Minimum Weight Perfect Matching via Blossom Belief Propagation

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs

Recursive Chain-of-Feedback Prevents Performance Degradation from Redundant Prompting

Large Language Models (LLMs) frequently struggle with complex reasoning tasks, failing to construct logically sound steps towards the solution. In response to this behavior, users often try prompting the LLMs repeatedly in hopes of reaching a better response. This paper studies such repetitive behavior and its effect by defining a novel setting, Chain-of-Feedback (CoF). The setting takes questions that require multi-step reasoning as an input. Upon response, we repetitively prompt meaningless feedback (e.g. 'make another attempt') requesting additional trials. Surprisingly, our preliminary results show that repeated meaningless feedback gradually decreases the quality of the responses, eventually leading to a larger deviation from the intended outcome. To alleviate these troubles, we propose a novel method, Recursive Chain-of-Feedback (R-CoF). Following the logic of recursion in computer science, R-CoF recursively revises the initially incorrect response by breaking down each incorrect reasoning step into smaller individual problems. Our preliminary results show that majority of questions that LLMs fail to respond correctly can be answered using R-CoF without any sample data outlining the logical process.Comment: Still Ongoing Work; 8 Pages; 2 Figure

A Digital Twin City Model for Age-Friendly Communities: Capturing Environmental Distress from Multimodal Sensory Data

As the worldwide population is aging, the demands of aging-in-place are also increasing and require smarter and more connected cities to keep mobility independence of older adults. However, today’s aging built environment often poses great environmental demands to older adults’ mobility and causes their distresses. To better understand and help mitigating older adults’ distress in their daily trips, this paper proposes constructing the digital twin city (DTC) model that integrates multimodal data (i.e., physiological sensing, visual sensing) on environmental demands in urban communities, so that such environmental demands can be considered in mobility planning of older adults. Specifically, this paper examines how data acquired from various modalities (i.e., electrodermal activity, gait patterns, visual sensing) can portray environmental demands associated with older adults’ mobility. In addition, it discusses the challenges and opportunities of multimodal data fusion in capturing environmental distresses in urban communities

Goal Driven Discovery of Distributional Differences via Language Descriptions

Mining large corpora can generate useful discoveries but is time-consuming for humans. We formulate a new task, D5, that automatically discovers differences between two large corpora in a goal-driven way. The task input is a problem comprising a research goal "$\textit{comparing the side effects of drug A and drug B}$" and a corpus pair (two large collections of patients' self-reported reactions after taking each drug). The output is a language description (discovery) of how these corpora differ (patients taking drug A "$\textit{mention feelings of paranoia}$" more often). We build a D5 system, and to quantitatively measure its performance, we 1) contribute a meta-dataset, OpenD5, aggregating 675 open-ended problems ranging across business, social sciences, humanities, machine learning, and health, and 2) propose a set of unified evaluation metrics: validity, relevance, novelty, and significance. With the dataset and the unified metrics, we confirm that language models can use the goals to propose more relevant, novel, and significant candidate discoveries. Finally, our system produces discoveries previously unknown to the authors on a wide range of applications in OpenD5, including temporal and demographic differences in discussion topics, political stances and stereotypes in speech, insights in commercial reviews, and error patterns in NLP models

Protease Cleavage Leads to Formation of Mature Trimer Interface in HIV-1 Capsid

During retrovirus particle maturation, the assembled Gag polyprotein is cleaved by the viral protease into matrix (MA), capsid (CA), and nucleocapsid (NC) proteins. To form the mature viral capsid, CA rearranges, resulting in a lattice composed of hexameric and pentameric CA units. Recent structural studies of assembled HIV-1 CA revealed several inter-subunit interfaces in the capsid lattice, including a three-fold interhexamer interface that is critical for proper capsid stability. Although a general architecture of immature particles has been provided by cryo-electron tomographic studies, the structural details of the immature particle and the maturation pathway remain unknown. Here, we used cryo-electron microscopy (cryoEM) to determine the structure of tubular assemblies of the HIV-1 CA-SP1-NC protein. Relative to the mature assembled CA structure, we observed a marked conformational difference in the position of the CA-CTD relative to the NTD in the CA-SP1-NC assembly, involving the flexible hinge connecting the two domains. This difference was verified via engineered disulfide crosslinking, revealing that inter-hexamer contacts, in particular those at the pseudo three-fold axis, are altered in the CA-SP1-NC assemblies compared to the CA assemblies. Results from crosslinking analyses of mature and immature HIV-1 particles containing the same Cys substitutions in the Gag protein are consistent with these findings. We further show that cleavage of preassembled CA-SP1-NC by HIV-1 protease in vitro leads to release of SP1 and NC without disassembly of the lattice. Collectively, our results indicate that the proteolytic cleavage of Gag leads to a structural reorganization of the polypeptide and creates the three-fold interhexamer interface, important for the formation of infectious HIV-1 particles. © 2012 Meng et al