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In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs…

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Adaptive optimization methods (such as Adam) play a major role in LLM pretraining, significantly outperforming Gradient Descent (GD). Recent studies have proposed new smoothness assumptions on the loss function to explain the advantages of…

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

Despite the widespread adoption of neural networks, their training dynamics remain poorly understood. We show experimentally that as the size of the dataset increases, a point forms where the magnitude of the gradient of the loss becomes…

The spherical noise added to gradients in differentially private (DP) training undermines the performance of adaptive optimizers like AdaGrad and Adam, and hence many recent works have proposed algorithms to address this challenge. However,…

Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…

Time-series forecasting often faces challenges from non-stationarity, particularly distributional drift, where the data distribution evolves over time. This dynamic behavior can undermine the effectiveness of adaptive optimizers, such as…

We identity a by-far-unrecognized problem of Adam-style optimizers which results from unnecessary coupling between momentum and adaptivity. The coupling leads to instability and divergence when the momentum and adaptivity parameters are…

In adaptive dynamic programming, neurocontrol and reinforcement learning, the objective is for an agent to learn to choose actions so as to minimise a total cost function. In this paper we show that when discretized time is used to model…

Precursor gradients in a reaction-diffusion system are spatially varying coefficients in the reaction-kinetics. Such gradients have been used in various applications, such as the head formation in the Hydra, to model the effect of…

Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…

A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…

Adaptive optimizers with decoupled weight decay, such as AdamW, are the de facto standard for pre-training large transformer-based generative models. Yet the quadratic nature of the $\ell_2$ penalty embedded in weight decay drives all…

Adaptive gradient-descent optimizers are the standard choice for training neural network models. Despite their faster convergence than gradient-descent and remarkable performance in practice, the adaptive optimizers are not as well…

Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms…

Predicting high-fidelity future human poses, from a historically observed sequence, is decisive for intelligent robots to interact with humans. Deep end-to-end learning approaches, which typically train a generic pre-trained model on…

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of…

An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…

The adaptive fitness of an organism in its ecological niche is highly reliant upon its ability to associate an environmental or internal stimulus with a behavior response through reinforcement. This simple but powerful observation has been…