Recent advances in quantum computing and in particular, the introduction of quantum GANs, have led to increased interest in quantum zero-sum game theory, extending the scope of learning algorithms for classical games into the quantum realm. In this paper, we focus on learning in quantum zero-sum games under Matrix Multiplicative Weights Update (a generalization of the multiplicative weights update method) and its continuous analogue, Quantum Replicator Dynamics. When each player selects their state according to quantum replicator dynamics, we show that the system exhibits conservation laws in a quantum-information theoretic sense. Moreover, we show that the system exhibits Poincaré recurrence, meaning that almost all orbits return arbitrarily close to their initial conditions infinitely often.

We study the design of computationally efficient online learning algorithms under smoothed analysis. In this setting, at every step an adversary generates a sample from an adaptively chosen distribution whose density is upper bounded by 1/ times the uniform density. Given access to an offline optimization (ERM) oracle, we give the first computationally efficient online algorithms whose sublinear regret depends only on the pseudo/VC dimension dof the class and the smoothness parameter .

Knowledge Distillation (KD) is a well-known training paradigm in deep neural networks where knowledge acquired by a large teacher model is transferred to a small student. KD has proven to be an effective technique to significantly improve the student's performance for various tasks including object detection. As such, KD techniques mostly rely on guidance at the intermediate feature level, which is typically implemented by minimizing an ℓp-norm distance between teacher and student activations during training. In this paper, we propose a replacement for the pixel-wise independent ℓp-norm based on the structural similarity (SSIM) [28]. By taking into account additional contrast and structural cues, feature importance, correlation and spatial dependence in the feature space are considered in the loss formulation. Extensive experiments on MSCOCO [16] demonstrate the effectiveness of our method across different training schemes and architectures. Our method adds only little computational overhead, is straightforward to implement and at the same time it significantly outperforms the standard ℓp-norms. Moreover, more complex state-of-the-art KD methods [13, 33] using attention-based sampling mechanisms are outperformed, including a +3.5 AP gain using a Faster R-CNN R-50 [21] compared to a vanilla model.