No Free Prune: Information-Theoretic Barriers to Pruning at Initialization

The existence of "lottery tickets" arXiv:1803.03635 at or near initialization raises the tantalizing question of whether large models are necessary in deep learning, or whether sparse networks can be quickly identified and trained without ever training the dense models that contain them. However, efforts to find these sparse subnetworks without training the dense model ("pruning at initialization") have been broadly unsuccessful arXiv:2009.08576. We put forward a theoretical explanation for this, based on the model's effective parameter count, $p_\text{eff}$, given by the sum of the number of non-zero weights in the final network and the mutual information between the sparsity mask and the data. We show the Law of Robustness of arXiv:2105.12806 extends to sparse networks with the usual parameter count replaced by $p_\text{eff}$, meaning a sparse neural network which robustly interpolates noisy data requires a heavily data-dependent mask. We posit that pruning during and after training outputs masks with higher mutual information than those produced by pruning at initialization. Thus two networks may have the same sparsities, but differ in effective parameter count based on how they were trained. This suggests that pruning near initialization may be infeasible and explains why lottery tickets exist, but cannot be found fast (i.e. without training the full network). Experiments on neural networks confirm that information gained during training may indeed affect model capacity.

Grokking as the Transition from Lazy to Rich Training Dynamics

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function $y(x)$. We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels $y(x)$ are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

Human or Machine? Turing Tests for Vision and Language

As AI algorithms increasingly participate in daily activities that used to be the sole province of humans, we are inevitably called upon to consider how much machines are really like us. To address this question, we turn to the Turing test and systematically benchmark current AIs in their abilities to imitate humans. We establish a methodology to evaluate humans versus machines in Turing-like tests and systematically evaluate a representative set of selected domains, parameters, and variables. The experiments involved testing 769 human agents, 24 state-of-the-art AI agents, 896 human judges, and 8 AI judges, in 21,570 Turing tests across 6 tasks encompassing vision and language modalities. Surprisingly, the results reveal that current AIs are not far from being able to impersonate human judges across different ages, genders, and educational levels in complex visual and language challenges. In contrast, simple AI judges outperform human judges in distinguishing human answers versus machine answers. The curated large-scale Turing test datasets introduced here and their evaluation metrics provide valuable insights to assess whether an agent is human or not. The proposed formulation to benchmark human imitation ability in current AIs paves a way for the research community to expand Turing tests to other research areas and conditions. All of source code and data are publicly available at https://tinyurl.com/8x8nha7p