### Generative Adversarial Networks (GANs), Some Open Questions

Since ability to generate “realistic-looking” data may be a step towards understanding its structure and exploiting it, generative models are an important component of unsupervised learning, which has been a frequent theme on this blog....### Back-propagation, an introduction

Given the sheer number of backpropagation tutorials on the internet, is there really need for another? One of us (Sanjeev) recently taught backpropagation in undergrad AI and couldn’t find any account he was happy with....### The search for biologically plausible neural computation: The conventional approach

Inventors of the original artificial neural networks (NNs) derived their inspiration from biology. However, as artificial NNs progressed, their design was less guided by neuroscience facts. Meanwhile, progress in neuroscience has altered our conceptual understanding...### Gradient Descent Learns Linear Dynamical Systems

From text translation to video captioning, learning to map one sequence to another is an increasingly active research area in machine learning. Fueled by the success of recurrent neural networks in its many variants, the...### Linear algebraic structure of word meanings

Word embeddings capture the meaning of a word using a low-dimensional vector and are ubiquitous in natural language processing (NLP). (See my earlier post 1 and post2.) It has always been unclear how to interpret...### A Framework for analysing Non-Convex Optimization

Previously Rong’s post and Ben’s post show that (noisy) gradient descent can converge to local minimum of a non-convex function, and in (large) polynomial time (Ge et al.’15). This post describes a simple framework that...### Markov Chains Through the Lens of Dynamical Systems: The Case of Evolution

In this post, we will see the main technical ideas in the analysis of the mixing time of evolutionary Markov chains introduced in a previous post. We start by introducing the notion of the expected...### Saddles Again

Thanks to Rong for the very nice blog post describing critical points of nonconvex functions and how to avoid them. I’d like to follow up on his post to highlight a fact that is not...### Escaping from Saddle Points

Convex functions are simple — they usually have only one local minimum. Non-convex functions can be much more complicated. In this post we will discuss various types of critical points that you might encounter when...
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