arXiv subjects

Qi Deng

Publications and source records attributed to Qi Deng.

At least 19 recordsLinked to original sources

arXiv2026

Infeasible Momentum Orthogonalized Methods for Optimization on the Stiefel Manifold

We study deterministic and stochastic optimization over the Stiefel manifold, explicitly allowing iterates to deviate from the manifold rather than enforcing feasibility via retraction at each step. We introduce Landom, a Landing-type method that constructs momentum in the relative-gradient direction, maps this update to its compact polar factor, and combines the resulting tangential step with a step along the negative gradient of the orthogonality penalty to improve feasibility. Under operator-to-nuclear smoothness, Landom achieves an $O(T^{-1/2})$ bound on the averaged nuclear norm of the relative gradient with exact gradients, and an $O(T^{-1/4})$ bound in expectation with stochastic momentum, bounded variance, and a fixed batch size. Our analysis also provides explicit pathwise bounds on the orthogonality residual, including its dependence on the step size and initial infeasibility. To address the coupling between objective and feasibility correction in Landom, we further propose Landom+, a two-timescale variant in which the tangential and normal step sizes are decoupled. By keeping the normal step size fixed, Landom+ achieves tighter control over the orthogonality residual following an initial transient while maintaining the respective convergence rates for stationarity. Numerical experiments across a range of applications illustrate that the proposed algorithms remain competitive with established manifold optimization approaches.

math.OC↗

arXiv2026

ProLand: A New Infeasible Manifold Optimization Method for LoRA Fine-Tuning

Low-rank adaptation (LoRA) enables parameter-efficient fine-tuning but can suffer from redundant basis directions. Constraining the basis factor to the Stiefel manifold addresses this redundancy through orthonormality. Landing methods allow temporarily infeasible iterates to explore a neighborhood of the manifold while progressively restoring orthogonality without per-step retractions. To improve optimization efficiency while retaining this flexibility, we introduce ProLand (Product-space Landing), a retraction-free optimizer that combines coordinated factor updates with Muon-style spectral directions. By designing the updates in the space of the represented weight increment, ProLand separates objective optimization from orthogonality restoration, supporting efficient feasibility recovery. This coordinated construction also enables Muon-style directions to guide objective optimization while preserving that separation. Experiments cover four GLUE validation tasks on DeBERTa-v3-base and seven language benchmarks on Qwen2.5-3B, Llama-3.2-3B, and Moonlight-16B-A3B across multiple adapter ranks. Across these 11 tasks, ProLand achieves the highest average score among the compared methods in every tested encoder and decoder model-rank configuration.

cs.LG↗

arXiv2026

Hybrid Momentum Methods for Optimizing Deep Learning Models

Momentum is central to stochastic optimization in deep learning, including the training of large language models. Classical momentum methods typically rely on a fast exponential moving average (EMA) scheme, which discounts past gradients on a fixed timescale and may underweight older gradients that remain informative. This creates a trade-off between retaining long-term history and adapting to recent changes. We introduce Hybrid Momentum (HyM), which combines a linearly weighted average of past gradients with a geometrically discounted fast momentum. The former assigns weights proportional to the gradients' iteration indices and retains a growing span of history, while the latter emphasizes recent gradients. This hybrid construction is modular and can be combined with adaptive preconditioning and other update transformations. In particular, we propose HyMUON, which applies Newton--Schulz orthogonalization to the hybrid direction. Illustrative examples and controlled experiments demonstrate the benefits of combining gradient information across these two timescales. Across image classification, machine translation, and language modeling, HyM and HyMUON match or improve upon strong baselines. HyMUON improves over Muon on IWSLT14, and in both the 100k- and 600k-step GPT-2 124M OpenWebText regimes. For LLaMA-1.3B pretraining on C4, HyMUON achieves a final validation loss of 2.777, compared with 2.903 for Muon.

