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

The factor graph of an instance of a constraint satisfaction problem (CSP) is the bipartite graph indicating which variables appear in each constraint. An instance of the CSP is given by the factor graph together with a list of which predicate is applied for each constraint. We establish that many Max-CSPs remains as hard to approximate as in the general case even when the factor graph is fixed (depending only on the size of the instance) and known in advance. Examples of results obtained for this restricted setting are: 1. Optimal inapproximability for Max-3-Lin and Max-3-Sat (Håstad, J. ACM 2001). 2. Approximation resistance for predicates supporting pairwise independent subgroups (Chan, J. ACM 2016). 3. Hardness of the “(2 + ε)-Sat” problem and other Promise CSPs (Austrin et al., SIAM J. Comput. 2017). The main technical tool used to establish these results is a new way of folding the long code which we call “functional folding”.

Optimal Inapproximability with Universal Factor Graphs.

1. A CORRECTION Theorem 3.6 in [1] contains an error in the stated bound. As is argued above the theorem, the statistical distance to the uniform distribution decreases by a factor O ( (m/ log m)−1/2 ) = O ((log n)1/2n−1/4) for every two iterations. This implies that the bound obtained for Theorem 3.6 should read O ( n1− t−1 2 1 4 (log n) t−1 2 1 2 ) . I am grateful to Justin Holmgren for pointing out this correction.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/rsa.20620

The square lattice shuffle, correction

In this paper we generalize the quantum algorithm for computing short discrete logarithms previously introduced by Ekera so as to allow for various tradeoffs between the number of times that the algorithm need be executed on the one hand, and the complexity of the algorithm and the requirements it imposes on the quantum computer on the other hand. 
Furthermore, we describe applications of algorithms for computing short discrete logarithms. In particular, we show how other important problems such as those of factoring RSA integers and of finding the order of groups under side information may be recast as short discrete logarithm problems. This immediately gives rise to an algorithm for factoring RSA integers that is less complex than Shor's general factoring algorithm in the sense that it imposes smaller requirements on the quantum computer. 
In both our algorithm and Shor's algorithm, the main hurdle is to compute a modular exponentiation in superposition. When factoring an n bit integer, the exponent is of length 2n bits in Shor's algorithm, compared to slightly more than n/2 bits in our algorithm.

Quantum algorithms for computing short discrete logarithms and factoring RSA integers

We survey some of the recent results in proving that approximating some NP-hard optimization problems remains NP-hard. This is a survey paper and it contains no new results.

Recent Results in Hardness of Approximation

We investigate the relationship between circuit bottom fan-in and circuit size when circuit depth is fixed. We show that in order to compute certain functions, a moderate reduction in circuit bottom fan-in will cause significant increase in circuit size. In particular, we prove that there are functions that are computable by circuits of linear size and depth k with bottom fan-in 2 but require exponential size for circuits of depth k with bottom fan-in 1. A general scheme is established to study the trade-off between circuit bottom fan-in and circuit size. Based on this scheme, we are able to prove, for example, that for any integer c, there are functions that are computable by circuits of linear size and depth k with bottom fan-in O(log n) but require exponential size for circuits of depth k with bottom fan-in c, and that for any constant /spl epsiv/>0, there are functions that are computable by circuits of linear size and depth k with bottom fan-in log n but require superpolynomial size for circuits of depth k with bottom fan-in O(log/sup 1-/spl epsiv//n). A consequence of these results is that the three input read-modes of alternating Turing machines proposed in the literature are all distinct.

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Johan Håstad

Papers

Optimal Inapproximability with Universal Factor Graphs.

The square lattice shuffle, correction

Quantum algorithms for computing short discrete logarithms and factoring RSA integers

Recent Results in Hardness of Approximation

Circuit bottom fan-in and computational power