On permutation-invariant neural networks

Conventional machine learning algorithms have traditionally been designed under the assumption that input data follows a vector-based format, with an emphasis on vector-centric paradigms. However, as the demand for tasks involving set-based inputs has grown, there has been a paradigm shift in the research community towards addressing these challenges. In recent years, the emergence of neural network architectures such as Deep Sets and Transformers has presented a significant advancement in the treatment of set-based data. These architectures are specifically engineered to naturally accommodate sets as input, enabling more effective representation and processing of set structures. Consequently, there has been a surge of research endeavors dedicated to exploring and harnessing the capabilities of these architectures for various tasks involving the approximation of set functions. This comprehensive survey aims to provide an overview of the diverse problem settings and ongoing research efforts pertaining to neural networks that approximate set functions. By delving into the intricacies of these approaches and elucidating the associated challenges, the survey aims to equip readers with a comprehensive understanding of the field. Through this comprehensive perspective, we hope that researchers can gain valuable insights into the potential applications, inherent limitations, and future directions of set-based neural networks. Indeed, from this survey we gain two insights: i) Deep Sets and its variants can be generalized by differences in the aggregation function, and ii) the behavior of Deep Sets is sensitive to the choice of the aggregation function. From these observations, we show that Deep Sets, one of the well-known permutation-invariant neural networks, can be generalized in the sense of a quasi-arithmetic mean

Outfit Completion via Conditional Set Transformation

In this paper, we formulate the outfit completion problem as a set retrieval task and propose a novel framework for solving this problem. The proposal includes a conditional set transformation architecture with deep neural networks and a compatibility-based regularization method. The proposed method utilizes a map with permutation-invariant for the input set and permutation-equivariant for the condition set. This allows retrieving a set that is compatible with the input set while reflecting the properties of the condition set. In addition, since this structure outputs the element of the output set in a single inference, it can achieve a scalable inference speed with respect to the cardinality of the output set. Experimental results on real data reveal that the proposed method outperforms existing approaches in terms of accuracy of the outfit completion task, condition satisfaction, and compatibility of completion results.Comment: 8 pages, 8 figure

Oxidation mechanisms of ZRB2-based ultra high temperature ceramic matrix composites

Ultra-high temperature ceramics (UHTCs) are expected as the materials for the nose cones and leading edges for hypersonic and re-entry vehicles. Zirconium diboride (ZrB2) and its composites are a widely studied class of UHTCs. The oxidation of monolithic ZrB2 forms ZrO2 and B2O3. B2O3 acts as a surface protective layer; however, it evaporates above 1200℃. SiC particles are considered effective additives because the SiO2 formed by the oxidation of SiC protects the unreacted region. Simultaneously, excessive pores are formed under the surface in the SiC particle-dispersed ZrB2 matrix (hereafter denoted ZS) composites in a wide temperature range by the preferential oxidation of SiC (active oxidation of SiC) because solid SiO2 is not formed; instead, gaseous SiO forms by active oxidation because of the low oxygen partial pressure relative to that of the surface. The pore-rich porous layer is denoted the “SiC-depleted layer”. The SiC-depleted layer leads to spallation and delamination of the oxidized regions on the surface because strength and stiffness of this layer are quite low. Thus, excessive pore formation in ZS composites should be prevented to improve the oxidation resistance. The objective of this study is to understand oxidation mechanisms of ZrB2-based composites and to propose the way to prevent the formation of SiC-depleted layer in ZS composites. In the present study, we fabricated monolithic ZrB2, ZS, and ZrB2-SiC-ZrC (ZSZ) ternary composites by spark plasma sintering (SPS) technique. In addition, carbon fiber-reinforced ZSZ matrix (C/ZSZ) composites was also fabricated by Si melt infiltration (MI) process. Oxidation resistance of monolithic ZrB2, ZS, ZSZ, and C/ZSZ have specially designed fast heating system in order to characterize oxidation resistance above 2000℃. Please click Additional Files below to see the full abstract