arXiv subjects

Mengke Yang

Publications and source records attributed to Mengke Yang.

4 recordsLinked to original sources

arXiv2026

Averaging pre-Lie bialgebras

In this paper, we first introduce representations of averaging pre-Lie algebras and study their matched pairs, Manin triples, and bialgebra theories. We prove that these three notions are equivalent under certain conditions. Moreover, by introducing averaging operators on quadratic Rota-Baxter pre-Lie algebras, we show that such operators give rise to averaging pre-Lie bialgebras. Then we introduce the notion of admissible classical Yang-Baxter equations in averaging pre-Lie algebras, as well as the relative Rota-Baxter operators on averaging pre-Lie algebras, and show that the relative Rota-Baxter operators on averaging pre-Lie algebras yield symmetric solutions of admissible classical Yang-Baxter equations in averaging pre-Lie algebras. Finally, we show that every averaging pre-Lie bialgebra induces an averaging Lie bialgebra.

math.RA↗

arXiv2026

On spectral conditions for fractional $k$-extendable graphs

A fractional matching of a graph $G$ is a function $h: E(G) \to [0,1]$ such that $\sum_{e \in E_G(v)} h(e) \leq 1$ for every vertex $v \in V(G)$, where $E_G(v)$ is the set of edges incident to $v$. If $\sum_{e \in E_G(v)} h(e) = 1$ for all $v$, then $h$ is a fractional perfect matching. A graph $G$ is fractional $k$-extendable if it has a matching of size $k$ and every $k$-matching $M$ in $G$ is contained in a fractional perfect matching $h$ such that $h(e)=1$ for every $e \in M$. In this paper, we establish new sufficient conditions for a graph with minimum degree $\delta$ to be fractional $k$-extendable. Our main results provide spectral guarantees for this property based on the distance spectral radius and the signless Laplacian spectral radius.

math.CO↗

arXiv2024

State-space Decomposition Model for Video Prediction Considering Long-term Motion Trend

Stochastic video prediction enables the consideration of uncertainty in future motion, thereby providing a better reflection of the dynamic nature of the environment. Stochastic video prediction methods based on image auto-regressive recurrent models need to feed their predictions back into the latent space. Conversely, the state-space models, which decouple frame synthesis and temporal prediction, proves to be more efficient. However, inferring long-term temporal information about motion and generalizing to dynamic scenarios under non-stationary assumptions remains an unresolved challenge. In this paper, we propose a state-space decomposition stochastic video prediction model that decomposes the overall video frame generation into deterministic appearance prediction and stochastic motion prediction. Through adaptive decomposition, the model's generalization capability to dynamic scenarios is enhanced. In the context of motion prediction, obtaining a prior on the long-term trend of future motion is crucial. Thus, in the stochastic motion prediction branch, we infer the long-term motion trend from conditional frames to guide the generation of future frames that exhibit high consistency with the conditional frames. Experimental results demonstrate that our model outperforms baselines on multiple datasets.

cs.CV↗

arXiv2023

Landmark Guided Active Exploration with State-specific Balance Coefficient

Goal-conditioned hierarchical reinforcement learning (GCHRL) decomposes long-horizon tasks into sub-tasks through a hierarchical framework and it has demonstrated promising results across a variety of domains. However, the high-level policy's action space is often excessively large, presenting a significant challenge to effective exploration and resulting in potentially inefficient training. In this paper, we design a measure of prospect for sub-goals by planning in the goal space based on the goal-conditioned value function. Building upon the measure of prospect, we propose a landmark-guided exploration strategy by integrating the measures of prospect and novelty which aims to guide the agent to explore efficiently and improve sample efficiency. In order to dynamically consider the impact of prospect and novelty on exploration, we introduce a state-specific balance coefficient to balance the significance of prospect and novelty. The experimental results demonstrate that our proposed exploration strategy significantly outperforms the baseline methods across multiple tasks.

cs.LG↗