Automated fact extraction and verification is a challenging task that involves finding relevant evidence sentences from a reliable corpus to verify the truthfulness of a claim.Existing models either (i) concatenate all the evidence sentences, leading to the inclusion of redundant and noisy information; or (ii) process each claim-evidence sentence pair separately and aggregate all of them later, missing the early combination of related sentences for more accurate claim verification.Unlike the prior works, in this paper, we propose Hierarchical Evidence Set Modeling (HESM), a framework to extract evidence sets (each of which may contain multiple evidence sentences), and verify a claim to be supported, refuted or not enough info, by encoding and attending the claim and evidence sets at different levels of hierarchy.Our experimental results show that HESM outperforms 7 state-of-the-art methods for fact extraction and claim verification.Our source code is available at https://github.com/ ShyamSubramanian/HESM.

A 2-MITE is a multiple-input translinear element with two input gates. In this paper, different properties of networks of 2-MITEs are derived, especially in the case of product-of-power-law (POPL) networks, in which the output currents are products of the inputs raised to different powers. It is found that conditions ensuring the uniqueness and stability of the operating point in 2-MITE networks are less stringent than those for MITE networks with higher number of input gates. This simplifies the synthesis of these networks considerably. A graph-theoretic approach to the analysis of 2-MITE networks is presented. Necessary conditions for a set of power-law equations to be implementable by 2-MITE networks are derived. Sufficient conditions for the same are presented for the case of POPL networks with one output

A procedure for synthesizing multiple-input translinear element (MITE) networks that implement a given system of translinear-loop equations (STLE) is presented. The minimum number of MITEs required for implementing the STLE, which is equal to the number of current variables in the STLE, is attained. The number of input gates of the MITEs is minimal amongst those MITE networks that satisfy the STLE and have the minimum number of MITEs. The synthesized MITE networks have a unique operating point and, in many cases, the network is guaranteed to be stable in a particular sense. This synthesis procedure exploits the relationship between MITE product-of-power-law (POPL) networks and linear diophantine equations which is explored in detail here.