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Ling Liang

Publications and source records attributed to Ling Liang.

At least 37 records · Page 2Linked to original sources

Do Less, Achieve More: Do We Need Every-Step Optimization for RL Fine-tuning of Diffusion Models?

Despite strong image-generation performance, diffusion models' reconstruction objectives limit alignment with human preferences. RL enables such alignment through explicit rewards. However, most studies apply RL to the full denoising trajectory, making it computationally costly and weakening preference alignment, i.e., doing more but achieving less. We observe that the impact of RL fine-tuning varies significantly across denoising stages. In the early stage, image structures are unstable and distant from the final reward signal. Applying RL at this stage leads to delayed rewards and action-reward mismatching, resulting in high variance and inefficient updates. Conversely, in the later stage, reward gains saturate, and continued training tends to overfit local details, intensifying reward hacking. To tackle these challenges, we propose AdaScope, an RL-enhanced plug-in that improves generation quality while reducing computational cost. Specifically, AdaScope adaptively identifies the optimal intervention timing for RL by perceiving the structural evolution and semantic consistency during denoising, and dynamically terminates training once the denoising converges and reward gains saturate. As a result, it achieves a rare 'dual benefit': a reduction in computational costs alongside a significant performance improvement. We offer theoretical grounds for the design of AdaScope. Compared with state-of-the-art methods, AdaScope improves performance by 66% while cutting computational cost by 59%.

cs.CV↗

PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the regularization parameter is small, Sinkhorn convergence slows, and the iterates approach an entropic solution that remains separated from the true OT plan by an entropic-bias plateau. We introduce PINS (Proximal Iterations with sparse Newton and Sinkhorn), a two-loop solver designed to move beyond this plateau. The outer loop applies an entropic proximal-point method, solving the original OT problem through a sequence of entropic subproblems with shifted cost matrices. Each inner subproblem is then solved by a Sinkhorn warm-up followed by sparse-Newton refinement. We prove that PINS converges globally to an optimal solution of the unregularized OT problem and that the inner Hessian admits a sparsification at every outer iteration with a structure independent of the cost matrix. On synthetic and augmented-MNIST instances, PINS achieves much lower relative cost errors than Sinkhorn-type baselines, which stall at the entropic-bias plateau, and is $5$--$73\times$ faster than Sinkhorn with the same outer loop at matched accuracy. On large-scale DOTmark instances, a streaming implementation reduces peak memory by $24$--$54\%$ compared with the network-simplex linear programming (LP) solver and remains feasible under per-process memory budgets for which the LP solver fails.

cs.LG↗

ripALM: A Relative-Type Inexact Proximal Augmented Lagrangian Method for Linearly Constrained Convex Optimization

Inexact proximal augmented Lagrangian methods (ipALMs) have been widely used for solving linearly constrained convex optimization problems, owing to their strong theoretical guarantees and excellent numerical performance. In practice, however, existing ipALMs typically employ Rockafellar-type absolute error criteria for solving the subproblems, which require delicate problem-dependent tuning of error-tolerance sequences. In this paper, we propose ripALM, a relative-type ipALM whose subproblem error criterion has only a \textit{single} tolerance parameter in $[0,1)$. This makes the method simpler to implement and less sensitive to parameter tuning in practice. On the other hand, the use of such a relative-type error criterion renders the convergence of our ripALM beyond the scope of the convergence theory of existing ipALMs. To address this gap, we develop a new analysis framework under which ripALM is shown to admit desirable global convergence properties and it achieves an asymptotic (super)linear convergence rate under a standard error bound condition. While there exist other relative-type inexact pALMs, to ensure convergence, they require additional correct steps that generally impede the convergence speed. To the best of our knowledge, ripALM is the first relative-type inexact version of the vanilla pALM that avoids both summable tolerance parameter sequences and correction steps, while retaining rigorous convergence guarantees. Numerical experiments on quadratically regularized optimal transport and basis pursuit denoising problems demonstrate the effectiveness and robustness of our proposed method.

