Investigating the Capabilities of Deep Learning for Processing and Interpreting One-Shot Multi-offset GPR Data: A Numerical Case Study for Lunar and Martian Environments

Ground-penetrating radar (GPR) is a mature geophysical method that has gained increasing popularity in planetary science over the past decade. GPR has been utilised both for Lunar and Martian missions providing pivotal information regarding the near surface geology of Terrestrial planets. Within that context, numerous processing pipelines have been suggested to address the unique challenges present in planetary setups. These processing pipelines often require manual tuning resulting to ambiguous outputs open to non-unique interpretations. These pitfalls combined with the large number of planetary GPR data (kilometers in magnitude), highlight the necessity for automatic, objective and advanced processing and interpretation schemes. The current paper investigates the potential of deep learning for interpreting and processing GPR data. The one-shot multi-offset configuration is investigated via a coherent numerical case study, showcasing the potential of deep learning for A) reconstructing the dielectric distribution of the the near surface of Terrestrial planets, and B) filling missing or bad-quality traces. Special care was taken for the numerical data to be both realistic and challenging. Moreover, the generated synthetic data are properly labelled and made publicly available for training future data-driven pipelines and contributing towards developing pre-trained foundation models for GPR.

Capsule Network Projectors are Equivariant and Invariant Learners

Learning invariant representations has been the longstanding approach to self-supervised learning. However, recently progress has been made in preserving equivariant properties in representations, yet do so with highly prescribed architectures. In this work, we propose an invariant-equivariant self-supervised architecture that employs Capsule Networks (CapsNets) which have been shown to capture equivariance with respect to novel viewpoints. We demonstrate that the use of CapsNets in equivariant self-supervised architectures achieves improved downstream performance on equivariant tasks with higher efficiency and fewer network parameters. To accommodate the architectural changes of CapsNets, we introduce a new objective function based on entropy minimisation. This approach, which we name CapsIE (Capsule Invariant Equivariant Network), achieves state-of-the-art performance across all invariant and equivariant downstream tasks on the 3DIEBench dataset, while outperforming supervised baselines. Our results demonstrate the ability of CapsNets to learn complex and generalised representations for large-scale, multi-task datasets compared to previous CapsNet benchmarks. Code is available at https://github.com/AberdeenML/CapsIE.

LeOCLR: Leveraging Original Images for Contrastive Learning of Visual Representations

Contrastive instance discrimination outperforms supervised learning in downstream tasks like image classification and object detection. However, this approach heavily relies on data augmentation during representation learning, which may result in inferior results if not properly implemented. Random cropping followed by resizing is a common form of data augmentation used in contrastive learning, but it can lead to degraded representation learning if the two random crops contain distinct semantic content. To address this issue, this paper introduces LeOCLR (Leveraging Original Images for Contrastive Learning of Visual Representations), a framework that employs a new instance discrimination approach and an adapted loss function that ensures the shared region between positive pairs is semantically correct. The experimental results show that our approach consistently improves representation learning across different datasets compared to baseline models. For example, our approach outperforms MoCo-v2 by 5.1% on ImageNet-1K in linear evaluation and several other methods on transfer learning tasks.

Masked Capsule Autoencoders

We propose Masked Capsule Autoencoders (MCAE), the first Capsule Network that utilises pretraining in a self-supervised manner. Capsule Networks have emerged as a powerful alternative to Convolutional Neural Networks (CNNs), and have shown favourable properties when compared to Vision Transformers (ViT), but have struggled to effectively learn when presented with more complex data, leading to Capsule Network models that do not scale to modern tasks. Our proposed MCAE model alleviates this issue by reformulating the Capsule Network to use masked image modelling as a pretraining stage before finetuning in a supervised manner. Across several experiments and ablations studies we demonstrate that similarly to CNNs and ViTs, Capsule Networks can also benefit from self-supervised pretraining, paving the way for further advancements in this neural network domain. For instance, pretraining on the Imagenette dataset, a dataset of 10 classes of Imagenet-sized images, we achieve not only state-of-the-art results for Capsule Networks but also a 9% improvement compared to purely supervised training. Thus we propose that Capsule Networks benefit from and should be trained within a masked image modelling framework, with a novel capsule decoder, to improve a Capsule Network's performance on realistic-sized images.

ProtoCaps: A Fast and Non-Iterative Capsule Network Routing Method

Capsule Networks have emerged as a powerful class of deep learning architectures, known for robust performance with relatively few parameters compared to Convolutional Neural Networks (CNNs). However, their inherent efficiency is often overshadowed by their slow, iterative routing mechanisms which establish connections between Capsule layers, posing computational challenges resulting in an inability to scale. In this paper, we introduce a novel, non-iterative routing mechanism, inspired by trainable prototype clustering. This innovative approach aims to mitigate computational complexity, while retaining, if not enhancing, performance efficacy. Furthermore, we harness a shared Capsule subspace, negating the need to project each lower-level Capsule to each higher-level Capsule, thereby significantly reducing memory requisites during training. Our approach demonstrates superior results compared to the current best non-iterative Capsule Network and tests on the Imagewoof dataset, which is too computationally demanding to handle efficiently by iterative approaches. Our findings underscore the potential of our proposed methodology in enhancing the operational efficiency and performance of Capsule Networks, paving the way for their application in increasingly complex computational scenarios.

