Shane Josias

I am a junior lecturer in Applied Mathematics at Stellenbosch University, South Africa. I recently completed my PhD in Applied Mathematics, where I focused on the computational efficiency and likelihood reliability problem in continuous-time normalising flows.

Prior to the above, I've worked as a software engineer writing complex events processing applications, as well as adding functionality to the framework on top of which those applications run. In addition, I also worked on various aspects of database integration.

news

Sep 19, 2024	Our work on multimodal base distributions in conditional flow matching generative models will be presented at the British Machine Vision Conference.
Dec 16, 2023	Presented our work at the Symbiosis of Deep Learning and Differential Equations workshop at NeurIPS.
Dec 8, 2022	Awarded a poster prize at the 65th Annual SAMS Congress.
Oct 24, 2022	Research assistant position available [closed].
Oct 23, 2022	Invited to attend the Nobel Symposium on Predictability in Science in the Age of AI.

selected publications

Multimodal base distributions in conditional flow matching generative models

Shane Josias, and Willie Brink

British Machine Vision Conference, 2024

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Normalising flows are a flexible class of generative models that provide exact likelihoods, and are often trained through maximum likelihood estimation. Recent work suggests that these models can assign undesirably high likelihood to out-of-distribution data, questioning their reliability for applications where likelihoods are important (e.g. outlier detection). We show that continuous normalising flows trained with the conditional flow matching objective, instead of maximum likelihood, also provide unreliable likelihoods. We then argue for and investigate the utility of incorporating multimodality in the base distribution, through a Gaussian mixture model (GMM) centred at the empirical means of a target distribution’s modes. The GMM has an additional benefit in that samples can be generated from specified modes. We find that the GMM base distribution leads to performance comparable to a standard (unimodal) base distribution for in- and out-of-distribution likelihoods, at little to no extra cost in training and inference times. Interestingly, samples generated by models that use a GMM base have higher precision but significantly lower recall compared to the standard base. We also find support for the hypothesis that continuous flows depend too strongly on pixel values, rather than semantic content.
Jacobian norm regularisation and conditioning in neural ODEs

Shane Josias, and Willie Brink

Communications in Computer and Information Science, 2022

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A recent line of work regularises the dynamics of neural ordinary differential equations (neural ODEs), in order to reduce the number of function evaluations needed by a numerical ODE solver during training. For instance, in the context of continuous normalising flows, the Frobenius norm of Jacobian matrices are regularised under the hypothesis that complex dynamics relate to an ill-conditioned ODE and require more function evaluations from the solver. Regularising the Jacobian norm also relates to sensitivity analysis in the broader neural network literature, where it is believed that regularised models should be more robust to random and adversarial perturbations in their input. We investigate the conditioning of neural ODEs under different Jacobian regularisation strategies, in a binary classification setting. Regularising the Jacobian norm indeed reduces the number of function evaluations required, but at a cost to generalisation. Moreover, naively regularising the Jacobian norm can make the ODE system more ill-conditioned, contrary to what is believed in the literature. As an alternative, we regularise the condition number of the Jacobian and observe a lower number of function evaluations without a significant decrease in generalisation performance. We also find that Jacobian regularisation does not guarantee adversarial robustness, but it can lead to larger margin classifiers.
Class-Selective Mini-Batching and Multitask Learning for Visual Relationship Recognition

Shane Josias, and Willie Brink

SAIEE Africa Research Journal, 2021

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An image can be described by the objects within it, and interactions between those objects. A pair of object labels together with an interaction label is known as a visual relationship, and is represented as a triplet of the form (subject, predicate, object). Recognising visual relationships in images is a challenging task, owing to the combinatorially large number of possible relationship triplets, which leads to an extreme multiclass classification problem. In addition, the distribution of visual relationships in a dataset tends to be long-tailed, i.e. most triplets occur rarely compared to a small number of dominating triplets. Three strategies to address these issues are investigated. Firstly, instead of predicting the full triplet, models can be trained to predict each of the three elements separately. Secondly a multitask learning strategy is investigated, where shared network parameters are used to perform the three separate predictions. Thirdly, a class-selective mini-batch construction strategy is used to expose the network to more of the rare classes during training. Experiments demonstrate that class-selective mini-batch construction can improve performance on classes in the long tail of the data distribution, possibly at the expense of accuracy on the small number of dominating classes. It is also found that a multitask model neither improves nor impedes performance in any significant way, but that its smaller size may be beneficial. In an effort to better understand the behaviour of the various models, a novel evaluation approach for visual relationship recognition is introduced. We conclude that the use of semantics can be helpful in the modelling and evaluation process.