Artificial Recurrent Neural Networks (1989-2010). Most work in machine learning focuses on machines with reactive behavior. RNNs, however, are more general sequence processors inspired by human brains. They have adaptive feedback connections and are in principle as powerful as any computer. The first RNNs could not learn to look far back into the past. But our RNN called "Long Short-Term Memory" (LSTM) overcomes this fundamental problem, and efficiently learns to solve many previously unlearnable tasks. It can be used for speech recognition, time series prediction, music composition, etc. For example, our LSTM RNN outperform all other known methods on the difficult problem of recognizing unsegmented cursive handwriting; they won several recent handwriting competitions. They learn through gradient descent and / or evolution or both. Compare the RNN Book Preface.

Gödel machine: An old dream of computer scientists is to build an optimally efficient universal problem solver. The Gödel machine can be implemented on a traditional computer and solves any given computational problem in an optimal fashion inspired by Kurt Gödel's celebrated self-referential formulas (1931). It starts with an axiomatic description of itself, and we may plug in any utility function, such as the expected future reward of a robot. Using an efficient proof searcher, the Gödel machine will rewrite any part of its software (including the proof searcher) as soon as it has found a proof that this will improve its future performance, given the utility function and the typically limited computational resources. Self-rewrites are globally optimal (no local maxima!) since provably none of all the alternative rewrites and proofs (those that could be found by continuing the proof search) are worth waiting for. The Gödel machine formalizes I. J. Good's informal remarks (1965) on an "intelligence explosion" through self-improving "super-intelligences". Summary. FAQ.

Optimal Ordered Problem Solver. OOPS solves one task after another, through search for solution- computing programs. The incremental method optimally exploits solutions to earlier tasks when possible - compare principles of Levin's optimal universal search. OOPS can temporarily rewrite its own search procedure, efficiently searching for faster search methods (metasearching or metalearning). It is applicable to problems of optimization or prediction. Talk slides.

Super Omegas and Generalized Kolmogorov Complexity and Algorithmic Probability. Kolmogorov's (left) complexity K(x) of a bitstring x is the length of the shortest program that computes x and halts. Solomonoff's algorithmic probability of x is the probability of guessing a program for x. Chaitin's Omega is the halting probability of a Turing machine with random input (Omega is known as the "number of wisdom" because it compactly encodes all mathematical truth). Schmidhuber generalized all of this to non-halting but converging programs. This led to the shortest possible formal descriptions and to non-enumerable but limit-computable measures and Super Omegas, and even has consequences for computable universes and optimal inductive inference. Slides.

Universal Learning Algorithms. There is a theoretically optimal way of predicting the future, given the past. It can be used to define an optimal (though noncomputable) rational agent that maximizes its expected reward in almost arbitrary environments sampled from computable probability distributions. This work represents the first mathematically sound theory of universal artificial intelligence - most previous work on AI was either heuristic or very limited.

Speed Prior. Occam's Razor: prefer simple solutions to complex ones. But what exactly does "simple" mean? According to tradition something is simple if it has a short description or program, that is, it has low Kolmogorov complexity. This leads to Solomonoff's & Levin's miraculous probability measure which yields optimal though noncomputable predictions, given past observations. The Speed Prior is different though: it is a new simplicity measure based on the fastest way of describing objects, not the shortest. Unlike the traditional one, it leads to near-optimal computable predictions, and provokes unusual prophecies concerning the future of our universe. Talk slides.

In the Beginning was the Code. In 1996 Schmidhuber wrote the first paper about all possible computable universes. His `Great Programmer' is consistent with Zuse's thesis (1967) of computable physics, against which there is no physical evidence, contrary to common belief. If everything is computable, then which exactly is our universe's program? It turns out that the simplest program computes all universes, not just ours. Later work (2000) on Algorithmic Theories of Everything analyzed all the universes with limit-computable probabilities as well as the very limits of formal describability. This paper led to above-mentioned generalizations of algorithmic information and probability and Super Omegas as well as the Speed Prior. See comments on Wolfram's 2002 book and letter on randomness in physics (Nature 439, 2006). Talk slides.

