We propose a new approach to model and learn, without manual supervision, the symmetries of natural objects, such as faces or flowers, given only images as input. It is well known that objects that have a symmetric structure do not usually result in symmetric images due to articulation and perspective effects. This is often tackled by seeking the intrinsic symmetries of the underlying 3D shape, which is very difficult to do when the latter cannot be recovered reliably from data. We show that, if only raw images are given, it is possible to look instead for symmetries in the space of object deformations. We can then learn symmetries from an unstructured collection of images of the object as an extension of the recently-introduced object frame representation, modified so that object symmetries reduce to the obvious symmetry groups in the normalized space. We also show that our formulation provides an explanation of the ambiguities that arise in recovering the pose of symmetric objects from their shape or images and we provide a way of discounting such ambiguities in learning.

Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters. While two properly rescaled weights implement the same function, the training dynamics can be dramatically different. To offer a fresh perspective on exploiting this phenomenon, we build on the recent path-lifting framework, which provides a compact factorization of ReLU networks. We introduce a geometrically motivated criterion to rescale neural network parameters which minimization leads to a conditioning strategy that aligns a kernel in the path-lifting space with a chosen reference. We derive an efficient algorithm to perform this alignment. In the context of random network initialization, we analyze how the architecture and the initialization scale jointly impact the output of the proposed method. Numerical experiments illustrate its potential to speed up training.

Symmetries have proven useful in machine learning models, improving generalisation and overall performance.

However, it may not be available in practice.

The word embedding space in neural models is skewed, and correcting this can improve task performance.

However, developing models that can process weight-space objects is challenging due to their high dimensional nature.