math.OC↗

A Breast Vision Pathology Foundation Model for Real-world Clinical Utility

Pathology foundation models have shown strong retrospective performance, but whether such systems can support clinically relevant use remains unclear. This challenge is particularly important in breast cancer, where pathological assessment serves as the gold standard for diagnosis and guides treatment planning, surgical decision-making and risk stratification across pre-, intra- and post-operative stages. Here we present \textbf{BRAVE}, a breast-adaptive pathology foundation model developed and evaluated using a total resource of 101,638 breast whole-slide images from 32 sources across Asia, Europe and North America. We assessed BRAVE across 34 tasks in 82 cohorts spanning pre-operative biopsy, intra-operative frozen section and post-operative resection, using an evidence chain comprising retrospective benchmarking, clinically challenging scenarios, workflow-oriented clinical impact simulations, prospective observational validation with the thresholds locked in the retrospective cohorts and crossover pathologist-AI interaction studies. Across these settings, BRAVE supported practical roles in the clinical workflow, including safe exclusion of low-risk cases from routine review, AI-assisted second-review rescue of initially missed positives and prioritization of cases for further assessment. In prospective validation across three centres, BRAVE excluded 76.9% of negative biopsy cases (NPV 0.953) and 70.1% of negative frozen-section cases (NPV 0.973), and triaged 78.8% of post-operative subtyping cases as high-confidence clear-cut cases (NPV 1.000). In reader studies, AI assistance improved balanced accuracy from 88.5% to 95.1% (OR 3.14, P<0.001), with better efficiency, confidence and inter-rater agreement. BRAVE-derived scores also independently predicted disease-free survival (adjusted HR 4.79, P<0.001) and overall survival (adjusted HR 8.14, P<0.001).

cs.CV↗

A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport

Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport polytope is often solved only approximately in practice. This leads to a gap between practical projected-gradient implementations and convergence theory, which typically assumes exact projections. For squared-loss GWOT, we propose an inexact projected-gradient framework with a verifiable feasibility-residual-based inexact condition for the projection subproblem. This condition is directly computable and avoids unknown quantities such as the exact projection point. Under this implementable condition, we prove subsequential convergence to stationary points and, with a mild tolerance-decay condition, convergence of the whole sequence. The resulting method retains the simplicity and sparsity of projected-gradient schemes while providing rigorous convergence guarantees, turning projected-gradient methods into a principled and scalable approach for GWOT with provable reliability.

cs.LG↗

Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions

Bayesian Optimal Experimental Design (BOED) provides a rigorous framework for decision-making tasks in which data acquisition is often the critical bottleneck, especially in resource-constrained settings. Traditionally, BOED typically selects designs by maximizing expected information gain (EIG), commonly defined through the Kullback-Leibler (KL) divergence. However, classical evaluation of EIG often involves challenging nested expectations, and even advanced variational methods leave the underlying log-density-ratio objective unchanged. As a result, support mismatch, tail underestimation, and rare-event sensitivity remain intrinsic concerns for KL-based BOED. To address these fundamental bottlenecks, we introduce an IPM-based BOED framework that replaces density-based divergences with integral probability metrics (IPMs), including the Wasserstein distance, Maximum Mean Discrepancy, and Energy Distance, resulting in a highly flexible plug-and-play BOED framework. We establish theoretical guarantees showing that IPM-based utilities provide stronger geometry-aware stability under surrogate-model error and prior misspecification than classical EIG-based utilities. We also validate the proposed framework empirically, demonstrating that IPM-based designs yield highly concentrated credible sets. Furthermore, by extending the same sample-based BOED template in a plug-and-play manner to geometry-aware discrepancies beyond the IPM class, illustrated by a neural optimal transport estimator, we achieve accurate optimal designs in high-dimensional settings where conventional nested Monte Carlo estimators and advanced variational methods fail.

stat.ML↗

Convergence Analysis of a Relative-type Inexact Preconditioned Proximal ALM for Convex Nonlinear Programming

This article investigates the convergence properties of a relative-type inexact preconditioned proximal augmented Lagrangian method (rip$^2$ALM) for convex nonlinear programming, a fundamental class of optimization problems with broad applications in science and engineering. Inexact proximal augmented Lagrangian methods have proven to be highly effective for solving such problems, owing to their attractive theoretical properties and strong practical performance. However, the convergence behavior of the relative-type inexact preconditioned variant remains insufficiently understood. This work aims to reduce this gap by rigorously establishing the global convergence of the sequence generated by rip$^2$ALM and proving its asymptotic (super)linear convergence rate under standard assumptions. In addition, we derive the global ergodic convergence rate with respect to both the primal feasibility violation and the primal objective residual, thereby offering a more comprehensive understanding of the overall performance of rip$^2$ALM. These results deepen our theoretical understanding of the family of proximal augmented Lagrangian methods and motivate their development for practical, large-scale structured application problems.

