arXiv subjects

Bingcong Li

Publications and source records attributed to Bingcong Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

PoLAR: Polar-Decomposed Low-Rank Adapter Representation

We show that low-rank adaptation of large-scale models suffers from a low stable rank that is well below the linear algebraic rank of the subspace, degrading fine-tuning performance. To mitigate the underutilization of the allocated subspace, we propose PoLAR, a parameterization inspired by the polar decomposition that factorizes the low-rank update into two direction matrices constrained to Stiefel manifolds and an unconstrained scale matrix. Our theory shows that PoLAR yields an exponentially faster convergence rate on a canonical low-rank adaptation problem. Pairing the parameterization with Riemannian optimization leads to consistent gains on three different benchmarks testing general language understanding, commonsense reasoning, and mathematical problem solving with base model sizes ranging from 350M to 27B.

cs.LG↗

arXiv2025

Learnable Loss Geometries with Mirror Descent for Scalable and Convergent Meta-Learning

Utilizing task-invariant knowledge acquired from related tasks as prior information, meta-learning offers a principled approach to learning a new task with limited data records. Sample-efficient adaptation of this prior information is a major challenge facing meta-learning, and plays an important role because it facilitates training the sought task-specific model with just a few optimization steps. Past works deal with this challenge through preconditioning that speeds up convergence of the per-task training. Though effective in representing locally quadratic loss curvatures, simple linear preconditioning can be hardly potent with complex loss geometries. Instead of relying on a quadratic distance metric, the present contribution copes with complex loss metrics by learning a versatile distance-generating function, which induces a nonlinear mirror map to effectively capture and optimize a wide range of loss geometries. With suitable parameterization, this generating function is effected by an expressive neural network that is provably a valid distance. Analytical results establish convergence of not only the proposed method, but also all meta-learning approaches based on preconditioning. To attain gradient norm less than $ε$, the convergence rate of $\mathcal{O}(ε^{-2})$ is on par with standard gradient-based meta-learning methods. Numerical tests on few-shot learning datasets demonstrate the superior empirical performance of the novel algorithm, as well as its rapid per-task convergence, which markedly reduces the number of adaptation steps, hence also accommodating large-scale meta-learning models.

cs.LG↗

arXiv2025

VASSO: Variance Suppression for Sharpness-Aware Minimization

Sharpness-aware minimization (SAM) has well-documented merits in enhancing generalization of deep neural network models. Accounting for sharpness in the loss function geometry, where neighborhoods of `flat minima' heighten generalization ability, SAM seeks `flat valleys' by minimizing the maximum loss provoked by an adversarial perturbation within the neighborhood. Although critical to account for sharpness of the loss function, in practice SAM suffers from `over-friendly adversaries,' which can curtail the outmost level of generalization. To avoid such `friendliness,' the present contribution fosters stabilization of adversaries through variance suppression (VASSO). VASSO offers a general approach to provably stabilize adversaries. In particular, when integrating VASSO with SAM, improved generalizability is numerically validated on extensive vision and language tasks. Once applied on top of a computationally efficient SAM variant, VASSO offers a desirable generalization-computation tradeoff.

cs.LG↗

arXiv2025

Can RLHF be More Efficient with Imperfect Reward Models? A Policy Coverage Perspective

Sample efficiency is critical for online Reinforcement Learning from Human Feedback (RLHF). While existing works investigate sample-efficient online exploration strategies, the potential of utilizing misspecified yet relevant reward models to accelerate learning remains underexplored. This paper studies how to transfer knowledge from those imperfect reward models in online RLHF. We start by identifying a novel property due to KL-regularization in the RLHF objective: \emph{a policy's coverability of the optimal policy is captured by its sub-optimality}. Building on this insight, we propose novel transfer learning principles and a theoretical algorithm -- \emph{\textbf{T}ransfer \textbf{P}olicy \textbf{O}ptimization (\textbf{TPO})} -- with provable benefits compared to standard online learning. Empirically, inspired by our theoretical findings, we develop a win-rate-based transfer policy selection strategy with improved computational efficiency. Moreover, our empirical transfer learning technique is modular and can be integrated with various policy optimization methods, such as DPO, IPO and XPO, to further enhance their performance. We validate the effectiveness of our method through experiments on summarization tasks.