Interestingness & Active Exploration & Artificial Curiosity & Theory of Surprise (1990-2010). Schmidhuber's curious learning agents like to go where they expect to learn something. These rudimentary artificial scientists or artists are driven by intrinsic motivation, losing interest in both predictable and unpredictable things. A basis for much of the recent work in Developmental Robotics since 2004. According to Schmidhuber's formal theory of creativity, art and science and humor are just by-products of the desire to create / discover more data that is predictable or compressible in hitherto unknown ways!

Learning attentive vision. Humans and other biological systems use sequential gaze shifts for pattern recognition. This can be much more efficient than fully parallel approaches to vision. In 1990 we built an artificial fovea controlled by an adaptive neural controller. Without a teacher, it learns to find targets in a visual scene, and to track moving targets.

Reinforcement Learning in partially observable worlds. Just like humans, reinforcement learners are supposed to maximize expected pleasure and minimize expected pain. Most traditional work is limited to reactive mappings from sensory inputs to actions. Our approaches (1989-2003) for partially observable environments are more general: they learn how to use memory and internal states, sometimes through evolution of RNN. The first universal reinforcement learner is optimal if we ignore computation time, and here is one that is optimal if we don't. The novel Natural Evolution Strategies link policy gradients to evolution.

Non-linear ICA. Pattern recognition works better on non-redundant data with independent components. Schmidhuber's Predictability Minimization (1992) was the first non-linear neural algorithm for learning to encode redundant inputs in this way. It is based on co-evolution of predictors and feature detectors that fight each other: the detectors try to extract features that make them unpredictable. His neural history compressors (1991) compactly encode sequential data. And Lococode unifies regularization and unsupervised learning. The feature detectors generated by such unsupervised methods resemble those of our more recent supervised neural computer vision systems.

Metalearning Machines / Learning to Learn / Self- Improvement. Can we construct metalearning algorithms that learn better learning algorithms? This question has been a main drive of Schmidhuber's research since his 1987 diploma thesis. In 1993 he introduced self-referential weight matrices, and in 1994 self-modifying policies trained by the "success-story algorithm" (talk slides). His first bias-optimal metalearner was the above-mentioned Optimal Ordered Problem Solver (2002), and the ultimate metalearner is the Gödel machine (2003).

Financial Forecasting. Our most lucrative neural network application employs a second-order method for finding the simplest model of stock market training data.

Automatic Subgoal Generators and Hierarchical Learning. There is no teacher providing useful intermediate subgoals for our reinforcement learning systems. In the early 1990s Schmidhuber introduced gradient-based (pictures) adaptive subgoal generators; later also discrete ones.

Program Evolution and Genetic Programming. As an undergrad Schmidhuber used Genetic Algorithms to evolve computer programs on a Symbolics LISP machine at SIEMENS AG. Two years later this was still novel: In 1987 he published world's 2nd paper on "Genetic Programming" (the first was Cramer's in 1985) and the first paper on Meta-Genetic Programming.

Learning Economies with Credit Conservation. In the late 1980s Schmidhuber developed the first credit-conserving reinforcement learning system based on market principles, and also the first neural one.

Fast weights instead of recurrent nets. A slowly changing feedforward neural net learns to quickly manipulate short-term memory in quickly changing synapses of another net. More fast weights. Evolution of fast weight control.

Neural Heat Exchanger. Like a physical heat exchanger, but with neurons instead of liquid. Perceptions warm up, expectations cool down.

Complexity-Based Theory of Beauty. In 1997 Schmidhuber claimed: among several patterns classified as "comparable" by some subjective observer, the subjectively most beautiful is the one with the simplest description, given the observer's particular method for encoding and memorizing it. Exemplary applications include low-complexity faces and Low-Complexity Art, the computer-age equivalent of minimal art (Leonardo, 1997). A low-complexity artwork such as this Femme Fractale both `looks right' and is computable by a short program; a typical observer should be able to see its simplicity. The drive to create such art is explained by the formal theory of creativity.