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]: We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition to other elementary functions. Differentiable features are trained via gradient descent, and the performance of features in a linear model is used to weight the rate of change among subcomponents of each representation. The search process maintains an archive of representations with accuracy-complexity trade-offs to assist in generalization and interpretation. We compare several stochastic optimization approaches within this framework. We benchmark these variants on 100 open-source regression problems in comparison to state-of-the-art machine learning approaches. Our main finding is that this approach produces the highest average test scores across problems while producing representations that are orders of magnitude smaller than the next best performing method (gradient boosting). We also report a negative result in which attempts to directly optimize the disentanglement of the representation result in more highly correlated features.
[A]: Representing the network architecture as a set of syntax trees and optimizing their structure leads to accurate and concise regression models.

[Q]: We study SGD and Adam for estimating a rank one signal planted in matrix or tensor noise. The extreme simplicity of the problem setup allows us to isolate the effects of various factors: signal to noise ratio, density of critical points, stochasticity and initialization. We observe a surprising phenomenon: Adam seems to get stuck in local minima as soon as polynomially many critical points appear (matrix case), while SGD escapes those. However, when the number of critical points degenerates to exponentials (tensor case), then both algorithms get trapped. Theory tells us that at fixed SNR the problem becomes intractable for large $d$ and in our experiments SGD does not escape this. We exhibit the benefits of warm starting in those situations. We conclude that in this class of problems, warm starting cannot be replaced by stochasticity in gradients to find the basin of attraction.
[A]:
SGD and Adam under single spiked model for tensor PCA