human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "the limits of depth reduction for arithmetic formulas it s all about the top fan in"):
  Abstract: In recent years, a very exciting and promising method for proving lower bounds for arithmetic circuits has been proposed. This method combines the method of {\it depth reduction} developed in the works of Agrawal-Vinay [AV08], Koiran [Koi12] and Tavenas [Tav13], and the use of the shifted partial derivative complexity measure developed in the works of Kayal [Kay12] and Gupta et al [GKKS13a]. These results inspired a flurry of other beautiful results and strong lower bounds for various classes of arithmetic circuits, in particular a recent work of Kayal et al [KSS13] showing superpolynomial lower bounds for {\it regular} arithmetic formulas via an {\it improved depth reduction} for these formulas. It was left as an intriguing question if these methods could prove superpolynomial lower bounds for general (homogeneous) arithmetic formulas, and if so this would indeed be a breakthrough in arithmetic circuit complexity. #R##N#In this paper we study the power and limitations of depth reduction and shifted partial derivatives for arithmetic formulas. We do it via studying the class of depth 4 homogeneous arithmetic circuits. We show: (1) the first {\it superpolynomial lower bounds} for the class of homogeneous depth 4 circuits with top fan-in $o(\log n)$. The core of our result is to show {\it improved depth reduction} for these circuits. (2) We show that improved depth reduction {\it is not possible} when the top fan-in is $\Omega(\log n)$. In particular this shows that the depth reduction procedure of Koiran and Tavenas [Koi12, Tav13] cannot be improved even for homogeneous formulas, thus strengthening the results of Fournier et al [FLMS13] who showed that depth reduction is tight for circuits, and answering some of the main open questions of [KSS13, FLMS13].

Includes members:
  Member "depth 4 lower bounds determinantal complexity a unified approach":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new exponential size lower bounds against depth four circuits of bounded individual degree")
  Member "improved bounds for reduction to depth 4 and depth 3":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds for matrix factorization")
  Member "arithmetic circuits the chasm at depth four gets wider":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lower bounds for matrix factorization")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.CC(Computational Complexity)