Knowledge distillation is an effective method for training small and efficient deep learning models. However, the efficacy of a single method can degenerate when transferring to other tasks, modalities, or even other architectures. To address this limitation, we propose a novel constrained feature distillation method. This method is derived from a small set of core principles, which results in two emerging components: an orthogonal projection and a task-specific normalisation. Equipped with both of these components, our transformer models can outperform all previous methods on ImageNet and reach up to a 4.4% relative improvement over the previous state-of-the-art methods. To further demonstrate the generality of our method, we apply it to object detection and image generation, whereby we obtain consistent and substantial performance improvements over state-of-the-art. Code and models are publicly available: https://github.com/roymiles/vkd

Recently, Zhang and Chen [25] have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE) in order to greatly reduce integration error and improve generation quality at low numbers of function evaluations (NFEs). Key to this approach is the score function reparameterisation, which reduces the integration error incurred from using a fixed score function estimate over each integration step. The original authors use the default parameterisation used by models trained for noise prediction - multiply the score by the standard deviation of the conditional forward noising distribution. We find that although the mean absolute value of this score parameterisation is close to constant for a large portion of the reverse sampling process, it changes rapidly at the end of sampling. As a simple fix, we propose to instead reparameterise the score (at inference) by dividing it by the average absolute value of previous score estimates at that time step collected from offline high NFE generations. We find that our score normalisation (DEIS-SN) consistently improves FID compared to vanilla DEIS, showing an improvement at 10 NFEs from 6.44 to 5.57 on CIFAR-10 and from 5.9 to 4.95 on LSUN-Church (64 64).

We place an Indian Buffet Process (IBP) prior over the neural structure of a Bayesian Neural Network (BNN), thus allowing the complexity of the BNN to increase and decrease automatically. We apply this methodology to the problem of resource allocation in continual learning, where new tasks occur and the network requires extra resources. Our BNN exploits online variational inference with relaxations to the Bernoulli and Beta distributions (which constitute the IBP prior), so allowing the use of the reparameterisation trick to learn variational posteriors via gradient-based methods. As we automatically learn the number of weights in the BNN, overfitting and underfitting problems are largely overcome. We show empirically that the method offers competitive results compared to Variational Continual Learning (VCL) in some settings.

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating data. However, the performance of inference algorithms can be dramatically affected by the parameterisation used to express a model, requiring users to transform their programs in non-intuitive ways. We argue for automating these transformations, and demonstrate that mechanisms available in recent modeling frameworks can implement non-centring and related reparameterisations. This enables new inference algorithms, and we propose two: a simple approach using interleaved sampling and a novel variational formulation that searches over a continuous space of parameterisations. We show that these approaches enable robust inference across a range of models, and can yield more efficient samplers than the best fixed parameterisation.

We derive a family of Monte Carlo estimators for gradients of expectations of univariate distributions, which is related to the log-derivative trick, but involves pairwise interactions between samples. The first of these comes from either a) introducing and approximating an integral representation based on the fundamental theorem of calculus, or b) applying the reparameterisation trick to an implicit parameterisation under infinitesimal perturbation of the parameters. From the former perspective we generalise to a reproducing kernel Hilbert space representation, giving rise to locality parameter in the pairwise interactions mentioned above. The resulting estimators are unbiased and shown to offer an independent component of useful information in comparison with the log-derivative estimator. Promising analytical and numerical examples confirm the intuitions behind the new estimators.

The Variational Auto-Encoder (VAE) model has become widely popular as a way to learn at once a generative model and embeddings for observations living in a high-dimensional space. In the real world, many such observations may be assumed to be hierarchically structured, such as living organisms data which are related through the evolutionary tree. Also, it has been theoretically and empirically shown that data with hierarchical structure can efficiently be embedded in hyperbolic spaces. We therefore endow the VAE with a hyperbolic geometry and empirically show that it can better generalise to unseen data than its Euclidean counterpart, and can qualitatively recover the hierarchical structure.