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Large language models (LLMs) have shown tremendous success in following user instructions and generating helpful responses. Nevertheless, their robustness is still far from optimal, as they may generate significantly inconsistent responses…

The dynamics of learning in modern large AI systems is hierarchical, often characterized by abrupt, qualitative shifts akin to phase transitions observed in physical systems. While these phenomena hold promise for uncovering the mechanisms…

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which…

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

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 gradient methods have achieved remarkable success in training deep neural networks on a wide variety of tasks. However, not much is known about the mathematical and statistical properties of this family of methods. This work aims…

The Adaptive Momentum Estimation (Adam) algorithm is highly effective in training various deep learning tasks. Despite this, there's limited theoretical understanding for Adam, especially when focusing on its vanilla form in non-convex…

As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…

A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…

The Adam optimizer is a cornerstone of modern deep learning, yet the empirical necessity of each of its individual components is often taken for granted. This paper presents a focused investigation into the role of bias-correction, a…

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

In quantum control, the robustness with respect to uncertainties in the system's parameters or driving field characteristics is of paramount importance and has been studied theoretically, numerically and experimentally. We test in this…

Large language models (LLMs) are currently at the forefront of intertwining artificial intelligence (AI) systems with human communication and everyday life. Thus, aligning them with human values is of great importance. However, given the…

The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its…

Aligning large language models (LLMs) with human intentions has become a critical task for safely deploying models in real-world systems. While existing alignment approaches have seen empirical success, theoretically understanding how these…

The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn't. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the…

Large Language Models (LLMs) are leading a new technological revolution as one of the most promising research streams toward artificial general intelligence. The scaling of these models, accomplished by increasing the number of parameters…

Artificial intelligence (AI) has achieved human-level performance in specialized tasks such as Go, image recognition, and protein folding, raising the prospect of an AI singularity-where machines not only match but surpass human reasoning.…

Large language models (LLMs) often exhibit abrupt emergent behavior, whereby new abilities arise at certain points during their training. This phenomenon, commonly referred to as a ''phase transition'', remains poorly understood. In this…

Large language models, comprising billions of parameters and pre-trained on extensive web-scale corpora, have been claimed to acquire certain capabilities without having been specifically trained on them. These capabilities, referred to as…