Distillation in neural networks using only the samples randomly drawn from a Gaussian distribution is possibly the most straightforward solution one can think of for the complex problem of knowledge transfer from one network (teacher) to the other (student). If successfully done, it can eliminate the requirement of teacher's training data for knowledge distillation and avoid often arising privacy concerns in sensitive applications such as healthcare. There have been some recent attempts at Gaussian noise-based data-free knowledge distillation, however, none of them offer a consistent or reliable solution. We identify the shift in the distribution of hidden layer activation as the key limiting factor, which occurs when Gaussian noise is fed to the teacher network instead of the accustomed training data. We propose a simple solution to mitigate this shift and show that for vision tasks, such as classification, it is possible to achieve a performance close to the teacher by just using the samples randomly drawn from a Gaussian distribution.

Feature importance (FI) estimates are a popular form of explanation, and they are commonly created and evaluated by computing the change in model confidence caused by removing certain input features at test time. For example, in the standard Sufficiency metric, only the top-k most important tokens are kept. In this paper, we study several under-explored dimensions of FI explanations, providing conceptual and empirical improvements for this form of explanation. First, we advance a new argument for why it can be problematic to remove features from an input when creating or evaluating explanations: the fact that these counterfactual inputs are out-of-distribution (OOD) to models implies that the resulting explanations are socially misaligned. The crux of the problem is that the model prior and random weight initialization influence the explanations (and explanation metrics) in unintended ways.

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.