Learning Multimodal VAEs through Mutual Supervision

Multimodal VAEs seek to model the joint distribution over heterogeneous data (e.g. vision, language), whilst also capturing a shared representation across such modalities. Prior work has typically combined information from the modalities by reconciling idiosyncratic representations directly in the recognition model through explicit products, mixtures, or other such factorisations. Here we introduce a novel alternative, the MEME, that avoids such explicit combinations by repurposing semi-supervised VAEs to combine information between modalities implicitly through mutual supervision. This formulation naturally allows learning from partially-observed data where some modalities can be entirely missing -- something that most existing approaches either cannot handle, or do so to a limited extent. We demonstrate that MEME outperforms baselines on standard metrics across both partial and complete observation schemes on the MNIST-SVHN (image-image) and CUB (image-text) datasets. We also contrast the quality of the representations learnt by mutual supervision against standard approaches and observe interesting trends in its ability to capture relatedness between data.

Gradient Matching for Domain Generalization

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

On Batch Normalisation for Approximate Bayesian Inference

We study batch normalisation in the context of variational inference methods in Bayesian neural networks, such as mean-field or MC Dropout. We show that batch-normalisation does not affect the optimum of the evidence lower bound (ELBO). Furthermore, we study the Monte Carlo Batch Normalisation (MCBN) algorithm, proposed as an approximate inference technique parallel to MC Dropout, and show that for larger batch sizes, MCBN fails to capture epistemic uncertainty. Finally, we provide insights into what is required to fix this failure, namely having to view the mini-batch size as a variational parameter in MCBN. We comment on the asymptotics of the ELBO with respect to this variational parameter, showing that as dataset size increases towards infinity, the batch-size must increase towards infinity as well for MCBN to be a valid approximate inference technique.

Relating by Contrasting: A Data-efficient Framework for Multimodal Generative Models

Multimodal learning for generative models often refers to the learning of abstract concepts from the commonality of information in multiple modalities, such as vision and language. While it has proven effective for learning generalisable representations, the training of such models often requires a large amount of related multimodal data that shares commonality, which can be expensive to come by. To mitigate this, we develop a novel contrastive framework for generative model learning, allowing us to train the model not just by the commonality between modalities, but by the distinction between related and unrelated multimodal data. We show in experiments that our method enables data-efficient multimodal learning on challenging datasets for various multimodal VAE models. We also show that under our proposed framework, the generative model can accurately identify related samples from unrelated ones, making it possible to make use of the plentiful unlabeled, unpaired multimodal data.

Meta-learning with differentiable closed-form solvers

Adapting deep networks to new concepts from a few examples is challenging, due to the high computational requirements of standard fine-tuning procedures. Most work on few-shot learning has thus focused on simple learning techniques for adaptation, such as nearest neighbours or gradient descent. Nonetheless, the machine learning literature contains a wealth of methods that learn non-deep models very efficiently. In this paper, we propose to use these fast convergent methods as the main adaptation mechanism for few-shot learning. The main idea is to teach a deep network to use standard machine learning tools, such as ridge regression, as part of its own internal model, enabling it to quickly adapt to novel data. This requires back-propagating errors through the solver steps. While normally the cost of the matrix operations involved in such a process would be significant, by using the Woodbury identity we can make the small number of examples work to our advantage. We propose both closed-form and iterative solvers, based on ridge regression and logistic regression components. Our methods constitute a simple and novel approach to the problem of few-shot learning and achieve performance competitive with or superior to the state of the art on three benchmarks.