Related papers: Solution Space Topology Guides CMTS Search
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The…
Modern SMT solvers, such as Z3, offer user-controllable strategies, enabling users to tailor solving strategies for their unique set of instances, thus dramatically enhancing solver performance for their use case. However, this approach of…
Monte Carlo Tree Search (MCTS) efficiently balances exploration and exploitation in tree search based on count-derived uncertainty. However, these local visit counts ignore a second type of uncertainty induced by the size of the subtree…
Architecture search is the process of automatically learning the neural model or cell structure that best suits the given task. Recently, this approach has shown promising performance improvements (on language modeling and image…
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
Monte Carlo Tree Search (MCTS) is an immensely popular search-based framework used for decision making. It is traditionally applied to domains where a perfect simulation model of the environment is available. We study and improve MCTS in…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
In many problem settings, most notably in game playing, an agent receives a possibly delayed reward for its actions. Often, those rewards are handcrafted and not naturally given. Even simple terminal-only rewards, like winning equals 1 and…
Identifying communities from temporal networks facilitates the understanding of potential dynamic relationships among entities, which has already received extensive applications. However, existing methods primarily rely on lower-order…
The standard cosmological model with cold dark matter posits a hierarchical formation of structures. We introduce topological neural networks (TNNs), implemented as message-passing neural networks on higher-order structures, to effectively…
Making changes to a program to optimize its performance is an unscalable task that relies entirely upon human intuition and experience. In addition, companies operating at large scale are at a stage where no single individual understands…
Understanding how the brain represents and processes information is crucial for advancing neuroscience and artificial intelligence. Representational similarity analysis (RSA) has been instrumental in characterizing neural representations,…
We propose SC-MCTS*: a novel Monte Carlo Tree Search (MCTS) reasoning algorithm for Large Language Models (LLMs), significantly improves both reasoning accuracy and speed. Our motivation comes from: 1. Previous MCTS LLM reasoning works…
Unstructured meshes are characterized by data points irregularly distributed in the Euclidian space. Due to the irregular nature of these data, computing connectivity information between the mesh elements requires much more time and memory…
Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…