Simulation of Hypergraph Algorithms with Looped Transformers

Looped Transformers have shown exceptional capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture to simulate hypergraph algorithms efficiently, addressing the gap between neural networks and combinatorial optimization over hypergraphs. In this paper, we extend the Loop Transformer architecture to simulate hypergraph algorithms efficiently, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. The paper establishes theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.

A novel particle swarm optimizer with multi-stage transformation and genetic operation for VLSI routing

As the basic model for very large scale integration (VLSI) routing, the Steiner minimal tree (SMT) can be used in various practical problems, such as wire length optimization, congestion, and time delay estimation. In this paper, a novel particle swarm optimization (PSO) algorithm based on multi-stage transformation and genetic operation is presented to construct two types of SMT, including non-Manhattan SMT and Manhattan SMT. Firstly, in order to be able to handle two types of SMT problems at the same time, an effective edge-vertex encoding strategy is proposed. Secondly, a multi-stage transformation strategy is proposed to both expand the algorithm search space and ensure the effective convergence. We have tested three types from two to four stages and various combinations under each type to highlight the best combination. Thirdly, the genetic operators combined with union-find partition are designed to construct the discrete particle update formula for discrete VLSI routing. Moreover, in order to introduce uncertainty and diversity into the search of PSO algorithm, we propose an improved mutation operation with edge transformation. Experimental results show that our algorithm from a global perspective of multilayer structure can achieve the best solution quality among the existing algorithms. Finally, to our best knowledge, it is the first work to address both manhattan and non-manhattan routing at the same time.