cs.LG↗

arXiv2025

Preconditioned Sharpness-Aware Minimization: Unifying Analysis and a Novel Learning Algorithm

Targeting solutions over `flat' regions of the loss landscape, sharpness-aware minimization (SAM) has emerged as a powerful tool to improve generalizability of deep neural network based learning. While several SAM variants have been developed to this end, a unifying approach that also guides principled algorithm design has been elusive. This contribution leverages preconditioning (pre) to unify SAM variants and provide not only unifying convergence analysis, but also valuable insights. Building upon preSAM, a novel algorithm termed infoSAM is introduced to address the so-called adversarial model degradation issue in SAM by adjusting gradients depending on noise estimates. Extensive numerical tests demonstrate the superiority of infoSAM across various benchmarks.

cs.LG↗

arXiv2024

On the Crucial Role of Initialization for Matrix Factorization

This work revisits the classical low-rank matrix factorization problem and unveils the critical role of initialization in shaping convergence rates for such nonconvex and nonsmooth optimization. We introduce Nystrom initialization, which significantly improves the global convergence of Scaled Gradient Descent (ScaledGD) in both symmetric and asymmetric matrix factorization tasks. Specifically, we prove that ScaledGD with Nystrom initialization achieves quadratic convergence in cases where only linear rates were previously known. Furthermore, we extend this initialization to low-rank adapters (LoRA) commonly used for finetuning foundation models. Our approach, NoRA, i.e., LoRA with Nystrom initialization, demonstrates superior performance across various downstream tasks and model scales, from 1B to 7B parameters, in large language and diffusion models.

cs.LG↗

arXiv2024

Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems

Sharpness-aware minimization (SAM) improves generalization of various deep learning tasks. Motivated by popular architectures such as LoRA, we explore the implicit regularization of SAM for scale-invariant problems involving two groups of variables. Instead of focusing on commonly used sharpness, this work introduces a concept termed balancedness, defined as the difference between the squared norm of two variables. This allows us to depict richer global behaviors of SAM. In particular, our theoretical and empirical findings reveal that i) SAM promotes balancedness; and ii) the regularization on balancedness is data-responsive -- outliers have stronger impact. The latter coincides with empirical observations that SAM outperforms SGD in the presence of outliers. Leveraging the implicit regularization, we develop a resource-efficient SAM variant, balancedness-aware regularization (BAR), tailored for scale-invariant problems such as finetuning language models with LoRA. BAR saves 95% computational overhead of SAM, with enhanced test performance across various tasks on RoBERTa, GPT2, and OPT-1.3B.

cs.LG↗

arXiv2024

DPZero: Private Fine-Tuning of Language Models without Backpropagation

The widespread practice of fine-tuning large language models (LLMs) on domain-specific data faces two major challenges in memory and privacy. First, as the size of LLMs continues to grow, the memory demands of gradient-based training methods via backpropagation become prohibitively high. Second, given the tendency of LLMs to memorize training data, it is important to protect potentially sensitive information in the fine-tuning data from being regurgitated. Zeroth-order methods, which rely solely on forward passes, substantially reduce memory consumption during training. However, directly combining them with standard differentially private gradient descent suffers more as model size grows. To bridge this gap, we introduce DPZero, a novel private zeroth-order algorithm with nearly dimension-independent rates. The memory efficiency of DPZero is demonstrated in privately fine-tuning RoBERTa and OPT on several downstream tasks. Our code is available at https://github.com/Liang137/DPZero.

cs.LG↗

arXiv2024

Meta-Learning with Versatile Loss Geometries for Fast Adaptation Using Mirror Descent

