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 "hardness amplification and the approximate degree of constant depth circuits"):
  Abstract: We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to within constant error in a certain one-sided sense, then an OR of disjoint copies of that circuit cannot be pointwise approximated even with very high error. As our main application, we show that for every sequence of degrees $d(n)$, there is an explicit depth-three circuit $F: \{-1,1\}^n \to \{-1,1\}$ of polynomial-size such that any degree-$d$ polynomial cannot pointwise approximate $F$ to error better than $1-\exp\left(-\tilde{\Omega}(nd^{-3/2})\right)$. As a consequence of our main result, we obtain an $\exp\left(-\tilde{\Omega}(n^{2/5})\right)$ upper bound on the the discrepancy of a function in AC$^0$, and an $\exp\left(\tilde{\Omega}(n^{2/5})\right)$ lower bound on the threshold weight of AC$^0$, improving over the previous best results of $\exp\left(-\Omega(n^{1/3})\right)$ and $\exp\left(\Omega(n^{1/3})\right)$ respectively. #R##N#Our techniques also yield a new lower bound of $\Omega\left(n^{1/2}/\log^{(d-2)/2}(n)\right)$ on the approximate degree of the AND-OR tree of depth $d$, which is tight up to polylogarithmic factors for any constant $d$, as well as new bounds for read-once DNF formulas. In turn, these results imply new lower bounds on the communication and circuit complexity of these classes, and demonstrate strong limitations on existing PAC learning algorithms.

Includes members:
  Member "distribution independent reliable learning":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")
  Member "dual lower bounds for approximate degree and markov bernstein inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "on arthur merlin games in communication complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "vanishing error approximate degree and qma complexity")
  Member "a separation of np and conp in multiparty communication complexity":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a nearly optimal lower bound on the approximate degree of ac 0")
  Member "strong direct product theorems for quantum communication and query complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a new minimax theorem for randomized algorithms")
  Member "the intersection of two halfspaces has high threshold degree":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "a note on the sign degree of formulas":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")
  Member "optimal bounds for sign representing the intersection of two halfspaces by polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "near optimal lower bounds on the threshold degree and sign rank of ac 0")

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)