Automatic differentiation in machine learning: a survey

Derivatives, mostly in the form of gradients and Hessians, are ubiquitous in machine learning. Automatic differentiation (AD), also called algorithmic differentiation or simply "autodiff", is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs. AD is a small but established field with applications in areas including computational fluid dynamics, atmospheric sciences, and engineering design optimization. Until very recently, the fields of machine learning and AD have largely been unaware of each other and, in some cases, have independently discovered each other's results. Despite its relevance, general-purpose AD has been missing from the machine learning toolbox, a situation slowly changing with its ongoing adoption under the names "dynamic computational graphs" and "differentiable programming". We survey the intersection of AD and machine learning, cover applications where AD has direct relevance, and address the main implementation techniques. By precisely defining the main differentiation techniques and their interrelationships, we aim to bring clarity to the usage of the terms "autodiff", "automatic differentiation", and "symbolic differentiation" as these are encountered more and more in machine learning settings.Comment: 43 pages, 5 figure

Defending Against Firmware Cyber Attacks on Safety-Critical Systems

In the past, it was not possible to update the underlying software in many industrial control devices. Engineering teams had to ‘rip and replace’ obsolete components. However, the ability to make firmware updates has provided significant benefits to the companies who use Programmable Logic Controllers (PLCs), switches, gateways and bridges as well as an array of smart sensor/actuators. These updates include security patches when vulnerabilities are identified in existing devices; they can be distributed by physical media but are increasingly downloaded over Internet connections. These mechanisms pose a growing threat to the cyber security of safety-critical applications, which are illustrated by recent attacks on safety-related infrastructures across the Ukraine. Subsequent sections explain how malware can be distributed within firmware updates. Even when attackers cannot reverse engineer the code necessary to disguise their attack, they can undermine a device by forcing it into a constant upload cycle where the firmware installation never terminates. In this paper, we present means of mitigating the risks of firmware attack on safety-critical systems as part of wider initiatives to secure national critical infrastructures. Technical solutions, including firmware hashing, must be augmented by organizational measures to secure the supply chain within individual plants, across companies and throughout safety-related industries

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

AI and OR in management of operations: history and trends

The last decade has seen a considerable growth in the use of Artificial Intelligence (AI) for operations management with the aim of finding solutions to problems that are increasing in complexity and scale. This paper begins by setting the context for the survey through a historical perspective of OR and AI. An extensive survey of applications of AI techniques for operations management, covering a total of over 1200 papers published from 1995 to 2004 is then presented. The survey utilizes Elsevier's ScienceDirect database as a source. Hence, the survey may not cover all the relevant journals but includes a sufficiently wide range of publications to make it representative of the research in the field. The papers are categorized into four areas of operations management: (a) design, (b) scheduling, (c) process planning and control and (d) quality, maintenance and fault diagnosis. Each of the four areas is categorized in terms of the AI techniques used: genetic algorithms, case-based reasoning, knowledge-based systems, fuzzy logic and hybrid techniques. The trends over the last decade are identified, discussed with respect to expected trends and directions for future work suggested

Implementation of the dissection theorem in cadence virtuoso

This paper describes a tool for the Cadence Virtuoso software that implements the Dissection Theorem (DT) or General Network Theorem (GNT) and its applications: the Extra Element Theorem (EET), Chain Theorem (CT) and General Feedback Theorem (GFT). The tool allows a circuit designer to gain additional circuit insight by providing all second- and third-level transfer functions of the DT. In particular, feedback networks are factored into their exact components, enabling a deeper insight into the structure of the loop gain, direct forward transmission and hence closed-loop behaviour

Recovering Grammar Relationships for the Java Language Specification

Grammar convergence is a method that helps discovering relationships between different grammars of the same language or different language versions. The key element of the method is the operational, transformation-based representation of those relationships. Given input grammars for convergence, they are transformed until they are structurally equal. The transformations are composed from primitive operators; properties of these operators and the composed chains provide quantitative and qualitative insight into the relationships between the grammars at hand. We describe a refined method for grammar convergence, and we use it in a major study, where we recover the relationships between all the grammars that occur in the different versions of the Java Language Specification (JLS). The relationships are represented as grammar transformation chains that capture all accidental or intended differences between the JLS grammars. This method is mechanized and driven by nominal and structural differences between pairs of grammars that are subject to asymmetric, binary convergence steps. We present the underlying operator suite for grammar transformation in detail, and we illustrate the suite with many examples of transformations on the JLS grammars. We also describe the extraction effort, which was needed to make the JLS grammars amenable to automated processing. We include substantial metadata about the convergence process for the JLS so that the effort becomes reproducible and transparent

AD in Fortran, Part 1: Design

We propose extensions to Fortran which integrate forward and reverse Automatic Differentiation (AD) directly into the programming model. Irrespective of implementation technology, embedding AD constructs directly into the language extends the reach and convenience of AD while allowing abstraction of concepts of interest to scientific-computing practice, such as root finding, optimization, and finding equilibria of continuous games. Multiple different subprograms for these tasks can share common interfaces, regardless of whether and how they use AD internally. A programmer can maximize a function F by calling a library maximizer, XSTAR=ARGMAX(F,X0), which internally constructs derivatives of F by AD, without having to learn how to use any particular AD tool. We illustrate the utility of these extensions by example: programs become much more concise and closer to traditional mathematical notation. A companion paper describes how these extensions can be implemented by a program that generates input to existing Fortran-based AD tools