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The surge of personalization techniques has allowed us to imagine how existing concepts would look in new scenes. However, an intriguing question remains: How can we generate a new, imaginary concept that has never been seen before? In this talk, we will present the task of creative text-to-image generation, where we seek to generate new and imaginary concepts.

Bio

Elad Richardson is a computer vision researcher.  In his MSc thesis, he explored the application of Deep Learning to 3D facial reconstruction under the supervision of Prof. Ron Kimmel. Elad is currently a PhD student under the supervision of Prof. Daniel Cohen-Or, focusing on generative models and their relation to computer-assisted creativity.

The talk is based on Nicolas Bergeron’s book, Section 4.

The title is a bit of a mouthful, so let us unpack it together:


A C*-correspondence is a certain kind of bimodule over a C*-algebra B that has a B-valued inner product.
Sub and super-product systems are families of C*-correspondences that enjoy certain semigroup-like properties under the tensor product. 
A CP-semigroup is a family of completely positive maps that form a semigroup under composition

Successful goal-directed navigation requires estimating one’s current position in the environment, representing the future goal location, and maintaining a map that preserves the topological relationship between positions. In addition, we often need to implement similar navigational strategies in a continuously changing environment, thereby necessitating certain invariance in the underlying spatial maps. Previous research has identified neurons in the hippocampus and parahippocampal cortices that fire specifically when an animal visits a particular location, implying the presence of a spatial map in the brain. However, this map largely encodes the current position of an animal and is context-dependent, whereby changing the room or shape of the arena results in a new map orthogonal to the previous one. These observations raise the question, are there other spatial maps that fulfill the cognitive requirements necessary for goal-directed navigation?
Using a goal-directed navigation task with multiple reward locations, we observed that neurons in the orbitofrontal cortex (OFC) exhibit distinct firing patterns depending on the goal location, and this goal-specific OFC activity originates even before the onset of the journey. Further, the difference in the ensemble firing patterns representing two target locations is proportional to the physical distance between these locations, implying the preservation of spatial topology. Finally, carrying out the task across different spatial contexts revealed that the mapping of target locations in the OFC is largely preserved and that the maps formed in two different contexts occupy similar neural subspaces and could be aligned by a linear transformation. Taken together, the OFC forms a topology-preserved schema of spatial locations that is used to represent the future spatial goal, making it a potentially crucial brain region for planning context-invariant goal-directed navigational strategies.

In this talk, we delve into several fundamental questions in deep learning. We start by addressing the question, "What are good representations of data?" Recent studies have shown that the representations learned by a single classifier over multiple classes can be easily adapted to new classes with very few samples. We offer a compelling explanation for this behavior by drawing a relationship between transferability and an emergent property known as neural collapse. Later, we explore why certain architectures, such as convolutional networks, outperform fully-connected networks, providing theoretical support for how their inherent sparsity aids learning with fewer samples. Lastly, I present recent findings on how training hyperparameters implicitly control the ranks of weight matrices, consequently affecting the model's compressibility and the dimensionality of the learned features.

Additionally, I will describe how this research integrates into a broader research program where I aim to develop realistic models of contemporary learning settings to guide practices in deep learning and artificial intelligence. Utilizing both theory and experiments, I study fundamental questions in the field of deep learning, including why certain architectural choices improve performance or convergence rates, when transfer learning and self-supervised learning work, and what kinds of data representations are learned in practical settings.