Jezabel Garcia

Jamie McGowan, Wei Sheng Lai, Weibin Chen et al.

In many domains, the most successful AI models tend to be the largest, indeed often too large to be handled by AI players with limited computational resources. To mitigate this, a number of compression methods have been developed, including methods that prune the network down to high sparsity whilst retaining performance. The best-performing pruning techniques are often those that use second-order curvature information (such as an estimate of the Fisher information matrix) to score the importance of each weight and to predict the optimal compensation for weight deletion. However, these methods are difficult to scale to high-dimensional parameter spaces without making heavy approximations. Here, we propose the FishLeg surgeon (FLS), a new second-order pruning method based on the Fisher-Legendre (FishLeg) optimizer. At the heart of FishLeg is a meta-learning approach to amortising the action of the inverse FIM, which brings a number of advantages. Firstly, the parameterisation enables the use of flexible tensor factorisation techniques to improve computational and memory efficiency without sacrificing much accuracy, alleviating challenges associated with scalability of most second-order pruning methods. Secondly, directly estimating the inverse FIM leads to less sensitivity to the amplification of stochasticity during inversion, thereby resulting in more precise estimates. Thirdly, our approach also allows for progressive assimilation of the curvature into the parameterisation. In the gradual pruning regime, this results in a more efficient estimate refinement as opposed to re-estimation. We find that FishLeg achieves higher or comparable performance against two common baselines in the area, most notably in the high sparsity regime when considering a ResNet18 model on CIFAR-10 (84% accuracy at 95% sparsity vs 60% for OBS) and TinyIM (53% accuracy at 80% sparsity vs 48% for OBS).

Sattar Vakili, Michael Bromberg, Jezabel Garcia et al.

An interesting observation in artificial neural networks is their favorable generalization error despite typically being extremely overparameterized. It is well known that the classical statistical learning methods often result in vacuous generalization errors in the case of overparameterized neural networks. Adopting the recently developed Neural Tangent (NT) kernel theory, we prove uniform generalization bounds for overparameterized neural networks in kernel regimes, when the true data generating model belongs to the reproducing kernel Hilbert space (RKHS) corresponding to the NT kernel. Importantly, our bounds capture the exact error rates depending on the differentiability of the activation functions. In order to establish these bounds, we propose the information gain of the NT kernel as a measure of complexity of the learning problem. Our analysis uses a Mercer decomposition of the NT kernel in the basis of spherical harmonics and the decay rate of the corresponding eigenvalues. As a byproduct of our results, we show the equivalence between the RKHS corresponding to the NT kernel and its counterpart corresponding to the Matérn family of kernels, showing the NT kernels induce a very general class of models. We further discuss the implications of our analysis for some recent results on the regret bounds for reinforcement learning and bandit algorithms, which use overparameterized neural networks.

Alexandru Cioba, Michael Bromberg, Qian Wang et al.

Meta-learning models transfer the knowledge acquired from previous tasks to quickly learn new ones. They are trained on benchmarks with a fixed number of data points per task. This number is usually arbitrary and it is unknown how it affects performance at testing. Since labelling of data is expensive, finding the optimal allocation of labels across training tasks may reduce costs. Given a fixed budget of labels, should we use a small number of highly labelled tasks, or many tasks with few labels each? Should we allocate more labels to some tasks and less to others? We show that: 1) If tasks are homogeneous, there is a uniform optimal allocation, whereby all tasks get the same amount of data; 2) At fixed budget, there is a trade-off between number of tasks and number of data points per task, with a unique solution for the optimum; 3) When trained separately, harder task should get more data, at the cost of a smaller number of tasks; 4) When training on a mixture of easy and hard tasks, more data should be allocated to easy tasks. Interestingly, Neuroscience experiments have shown that human visual skills also transfer better from easy tasks. We prove these results mathematically on mixed linear regression, and we show empirically that the same results hold for few-shot image classification on CIFAR-FS and mini-ImageNet. Our results provide guidance for allocating labels across tasks when collecting data for meta-learning.