Data-driven modelling and synthesis of motion is an active research area with applications that include animation, games, and social robotics. This paper introduces a new class of probabilistic, generative, and controllable motion-data models based on normalising flows. Models of this kind can describe highly complex distributions, yet can be trained efficiently using exact maximum likelihood, unlike GANs or VAEs. Our proposed model is autoregressive and uses LSTMs to enable arbitrarily long time-dependencies. Importantly, is is also causal, meaning that each pose in the output sequence is generated without access to poses or control inputs from future time steps; this absence of algorithmic latency is important for interactive applications with real-time motion control. The approach can in principle be applied to any type of motion since it does not make restrictive, task-specific assumptions regarding the motion or the character morphology. We evaluate the models on motion-capture datasets of human and quadruped locomotion. Objective and subjective results show that randomly-sampled motion from the proposed method outperforms task-agnostic baselines and attains a motion quality close to recorded motion capture.
Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for parametrization is needed. We propose block neural autoregressive flow (B-NAF), a much more compact universal approximator of density functions, where we model a bijection directly using a single feed-forward network. Invertibility is ensured by carefully designing each affine transformation with block matrices that make the flow autoregressive and (strictly) monotone. We compare B-NAF to NAF and other established flows on density estimation and approximate inference for latent variable models. Our proposed flow is competitive across datasets while using orders of magnitude fewer parameters.
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in practice. This paper employs normalising flows as a flexible likelihood model and presents an efficient method for fitting them to complex densities. These estimators must trade-off between modeling distributional complexity, functional complexity and heteroscedasticity without overfitting. We recognize these trade-offs as modeling decisions and develop a Bayesian framework for placing priors over these conditional density estimators using variational Bayesian neural networks. We evaluate this method on several small benchmark regression datasets, on some of which it obtains state of the art performance. Finally, we apply the method to two spatial density modeling tasks with over 1 million datapoints using the New York City yellow taxi dataset and the Chicago crime dataset.
Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such as Bayes by Backprop or Multiplicative Normalising Flows). However, current approaches have limitations regarding flexibility and scalability. We introduce Bayes by Hypernet (BbH), a new method of variational approximation that interprets hypernetworks as implicit distributions. It naturally uses neural networks to model arbitrarily complex distributions and scales to modern deep learning architectures. In our experiments, we demonstrate that our method achieves competitive accuracies and predictive uncertainties on MNIST and a CIFAR5 task, while being the most robust against adversarial attacks.