arXiv subjects

Renjie Ding

Publications and source records attributed to Renjie Ding.

6 recordsLinked to original sources

arXiv2026

A Step to Decouple Optimization in 3DGS

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for real-time novel view synthesis. As an explicit representation optimized through gradient propagation among primitives, optimization widely accepted in deep neural networks (DNNs) is actually adopted in 3DGS, such as synchronous weight updating and Adam with the adaptive gradient. However, considering the physical significance and specific design in 3DGS, there are two overlooked details in the optimization of 3DGS: (i) update step coupling, which induces optimizer state rescaling and costly attribute updates outside the viewpoints, and (ii) gradient coupling in the moment, which may lead to under- or over-effective regularization. Nevertheless, such a complex coupling is under-explored. After revisiting the optimization of 3DGS, we take a step to decouple it and recompose the process into: Sparse Adam, Re-State Regularization and Decoupled Attribute Regularization. Taking a large number of experiments under the 3DGS and 3DGS-MCMC frameworks, our work provides a deeper understanding of these components. Finally, based on the empirical analysis, we re-design the optimization and propose AdamW-GS by re-coupling the beneficial components, under which better optimization efficiency and representation effectiveness are achieved simultaneously.

cs.CV↗

arXiv2026

ToolPRM: Fine-Grained Inference Scaling of Structured Outputs for Function Calling

Large language models (LLMs) excel at function calling, but inference scaling has been explored mainly for unstructured generation. We propose an inference-scaling framework for structured outputs that combines fine-grained beam search with \textbf{ToolPRM}, a process reward model scoring each intra-call decision (function name and argument filling). We build the first fine-grained intra-call supervision dataset via function masking, rollout collection, and step-level annotation. ToolPRM outperforms outcome and coarse-grained reward models in predictive accuracy and yields consistent test-time gains on multiple function-calling benchmarks. We further show that structured generation follows ``\textbf{explore more but retain less}'', since early JSON errors are unrecoverable.

cs.AI↗

arXiv2026

Average block nonlinear Kaczmarz methods with adaptive momentum for nonlinear systems of equations

The Kaczmarz method is widely recognized as an efficient iterative algorithm for solving large-scale linear systems, owing to its simplicity and low memory requirements. However, the development of its nonlinear extensions for solving large-scale nonlinear systems has seen limited progress. In this work, we introduce a new family of momentum-accelerated averaging block nonlinear Kaczmarz methods tailored for large-scale nonlinear systems and ill-posed problems. Our contributions are twofold: (1) We develop an adaptive strategy for selecting step sizes and momentum coefficients, leading to a new average block nonlinear Kaczmarz method with adaptive momentum (ABNKAm). This algorithm achieves high computational efficiency by requiring only minimal inner-product computations per iteration, which significantly reduces both arithmetic complexity and memory usage. (2) We establish rigorous convergence of the ABNKAm under mild assumptions, proving that the method converges exponentially to the unique solution nearest to the initial point. Moreover, under suitable conditions, we provide a theoretical justification of acceleration of the proposed ABNKAm with momentum. Extensive numerical experiments demonstrate that ABNKAm outperforms existing nonlinear Kaczmarz variants in terms of both iteration count and computational time, with particularly notable gains in large-scale problems.

math.NA↗

arXiv2025

PARL-MT: Learning to Call Functions in Multi-Turn Conversation with Progress Awareness

Large language models (LLMs) have achieved impressive success in single-turn function calling, yet real-world applications such as travel planning or multi-stage data analysis typically unfold across multi-turn conversations. In these settings, LLMs must not only issue accurate function calls at each step but also maintain progress awareness, the ability to summarize past interactions and plan future actions to ensure coherent, long-horizon task execution. Existing approaches, however, either reduce multi-turn training to isolated single-turn samples, which neglects task-level planning, or employ end-to-end reinforcement learning (RL) that struggles with redundancy and lacks explicit integration of progress awareness. To overcome these limitations, we introduce PARL-MT, a framework that explicitly incorporates progress awareness into LLM training for multi-turn function calling. PARL-MT combines (i) a Progress Awareness Generation (PAG) pipeline, which automatically constructs datasets coupling conversation summaries with future task planning, and (ii) a Progress Awareness-Guided Reinforcement Learning (PAG-RL) algorithm, which integrates progress awareness into RL training to reduce contextual redundancy and improve alignment between local actions and global task completion. Empirical results on two public benchmarks demonstrate that PARL-MT significantly outperforms existing methods, highlighting the effectiveness of progress awareness in enabling robust and efficient multi-turn function calling.

cs.CL↗

arXiv2025

Random Greedy Fast Block Kaczmarz Method for Solving Large-Scale Nonlinear Systems

To efficiently solve large scale nonlinear systems, we propose a novel Random Greedy Fast Block Kaczmarz method. This approach integrates the strengths of random and greedy strategies while avoiding the computationally expensive pseudoinversion of Jacobian submatrices, thus enabling efficient solutions for large scale problems. Our theoretical analysis establishes that the proposed method achieves linear convergence in expectation, with its convergence rates upper bound determined by the stochastic greedy condition number and the relaxation parameter. Numerical experiments confirm that when the Jacobian matrix exhibits a favorable stochastic greedy condition number and an appropriate relaxation parameter is selected, the algorithm convergence is significantly accelerated. As a result, the proposed method outperforms other comparable algorithms in both efficiency and robustness.

math.NA↗

arXiv2025

Adaptive Residual-Driven Newton Solver for Nonlinear Systems of Equations

Newton-type solvers have been extensively employed for solving a variety of nonlinear system of algebraic equations. However, for some complex nonlinear system of algebraic equations, efficiently solving these systems remains a challenging task. The primary reason for this challenge arises from the unbalanced nonlinearities within the nonlinear system. Therefore, accurately identifying and balancing the unbalanced nonlinearities in the system is essential. In this work, we propose a residual-driven adaptive strategy to identify and balance the nonlinearities in the system. The fundamental idea behind this strategy is to assign an adaptive weight multiplier to each component of the nonlinear system, with these weight multipliers increasing according to a specific update rule as the residual components increase, thereby enabling the Newton-type solver to select a more appropriate step length, ensuring that each component in the nonlinear system experiences sufficient reduction rather than competing against each other. More importantly, our strategy yields negligible additional computational overhead and can be seamlessly integrated with other Newton-type solvers, contributing to the improvement of their efficiency and robustness. We test our algorithm on a variety of benchmark problems, including a chemical equilibrium system, a convective diffusion problem, and a series of challenging nonlinear systems. The experimental results demonstrate that our algorithm not only outperforms existing Newton-type solvers in terms of computational efficiency but also exhibits superior robustness, particularly in handling systems with highly imbalanced nonlinearities.

math.NA↗