A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom

A metadata-enhanced framework for high performance visual effects

This thesis is devoted to reducing the interactive latency of image processing computations in visual effects. Film and television graphic artists depend upon low-latency feedback to receive a visual response to changes in effect parameters. We tackle latency with a domain-specific optimising compiler which leverages high-level program metadata to guide key computational and memory hierarchy optimisations. This metadata encodes static and dynamic information about data dependence and patterns of memory access in the algorithms constituting a visual effect – features that are typically difficult to extract through program analysis – and presents it to the compiler in an explicit form. By using domain-specific information as a substitute for program analysis, our compiler is able to target a set of complex source-level optimisations that a vendor compiler does not attempt, before passing the optimised source to the vendor compiler for lower-level optimisation. Three key metadata-supported optimisations are presented. The first is an adaptation of space and schedule optimisation – based upon well-known compositions of the loop fusion and array contraction transformations – to the dynamic working sets and schedules of a runtimeparameterised visual effect. This adaptation sidesteps the costly solution of runtime code generation by specialising static parameters in an offline process and exploiting dynamic metadata to adapt the schedule and contracted working sets at runtime to user-tunable parameters. The second optimisation comprises a set of transformations to generate SIMD ISA-augmented source code. Our approach differs from autovectorisation by using static metadata to identify parallelism, in place of data dependence analysis, and runtime metadata to tune the data layout to user-tunable parameters for optimal aligned memory access. The third optimisation comprises a related set of transformations to generate code for SIMT architectures, such as GPUs. Static dependence metadata is exploited to guide large-scale parallelisation for tens of thousands of in-flight threads. Optimal use of the alignment-sensitive, explicitly managed memory hierarchy is achieved by identifying inter-thread and intra-core data sharing opportunities in memory access metadata. A detailed performance analysis of these optimisations is presented for two industrially developed visual effects. In our evaluation we demonstrate up to 8.1x speed-ups on Intel and AMD multicore CPUs and up to 6.6x speed-ups on NVIDIA GPUs over our best hand-written implementations of these two effects. Programmability is enhanced by automating the generation of SIMD and SIMT implementations from a single programmer-managed scalar representation

Efficient Linear Programming for Dense CRFs

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear programming (LP) relaxation, the state-of-the-art algorithm is too slow to be useful in practice. To alleviate this deficiency, we introduce an efficient LP minimization algorithm for dense CRFs. To this end, we develop a proximal minimization framework, where the dual of each proximal problem is optimized via block coordinate descent. We show that each block of variables can be efficiently optimized. Specifically, for one block, the problem decomposes into significantly smaller subproblems, each of which is defined over a single pixel. For the other block, the problem is optimized via conditional gradient descent. This has two advantages: 1) the conditional gradient can be computed in a time linear in the number of pixels and labels; and 2) the optimal step size can be computed analytically. Our experiments on standard datasets provide compelling evidence that our approach outperforms all existing baselines including the previous LP based approach for dense CRFs.Comment: 24 pages, 10 figures and 4 table

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design

A Domain Specific Approach to High Performance Heterogeneous Computing

Users of heterogeneous computing systems face two problems: firstly, in understanding the trade-off relationships between the observable characteristics of their applications, such as latency and quality of the result, and secondly, how to exploit knowledge of these characteristics to allocate work to distributed computing platforms efficiently. A domain specific approach addresses both of these problems. By considering a subset of operations or functions, models of the observable characteristics or domain metrics may be formulated in advance, and populated at run-time for task instances. These metric models can then be used to express the allocation of work as a constrained integer program, which can be solved using heuristics, machine learning or Mixed Integer Linear Programming (MILP) frameworks. These claims are illustrated using the example domain of derivatives pricing in computational finance, with the domain metrics of workload latency or makespan and pricing accuracy. For a large, varied workload of 128 Black-Scholes and Heston model-based option pricing tasks, running upon a diverse array of 16 Multicore CPUs, GPUs and FPGAs platforms, predictions made by models of both the makespan and accuracy are generally within 10% of the run-time performance. When these models are used as inputs to machine learning and MILP-based workload allocation approaches, a latency improvement of up to 24 and 270 times over the heuristic approach is seen.Comment: 14 pages, preprint draft, minor revisio

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be found at http://minty.caltech.edu/papers.ph