We investigate the prominent class of fair representation learning methods for bias mitigation. Using causal reasoning to define and formalise different sources of dataset bias, we reveal important implicit assumptions inherent to these methods. We prove fundamental limitations on fair representation learning when evaluation data is drawn from the same distribution as training data and run experiments across a range of medical modalities to examine the performance of fair representation learning under distribution shifts. Our results explain apparent contradictions in the existing literature and reveal how rarely considered causal and statistical aspects of the underlying data affect the validity of fair representation learning. We raise doubts about current evaluation practices and the applicability of fair representation learning methods in performance-sensitive settings. We argue that fine-grained analysis of dataset biases should play a key role in the field moving forward.

Counterfactual image generation presents significant challenges, including preserving identity, maintaining perceptual quality, and ensuring faithfulness to an underlying causal model. While existing auto-encoding frameworks admit semantic latent spaces which can be manipulated for causal control, they struggle with scalability and fidelity. Advancements in diffusion models present opportunities for improving counterfactual image editing, having demonstrated state-of-the-art visual quality, human-aligned perception and representation learning capabilities. Here, we present a suite of diffusion-based causal mechanisms, introducing the notions of spatial, semantic and dynamic abduction. We propose a general framework that integrates semantic representations into diffusion models through the lens of Pearlian causality to edit images via a counterfactual reasoning process. To the best of our knowledge, ours is the first work to consider high-level semantic identity preservation for diffusion counterfactuals and to demonstrate how semantic control enables principled trade-offs between faithful causal control and identity preservation.

We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.

Contrastive pretraining can substantially increase model generalisation and downstream performance. However, the quality of the learned representations is highly dependent on the data augmentation strategy applied to generate positive pairs. Positive contrastive pairs should preserve semantic meaning while discarding unwanted variations related to the data acquisition domain. Traditional contrastive pipelines attempt to simulate domain shifts through pre-defined generic image transformations. However, these do not always mimic realistic and relevant domain variations for medical imaging, such as scanner differences. To tackle this issue, we herein introduce counterfactual contrastive learning, a novel framework leveraging recent advances in causal image synthesis to create contrastive positive pairs that faithfully capture relevant domain variations. Our method, evaluated across five datasets encompassing both chest radiography and mammography data, for two established contrastive objectives (SimCLR and DINO-v2), outperforms standard contrastive learning in terms of robustness to acquisition shift. Notably, counterfactual contrastive learning achieves superior downstream performance on both in-distribution and external datasets, especially for images acquired with scanners under-represented in the training set. Further experiments show that the proposed framework extends beyond acquisition shifts, with models trained with counterfactual contrastive learning reducing subgroup disparities across biological sex.

The extraction of object-centric representations for downstream tasks is an emerging area of research. Learning grounded representations of objects that are guaranteed to be stable and invariant promises robust performance across different tasks and environments. Slot Attention (SA) learns object-centric representations by assigning objects to *slots*, but presupposes a *single* distribution from which all slots are randomly initialised. This results in an inability to learn *specialized* slots which bind to specific object types and remain invariant to identity-preserving changes in object appearance. To address this, we present *Conditional Slot Attention* (CoSA) using a novel concept of *Grounded Slot Dictionary* (GSD) inspired by vector quantization. Our proposed GSD comprises (i) canonical object-level property vectors and (ii) parametric Gaussian distributions, which define a prior over the slots. We demonstrate the benefits of our method in multiple downstream tasks such as scene generation, composition, and task adaptation, whilst remaining competitive with SA in object discovery.

Learning modular object-centric representations is said to be crucial for systematic generalization. Existing methods show promising object-binding capabilities empirically, but theoretical identifiability guarantees remain relatively underdeveloped. Understanding when object-centric representations can theoretically be identified is important for scaling slot-based methods to high-dimensional images with correctness guarantees. To that end, we propose a probabilistic slot-attention algorithm that imposes an *aggregate* mixture prior over object-centric slot representations, thereby providing slot identifiability guarantees without supervision, up to an equivalence relation. We provide empirical verification of our theoretical identifiability result using both simple 2-dimensional data and high-resolution imaging datasets.

We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals.

