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 "small depth multilinear formula lower bounds for iterated matrix multiplication with applications"):
  Abstract: In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show that the well-known divide-and-conquer algorithm cannot be significantly improved at any depth, as long as the formulas are multilinear. #R##N#Formally, for each depth $\Delta \leq \log d$, we show that any product-depth $\Delta$ multilinear formula for $\mathrm{IMM}_d$ must have size $\exp(\Omega(\Delta d^{1/\Delta})).$ It also follows from this that any multilinear circuit of product-depth $\Delta$ for the same polynomial of the above form must have a size of $\exp(\Omega(d^{1/\Delta})).$ In particular, any polynomial-sized multilinear formula for $\mathrm{IMM}_d$ must have depth $\Omega(\log d)$, and any polynomial-sized multilinear circuit for $\mathrm{IMM}_d$ must have depth $\Omega(\log d/\log \log d).$ Both these bounds are tight up to constant factors. #R##N#1. Depth-reduction: A well-known result of Brent (JACM 1974) implies that any formula of size $s$ can be converted to one of size $s^{O(1)}$ and depth $O(\log s)$; further, this reduction continues to hold for multilinear formulas. Our lower bound implies that any depth-reduction in the multilinear setting cannot reduce the depth to $o(\log s)$ without a superpolynomial blow-up in size. #R##N#2. Separations from general formulas: Our result, along with a non-trivial upper bound for $\mathrm{IMM}_{d}$ implied by a result of Gupta, Kamath, Kayal and Saptharishi (SICOMP 2016), shows that for any size $s$ and product-depth $\Delta = o(\log s),$ general formulas of size $s$ and product-depth $\Delta$ cannot be converted to multilinear formulas of size $s^{\omega(1)}$ and product-depth $\Delta,$ when the underlying field has characteristic zero.

Includes members:
  Member "the average sensitivity of bounded depth formulas":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved pseudorandom generators from pseudorandom multi switching lemmas")
  Member "on the power of homogeneous depth 4 arithmetic circuits":
    also connected through other hyperedges:
      - Hyperedge HE-2 (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-3 (induced by source paper "lower bounds for matrix factorization")
  Member "homogeneous formulas and symmetric polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new exponential size lower bounds against depth four circuits of bounded individual degree")

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)