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 "towards optimal depth reductions for syntactically multilinear circuits"):
  Abstract: We show that any $n$-variate polynomial computable by a syntactically multilinear circuit of size $\operatorname{poly}(n)$ can be computed by a depth-$4$ syntactically multilinear ($\Sigma\Pi\Sigma\Pi$) circuit of size at most $\exp\left({O\left(\sqrt{n\log n}\right)}\right)$. For degree $d = \omega(n/\log n)$, this improves upon the upper bound of $\exp\left({O(\sqrt{d}\log n)}\right)$ obtained by Tavenas~\cite{T15} for general circuits, and is known to be asymptotically optimal in the exponent when $d < n^{\epsilon}$ for a small enough constant $\epsilon$. Our upper bound matches the lower bound of $\exp\left({\Omega\left(\sqrt{n\log n}\right)}\right)$ proved by Raz and Yehudayoff~\cite{RY09}, and thus cannot be improved further in the exponent. Our results hold over all fields and also generalize to circuits of small individual degree. #R##N#More generally, we show that an $n$-variate polynomial computable by a syntactically multilinear circuit of size $\operatorname{poly}(n)$ can be computed by a syntactically multilinear circuit of product-depth $\Delta$ of size at most $\exp\left(O\left(\Delta \cdot (n/\log n)^{1/\Delta} \cdot \log n\right)\right)$. It follows from the lower bounds of Raz and Yehudayoff (CC 2009) that in general, for constant $\Delta$, the exponent in this upper bound is tight and cannot be improved to $o\left(\left(n/\log n\right)^{1/\Delta}\cdot \log n\right)$.

Includes members:
  Member "an almost quadratic lower bound for syntactically multilinear arithmetic circuits":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lower bounds for special cases of syntactic multilinear abps")
  Member "the chasm at depth four and tensor rank old results new insights":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on multilinear forms bias correlation and tensor rank")
  Member "on the power of homogeneous depth 4 arithmetic circuits":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (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-5 (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)