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Is Optimization a Sufficient Language for Understanding Deep Learning? In this Deep Learning era, machine learning usually boils down to defining a suitable objective/cost function for the learning task at hand, and then optimizing this function using some variant of gradient descent (implemented via backpropagation). Little wonder that hundreds of ML papers each year are devoted to various aspect
Deep-learning-free Text and Sentence Embedding, Part 1 Word embeddings (see my old post1 and post2) capture the idea that one can express “meaning” of words using a vector, so that the cosine of the angle between the vectors captures semantic similarity. (“Cosine similarity” property.) Sentence embeddings and text embeddings try to achieve something similar: use a fixed-dimensional vector to repre
Chi Jin and Michael Jordan • Jul 19, 2017 • 20 minute read A core, emerging problem in nonconvex optimization involves the escape of saddle points. While recent research has shown that gradient descent (GD) generically escapes saddle points asymptotically (see Rong Ge’s and Ben Recht’s blog posts), the critical open problem is one of efficiency — is GD able to move past saddle points quickly, or
Anima Anandkumar • Jan 25, 2016 • 12 minute read While convex analysis has received much attention by the machine learning community, theoretical analysis of non-convex optimization is still nascent. This blog as well as the recent NIPS 2015 workshop on non-convex optimization aim to accelerate research in this area. Along with Kamalika Chaudhuri, Percy Liang, Niranjan U Naresh, and Sewoong Oh,
Tensors are high dimensional generalizations of matrices. In recent years tensor decompositions were used to design learning algorithms for estimating parameters of latent variable models like Hidden Markov Model, Mixture of Gaussians and Latent Dirichlet Allocation (many of these works were considered as examples of “spectral learning”, read on to find out why). In this post I will briefly descri
Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Networks Jul 15, 2022 (Noam Razin). The ability of large neural networks to generalize is commonly believed to stem from an implicit regularization — a tendency... Continue Predicting Generalization using GANs Jun 6, 2022 (Sanjeev Arora and Yi Zhang). A central problem of generalization theory is the following: Giv
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