math.OC↗

Fast and Effective Computation of Generalized Symmetric Matrix Factorization

In this paper, we study a nonconvex, nonsmooth, and non-Lipschitz generalized symmetric matrix factorization model that unifies a broad class of matrix factorization formulations arising in machine learning, image science, engineering, and related areas. We first establish two exactness properties. On the modeling side, we prove an exact penalty property showing that, under suitable conditions, the symmetry-inducing quadratic penalty enforces symmetry whenever the penalty parameter is sufficiently large but finite, thereby exactly recovering the associated symmetric formulation. On the algorithmic side, we introduce an auxiliary-variable splitting formulation and establish an exact relaxation relationship that rigorously links stationary points of the original objective function to those of a relaxed potential function. Building on these exactness properties, we propose an average-type nonmonotone alternating updating method (A-NAUM) based on the relaxed potential function. At each iteration, A-NAUM alternately updates the two factor blocks by (approximately) minimizing the potential function, while the auxiliary block is updated in closed form. To ensure the convergence and enhance practical performance, we further incorporate an average-type nonmonotone line search and show that it is well-defined under mild conditions. Moreover, based on the Kurdyka-Łojasiewicz property and its associated exponent, we establish global convergence of the entire sequence to a stationary point and derive convergence rate results. Finally, numerical experiments on real datasets demonstrate the efficiency of A-NAUM.

math.OC↗

Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition

This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems. BM-Global efficiently decreases the objective value via low-cost steps leveraging the nonconvex but smooth Burer-Monteiro (BM) decomposition, while effectively escapes saddle points and spurious local minima ubiquitous in the BM form to obtain guarantees of fast convergence rates to the global optima of the original nuclear-norm-regularized problem through aperiodic inexact proximal gradient steps on it. The proposed approach adaptively adjusts the rank for the BM decomposition and can provably identify an optimal rank for the BM decomposition problem automatically in the course of optimization through tools of manifold identification. BM-Global hence also spends significantly less time on parameter tuning than existing matrix-factorization methods, which require an exhaustive search for finding this optimal rank. Extensive experiments on real-world large-scale problems of recommendation systems, regularized kernel estimation, and molecular conformation confirm that BM-Global can indeed effectively escapes spurious local minima at which existing BM approaches are stuck, and is a magnitude faster than state-of-the-art algorithms for low-rank matrix optimization problems involving a nuclear-norm regularizer. Based on this research, we have released an open-source package of the proposed BM-Global at https://www.github.com/leepei/BM-Global/.

cs.LG↗

D-ripALM: A Tuning-friendly Decentralized Relative-Type Inexact Proximal Augmented Lagrangian Method

This paper proposes D-ripALM, a Decentralized relative-type inexact proximal Augmented Lagrangian Method for consensus convex optimization over multi-agent networks. D-ripALM adopts a double-loop distributed optimization framework that accommodates a wide range of inner solvers, enabling efficient treatment of both smooth and nonsmooth objectives. In contrast to existing double-loop distributed augmented Lagrangian methods, D-ripALM employs a relative-type error criterion to regulate the switching between inner and outer iterations, resulting in a more practical and tuning-friendly algorithmic framework with enhanced numerical robustness. Moreover, we establish rigorous convergence guarantees for D-ripALM under general convexity assumptions, without requiring smoothness or strong convexity conditions commonly imposed in the distributed optimization literature. Numerical experiments further demonstrate the tuning-friendly nature of D-ripALM and its efficiency in attaining high-precision solutions with fewer communication rounds.

math.OC↗

OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents

Optimization plays a vital role in scientific research and practical applications. However, formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce OptimAI, a framework for solving Optimization problems described in natural language by leveraging LLM-powered AI agents, and achieve superior performance over current state-of-the-art methods. Our framework is built upon the following key roles: (1) a formulator that translates natural language problem descriptions into precise mathematical formulations; (2) a planner that constructs a high-level solution strategy prior to execution; and (3) a coder and a code critic capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in $5.8\times$ and $3.1\times$ drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional $3.3\times$ productivity gain. Our design emphasizes multi-agent collaboration, and our experiments confirm that combining diverse models leads to performance gains. Our approach attains 88.1% accuracy on the NLP4LP dataset and 82.3% on the Optibench dataset, reducing error rates by 58% and 52%, respectively, over prior best results.

