arXiv subjects

Xiaofeng Ma

Publications and source records attributed to Xiaofeng Ma.

5 recordsLinked to original sources

arXiv2025

Indeterminate Probability Theory

Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes the following contributions: (1) An observer-centered framework in which experimental outcomes are represented as distributions combining ground truth with observation error; (2) The introduction of three independence candidate axioms that enable a two-phase probabilistic inference framework; (3) The derivation of closed-form solutions for arbitrary complex joint distributions under this framework. Both the Indeterminate Probability Neural Network (IPNN) model and the non-neural multivariate time series forecasting application demonstrate IPT's effectiveness in modeling high-dimensional distributions, with successful validation up to 1000 dimensions. Importantly, IPT is consistent with classical probability theory and subsumes the frequentist equation in the limit of vanishing observation error.

cs.LG↗

arXiv2025

FreePRM: Training Process Reward Models Without Ground Truth Process Labels

Recent advancements in Large Language Models (LLMs) have demonstrated that Process Reward Models (PRMs) play a crucial role in enhancing model performance. However, training PRMs typically requires step-level labels, either manually annotated or automatically generated, which can be costly and difficult to obtain at scale. To address this challenge, we introduce FreePRM, a weakly supervised framework for training PRMs without access to ground-truth step-level labels. FreePRM first generates pseudo step-level labels based on the correctness of final outcome, and then employs Buffer Probability to eliminate impact of noise inherent in pseudo labeling. Experimental results show that FreePRM achieves an average F1 score of 53.0% on ProcessBench, outperforming fully supervised PRM trained on Math-Shepherd by +24.1%. Compared to other open-source PRMs, FreePRM outperforms upon RLHFlow-PRM-Mistral-8B (28.4%) by +24.6%, EurusPRM (31.3%) by +21.7%, and Skywork-PRM-7B (42.1%) by +10.9%. This work introduces a new paradigm in PRM training, significantly reducing reliance on costly step-level annotations while maintaining strong performance.

cs.CL↗

arXiv2025

Logical Consistency is Vital: Neural-Symbolic Information Retrieval for Negative-Constraint Queries

Information retrieval plays a crucial role in resource localization. Current dense retrievers retrieve the relevant documents within a corpus via embedding similarities, which compute similarities between dense vectors mainly depending on word co-occurrence between queries and documents, but overlook the real query intents. Thus, they often retrieve numerous irrelevant documents. Particularly in the scenarios of complex queries such as \emph{negative-constraint queries}, their retrieval performance could be catastrophic. To address the issue, we propose a neuro-symbolic information retrieval method, namely \textbf{NS-IR}, that leverages first-order logic (FOL) to optimize the embeddings of naive natural language by considering the \emph{logical consistency} between queries and documents. Specifically, we introduce two novel techniques, \emph{logic alignment} and \emph{connective constraint}, to rerank candidate documents, thereby enhancing retrieval relevance. Furthermore, we construct a new dataset \textbf{NegConstraint} including negative-constraint queries to evaluate our NS-IR's performance on such complex IR scenarios. Our extensive experiments demonstrate that NS-IR not only achieves superior zero-shot retrieval performance on web search and low-resource retrieval tasks, but also performs better on negative-constraint queries. Our scource code and dataset are available at https://github.com/xgl-git/NS-IR-main.

cs.IR↗

arXiv2024

Order-lifted data inversion/retrieval method of neighbor cells to implement general high-order schemes in unstructured-mesh-based finite-volume solution framework

This study introduces an order-lifted inversion/retrieval method for implementing high-order schemes within the framework of an unstructured-mesh-based finite-volume method. This method defines a special representation called the data order-lifted inversion of neighbor cells (DOLINC) differential, which transforms the degrees of freedom of wide templates into differentials of various orders stored in local grid cells. Furthermore, to retrieve the original far-field information without bias during the reconstruction/interpolation of face values, the corresponding accurate inversion formulas are derived based on the defined DOLINC differentials. The order-lifted inversion method can be applied to multi-dimensional polyhedral-mesh solvers by considering the influence of grid non-uniformity on high-order schemes. It seamlessly accommodates multi-process parallel computing for high-order methods without requiring special consideration for the boundary interface. This method not only enhances the numerical accuracy of second-order finite-volume methods, but also demonstrates a significant computational-speed advantage over similar methods. A series of benchmark cases, including the linear advection, Burgers, and Euler equations, are comprehensively validated to assess the practical performance of the method. The results indicate that the unstructured-mesh high-order schemes implemented based on this method achieve theoretical accuracy in practical computations and substantially reduce computational costs compared with methods that increase grid resolution.

physics.flu-dyn↗

arXiv2020

The flag manifold as a tool for analyzing and comparing data sets

The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However, this usefulness begins to falter when the data cloud contains sufficiently many outliers corresponding to stray elements from another class or when the number of data points is larger than the number of features. We illustrate how nested subspace methods, utilizing flag manifolds, can help to deal with such additional confounding factors. Flag manifolds, which are parameter spaces for nested subspaces, are a natural geometric generalization of Grassmann manifolds. To make practical comparisons on a flag manifold, algorithms are proposed for determining the distances between points $[A], [B]$ on a flag manifold, where $A$ and $B$ are arbitrary orthogonal matrix representatives for $[A]$ and $[B]$, and for determining the initial direction of these minimal length geodesics. The approach is illustrated in the context of (hyper) spectral imagery showing the impact of ambient dimension, sample dimension, and flag structure.

cs.CV↗