Related papers: Deep Minds and Shallow Probes

Neural networks often learn task-specific latent representations that fail to generalize to novel settings or tasks. Conversely, humans learn discrete representations (i.e., concepts or words) at a variety of abstraction levels (e.g.,…

Implicit neural representations are a promising new avenue of representing general signals by learning a continuous function that, parameterized as a neural network, maps the domain of a signal to its codomain; the mapping from spatial…

We explore and expand the $\textit{Soft Nearest Neighbor Loss}$ to measure the $\textit{entanglement}$ of class manifolds in representation space: i.e., how close pairs of points from the same class are relative to pairs of points from…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

David Marr's seminal theory of vision proposes that the human visual system operates through a sequence of three stages, known as the 2D sketch, the 2.5D sketch, and the 3D model. In recent years, Deep Neural Networks (DNN) have been widely…

Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these…

Although deep learning has shown its powerful performance in many applications, the mathematical principles behind neural networks are still mysterious. In this paper, we consider the problem of learning a one-hidden-layer neural network…

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…

The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…

In the algorithmic (Kolmogorov) view, agents are programs that track and compress sensory streams using generative programs. We propose a framework where the relevant structural prior is simplicity (Solomonoff) understood as…

Collision detection is essential to virtually all robotics applications. However, traditional geometric collision detection methods generally require pre-existing workspace geometry representations; thus, they are unable to infer the…

Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that…

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient…

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based…

Despite impressive performance as evaluated on i.i.d. holdout data, deep neural networks depend heavily on superficial statistics of the training data and are liable to break under distribution shift. For example, subtle changes to the…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…

Capsule networks are a type of neural network that identify image parts and form the instantiation parameters of a whole hierarchically. The goal behind the network is to perform an inverse computer graphics task, and the network parameters…

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by…