Tabular Machine Learning Methods for Predicting Gas Turbine Emissions

Predicting emissions for gas turbines is critical for monitoring harmful pollutants being released into the atmosphere. In this study, we evaluate the performance of machine learning models for predicting emissions for gas turbines. We compare an existing predictive emissions model, a first principles-based Chemical Kinetics model, against two machine learning models we developed based on SAINT and XGBoost, to demonstrate improved predictive performance of nitrogen oxides (NOx) and carbon monoxide (CO) using machine learning techniques. Our analysis utilises a Siemens Energy gas turbine test bed tabular dataset to train and validate the machine learning models. Additionally, we explore the trade-off between incorporating more features to enhance the model complexity, and the resulting presence of increased missing values in the dataset.

Semantic Positive Pairs for Enhancing Contrastive Instance Discrimination

Self-supervised learning algorithms based on instance discrimination effectively prevent representation collapse and produce promising results in representation learning. However, the process of attracting positive pairs (i.e., two views of the same instance) in the embedding space and repelling all other instances (i.e., negative pairs) irrespective of their categories could result in discarding important features. To address this issue, we propose an approach to identifying those images with similar semantic content and treating them as positive instances, named semantic positive pairs set (SPPS), thereby reducing the risk of discarding important features during representation learning. Our approach could work with any contrastive instance discrimination framework such as SimCLR or MOCO. We conduct experiments on three datasets: ImageNet, STL-10 and CIFAR-10 to evaluate our approach. The experimental results show that our approach consistently outperforms the baseline method vanilla SimCLR across all three datasets; for example, our approach improves upon vanilla SimCLR under linear evaluation protocol by 4.18% on ImageNet with a batch size 1024 and 800 epochs.

S-JEA: Stacked Joint Embedding Architectures for Self-Supervised Visual Representation Learning

The recent emergence of Self-Supervised Learning (SSL) as a fundamental paradigm for learning image representations has, and continues to, demonstrate high empirical success in a variety of tasks. However, most SSL approaches fail to learn embeddings that capture hierarchical semantic concepts that are separable and interpretable. In this work, we aim to learn highly separable semantic hierarchical representations by stacking Joint Embedding Architectures (JEA) where higher-level JEAs are input with representations of lower-level JEA. This results in a representation space that exhibits distinct sub-categories of semantic concepts (e.g., model and colour of vehicles) in higher-level JEAs. We empirically show that representations from stacked JEA perform on a similar level as traditional JEA with comparative parameter counts and visualise the representation spaces to validate the semantic hierarchies.

HMSN: Hyperbolic Self-Supervised Learning by Clustering with Ideal Prototypes

Hyperbolic manifolds for visual representation learning allow for effective learning of semantic class hierarchies by naturally embedding tree-like structures with low distortion within a low-dimensional representation space. The highly separable semantic class hierarchies produced by hyperbolic learning have shown to be powerful in low-shot tasks, however, their application in self-supervised learning is yet to be explored fully. In this work, we explore the use of hyperbolic representation space for self-supervised representation learning for prototype-based clustering approaches. First, we extend the Masked Siamese Networks to operate on the Poincar\'e ball model of hyperbolic space, secondly, we place prototypes on the ideal boundary of the Poincar\'e ball. Unlike previous methods we project to the hyperbolic space at the output of the encoder network and utilise a hyperbolic projection head to ensure that the representations used for downstream tasks remain hyperbolic. Empirically we demonstrate the ability of these methods to perform comparatively to Euclidean methods in lower dimensions for linear evaluation tasks, whilst showing improvements in extreme few-shot learning tasks.

Vanishing Activations: A Symptom of Deep Capsule Networks

Capsule Networks, an extension to Neural Networks utilizing vector or matrix representations instead of scalars, were initially developed to create a dynamic parse tree where visual concepts evolve from parts to complete objects. Early implementations of Capsule Networks achieved and maintain state-of-the-art results on various datasets. However, recent studies have revealed shortcomings in the original Capsule Network architecture, notably its failure to construct a parse tree and its susceptibility to vanishing gradients when deployed in deeper networks. This paper extends the investigation to a range of leading Capsule Network architectures, demonstrating that these issues are not confined to the original design. We argue that the majority of Capsule Network research has produced architectures that, while modestly divergent from the original Capsule Network, still retain a fundamentally similar structure. We posit that this inherent design similarity might be impeding the scalability of Capsule Networks. Our study contributes to the broader discussion on improving the robustness and scalability of Capsule Networks.