Utilizing task-invariant prior knowledge extracted from related tasks, meta-learning is a principled framework that empowers learning a new task especially when data records are limited. A fundamental challenge in meta-learning is how to quickly "adapt" the extracted prior in order to train a task-specific model within a few optimization steps. Existing approaches deal with this challenge using a preconditioner that enhances convergence of the per-task training process. Though effective in representing locally a quadratic training loss, these simple linear preconditioners can hardly capture complex loss geometries. The present contribution addresses this limitation by learning a nonlinear mirror map, which induces a versatile distance metric to enable capturing and optimizing a wide range of loss geometries, hence facilitating the per-task training. Numerical tests on few-shot learning datasets demonstrate the superior expressiveness and convergence of the advocated approach.

cs.LG↗

arXiv2023

Enhancing Sharpness-Aware Optimization Through Variance Suppression

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of 'flat minima' heighten generalization ability, SAM seeks 'flat valleys' by minimizing the maximum loss caused by an adversary perturbing parameters within the neighborhood. Although critical to account for sharpness of the loss function, such an 'over-friendly adversary' can curtail the outmost level of generalization. The novel approach of this contribution fosters stabilization of adversaries through variance suppression (VaSSO) to avoid such friendliness. VaSSO's provable stability safeguards its numerical improvement over SAM in model-agnostic tasks, including image classification and machine translation. In addition, experiments confirm that VaSSO endows SAM with robustness against high levels of label noise.

cs.LG↗

arXiv2023

Contractive error feedback for gradient compression

On-device memory concerns in distributed deep learning have become severe due to (i) the growth of model size in multi-GPU training, and (ii) the wide adoption of deep neural networks for federated learning on IoT devices which have limited storage. In such settings, communication efficient optimization methods are attractive alternatives, however they still struggle with memory issues. To tackle these challenges, we propose an communication efficient method called contractive error feedback (ConEF). As opposed to SGD with error-feedback (EFSGD) that inefficiently manages memory, ConEF obtains the sweet spot of convergence and memory usage, and achieves communication efficiency by leveraging biased and all-reducable gradient compression. We empirically validate ConEF on various learning tasks that include image classification, language modeling, and machine translation and observe that ConEF saves 80\% - 90\% of the extra memory in EFSGD with almost no loss on test performance, while also achieving 1.3x - 5x speedup of SGD. Through our work, we also demonstrate the feasibility and convergence of ConEF to clear up the theoretical barrier of integrating ConEF to popular memory efficient frameworks such as ZeRO-3.

cs.LG↗

arXiv2023

Conic Descent Redux for Memory-Efficient Optimization

Conic programming has well-documented merits in a gamut of signal processing and machine learning tasks. This contribution revisits a recently developed first-order conic descent (CD) solver, and advances it in three aspects: intuition, theory, and algorithmic implementation. It is found that CD can afford an intuitive geometric derivation that originates from the dual problem. This opens the door to novel algorithmic designs, with a momentum variant of CD, momentum conic descent (MOCO) exemplified. Diving deeper into the dual behavior CD and MOCO reveals: i) an analytically justified stopping criterion; and, ii) the potential to design preconditioners to speed up dual convergence. Lastly, to scale semidefinite programming (SDP) especially for low-rank solutions, a memory efficient MOCO variant is developed and numerically validated.

math.OC↗

arXiv2023

Scalable Bayesian Meta-Learning through Generalized Implicit Gradients

Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.

cs.LG↗

arXiv2021

Distributionally Robust Semi-Supervised Learning Over Graphs

Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly encoding local graph structures and features of nodes, state-of-the-art GNNs can scale linearly with the size of graph. Despite their success in practice, most of existing methods are unable to handle graphs with uncertain nodal attributes. Specifically whenever mismatches between training and testing data distribution exists, these models fail in practice. Challenges also arise due to distributional uncertainties associated with data acquired by noisy measurements. In this context, a distributionally robust learning framework is developed, where the objective is to train models that exhibit quantifiable robustness against perturbations. The data distribution is considered unknown, but lies within a Wasserstein ball centered around empirical data distribution. A robust model is obtained by minimizing the worst expected loss over this ball. However, solving the emerging functional optimization problem is challenging, if not impossible. Advocating a strong duality condition, we develop a principled method that renders the problem tractable and efficiently solvable. Experiments assess the performance of the proposed method.

