multi-block ADMM-type methods remains largely unexplored. Such an extension is critical, as multi-block methods leverage the separable structure of optimization problems, offering substantial reductions in per-iteration complexity. Given that classical multi-block ADMM does not guarantee convergence, the Majorized Proximal Augmented Lagrangian Method (MPALM), which shares a similar form with multi-block ADMM and ensures convergence, is more suitable in this setting. Despite its theoretical advantages, MPALM's performance is highly sensitive to the choice of penalty parameters. To address this limitation, we propose a novel L2O approach that adaptively selects this hyperparameter using supervised learning. We demonstrate the versatility and effectiveness of our method by applying it to the Lasso problem and the optimal transport problem. Our numerical results show that the proposed framework outperforms popular alternatives. Given its applicability to generic linearly constrained composite optimization problems, this work opens the door to a wide range of potential real-world applications.

math.OC↗

arXiv2024

Fast and Certifiable Trajectory Optimization

We propose semidefinite trajectory optimization (STROM), a framework that computes fast and certifiably optimal solutions for nonconvex trajectory optimization problems defined by polynomial objectives and constraints. STROM employs sparse second-order Lasserre's hierarchy to generate semidefinite program (SDP) relaxations of trajectory optimization. Different from existing tools (e.g., YALMIP and SOSTOOLS in Matlab), STROM generates chain-like multiple-block SDPs with only positive semidefinite (PSD) variables. Moreover, STROM does so two orders of magnitude faster. Underpinning STROM is cuADMM, the first ADMM-based SDP solver implemented in CUDA and runs in GPUs (with C/C++ extension). cuADMM builds upon the symmetric Gauss-Seidel ADMM algorithm and leverages GPU parallelization to speedup solving sparse linear systems and projecting onto PSD cones. In five trajectory optimization problems (inverted pendulum, cart-pole, vehicle landing, flying robot, and car back-in), cuADMM computes optimal trajectories (with certified suboptimality below 1%) in minutes (when other solvers take hours or run out of memory) and seconds (when others take minutes). Further, when warmstarted by data-driven initialization in the inverted pendulum problem, cuADMM delivers real-time performance: providing certifiably optimal trajectories in 0.66 seconds despite the SDP has 49,500 variables and 47,351 constraints.

math.OC↗

arXiv2024

On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization

We consider a regularized expected reward optimization problem in the non-oblivious setting that covers many existing problems in reinforcement learning (RL). In order to solve such an optimization problem, we apply and analyze the classical stochastic proximal gradient method. In particular, the method has shown to admit an $O(ε^{-4})$ sample complexity to an $ε$-stationary point, under standard conditions. Since the variance of the classical stochastic gradient estimator is typically large, which slows down the convergence, we also apply an efficient stochastic variance-reduce proximal gradient method with an importance sampling based ProbAbilistic Gradient Estimator (PAGE). Our analysis shows that the sample complexity can be improved from $O(ε^{-4})$ to $O(ε^{-3})$ under additional conditions. Our results on the stochastic (variance-reduced) proximal gradient method match the sample complexity of their most competitive counterparts for discounted Markov decision processes under similar settings. To the best of our knowledge, the proposed methods represent a novel approach in addressing the general regularized reward optimization problem.

cs.LG↗

arXiv2024

The Exploration-Exploitation Dilemma Revisited: An Entropy Perspective

The imbalance of exploration and exploitation has long been a significant challenge in reinforcement learning. In policy optimization, excessive reliance on exploration reduces learning efficiency, while over-dependence on exploitation might trap agents in local optima. This paper revisits the exploration-exploitation dilemma from the perspective of entropy by revealing the relationship between entropy and the dynamic adaptive process of exploration and exploitation. Based on this theoretical insight, we establish an end-to-end adaptive framework called AdaZero, which automatically determines whether to explore or to exploit as well as their balance of strength. Experiments show that AdaZero significantly outperforms baseline models across various Atari and MuJoCo environments with only a single setting. Especially in the challenging environment of Montezuma, AdaZero boosts the final returns by up to fifteen times. Moreover, we conduct a series of visualization analyses to reveal the dynamics of our self-adaptive mechanism, demonstrating how entropy reflects and changes with respect to the agent's performance and adaptive process.

