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 "constrained deep networks lagrangian optimization via log barrier extensions"):
  Abstract: This study investigates imposing inequality constraints on the outputs of CNNs, with application to weakly supervised segmentation. In the context of deep networks, constraints are commonly handled with penalties for their simplicity, and despite their well-known limitations. Lagrangian-dual optimization has been largely avoided, mainly due to the computational complexity and stability/convergence issues caused by alternating explicit dual updates/projections and stochastic optimization. Several studies showed that, for deep CNNs, the theoretical and practical advantages of Lagrangian optimization over penalties do not materialize in practice. We propose log-barrier extensions, which approximate Lagrangian optimization of constrained-CNN problems with a sequence of unconstrained losses. Unlike standard interior-point and log-barrier methods, our formulation does not need an initial feasible solution. Furthermore, we provide a new technical result, which shows that the proposed extensions yield an upper bound on the duality gap. This generalizes the duality-gap result of standard log-barriers, yielding sub-optimality certificates for feasible solutions. While sub-optimality is not guaranteed for non-convex problems, our result shows that log-barrier extensions are a principled way to approximate Lagrangian optimization for constrained CNNs via implicit dual variables. We report comprehensive constrained-CNN experiments, showing that our formulation outperforms several penalty-based methods, in terms of accuracy and training stability.

Includes members:
  Member "constrained cnn losses for weakly supervised segmentation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an interpretable classifier for high resolution breast cancer screening images utilizing weakly supervised localization")
  Member "constrained deep learning using conditional gradient and applications in computer vision":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the empirical duality gap of constrained statistical learning")
  Member "a curriculum domain adaptation approach to the semantic segmentation of urban scenes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lidarnet a boundary aware domain adaptation model for lidar point cloud semantic segmentation")
  Member "normalized cut loss for weakly supervised cnn segmentation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "weakly supervised salient object detection via scribble annotations")
  Member "decoupling direction and norm for efficient gradient based l2 adversarial attacks and defenses":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "increasing the robustness of dnns against image corruptions by playing the game of noise")
  Member "on regularized losses for weakly supervised cnn segmentation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "weakly supervised salient object detection via scribble annotations")
  Member "beyond gradient descent for regularized segmentation losses":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "belief propagation reloaded learning bp layers for labeling problems")
  Member "imposing hard constraints on deep networks promises and limitations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "non parametric uni modality constraints for deep ordinal classification")

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.CV(Computer Vision and Pattern Recognition)