Small polaron with generic open boundary conditions revisit: exact solution via the off-diagonal Bethe ansatz

The small polaron, an one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical $U(1)$-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous $T-Q$ relation.Comment: 12 pages, no figure, published versio

Learning to Collaborate by Grouping: a Consensus-oriented Strategy for Multi-agent Reinforcement Learning

Multi-agent systems require effective coordination between groups and individuals to achieve common goals. However, current multi-agent reinforcement learning (MARL) methods primarily focus on improving individual policies and do not adequately address group-level policies, which leads to weak cooperation. To address this issue, we propose a novel Consensus-oriented Strategy (CoS) that emphasizes group and individual policies simultaneously. Specifically, CoS comprises two main components: (a) the vector quantized group consensus module, which extracts discrete latent embeddings that represent the stable and discriminative group consensus, and (b) the group consensus-oriented strategy, which integrates the group policy using a hypernet and the individual policies using the group consensus, thereby promoting coordination at both the group and individual levels. Through empirical experiments on cooperative navigation tasks with both discrete and continuous spaces, as well as Google research football, we demonstrate that CoS outperforms state-of-the-art MARL algorithms and achieves better collaboration, thus providing a promising solution for achieving effective coordination in multi-agent systems

Modularity-Guided Graph Topology Optimization And Self-Boosting Clustering

Existing modularity-based community detection methods attempt to find community memberships which can lead to the maximum of modularity in a fixed graph topology. In this work, we propose to optimize the graph topology through the modularity maximization process. We introduce a modularity-guided graph optimization approach for learning sparse high modularity graph from algorithmically generated clustering results by iterative pruning edges between two distant clusters. To the best of our knowledge, this represents a first attempt for using modularity to guide graph topology learning. Extensive experiments conducted on various real-world data sets show that our method outperforms the state-of-the-art graph construction methods by a large margin. Our experiments show that with increasing modularity, the accuracy of graph-based clustering algorithm is simultaneously increased, demonstrating the validity of modularity theory through numerical experimental results of real-world data sets. From clustering perspective, our method can also be seen as a self-boosting clustering method

Bethe ansatz solutions of the τ 2-model with arbitrary boundary fields

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.Comment: 26 pages, no figures, published versio

From Few to More: Large-scale Dynamic Multiagent Curriculum Learning

A lot of efforts have been devoted to investigating how agents can learn effectively and achieve coordination in multiagent systems. However, it is still challenging in large-scale multiagent settings due to the complex dynamics between the environment and agents and the explosion of state-action space. In this paper, we design a novel Dynamic Multiagent Curriculum Learning (DyMA-CL) to solve large-scale problems by starting from learning on a multiagent scenario with a small size and progressively increasing the number of agents. We propose three transfer mechanisms across curricula to accelerate the learning process. Moreover, due to the fact that the state dimension varies across curricula,, and existing network structures cannot be applied in such a transfer setting since their network input sizes are fixed. Therefore, we design a novel network structure called Dynamic Agent-number Network (DyAN) to handle the dynamic size of the network input. Experimental results show that DyMA-CL using DyAN greatly improves the performance of large-scale multiagent learning compared with state-of-the-art deep reinforcement learning approaches. We also investigate the influence of three transfer mechanisms across curricula through extensive simulations.Comment: Accepted by AAAI202