cs.LG↗

arXiv2024

AdapMoE: Adaptive Sensitivity-based Expert Gating and Management for Efficient MoE Inference

Mixture-of-Experts (MoE) models are designed to enhance the efficiency of large language models (LLMs) without proportionally increasing the computational demands. However, their deployment on edge devices still faces significant challenges due to high on-demand loading overheads from managing sparsely activated experts. This paper introduces AdapMoE, an algorithm-system co-design framework for efficient MoE inference. AdapMoE features adaptive expert gating and management to reduce the on-demand loading overheads. We observe the heterogeneity of experts loading across layers and tokens, based on which we propose a sensitivity-based strategy to adjust the number of activated experts dynamically. Meanwhile, we also integrate advanced prefetching and cache management techniques to further reduce the loading latency. Through comprehensive evaluations on various platforms, we demonstrate AdapMoE consistently outperforms existing techniques, reducing the average number of activated experts by 25% and achieving a 1.35x speedup without accuracy degradation. Code is available at: https://github.com/PKU-SEC-Lab/AdapMoE.

cs.LG↗

arXiv2024

TensorTEE: Unifying Heterogeneous TEE Granularity for Efficient Secure Collaborative Tensor Computing

Heterogeneous collaborative computing with NPU and CPU has received widespread attention due to its substantial performance benefits. To ensure data confidentiality and integrity during computing, Trusted Execution Environments (TEE) is considered a promising solution because of its comparatively lower overhead. However, existing heterogeneous TEE designs are inefficient for collaborative computing due to fine and different memory granularities between CPU and NPU. 1) The cacheline granularity of CPU TEE intensifies memory pressure due to its extra memory access, and 2) the cacheline granularity MAC of NPU escalates the pressure on the limited memory storage. 3) Data transfer across heterogeneous enclaves relies on the transit of non-secure regions, resulting in cumbersome re-encryption and scheduling. To address these issues, we propose TensorTEE, a unified tensor-granularity heterogeneous TEE for efficient secure collaborative tensor computing. First, we virtually support tensor granularity in CPU TEE to eliminate the off-chip metadata access by detecting and maintaining tensor structures on-chip. Second, we propose tensor-granularity MAC management with predictive execution to avoid computational stalls while eliminating off-chip MAC storage and access. Moreover, based on the unified granularity, we enable direct data transfer without re-encryption and scheduling dilemmas. Our evaluation is built on enhanced Gem5 and a cycle-accurate NPU simulator. The results show that TensorTEE improves the performance of Large Language Model (LLM) training workloads by 4.0x compared to existing work and incurs only 2.1% overhead compared to non-secure training, offering a practical security assurance for LLM training.

cs.CR↗

arXiv2024

A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems

The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications. This paper proposes to solve the discrete OT problem by applying a squared smoothing Newton method via the Huber smoothing function for solving the corresponding KKT system directly. The proposed algorithm admits appealing convergence properties and is able to take advantage of the solution sparsity to greatly reduce computational costs. Moreover, the algorithm can be extended to solve problems with similar structures including the Wasserstein barycenter (WB) problem with fixed supports. To verify the practical performance of the proposed method, we conduct extensive numerical experiments to solve a large set of discrete OT and WB benchmark problems. Our numerical results show that the proposed method is efficient compared to state-of-the-art linear programming (LP) solvers. Moreover, the proposed method consumes less memory than existing LP solvers, which demonstrates the potential usage of our algorithm for solving large-scale OT and WB problems.

math.OC↗

arXiv2024

A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-quadratic Regularized Optimal Transport Problems

