12 citations · 67 across the 40 of their papers we have counts for
25 papers · 1 filter
Behavioral Monitoring of JEPA World Models with Jacobian Centroids
Thomas Walker, Randall Balestriero, Richard Baraniuk
Detecting failures in World Model (WM)-based planning requires monitoring whether the model is behaviorally aligned with the current task, which in turn requires studying its inter…
The Geometric Structure of Models Learning Sparse Data
Thomas Walker, T. Mitchell Roddenberry, Ahmed Imtiaz Humayun +2
The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the trainin…
The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts
Thomas Walker, Ahmed Imtiaz Humayun, Randall Balestriero +1
The Linear Representation Hypothesis (LRH) identifies features of a trained deep network (DN) as linear directions in the activation spaces, i.e., output spaces of intermediate lay…
GrokAlign: Geometric Characterisation and Acceleration of Grokking
Thomas Walker, Ahmed Imtiaz Humayun, Randall Balestriero +1
A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustnes…
On the Geometry of Deep Learning
Randall Balestriero, Ahmed Imtiaz Humayun, Richard Baraniuk
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affi…
Mitigating over-exploration in latent space optimization using LES
Omer Ronen, Ahmed Imtiaz Humayun, Richard Baraniuk +2
We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LS…
Deep Networks Always Grok and Here is Why
Ahmed Imtiaz Humayun, Randall Balestriero, Richard Baraniuk
Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have…
Training Dynamics of Deep Network Linear Regions
Ahmed Imtiaz Humayun, Randall Balestriero, Richard Baraniuk
The study of Deep Network (DN) training dynamics has largely focused on the evolution of the loss function, evaluated on or around train and test set data points. In fact, many DN…
Batch Normalization Explained
Randall Balestriero, Richard G. Baraniuk
A critically important, ubiquitous, and yet poorly understood ingredient in modern deep networks (DNs) is batch normalization (BN), which centers and normalizes the feature maps. T…
Singular Value Perturbation and Deep Network Optimization
Rudolf H. Riedi, Randall Balestriero, Richard G. Baraniuk
We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically w…
No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds
Ahmed Imtiaz Humayun, Randall Balestriero, Anastasios Kyrillidis +1
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used t…
NeuroView-RNN: It's About Time
CJ Barberan, Sina Alemohammad, Naiming Liu +2
Recurrent Neural Networks (RNNs) are important tools for processing sequential data such as time-series or video. Interpretability is defined as the ability to be understood by a p…
Spatial Transformer K-Means
Romain Cosentino, Randall Balestriero, Yanis Bahroun +3
K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $…
MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining
Ahmed Imtiaz Humayun, Randall Balestriero, Richard Baraniuk
Deep Generative Networks (DGNs) are extensively employed in Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and their variants to approximate the data mani…
Fast Jacobian-Vector Product for Deep Networks
Randall Balestriero, Richard Baraniuk
Jacobian-vector products (JVPs) form the backbone of many recent developments in Deep Networks (DNs), with applications including faster constrained optimization, regularization wi…
Max-Affine Spline Insights Into Deep Network Pruning
Haoran You, Randall Balestriero, Zhihan Lu +6
In this paper, we study the importance of pruning in Deep Networks (DNs) and the yin & yang relationship between (1) pruning highly overparametrized DNs that have been trained from…
Enhanced Recurrent Neural Tangent Kernels for Non-Time-Series Data
Sina Alemohammad, Randall Balestriero, Zichao Wang +1
Kernels derived from deep neural networks (DNNs) in the infinite-width regime provide not only high performance in a range of machine learning tasks but also new theoretical insigh…
Deep Autoencoders: From Understanding to Generalization Guarantees
Romain Cosentino, Randall Balestriero, Richard Baraniuk +1
A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work…
Ensembles of Generative Adversarial Networks for Disconnected Data
Lorenzo Luzi, Randall Balestriero, Richard G. Baraniuk
Most current computer vision datasets are composed of disconnected sets, such as images from different classes. We prove that distributions of this type of data cannot be represent…
Analytical Probability Distributions and EM-Learning for Deep Generative Networks
Randall Balestriero, Sebastien Paris, Richard G. Baraniuk
Deep Generative Networks (DGNs) with probabilistic modeling of their output and latent space are currently trained via Variational Autoencoders (VAEs). In the absence of a known an…
The Recurrent Neural Tangent Kernel
Sina Alemohammad, Zichao Wang, Randall Balestriero +1
The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learnin…
The Geometry of Deep Networks: Power Diagram Subdivision
Randall Balestriero, Romain Cosentino, Behnaam Aazhang +1
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators…
Implicit Rugosity Regularization via Data Augmentation
Daniel LeJeune, Randall Balestriero, Hamid Javadi +1
Deep (neural) networks have been applied productively in a wide range of supervised and unsupervised learning tasks. Unlike classical machine learning algorithms, deep networks typ…
From Hard to Soft: Understanding Deep Network Nonlinearities via Vector Quantization and Statistical Inference
Randall Balestriero, Richard G. Baraniuk
Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but rece…