Related papers: Gauge theory and twins paradox of disentangled rep…
Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
The geometrical picture of gauge theories must be enlarged when a gauge potential ceases to behave like a connection, as it does in electroweak interactions. When the gauge group has dimension four, the vector space isomorphism between…
How can intelligent agents solve a diverse set of tasks in a data-efficient manner? The disentangled representation learning approach posits that such an agent would benefit from separating out (disentangling) the underlying structure of…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
Intelligent perception and interaction with the world hinges on internal representations that capture its underlying structure (''disentangled'' or ''abstract'' representations). Disentangled representations serve as world models, isolating…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…
Graph Neural Networks (GNNs) have become essential tools for graph representation learning in various domains, such as social media and healthcare. However, they often suffer from fairness issues due to inherent biases in node attributes…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…
We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are…
Latent traversal is a popular approach to visualize the disentangled latent representations. Given a bunch of variations in a single unit of the latent representation, it is expected that there is a change in a single factor of variation of…
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories,…
I introduce a way of constructing a fiber bundle whose fibers are given by hypercomplex algebras and woven by appropriate structure group, and present that a novel gauge theory can be built on the hypercomplex fiber bundle. In this work, I…
In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…
Disentangled representation learning has recently attracted a significant amount of attention, particularly in the field of image representation learning. However, learning the disentangled representations behind a graph remains largely…
One of the main arguments behind studying disentangled representations is the assumption that they can be easily reused in different tasks. At the same time finding a joint, adaptable representation of data is one of the key challenges in…
Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning. This study introduces a novel approach by applying the principles of gauge symmetries, a key…