In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized space, remains limited. For instance, in deep neural networks (DNNs), their internal representations, decision-making mechanism, absence of overfitting in an over-parametrized space, superior generalizability, etc., remain less understood. Successful applications are often considered as empirical rather than scientific achievement. This paper delves into the loss landscape of DNNs through the lens of spin glass in statistical physics, a system characterized by a complex energy landscape with numerous metastable states, as a novel perspective in understanding how DNNs work. We investigated the loss landscape of single hidden layer neural networks activated by Rectified Linear Unit (ReLU) function, and introduced several protocols to examine the analogy between DNNs and spin glass. Specifically, we used (1) random walk in the parameter space of DNNs to unravel the structures in their loss landscape; (2) a permutation-interpolation protocol to study the connection between copies of identical regions in the loss landscape due to the permutation symmetry in the hidden layers; (3) hierarchical clustering to reveal the hierarchy among trained solutions of DNNs, reminiscent of the so-called Replica Symmetry Breaking (RSB) phenomenon (i.e. the Parisi solution) in spin glass; (4) finally, we examine the relationship between the ruggedness of DNN's loss landscape and its generalizability, showing an improvement of flattened minima.

ChatGPT is a state-of-the-art language model developed by OpenAI, designed to generate human-like text in response to questions and prompts. The model is built on a transformer architecture and is trained on a large corpus of text data, allowing it to generate text that is both coherent and contextually appropriate. In this post, we'll explore how ChatGPT works and the type of model it uses, as well as the accuracy rate of the Adam optimization algorithm used in its training process. ChatGPT is based on the transformer architecture, which was introduced in 2017 by Vaswani et al. in their paper "Attention is All You Need". The transformer architecture is an attention-based neural network that has proven to be highly effective for natural language processing tasks, such as language translation and text generation.

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that a single step size (learning rate) is used for all input variables. Extensions to gradient descent like AdaGrad and RMSProp update the algorithm to use a separate step size for each input variable but may result in a step size that rapidly decreases to very small values. The Adaptive Movement Estimation algorithm, or Adam for short, is an extension to gradient descent and a natural successor to techniques like AdaGrad and RMSProp that automatically adapts a learning rate for each input variable for the objective function and further smooths the search process by using an exponentially decreasing moving average of the gradient to make updates to variables. In this tutorial, you will discover how to develop gradient descent with Adam optimization algorithm from scratch.

Adam is the super star optimization algorithm of Deep Learning. Optimization algorithms aim to find optimum weights, minimize error and maximize accuracy. We find partial derivative of total error with respect to each weight and use this calculation to update weights. This is common because it works slowly but surely. In 2015, Adam optimization algorithm is raised. The name of the algorithm refers to adaptive moment estimation.