Thesis seminar - The Sparse Manifold Transform and Unsupervised Learning for Signal Representation
In this talk, I will first present a signal representation framework called the Sparse Manifold Transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maintaining approximate invertibility. The sparse manifold transform is an unsupervised and generative framework that explicitly and simultaneously models the sparse discreteness and low-dimensional manifold structure found in natural scenes. When stacked, it also models hierarchical composition. The proposed framework also provides new geometric insights in understanding the simple cells, complex cells and beyond.
Signal representation is a broad and comprehensive topic. Besides this major quest to build a principled representation for natural signals, I will also present a series of exciting projects I have worked on along the way to understand the representation of different signal modalities from different angles. This involves explainable word embeddings visualization, energy-based generative models, model superpositions, etc.
Rudiger von der Heydt
Sparse Deep Predictive Coding: a model of visual perception
Building models to efficiently represent images is a central problem in the machine learning community. The brain and especially the visual cortex, has long find economical and robust solutions to solve such a problem. At the local scale, Sparse Coding is one of the most successful framework to model neural computation in the visual cortex. It directly derives from the efficient coding hypothesis, and could be thought as a competitive mechanism that describes visual stimulus using a limited number of neurons. At the structural scale Predictive Coding theory has been proposed to model the interconnection between cortical layers using feedforward and feedback connections.
The presentation introduces a model combining Sparse Coding and Predictive Coding in a hierarchical and convolutional architecture. Our model, called the Sparse Deep Predictive Coding (SDPC) was trained on several challenging databases including faces and natural images. The SDPC allows us to analyze the impact of recurrent processing at both neural organization level and perceptual level. At neural organization level, the feedback signal of the model accounted for a reorganization of the V1 association fields that promotes contour integration. At the higher level of perception, the SDPC exhibited significant denoising ability, highly correlated with the strength of the feedback from V2 to V1. The SDPC demonstrates that neuro-inspiration might be the right path to design more powerful and more robust computer vision algorithms.