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 "quantified derandomization of linear threshold circuits"):
  Abstract: One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing approach to prove such lower bounds is to construct a non-trivial derandomization algorithm for $TC^0$. In this work we take a first step towards the latter goal, by proving the first positive results regarding the derandomization of $TC^0$ circuits of depth $d>2$. #R##N#Our first main result is a quantified derandomization algorithm for $TC^0$ circuits with a super-linear number of wires. Specifically, we construct an algorithm that gets as input a $TC^0$ circuit $C$ over $n$ input bits with depth $d$ and $n^{1+\exp(-d)}$ wires, runs in almost-polynomial-time, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs. In fact, our algorithm works even when the circuit $C$ is a linear threshold circuit, rather than just a $TC^0$ circuit (i.e., $C$ is a circuit with linear threshold gates, which are stronger than majority gates). #R##N#Our second main result is that even a modest improvement of our quantified derandomization algorithm would yield a non-trivial algorithm for standard derandomization of all of $TC^0$, and would consequently imply that $NEXP\not\subseteq TC^0$. Specifically, if there exists a quantified derandomization algorithm that gets as input a $TC^0$ circuit with depth $d$ and $n^{1+O(1/d)}$ wires (rather than $n^{1+\exp(-d)}$ wires), runs in time at most $2^{n^{\exp(-d)}}$, and distinguishes between the case that $C$ rejects at most $2^{n^{1-1/5d}}$ inputs and the case that $C$ accepts at most $2^{n^{1-1/5d}}$ inputs, then there exists an algorithm with running time $2^{n^{1-\Omega(1)}}$ for standard derandomization of $TC^0$.

Includes members:
  Member "deterministic search for cnf satisfying assignments in almost polynomial time":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "statistical physics approaches to unique games")
  Member "average case lower bounds and satisfiability algorithms for small threshold circuits":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "fooling intersections of low weight halfspaces")
  Member "randomness extraction in ac0 and with small locality":
    also connected through other hyperedges:
      (none)
  Member "pseudorandomness via the discrete fourier transform":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "fourier bounds and pseudorandom generators for product tests")
  Member "super linear gate and super quadratic wire lower bounds for depth two and depth three threshold circuits":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a deep conditioning treatment of neural networks")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (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-6 (induced by source paper "lower bounds against sparse symmetric functions of acc circuits expanding the reach of sat algorithms")
  Member "almost optimal pseudorandom generators for spherical caps":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "beating the perils of non convexity guaranteed training of neural networks using tensor methods")

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)