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Ang Gao

Ang Gao contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence Machine Learning

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preprint2026arXiv

Flow Matching with Arbitrary Auxiliary Paths

We introduce a new generative modeling framework, \textbf{Flow Matching with Arbitrary Auxiliary Paths (AuxPath-FM)}, which generalizes conditional flow matching by incorporating an auxiliary variable drawn from an arbitrary distribution into the probability path. Unlike prior methods that restrict auxiliary components to Gaussian noise, AuxPath-FM allows the variable $η$ to follow any distribution, producing trajectories of the form $X_t = a(t)X_1 + b(t)X_0 + c(t)η$. We theoretically demonstrate that this construction preserves the continuity equation and maintains a training objective consistent with the marginal formulation. This flexibility enables the design of diverse probability paths using various priors, including Gaussian, Uniform, Laplace, and discrete Rademacher distributions, each offering unique geometric properties for generative flows. Furthermore, our framework allows for specialized tasks such as label-guided generation by encoding structured semantic information into the auxiliary distribution. Overall, AuxPath-FM provides a principled and general foundation for probability path design, offering both theoretical generality and practical flexibility for diverse generative modeling tasks.

preprint2026arXiv

P-Guide: Parameter-Efficient Prior Steering for Single-Pass CFG Inference

Classifier-Free Guidance (CFG) is essential for high-fidelity conditional generation in flow matching, yet it imposes significant computational overhead by requiring dual forward passes at each sampling step. In this work, we address this bottleneck by introducing \textbf{P-Guide}, a framework that achieves high-quality guidance through a single inference pass by modulating only the initial latent state. We further show that, under a first-order approximation, P-Guide is equivalent to CFG in the sense that it steers generation from the prior space, without requiring explicit velocity field extrapolation during sampling. We consider both homoscedastic and \textbf{heteroscedastic} priors, and find that jointly modeling the mean and variance enables adaptive loss attenuation and improved robustness to data uncertainty. Extensive experiments demonstrate that P-Guide reduces inference latency by approximately 50\% while maintaining fidelity and prompt alignment competitive with standard dual-pass CFG baselines.

preprint2026arXiv

Process In-Context Learning: Enhancing Mathematical Reasoning via Dynamic Demonstration Insertion

In-context learning (ICL) has proven highly effective across diverse large language model (LLM) tasks. However, its potential for enhancing tasks that demand step-by-step logical deduction, such as mathematical reasoning, remains underexplored. A core limitation of existing ICL approaches is their static use of demonstrations: examples are pre-selected before inference and remain fixed, failing to adapt to the dynamic confusion points that often arise during multi-step reasoning such as ambiguous calculations or logical gaps. These unresolved confusion points can lead to cascading errors that degrade final accuracy. To tackle this issue, we propose Process In-Context Learning (PICL), a dynamic demonstration integration framework designed to boost mathematical reasoning by responding to real-time inference needs. PICL operates in two stages: 1)~it identifies potential confusion points by analyzing semantics and entropy in the reasoning process and summarizes their core characteristics; 2)~upon encountering these points, it retrieves relevant demonstrations from the demonstration pool that match the confusion context and inserts them directly into the ongoing reasoning process to guide subsequent steps. Experiments show that PICL outperforms baseline methods by mitigating mid-inference confusion, highlighting the value of adaptive demonstration insertion in complex mathematical reasoning.

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