The game of Contract Bridge is played with a standard 52-card deck (4 suits,,, and, with 13 cards in each suit) and 4 players (North, East, South, West). North-South and East-West are two competitive teams. Each player is dealt with 13 cards. There are two phases during the game, namely bidding and playing. After the game, scoring is done based on the won tricks in the playing phase and whether it matches with the contract made in the bidding phase. An example of contract bridge bidding and playing in shown in Figure 1.

We thank reviewers (R1,R2,R3,R5) for their insightful comments. We thank R5 for pointing out that the "decomposition challenges" in IIG are critical for equilibrium construction where Therefore, our paper could have stronger implications than we expect. We disagree with R2 that the tabular form of JPS indeed has theoretical guarantees, as appreciated by other reviewers. Full game AI is a future work. R5 makes a great point that similarity exists between our policy-change density (Eqn.

We introduce a method called TracIn that computes the influence of a training example on a prediction made by the model. The idea is to trace how the loss on the test point changes during the training process whenever the training example of interest was utilized. We provide a scalable implementation of TracIn via: (a) a first-order gradient approximation to the exact computation, (b) saved checkpoints of standard training procedures, and (c) cherry-picking layers of a deep neural network. In contrast with previously proposed methods, TracIn is simple to implement; all it needs is the ability to work with gradients, checkpoints, and loss functions.

This paper considers the setting of jointly matching and clustering multiple graphs belonging to different groups, which naturally rises in many realistic problems. Both graph matching and clustering are challenging (NP-hard) and a joint solution is appealing due to the natural connection of the two tasks. In this paper, we resort to a graduated assignment procedure for soft matching and clustering over iterations, whereby the two-way constraint and clustering confidence are modulated by two separate annealing parameters, respectively. Our technique can be further utilized for end-to-end learning whose loss refers to the cross-entropy between two lines of matching pipelines, as such the keypoint feature extraction CNNs can be learned without ground-truth supervision. Experimental results on real-world benchmarks show our method outperforms learning-free algorithms and performs comparatively against two-graph based supervised graph matching approaches. Source code is publicly available as a module of ThinkMatch.