cs.CL↗

Inner-Probe: Discovering Copyright-related Data Generation in LLM Architecture

Large Language Models (LLMs) utilize extensive knowledge databases and show powerful text generation ability. However, their reliance on high-quality copyrighted datasets raises concerns about copyright infringements in generated texts. Current research often employs prompt engineering or semantic classifiers to identify copyrighted content, but these approaches have two significant limitations: (1) Challenging to identify which specific subdataset (e.g., works from particular authors) influences an LLM's output. (2) Treating the entire training database as copyrighted, hence overlooking the inclusion of non-copyrighted training data. We propose Inner-Probe, a lightweight framework designed to evaluate the influence of copyrighted sub-datasets on LLM-generated texts. Unlike traditional methods relying solely on text, we discover that the results of multi-head attention (MHA) during LLM output generation provide more effective information. Thus, Inner-Probe performs sub-dataset contribution analysis using a lightweight LSTM based network trained on MHA results in a supervised manner. Harnessing such a prior, Inner-Probe enables non-copyrighted text detection through a concatenated global projector trained with unsupervised contrastive learning. Inner-Probe demonstrates 3x improved efficiency compared to semantic model training in sub-dataset contribution analysis on Books3, achieves 15.04% - 58.7% higher accuracy over baselines on the Pile, and delivers a 0.104 increase in AUC for non-copyrighted data filtering.

cs.CL↗

A Sanity Check for Multi-In-Domain Face Forgery Detection in the Real World

Existing methods for deepfake detection aim to develop generalizable detectors. Although "generalizable" is the ultimate target once and for all, with limited training forgeries and domains, it appears idealistic to expect generalization that covers entirely unseen variations, especially given the diversity of real-world deepfakes. Therefore, introducing large-scale multi-domain data for training can be feasible and important for real-world applications. However, within such a multi-domain scenario, the differences between multiple domains, rather than the subtle real/fake distinctions, dominate the feature space. As a result, despite detectors being able to relatively separate real and fake within each domain (i.e., high AUC), they struggle with single-image real/fake judgments in domain-unspecified conditions (i.e., low ACC). In this paper, we first define a new research paradigm named Multi-In-Domain Face Forgery Detection (MID-FFD), which includes sufficient volumes of real-fake domains for training. Then, the detector should provide definitive real-fake judgments to the domain-unspecified inputs, which simulate the frame-by-frame independent detection scenario in the real world. Meanwhile, to address the domain-dominant issue, we propose a model-agnostic framework termed DevDet (Developer for Detector) to amplify real/fake differences and make them dominant in the feature space. DevDet consists of a Face Forgery Developer (FFDev) and a Dose-Adaptive detector Fine-Tuning strategy (DAFT). Experiments demonstrate our superiority in predicting real-fake under the MID-FFD scenario while maintaining original generalization ability to unseen data.

cs.CV↗

From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs

Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention. While most existing research concentrates on theoretical properties (such as well-posedness, regularity, and continuity) of the solutions, alongside direct AI-driven methods for solving PDEs, the challenge of uncovering symbolic relationships within these equations remains largely unexplored. In this paper, we propose leveraging large language models (LLMs) to learn such symbolic relationships. Our results demonstrate that LLMs can effectively predict the operators involved in PDE solutions by utilizing the symbolic information in the PDEs both theoretically and numerically. Furthermore, we show that discovering these symbolic relationships can substantially improve both the efficiency and accuracy of symbolic machine learning for finding analytical approximation of PDE solutions, delivering a fully interpretable solution pipeline. This work opens new avenues for understanding the symbolic structure of scientific problems and advancing their solution processes.

cs.LG↗

Nesterov's Accelerated Jacobi-Type Methods for Large-scale Symmetric Positive Semidefinite Linear Systems

Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their forms and friendliness to parallelization, they are not attractive either because of the potential convergence failure or their slow convergence rate. This paper aims to showcase the possibility of improving classical Jacobi-type methods by employing Nesterov's acceleration technique that results in an accelerated Jacobi-type method with improved convergence properties. Simultaneously, it preserves the appealing features for parallel implementation. In particular, we show that the proposed method has an $O\left(t^{-2}\right)$ convergence rate in terms of objective function values of the associated convex quadratic optimization problem, where $t\geq 1$ denotes the iteration counter. To further improve the practical performance of the proposed method, we also develop and analyze a restarted variant of the method, which is shown to have an $O\left((\log_2(t))^2t^{-2}\right)$ convergence rate when the coefficient matrix is positive definite. Furthermore, we conduct appropriate numerical experiments to evaluate the efficiency of the proposed method. Our numerical results demonstrate that the proposed method outperforms the classical Jacobi-type methods and the conjugate gradient method, and shows a comparable performance as the preconditioned conjugate gradient method with a diagonal preconditioner. Finally, we develop a parallel implementation and conduct speed-up tests on some large-scale systems. Our results indicate that the proposed framework is highly scalable.

math.OC↗

NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems

We propose \textbf{NewVEM}, a Newton vertex exchange method for efficiently solving self-concordant minimization problems under generalized simplex constraints. The algorithm features a two-level structure: the outer loop employs a projected Newton method, and the inner loop uses a vertex exchange approach to solve strongly convex quadratic subproblems. Both loops converge locally at linear rates under technical conditions, resulting in a ``fast $\times$ fast'' framework that demonstrates high efficiency and scalability in practice. To get a feasible initial point to execute the algorithm, we also present and analyze a highly efficient semismooth Newton method for computing the projection onto the generalized simplex. The excellent practical performance of the proposed algorithms is demonstrated by a set of numerical experiments. Our results further motivate the potential real-world applications of the considered model and the proposed algorithms.

math.OC↗

Ironman: Accelerating Oblivious Transfer Extension for Privacy-Preserving AI with Near-Memory Processing

With the wide application of machine learning (ML), privacy concerns arise with user data as they may contain sensitive information. Privacy-preserving ML (PPML) based on cryptographic primitives has emerged as a promising solution in which an ML model is directly computed on the encrypted data to provide a formal privacy guarantee. However, PPML frameworks heavily rely on the oblivious transfer (OT) primitive to compute nonlinear functions. OT mainly involves the computation of single-point correlated OT (SPCOT) and learning parity with noise (LPN) operations. As OT is still computed extensively on general-purpose CPUs, it becomes the latency bottleneck of modern PPML frameworks. In this paper, we propose a novel OT accelerator, dubbed Ironman, to significantly increase the efficiency of OT and the overall PPML framework. We observe that SPCOT is computation-bounded, and thus propose a hardware-friendly SPCOT algorithm with a customized accelerator to improve SPCOT computation throughput. In contrast, LPN is memory-bandwidth-bounded due to irregular memory access patterns. Hence, we further leverage the near-memory processing (NMP) architecture equipped with memory-side cache and index sorting to improve effective memory bandwidth. With extensive experiments, we demonstrate Ironman achieves a 39.2-237.4 times improvement in OT throughput across different NMP configurations compared to the full-thread CPU implementation. For different PPML frameworks, Ironman demonstrates a 2.1-3.4 times reduction in end-to-end latency for both CNN and Transformer models.

cs.AR↗

Group zero-norm regularized robust loss minimization: proximal MM method and statistical error bound

This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization problems. First, we present the core principles and iterative framework of the PMM method. Under the Kurdyka-Łojasiewicz (KL) property assumption of the potential function, we establish the global convergence of the algorithm and characterize its local (sub)linear convergence rate. Furthermore, for linear observation models with design matrices satisfying restricted eigenvalue conditions, we derive statistical estimation error bounds between the PMM-generated iterates (including their limit points) and the ground truth solution. These bounds not only rigorously quantify the approximation accuracy of the algorithm but also extend previous results on element-wise sparse composite optimization from reference [57]. To efficiently implement the PMM framework, we develop a proximal dual semismooth Newton method for solving critical subproblems. Extensive numerical experiments on both synthetic data and the UCI benchmark demonstrate the superior computational efficiency of our PMM method compared to the proximal Alternating Direction Method of Multipliers (pADMM).

math.OC↗