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For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…
Overparameterized deep networks have the capacity to memorize training data with zero \emph{training error}. Even after memorization, the \emph{training loss} continues to approach zero, making the model overconfident and the test…
The implicit bias towards solutions with favorable properties is believed to be a key reason why neural networks trained by gradient-based optimization can generalize well. While the implicit bias of gradient flow has been widely studied…
Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…
The infrequent occurrence of overfit in deep neural networks is perplexing. On the one hand, theory predicts that as models get larger they should eventually become too specialized for a specific training set, with ensuing decrease in…
Deep kernel learning (DKL) and related techniques aim to combine the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. One crucial aspect of these models is an expectation that, because…
This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the…
The broad range of neural network training techniques that invoke optimization but rely on ad hoc modification for validity suggests that optimization-based training is misguided. Shortcomings of optimization-based training are brought to…
Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…
Many deep reinforcement learning algorithms contain inductive biases that sculpt the agent's objective and its interface to the environment. These inductive biases can take many forms, including domain knowledge and pretuned…
Due to the unprecedented success of deep learning, it has become an integral component in several multimedia computing applications in todays world. Unfortunately, deep learning systems are not perfect and can fail, sometimes abruptly,…
We study the relationship between the frequency of a function and the speed at which a neural network learns it. We build on recent results that show that the dynamics of overparameterized neural networks trained with gradient descent can…
Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…
In latest years, deep learning has gained a leading role in the pansharpening of multiresolution images. Given the lack of ground truth data, most deep learning-based methods carry out supervised training in a reduced-resolution domain.…
In the context of neural network models, overparametrization refers to the phenomena whereby these models appear to generalize well on the unseen data, even though the number of parameters significantly exceeds the sample sizes, and the…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Many real world data analysis problems exhibit invariant structure, and models that take advantage of this structure have shown impressive empirical performance, particularly in deep learning. While the literature contains a variety of…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
Graph Convolutional Networks (GCNs) are known to suffer from performance degradation as the number of layers increases, which is usually attributed to over-smoothing. Despite the apparent consensus, we observe that there exists a…