cs.LG↗

arXiv2026

Optimal First-Order Methods for a Class of Structured Hölder-Smooth Problems

Convex optimization with Hölder-continuous gradients has attracted considerable attention as a framework bridging smooth and nonsmooth optimization. For this class, Nesterov's universal fast gradient method attains the optimal black-box complexity, and we study whether exploiting further problem structure can further improve this bound. In this paper, we study an important class of Hölder-smooth problems, namely regularized $\ell_p$ regression with $p\in(1,2)$, whose loss has a $(p-1)$-Hölder-continuous gradient and for which the universal method requires $\mathcal{O}(\varepsilon^{-2/(3p-2)})$ iterations. Exploiting the problem structure, we characterize a family of smooth approximations based on $p$-Huber smoothing and prove that, for any prescribed smoothness level, it minimizes the worst-case approximation error among smooth lower approximations of the scalar loss. Combined with accelerated proximal gradients, the smoothing approach attains an $\varepsilon$-optimal solution in $\mathcal{O}(\varepsilon^{-1/p})$ matrix--vector products, which significantly improves the complexity guarantee for $1<p<2$. We show that this bound is optimal by providing a matching lower bound. Numerical experiments on synthetic and real data demonstrate the practical performance of the proposed methods.

math.OC↗

arXiv2026

Learning Ordinal Probabilistic Reward from Preferences

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically demand costly point-wise supervision, while DRMs produce uncalibrated relative scores that lack probabilistic interpretation. To address these challenges, we introduce a novel reward modeling paradigm: Probabilistic Reward Model (PRM). Instead of modeling reward as a deterministic scalar, our approach treats it as a random variable, learning a full probability distribution for the quality of each response. To make this paradigm practical, we present its closed-form, discrete realization: the Ordinal Probabilistic Reward Model (OPRM), which discretizes the quality score into a finite set of ordinal ratings. Building on OPRM, we propose a data-efficient training strategy called Region Flooding Tuning (RgFT). It enables rewards to better reflect absolute text quality by incorporating quality-level annotations, which guide the model to concentrate the probability mass within corresponding rating sub-regions. Experiments on various reward model benchmarks show that our method improves accuracy by $\textbf{2.9%}\sim\textbf{7.4%}$ compared to prior reward models, demonstrating strong performance and data efficiency. Analysis of the score distribution provides evidence that our method captures not only relative rankings but also absolute quality.

cs.CL↗

arXiv2026

Integrated Prediction and Multi-period Portfolio Optimization

Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture. Classical methods usually follow a two-stage framework: machine learning algorithms are employed to produce forecasts that closely fit the realized returns, and the predicted values are then used in a downstream portfolio optimization problem to determine the asset weights. This separation leads to a fundamental misalignment between predictions and decision outcomes, while also ignoring the impact of transaction costs. To bridge this gap, recent studies have proposed the idea of end-to-end learning, integrating the two stages into a single pipeline. This paper introduces IPMO (Integrated Prediction and Multi-period Portfolio Optimization), a model for multi-period mean-variance portfolio optimization with turnover penalties. The predictor generates multi-period return forecasts that parameterize a differentiable convex optimization layer, which in turn drives learning via portfolio performance. For scalability, we introduce a mirror-descent fixed-point (MDFP) differentiation scheme that avoids factorizing the Karush-Kuhn-Tucker (KKT) systems, which thus yields stable implicit gradients and nearly scale-insensitive runtime as the decision horizon grows. In experiments with real market data and two representative time-series prediction models, the IPMO method consistently outperforms the two-stage benchmarks in risk-adjusted performance net of transaction costs and achieves more coherent allocation paths. Our results show that integrating machine learning prediction with optimization in the multi-period setting improves financial outcomes and remains computationally tractable.

