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 "sum of squares certificates for maxima of random tensors on the sphere"):
  Abstract: For an $n$-variate order-$d$ tensor $A$, define $ A_{\max} := \sup_{\| x \|_2 = 1} \langle A , x^{\otimes d} \rangle$ to be the maximum value taken by the tensor on the unit sphere. It is known that for a random tensor with i.i.d $\pm 1$ entries, $A_{\max} \lesssim \sqrt{n\cdot d\cdot\log d}$ w.h.p. We study the problem of efficiently certifying upper bounds on $A_{\max}$ via the natural relaxation from the Sum of Squares (SoS) hierarchy. Our results include: #R##N#- When $A$ is a random order-$q$ tensor, we prove that $q$ levels of SoS certifies an upper bound $B$ on $A_{\max}$ that satisfies \[ B ~~~~\leq~~ #R##N#A_{\max} \cdot \biggl(\frac{n}{q^{\,1-o(1)}}\biggr)^{q/4-1/2} \quad \text{w.h.p.} \] Our upper bound improves a result of Montanari and Richard (NIPS 2014) when $q$ is large. #R##N#- We show the above bound is the best possible up to lower order terms, namely the optimum of the level-$q$ SoS relaxation is at least \[ A_{\max} \cdot \biggl(\frac{n}{q^{\,1+o(1)}}\biggr)^{q/4-1/2} \ . \] #R##N#- When $A$ is a random order-$d$ tensor, we prove that $q$ levels of SoS certifies an upper bound $B$ on $A_{\max}$ that satisfies \[ #R##N#B ~~\leq ~~ A_{\max} \cdot \biggl(\frac{\widetilde{O}(n)}{q}\biggr)^{d/4 - 1/2} \quad \text{w.h.p.} \] For growing $q$, this improves upon the bound certified by constant levels of SoS. This answers in part, a question posed by Hopkins, Shi, and Steurer (COLT 2015), who established the tight characterization for constant levels of SoS.

Includes members:
  Member "sum of squares lower bounds for refuting any csp":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "sum of squares meets square loss fast rates for agnostic tensor completion")
  Member "strongly refuting random csps below the spectral threshold":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "tensor principal component analysis via sum of squares proofs":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "computational hardness of certifying bounds on constrained pca problems")
  Member "dictionary learning and tensor decomposition via the sum of squares method":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "a statistical model for tensor pca":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "community detection on mixture multi layer networks via regularized tensor decomposition")
  Member "sum of squares proofs and the quest toward optimal algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "sum of squares bounds for the ordering principle")
  Member "rounding sum of squares relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "hypercontractivity sum of squares proofs and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "sum of squares bounds for the ordering principle")

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)