In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

[Q]: Extreme Classification Methods have become of paramount importance, particularly for Information Retrieval (IR) problems, owing to the development of smart algorithms that are scalable to industry challenges. One of the prime class of models that aim to solve the memory and speed challenge of extreme multi-label learning is Group Testing. Multi-label Group Testing (MLGT) methods construct label groups by grouping original labels either randomly or based on some similarity and then train smaller classifiers to first predict the groups and then recover the original label vectors. Recently, a novel approach called MACH (Merged Average Classifiers via Hashing) was proposed which projects the huge label vectors to a small and manageable count-min sketch (CMS) matrix and then learns to predict this matrix to recover the original prediction probabilities. Thereby, the model memory scales O(logK) for K classes. MACH is a simple algorithm which works exceptionally well in practice. Despite this simplicity of MACH, there is a big gap between the theoretical understanding of the trade-offs with MACH. In this paper we fill this gap. Leveraging the theory of count-min sketch we provide precise quantification of the memory-identifiablity tradeoffs. We extend the theory to the case of multi-label classification, where the dependencies make the estimators hard to calculate in closed forms. To mitigate this issue, we propose novel quadratic approximation using the Inclusion-Exclusion Principle. Our estimator has significantly lower reconstruction error than the typical CMS estimator across various values of number of classes K, label sparsity and compression ratio.
[A]: How to estimate original probability vector for millions of classes from count-min sketch measurements -  a theoretical and practical setup.


[Q]: Program verification offers a framework for ensuring program correctness and therefore systematically eliminating different classes of bugs. Inferring loop invariants is one of the main challenges behind automated verification of real-world programs which often contain many loops. In this paper, we present Continuous Logic Network (CLN), a novel neural architecture for automatically learning loop invariants directly from program execution traces. Unlike existing neural networks, CLNs can learn precise and explicit representations of formulas in Satisfiability Modulo Theories (SMT)  for loop invariants from program execution traces. We develop a new sound and complete semantic mapping for assigning SMT formulas to continuous truth values that allows CLNs to be trained efficiently. We use CLNs to implement a new inference system for loop invariants, CLN2INV, that significantly outperforms existing approaches on the popular Code2Inv dataset. CLN2INV is the first tool to solve all 124 theoretically solvable problems in the Code2Inv dataset. Moreover, CLN2INV takes only 1.1 second on average for each problem, which is 40 times faster than existing approaches. We further demonstrate that CLN2INV can even learn 12 significantly more complex loop invariants than the ones required for the Code2Inv dataset.
[A]: We introduce the Continuous Logic Network (CLN), a novel neural architecture for automatically learning loop invariants and general SMT formulas.


[Q]: Variational Auto Encoders (VAE) are capable of generating realistic images, sounds and video sequences. From practitioners point of view, we are usually interested in solving problems where tasks are learned sequentially, in a way that avoids revisiting all previous data at each stage. We address this problem by introducing a conceptually simple and scalable end-to-end approach of incorporating past knowledge by learning prior directly from the data.   We consider scalable boosting-like approximation for intractable theoretical optimal prior. We provide empirical studies on two commonly used benchmarks, namely  MNIST and Fashion MNIST on disjoint sequential image generation tasks. For each dataset proposed method delivers the best results among comparable approaches,  avoiding catastrophic forgetting in a fully automatic way with a fixed model architecture.
[A]:
Novel algorithm for Incremental learning of VAE with fixed architecture