Capsule networks are a recently proposed type of neural network shown to outperform alternatives in challenging shape recognition tasks. In capsule networks, scalar neurons are replaced with capsule vectors or matrices, whose entries represent different properties of objects. The relationships between objects and their parts are learned via trainable viewpoint-invariant transformation matrices, and the presence of a given object is decided by the level of agreement among votes from its parts. This interaction occurs between capsule layers and is a process called routing-by-agreement. In this paper, we propose a new capsule routing algorithm derived from Variational Bayes for fitting a mixture of transforming gaussians, and show it is possible transform our capsule network into a Capsule-VAE. Our Bayesian approach addresses some of the inherent weaknesses of MLE based models such as the variance-collapse by modelling uncertainty over capsule pose parameters. We outperform the state-of-the-art on smallNORB using ≃50% fewer capsules than previously reported, achieve competitive performances on CIFAR-10, Fashion-MNIST, SVHN, and demonstrate significant improvement in MNIST to affNIST generalisation over previous works.1

Rather than performing inefficient local iterative routing between adjacent capsule layers, we propose an alternative global view based on representing the inherent uncertainty in part-object assignment. In our formulation, the local routing iterations are replaced with variational inference of part-object connections in a probabilistic capsule network, leading to a significant speedup without sacrificing performance. In this way, global context is also considered when routing capsules by introducing global latent variables that have direct influence on the objective function, and are updated discriminatively in accordance with the minimum description length (MDL) principle. We focus on enhancing capsule network properties, and perform a thorough evaluation on pose-aware tasks, observing improvements in performance over previous approaches whilst being more computationally efficient.

Acknowledgements The authors would like to thank Mr. George Marandianos, Mrs. Mamatha Thota and Mr. Samuel Bond-Taylor for manually annotating datasets used in this study and of course the reviewers for their constructive feedback that helped to improve the manuscript. We would also like to thank Professor Luc Bidaut for enabling this collaboration. Funding The research presented in this paper was funded by Engineering and Physical Sciences Research Council (Reference Number EP/R005524/1) and Innovate UK (Reference Number 102908), in collaboration with the Olympus Automation Limited Company, for the project Automated Robotic Food Manufacturing System.

There exist various types of information in retail food packages, including food product name, ingredients list and use by date. The correct recognition and coding of use by dates is especially critical in ensuring proper distribution of the product to the market and eliminating potential health risks caused by erroneous mislabelling. The latter can have a major negative effect on the health of consumers and consequently raise legal issues for suppliers. In this work, an end-to-end architecture, composed of a dual deep neural network based system is proposed for automatic recognition of use by dates in food package photos. The system includes: a Global level convolutional neural network (CNN) for high-level food package image quality evaluation (blurry/clear/missing use by date statistics); a Local level fully convolutional network (FCN) for use by date ROI localisation. Post ROI extraction, the date characters are then segmented and recognised. The proposed framework is the first to employ deep neural networks for end-to-end automatic use by date recognition in retail packaging photos. It is capable of achieving very good levels of performance on all the aforementioned tasks, despite the varied textual/pictorial content complexity found in food packaging design.

In this work, a novel deep learning approach to unfold nuclear power reactor signals is proposed. It includes a combination of convolutional neural networks (CNN), denoising autoencoders (DAE) and $k$-means clustering of representations. Monitoring nuclear reactors while running at nominal conditions is critical. Based on analysis of the core reactor neutron flux, it is possible to derive useful information for building fault/anomaly detection systems. By leveraging signal and image pre-processing techniques, the high and low energy spectra of the signals were appropriated into a compatible format for CNN training. Firstly, a CNN was employed to unfold the signal into either twelve or forty-eight perturbation location sources, followed by a $k$-means clustering and $k$-Nearest Neighbour coarse-to-fine procedure, which significantly increases the unfolding resolution. Secondly, a DAE was utilised to denoise and reconstruct power reactor signals at varying levels of noise and/or corruption. The reconstructed signals were evaluated w.r.t. their original counter parts, by way of normalised cross correlation and unfolding metrics. The results illustrate that the origin of perturbations can be localised with high accuracy, despite limited training data and obscured$/$noisy signals, across various levels of granularity.