The optimal transport (OT) problem and its related problems have attracted significant attention and have been extensively studied in various applications. In this paper, we focus on a class of group-quadratic regularized OT problems which aim to find solutions with specialized structures that are advantageous in practical scenarios. To solve this class of problems, we propose a corrected inexact proximal augmented Lagrangian method (ciPALM), with the subproblems being solved by the semi-smooth Newton ({\sc Ssn}) method. We establish that the proposed method exhibits appealing convergence properties under mild conditions. Moreover, our ciPALM distinguishes itself from the recently developed semismooth Newton-based inexact proximal augmented Lagrangian ({\sc Snipal}) method for linear programming. Specifically, {\sc Snipal} uses an absolute error criterion for the approximate minimization of the subproblem for which a summable sequence of tolerance parameters needs to be pre-specified for practical implementations. In contrast, our ciPALM adopts a relative error criterion with a \textit{single} tolerance parameter, which would be more friendly to tune from computational and implementation perspectives. These favorable properties position our ciPALM as a promising candidate for tackling large-scale problems. Various numerical studies validate the effectiveness of employing a relative error criterion for the inexact proximal augmented Lagrangian method, and also demonstrate that our ciPALM is competitive for solving large-scale group-quadratic regularized OT problems.

math.OC↗

arXiv2023

NP-Hardness of Tensor Network Contraction Ordering

We study the optimal order (or sequence) of contracting a tensor network with a minimal computational cost. We conclude 2 different versions of this optimal sequence: that minimize the operation number (OMS) and that minimize the time complexity (CMS). Existing results only shows that OMS is NP-hard, but no conclusion on CMS problem. In this work, we firstly reduce CMS to CMS-0, which is a sub-problem of CMS with no free indices. Then we prove that CMS is easier than OMS, both in general and in tree cases. Last but not least, we prove that CMS is still NP-hard. Based on our results, we have built up relationships of hardness of different tensor network contraction problems.

cs.CC↗

arXiv2023

Computing one-bit compressive sensing via zero-norm regularized DC loss model and its surrogate

One-bit compressed sensing is very popular in signal processing and communications due to its low storage costs and low hardware complexity, but it is a challenging task to recover the signal by using the one-bit information. In this paper, we propose a zero-norm regularized smooth difference of convexity (DC) loss model and derive a family of equivalent nonconvex surrogates covering the MCP and SCAD surrogates as special cases. Compared to the existing models, the new model and its SCAD surrogate have better robustness. To compute their $τ$-stationary points, we develop a proximal gradient algorithm with extrapolation and establish the convergence of the whole iterate sequence. Also, the convergence is proved to have a linear rate under a mild condition by studying the KL property of exponent 0 of the models. Numerical comparisons with several state-of-art methods show that in terms of the quality of solution, the proposed model and its SCAD surrogate are remarkably superior to the $\ell_p$-norm regularized models, and are comparable even superior to those sparsity constrained models with the true sparsity and the sign flip ratio as inputs.

math.OC↗

arXiv2022

An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving large-scale CMOT problems. The experiments on the discrete tomography problem also highlight the potential modeling power of our model.

math.OC↗

arXiv2022

Toward Robust Spiking Neural Network Against Adversarial Perturbation

As spiking neural networks (SNNs) are deployed increasingly in real-world efficiency critical applications, the security concerns in SNNs attract more attention. Currently, researchers have already demonstrated an SNN can be attacked with adversarial examples. How to build a robust SNN becomes an urgent issue. Recently, many studies apply certified training in artificial neural networks (ANNs), which can improve the robustness of an NN model promisely. However, existing certifications cannot transfer to SNNs directly because of the distinct neuron behavior and input formats for SNNs. In this work, we first design S-IBP and S-CROWN that tackle the non-linear functions in SNNs' neuron modeling. Then, we formalize the boundaries for both digital and spike inputs. Finally, we demonstrate the efficiency of our proposed robust training method in different datasets and model architectures. Based on our experiment, we can achieve a maximum $37.7\%$ attack error reduction with $3.7\%$ original accuracy loss. To the best of our knowledge, this is the first analysis on robust training of SNNs.

cs.NE↗