cs.CE↗

arXiv2026

ZOTTA: Test-Time Adaptation with Gradient-Free Zeroth-Order Optimization

Test-time adaptation (TTA) aims to improve model robustness under distribution shifts by adapting to unlabeled test data, but most existing methods rely on backpropagation (BP), which is computationally costly and incompatible with non-differentiable models such as quantized models, limiting practical deployment on numerous edge devices. Recent BP-free approaches alleviate overhead but remain either architecture-specific or limited in optimization capacity to handle high-dimensional models. We propose ZOTTA, a fully BP-free TTA framework that performs efficient adaptation using only forward passes via Zeroth-Order Optimization (ZOO). While ZOO is theoretically appealing, naive application leads to slow convergence under high-dimensional parameter spaces and unstable optimization due to the lack of labels. ZOTTA overcomes these challenges through 1) Distribution-Robust Layer Selection, which automatically identifies and freezes layers that already extract distribution-invariant features, updating only domain-sensitive layers to reduce the optimization dimensionality and accelerate convergence; 2) Spatial Feature Aggregation Alignment, which stabilizes ZOO by aligning globally aggregated spatial features between source and target to reduce gradient variance. Together, these components enable architecture-agnostic and stable BP-free adaptation. Extensive experiments on ImageNet-C/R/Sketch/A show that ZOTTA outperforms or matches BP-based methods, e.g., it reduces memory usage by 84% and improves accuracy by 3.9% over SAR on ImageNet-C. Code:https://github.com/Zhang-Ronghao/zotta.

cs.CV↗

arXiv2026

A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers

Differentiating through the solution of a quadratic program (QP) is a central problem in differentiable optimization. Most existing approaches differentiate through the Karush--Kuhn--Tucker (KKT) system, but their computational cost and numerical robustness can degrade at scale. To address these limitations, we propose dXPP, a penalty-based differentiation framework that decouples QP solving from differentiation. In the solving step (forward pass), dXPP is solver-agnostic and can leverage any black-box QP solver. In the differentiation step (backward pass), we map the solution to a smooth approximate penalty problem and implicitly differentiate through it, requiring only the solution of a much smaller linear system in the primal variables. This approach bypasses the difficulties inherent in explicit KKT differentiation and significantly improves computational efficiency and robustness. We evaluate dXPP on various tasks, including randomly generated QPs, large-scale sparse projection problems, and a real-world multi-period portfolio optimization task. Empirical results demonstrate that dXPP is competitive with KKT-based differentiation methods and achieves substantial speedups on large-scale problems. Our implementation is open source and available at https://github.com/mmmmmmlinghu/dXPP.

cs.LG↗

arXiv2026

Agentopia: Long-Term Life Simulation and Learning in Agent Societies

Humans learn from social life. Simulating this process with LLM-powered agents represents a promising research direction, raising a natural question: whether LLMs can learn from such simulated social experience to better understand and replicate human behavior. However, prior agent society simulations typically operate at the scale of days, limiting the depth of social interactions and long-term growth. In this paper, we study long-term life simulation and LLM learning in agent societies, with two goals: (1) investigating social behaviors that emerge from life-long simulation, and (2) developing anthropomorphic capabilities in LLMs, particularly intelligence in social life, through years of simulated social experience. Specifically, we present Agentopia, a comprehensive framework for long-term life simulation in multi-agent societies, where 100 agents autonomously pursue personal growth, develop social relationships, and fulfill their needs and goals over 10 simulated years. We define life reward to mirror human well-being, and leverage this reward to train LLMs via rejection sampling. Extensive experiments show that agents exhibit rich emergent social behaviors. Furthermore, life reward training effectively enhances the underlying LLM, which leads to improved agent well-being in simulation, and generalizes to downstream role-playing benchmarks with +15.6% improvement.

cs.CL↗

arXiv2026

Uniformly Optimal and Parameter-free First-order Methods for Convex and Function-constrained Optimization

This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve this, we enable first-order methods to utilize computational oracles for solving diagonal quadratic programs in subproblems. For problems where the optimal value $f^*$ is known, such as those in overparameterized models and feasibility problems, we propose an accelerated first-order method that incorporates a modified Polyak step size and Nesterov's momentum. Notably, our method does not require knowledge of smoothness levels, Hölder continuity parameter of the gradient, or additional line search, yet achieves the optimal oracle complexity bound of $\mathcal{O}(\varepsilon^{-2/(1+3ρ)})$ under Hölder smoothness conditions. When $f^*$ is unknown, we reformulate the problem as finding the root of the optimal value function and develop inexact fixed-point iteration and secant method to compute $f^*$. These root-finding subproblems are solved inexactly using first-order methods to a specified relative accuracy. We employ the accelerated prox-level (APL) method, which is proven to be uniformly optimal for convex optimization with simple constraints. Our analysis demonstrates that APL-based level-set methods also achieve the optimal oracle complexity of $\mathcal{O}(\varepsilon^{-2/(1+3ρ)})$ for convex function-constrained optimization, without requiring knowledge of any problem-specific structures. Through experiments on various tasks, we demonstrate the advantages of our methods over existing approaches in function-constrained optimization.

