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 "average case lower bounds and satisfiability algorithms for small threshold circuits"):
  Abstract: $ \newcommand{\cclass}[1]{\normalfont\textsf{##1}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there is a constant $\varepsilon_d > 0$ such that the Parity function on $n$ bits has correlation at most $n^{-\varepsilon_d}$ with depth-$d$ threshold circuits which have at most $n^{1+\varepsilon_d}$ wires, and the Generalized Andreev function on $n$ bits has correlation at most $\exp(-{n^{\varepsilon_d}})$ with depth-$d$ threshold circuits which have at most $n^{1+\varepsilon_d}$ wires. Previously, only worst-case lower bounds in this setting were known (Impagliazzo, Paturi, and Saks (SICOMP 1997)). #R##N#We use our ideas to make progress on several related questions. We give satisfiability algorithms beating brute force search for depth-$d$ threshold circuits with a superlinear number of wires. These are the first such algorithms for depth greater than 2. We also show that Parity on $n$ bits cannot be computed by polynomial-size $\textsf{AC}^0$ circuits with $n^{o(1)}$ general threshold gates. Previously no lower bound for Parity in this setting could handle more than $\log(n)$ gates. This result also implies subexponential-time learning algorithms for $\textsf{AC}^0$ with $n^{o(1)}$ threshold gates under the uniform distribution. In addition, we give almost optimal bounds for the number of gates in a depth-$d$ threshold circuit computing Parity on average, and show average-case lower bounds for threshold formulas of any depth. #R##N#Our techniques include adaptive random restrictions, anti-concentration and the structural theory of linear threshold functions, and bounded-read Chernoff bounds.

Includes members:
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "new algorithms and lower bounds for circuits with linear threshold gates":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds against sparse symmetric functions of acc circuits expanding the reach of sat algorithms")
  Member "a tail bound for read k families of functions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "joint alignment from pairwise differences with a noisy oracle")
  Member "a satisfiability algorithm for sparse depth two threshold circuits":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "more consequences of falsifying seth and the orthogonal vectors conjecture")
  Member "a satisfiability algorithm for ac 0":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "more consequences of falsifying seth and the orthogonal vectors conjecture")
  Member "average sensitivity and noise sensitivity of polynomial threshold functions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "kruskal katona for convex sets with applications")
  Member "bounded independence fools halfspaces":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "list decodable subspace recovery via sum of squares")
  Member "bounding the sensitivity of polynomial threshold functions":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "degree d chow parameters robustly determine degree d ptfs and algorithmic applications")

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)