Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks. This motivates longer term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation, and manifold learning.

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Representation Learning: A Review and New Perspectives

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

Can machine learning deliver AI? Theoretical results, inspiration from the brain and cognition, as well as machine learning experiments suggest that in order to learn the kind of complicated functions that can represent high-level abstractions (e.g. in vision, language, and other AI-level tasks), one would need deep architectures. Deep architectures are composed of multiple levels of non-linear operations, such as in neural nets with many hidden layers, graphical models with many levels of latent variables, or in complicated propositional formulae re-using many sub-formulae. Each level of the architecture represents features at a different level of abstraction, defined as a composition of lower-level features. Searching the parameter space of deep architectures is a difficult task, but new algorithms have been discovered and a new sub-area has emerged in the machine learning community since 2006, following these discoveries. Learning algorithms such as those for Deep Belief Networks and other related unsupervised learning algorithms have recently been proposed to train deep architectures, yielding exciting results and beating the state-of-the-art in certain areas. Learning Deep Architectures for AI discusses the motivations for and principles of learning algorithms for deep architectures. By analyzing and comparing recent results with different learning algorithms for deep architectures, explanations for their success are proposed and discussed, highlighting challenges and suggesting avenues for future explorations in this area.

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Learning Deep Architectures for AI

We consider the problem of solving systems of equations Pi(x) ? 0 (mod ni) i = 1... k where Pi are polynomials of degree d and the ni are distinct relatively prime numbers and x d(d+1)/2 we can recover x in polynomial time provided ni ? 2k. This shows that RSA with low exponent is not a good alternative to use as a public key cryptosystem in a large network. It also shows that a protocol by Broder and Dolev [4] is insecure if RSA with low exponent is used.

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On Using RSA with Low Exponent in a Public Key Network

In the paper, we analyze the stochastic behavior of backoff protocols for multiple access channels such as the Ethernet In particular, we prove that binary exponential backoff is unstable if the arrival rate of new messages at each station is l/N for any number of stations N exceeding 1 and any overall arrival rate l exceeding 567 + 1/4N - 2 More importantly, we also prove that any superlinear polynomial backoff protocol (eg, quadratic backoff) is stable for any set of arrival rates that sum to less than one, and any number of stations The results significantly extend the previous work in the area, and provide the first examples of acknowledgement based protocols known to be stable for a nonnegligible overall arrival rate distributed over an arbitrarily large number of stations The results also disprove a popular assumption that exponential backoff is the best choice among acknowledgement based protocols for systems with large overall arrival rates Finally, we prove that any linear or sublinear backoff protocol is unstable if the arrival rate at each station is l/N for any fixed l and sufficiently large N

Analysis of backoff protocols for multiple access channels

We propose a general polynomial time algorithm to find small integer solutions to systems of linear congruences. We use this algorithm to obtain two polynomial time algorithms for reconstructing the values of variables $x_1 , \cdots ,x_k $ when we are given some linear congruences relating them together with some bits obtained by truncating the binary expansions of the variables. The first algorithm reconstructs the variables when either the high order bits or the low order bits of the $x_i $ are known. It is essentially optimal in its use of information in the sense that it will solve most problems almost as soon as the variables become uniquely determined by their constraints. The second algorithm reconstructs the variables when an arbitrary window of consecutive bits of the variables is known. This algorithm will solve most problems when twice as much information as that necessary to uniquely determine the variables is available. Two cryptanalytic applications of the algorithms are given: predicting li...

Reconstructing truncated integer variables satisfying linear congruences

In this article we state and prove a corrected version of Theorem 3.5 in [SIAM J. Comput., 18 (1989), pp. 859--881].

Johan Håstad

Papers

On Using RSA with Low Exponent in a Public Key Network

Analysis of backoff protocols for multiple access channels

Reconstructing truncated integer variables satisfying linear congruences

Polynomial time algorithms for finding integer relations among real numbers

The Bit Extraction Problem of t-Resilient Functions (Preliminary Version)