math.OC↗

arXiv2026

A Smooth Approximation Framework for Weakly Convex Optimization

Standard complexity analyses for weakly convex optimization rely on the Moreau envelope technique proposed by Davis and Drusvyatskiy (2019). The main insight is that nonsmooth algorithms, such as proximal subgradient, proximal point, and their stochastic variants, implicitly minimize a smooth surrogate function induced by the Moreau envelope. Meanwhile, explicit smoothing, which directly minimizes a smooth approximation of the objective, has long been recognized as an efficient strategy for nonsmooth optimization. In this paper, we generalize the notion of smoothable functions, which was proposed by Beck and Teboulle (2012) for nonsmooth convex optimization. This generalization provides a unified viewpoint on several important smoothing techniques for weakly convex optimization, including Nesterov-type smoothing and Moreau envelope smoothing. Our theory yields a framework for designing smooth approximation algorithms for both deterministic and stochastic weakly convex problems with provable complexity guarantees. Furthermore, our theory extends to the smooth approximation of non-Lipschitz functions, allowing for complexity analysis even when global Lipschitz continuity does not hold.

math.OC↗

arXiv2025

Accelerated Distance-adaptive Methods for Hölder Smooth and Convex Optimization

This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits Hölder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we propose an accelerated distance-adaptive method which achieves optimal anytime convergence rates for Hölder smooth problems without requiring prior knowledge of smoothness parameters or explicit parameter tuning. Importantly, our parameter-free approach removes the necessity of specifying target accuracy in advance, addressing a limitation found in the universal fast gradient methods (Nesterov, Yu. \textit{Mathematical Programming}, 2015). For convex stochastic optimization, we further present a parameter-free accelerated method that eliminates the need for line-search procedures. Preliminary experimental results highlight the effectiveness of our approach on convex nonsmooth problems and its advantages over existing parameter-free or accelerated methods.

math.OC↗

arXiv2025

A Confidence-Constrained Cloud-Edge Collaborative Framework for Autism Spectrum Disorder Diagnosis

Autism Spectrum Disorder (ASD) diagnosis systems in school environments increasingly relies on IoT-enabled cameras, yet pure cloud processing raises privacy and latency concerns while pure edge inference suffers from limited accuracy. We propose Confidence-Constrained Cloud-Edge Knowledge Distillation (C3EKD), a hierarchical framework that performs most inference at the edge and selectively uploads only low-confidence samples to the cloud. The cloud produces temperature-scaled soft labels and distils them back to edge models via a global loss aggregated across participating schools, improving generalization without centralizing raw data. On two public ASD facial-image datasets, the proposed framework achieves a superior accuracy of 87.4\%, demonstrating its potential for scalable deployment in real-world applications.

cs.NI↗

arXiv2025

Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address this limitation, we introduce a new subgradient growth condition that naturally encompasses a wide range of locally Lipschitz functions, with the classical global Lipschitz function as a special case. Under this milder condition, we prove that randomized smoothing yields a differentiable function that satisfies certain generalized smoothness properties. To optimize such functions, we propose novel randomized smoothing gradient algorithms that, with high probability, converge to $(δ, ε)$-Goldstein stationary points and achieve a sample complexity of $\tilde{\mathcal{O}}(d^{5/2}δ^{-1}ε^{-4})$. By incorporating variance reduction techniques, we further improve the sample complexity to $\tilde{\mathcal{O}}(d^{3/2}δ^{-1}ε^{-3})$, matching the optimal $ε$-bound under the global Lipschitz assumption, up to a logarithmic factor. Experimental results validate the effectiveness of our proposed algorithms.

