human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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].

Connected through hyperedge HE-1 (induced by source paper "towards an algebraic natural proofs barrier via polynomial identity testing"):
  with members:
    - "succinct hitting sets and barriers to proving algebraic circuits lower bounds"
    - "arithmetic circuits with locally low algebraic rank"
    - "geometric complexity theory and matrix powering"
    - "functional lower bounds for arithmetic circuits and connections to boolean circuit complexity"
    - "no occurrence obstructions in geometric complexity theory"
    - "the chasm at depth four and tensor rank old results new insights"
    - "on minimal free resolutions and the method of shifted partial derivatives in complexity theory"
    - "rectangular kronecker coefficients and plethysms in geometric complexity theory"

Connected through hyperedge HE-2 (induced by source paper "arithmetic circuits with locally low algebraic rank"):
  with members:
    - "an exponential lower bound for homogeneous depth 5 circuits over finite fields"
    - "sums of products of polynomials in few variables lower bounds and polynomial identity testing"
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs"
    - "jacobian hits circuits hitting sets lower bounds for depth d occur k formulas depth 3 transcendence degree k circuits"
    - "algebraic independence and blackbox identity testing"

Connected through hyperedge HE-3 (induced by source paper "identity testing and lower bounds for read k oblivious algebraic branching programs"):
  with members:
    - "some lower bound results for set multilinear arithmetic computations"
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "pseudorandomness and fourier growth bounds for width 3 branching programs"
    - "hitting sets for roabp and sum of set multilinear circuits"
    - "deterministic identity testing for sum of read once oblivious arithmetic branching programs"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "pseudorandomness for regular branching programs via fourier analysis"
    - "improved bounds for reduction to depth 4 and depth 3"

Connected through hyperedge HE-4 (induced by source paper "sums of products of polynomials in few variables lower bounds and polynomial identity testing"):
  with members:
    - "subexponential size hitting sets for bounded depth multilinear formulas"
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "quasipolynomial time identity testing of non commutative and read once oblivious algebraic branching programs"
    - "on identity testing of tensors low rank recovery and compressed sensing"
    - "jacobian hits circuits hitting sets lower bounds for depth d occur k formulas depth 3 transcendence degree k circuits"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-5 (induced by source paper "an exponential lower bound for homogeneous depth 5 circuits over finite fields"):
  with members:
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "on the limits of depth reduction at depth 3 over small finite fields"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-6 (induced by source paper "lower bounds by birkhoff interpolation"):
  with members:
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-7 (induced by source paper "on the power of homogeneous depth 4 arithmetic circuits"):
  with members:
    - "depth 4 lower bounds determinantal complexity a unified approach"
    - "superpolynomial lower bounds for general homogeneous depth 4 arithmetic circuits"
    - "on the limits of depth reduction at depth 3 over small finite fields"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "arithmetic circuits the chasm at depth four gets wider"

Connected through hyperedge HE-8 (induced by source paper "on the limits of depth reduction at depth 3 over small finite fields"):
  with members:
    - "on the power of homogeneous depth 4 arithmetic circuits"
    - "depth 4 lower bounds determinantal complexity a unified approach"
    - "superpolynomial lower bounds for general homogeneous depth 4 arithmetic circuits"
    - "arithmetic circuit lower bounds via maxrank"
    - "improved bounds for reduction to depth 4 and depth 3"
    - "arithmetic circuits the chasm at depth four gets wider"

Question: Please tell me which class the center node 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)