cs.LG↗

arXiv2021

Heavy Ball Momentum for Conditional Gradient

Conditional gradient, aka Frank Wolfe (FW) algorithms, have well-documented merits in machine learning and signal processing applications. Unlike projection-based methods, momentum cannot improve the convergence rate of FW, in general. This limitation motivates the present work, which deals with heavy ball momentum, and its impact to FW. Specifically, it is established that heavy ball offers a unifying perspective on the primal-dual (PD) convergence, and enjoys a tighter per iteration PD error rate, for multiple choices of step sizes, where PD error can serve as the stopping criterion in practice. In addition, it is asserted that restart, a scheme typically employed jointly with Nesterov's momentum, can further tighten this PD error bound. Numerical results demonstrate the usefulness of heavy ball momentum in FW iterations.

math.OC↗

arXiv2021

PingAn-VCGroup's Solution for ICDAR 2021 Competition on Scientific Table Image Recognition to Latex

This paper presents our solution for the ICDAR 2021 Competition on Scientific Table Image Recognition to LaTeX. This competition has two sub-tasks: Table Structure Reconstruction (TSR) and Table Content Reconstruction (TCR). We treat both sub-tasks as two individual image-to-sequence recognition problems. We leverage our previously proposed algorithm MASTER \cite{lu2019master}, which is originally proposed for scene text recognition. We optimize the MASTER model from several perspectives: network structure, optimizer, normalization method, pre-trained model, resolution of input image, data augmentation, and model ensemble. Our method achieves 0.7444 Exact Match and 0.8765 Exact Match @95\% on the TSR task, and obtains 0.5586 Exact Match and 0.7386 Exact Match 95\% on the TCR task.

cs.CV↗

arXiv2021

Adversarial Linear Contextual Bandits with Graph-Structured Side Observations

This paper studies the adversarial graphical contextual bandits, a variant of adversarial multi-armed bandits that leverage two categories of the most common side information: \emph{contexts} and \emph{side observations}. In this setting, a learning agent repeatedly chooses from a set of $K$ actions after being presented with a $d$-dimensional context vector. The agent not only incurs and observes the loss of the chosen action, but also observes the losses of its neighboring actions in the observation structures, which are encoded as a series of feedback graphs. This setting models a variety of applications in social networks, where both contexts and graph-structured side observations are available. Two efficient algorithms are developed based on \texttt{EXP3}. Under mild conditions, our analysis shows that for undirected feedback graphs the first algorithm, \texttt{EXP3-LGC-U}, achieves the regret of order $\mathcal{O}(\sqrt{(K+α(G)d)T\log{K}})$ over the time horizon $T$, where $α(G)$ is the average \emph{independence number} of the feedback graphs. A slightly weaker result is presented for the directed graph setting as well. The second algorithm, \texttt{EXP3-LGC-IX}, is developed for a special class of problems, for which the regret is reduced to $\mathcal{O}(\sqrt{α(G)dT\log{K}\log(KT)})$ for both directed as well as undirected feedback graphs. Numerical tests corroborate the efficiency of proposed algorithms.

cs.LG↗

arXiv2020

Enhancing Parameter-Free Frank Wolfe with an Extra Subproblem

Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration, thanks to which the decision variable is updated in a prediction-correction (PC) format. Relying on no problem dependent parameters in the step sizes, the convergence rate of ExtraFW for general convex problems is shown to be ${\cal O}(\frac{1}{k})$, which is optimal in the sense of matching the lower bound on the number of solved FW subproblems. However, the merit of ExtraFW is its faster rate ${\cal O}\big(\frac{1}{k^2} \big)$ on a class of machine learning problems. Compared with other parameter-free FW variants that have faster rates on the same problems, ExtraFW has improved rates and fine-grained analysis thanks to its PC update. Numerical tests on binary classification with different sparsity-promoting constraints demonstrate that the empirical performance of ExtraFW is significantly better than FW, and even faster than Nesterov's accelerated gradient on certain datasets. For matrix completion, ExtraFW enjoys smaller optimality gap, and lower rank than FW.

math.OC↗