math.OC↗

arXiv2025

Exploring Audio Cues for Enhanced Test-Time Video Model Adaptation

Test-time adaptation (TTA) aims to boost the generalization capability of a trained model by conducting self-/unsupervised learning during the testing phase. While most existing TTA methods for video primarily utilize visual supervisory signals, they often overlook the potential contribution of inherent audio data. To address this gap, we propose a novel approach that incorporates audio information into video TTA. Our method capitalizes on the rich semantic content of audio to generate audio-assisted pseudo-labels, a new concept in the context of video TTA. Specifically, we propose an audio-to-video label mapping method by first employing pre-trained audio models to classify audio signals extracted from videos and then mapping the audio-based predictions to video label spaces through large language models, thereby establishing a connection between the audio categories and video labels. To effectively leverage the generated pseudo-labels, we present a flexible adaptation cycle that determines the optimal number of adaptation iterations for each sample, based on changes in loss and consistency across different views. This enables a customized adaptation process for each sample. Experimental results on two widely used datasets (UCF101-C and Kinetics-Sounds-C), as well as on two newly constructed audio-video TTA datasets (AVE-C and AVMIT-C) with various corruption types, demonstrate the superiority of our approach. Our method consistently improves adaptation performance across different video classification models and represents a significant step forward in integrating audio information into video TTA. Code: https://github.com/keikeiqi/Audio-Assisted-TTA.

cs.CV↗

arXiv2025

BenLOC: A Benchmark for Learning to Configure MIP Optimizers

The automatic configuration of Mixed-Integer Programming (MIP) optimizers has become increasingly critical as the large number of configurations can significantly affect solver performance. Yet the lack of standardized evaluation frameworks has led to data leakage and over-optimistic claims, as prior studies often rely on homogeneous datasets and inconsistent experimental setups. To promote a fair evaluation process, we present BenLOC, a comprehensive benchmark and open-source toolkit, which not only offers an end-to-end pipeline for learning instance-wise MIP optimizer configurations, but also standardizes dataset selection, train-test splits, feature engineering and baseline choice for unbiased and comprehensive evaluations. Leveraging this framework, we conduct an empirical analysis on five well-established MIP datasets and compare classical machine learning models with handcrafted features against state-of-the-art deep-learning techniques. The results demonstrate the importance of datasets, features and baseline criteria proposed by BenLOC and the effectiveness of BenLOC in providing unbiased and comprehensive evaluations.

math.OC↗

arXiv2025

Liquidity Adjustment in Multivariate Volatility Modeling: Evidence from Portfolios of Cryptocurrencies and US Stocks

We develop a liquidity-sensitive multivariate volatility framework to improve the estimation of time-varying covariance structures under market frictions. We introduce two novel portfolio-level liquidity measures, liquidity jump and liquidity diffusion, which capture magnitude and volatility of liquidity fluctuation, respectively, and construct liquidity-adjusted return and volatility that reflect real-time liquidity variability. These liquidity-adjusted inputs are integrated into a VECM-DCC/ADCC-Bayesian model, allowing for conditional and posterior covariance estimation under liquidity stress. Applying this framework to portfolios of cryptocurrencies and US stocks, we find that traditional models misrepresent volatility and co-movement, while liquidity-adjusted models yield more stable and interpretable risk structures, particularly for portfolios of cryptocurrencies. The findings support the use of liquidity-adjusted multivariate models as statistically grounded tools for assessing the propagation of portfolio risk under market frictions, with implications for asset pricing, market microstructure design, and portfolio management.

q-fin.ST↗

arXiv2025

Liquidity Jump, Liquidity Diffusion, and Crypto Wash Trading

We develop a new framework to detect wash trading in crypto assets through real-time liquidity fluctuation. We propose that short-term price jumps in crypto assets results from wash trading-induced liquidity fluctuation, and construct two complementary liquidity measures, liquidity jump (size of fluctuation) and liquidity diffusion (volatility of fluctuation), to capture the behavioral signature of wash trading. Using US stocks as a benchmark, we demonstrate that joint elevation in both liquidity metrics indicates wash trading in crypto assets. A simulated regulatory treatment that removes likely wash trades confirms this dynamic: it reduces liquidity diffusion significantly while leaving liquidity jump largely unaffected. These findings align with a theoretical model in which manipulative traders amplify both the level and variance of price pressure, whereas passive investors affect only the level. Our model offers practical tools for investors to assess market quality and for regulators to monitor manipulation risk on crypto exchanges without oversight.

q-fin.RM↗