Simplified priors for Object-Centric Learning

Humans excel at abstracting data and constructing \emph{reusable} concepts, a capability lacking in current continual learning systems. The field of object-centric learning addresses this by developing abstract representations, or slots, from data without human supervision. Different methods have been proposed to tackle this task for images, whereas most are overly complex, non-differentiable, or poorly scalable. In this paper, we introduce a conceptually simple, fully-differentiable, non-iterative, and scalable method called SAMP Simplified Slot Attention with Max Pool Priors). It is implementable using only Convolution and MaxPool layers and an Attention layer. Our method encodes the input image with a Convolutional Neural Network and then uses a branch of alternating Convolution and MaxPool layers to create specialized sub-networks and extract primitive slots. These primitive slots are then used as queries for a Simplified Slot Attention over the encoded image. Despite its simplicity, our method is competitive or outperforms previous methods on standard benchmarks.

Geometry-Informed Neural Networks

We introduce the concept of geometry-informed neural networks (GINNs), which encompass (i) learning under geometric constraints, (ii) neural fields as a suitable representation, and (iii) generating diverse solutions to under-determined systems often encountered in geometric tasks. Notably, the GINN formulation does not require training data, and as such can be considered generative modeling driven purely by constraints. We add an explicit diversity loss to mitigate mode collapse. We consider several constraints, in particular, the connectedness of components which we convert to a differentiable loss through Morse theory. Experimentally, we demonstrate the efficacy of the GINN learning paradigm across a range of two and three-dimensional scenarios with increasing levels of complexity.