Neurobiology: Efficiency measures

NEWS & VIEWS with photons’ or ‘not imaging the hair at all’4,5. One might think that the same Zeno trick could be used to improve counterfactual quantum computers, so that they could actually be useful for something — or at least, that the probability of their finding the right answer should be better than that achieved by flipping coins or tossing dice. But this hope proved misguided: the straightforward application of the Zeno idea to counterfactual quantum computing did not seem to beat the random-guessing limit, and things were at a standstill. Enter Hosten et al.1. These authors have discovered that chaining Zeno boosters together produces a super Zeno booster that is indeed capable of beating the random-guessing limit in counterfactual quantum computing. They also demonstrate that the idea works with a quantum-optical implementation of the Grover search algorithm. This algorithm proves that a quantum computer can always perform better than any classical computer in searching an unsorted database for a target datum7. It has a particularly simple implementation in NATURE|Vol 439|23 February 2006 quantum optical interferometry, as does the super-sized quantum Zeno effect. Hosten and colleagues show how the two can be married to locate the target element in a database — without running the quantum computer that searches for that element in the first place. So what is counterfactual quantum computing good for, other than to illustrate the conclusion of a rather obscure quantum paradox? The computer must still be programmed and turned on, even if it is not run, so the approach will not save on electricity bills or labour costs. In fact, the value of the experiment lies simply in furthering our understanding of quantum mechanics and its interface with computation. The entire field of quantum information arose from physicists trying to understand the implications of paradoxes in quantum theory, and already the field is beginning to evolve on its own. The first commercial applications of quantum information, such as real-world quantum cryptography, are now being deployed. A century ago, we saw the start of the first quantum revolution — the discovery of the NEUROBIOLOGY Efficiency measures Michael R. DeWeese and Anthony Zador The nervous system translates sensory information into electrical impulses. The neural ‘code’ involved seems to represent natural sounds and images efficiently, using the smallest number of impulses. Our perception of the outside world relies on the transformation of physical signals (such as light and sound) into a pattern of neural impulses, or spikes. These spikes are then transmitted to higher brain regions, where they are further transformed into other patterns of sensory spikes, and ultimately into the motor spikes that mediate behaviour. What is the relationship (the ‘neural code’) between these neural responses and the sensory signals they represent? Are there general principles underlying the neural code? The ‘efficient-coding hypothesis’1 proposes that sensory neurons are adapted to the statistical properties of sensory signals to which neurons are exposed. Two papers in this issue invoke this principle to predict how neurons encode natural auditory and visual stimuli, as opposed to the artificial stimuli often used in experiments. Smith and Lewicki (page 978)2 develop an algorithm to find an efficient representation of natural sounds and speech, and show that this theoretically predicted representation matches that observed experimentally in the auditory nerve of cats. Sharpee and colleagues (page 936)3 show that cortical neurons adapt over seconds or minutes during the course of an experiment to maximize the information they provide about the stimulus. 920 Together, the two papers show how the efficient-coding hypothesis can help to make sense of properties of the neural code on both evolutionary and behavioural timescales. In the cochlea, sound is encoded into spikes, which are transmitted along the auditory nerve to higher stations in the auditory system. Auditory nerve fibres each respond to a narrow range of sound frequencies, with the range generally increasing with the median frequency. The response of each auditory nerve fibre can therefore be modelled as a (nonlinear) ‘filter’ that removes frequencies outside a particular range. Why do the auditory nerve filters have the particular form they do? Smith and Lewicki reasoned that if the auditory code is indeed ‘efficient’, then they should be able to predict the form of the auditory filter bank by finding the sparsest code; that is, the one that requires the least activity. To obtain this prediction, Smith and Lewicki first expressed the efficient-coding hypothesis as an algorithm whose input is an ensemble of sounds, and whose output is a sparse encoding for transmitting or representing this ensemble. The algorithm discovers that the sparsest encoding of sounds is into brief events suggestive of spikes, the precise timing of which conveys much of the information. The sparsest ©2006 Nature Publishing Group quantum rules that underpin our world. We are now on the verge of a second revolution8, in which these rules spawn technological applications. Results such as those of Hosten and colleagues1 are significant markers on the road to that revolution. ■ Jonathan P. Dowling is at the Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA, and the Institute for Quantum Studies, Texas A&M University. e-mail: 1. Hosten, O., Rakher, M. T., Barreiro, J. T., Peters, N. A. & Kwiat, P. G. Nature 439, 949–952 (2006). 2. Elitzur, A. C. & Vaidman, L. Found. Phys. 23, 987–997 (1993). 3. Mitchison, G. & Jozsa, R. Proc. R. Soc. Lond. A 457, 1175–1193 (2001). 4. Kwiat, P. et al. Phys. Rev. Lett. 74, 4763–4766 (1995). 5. Kwiat, P., Weinfurter, H. & Zeilinger, A. Sci. Am. 275(5), 72–78 (1996). 6. Knight, P. Nature 344, 493–494 (1990). 7. Grover, L. K. Phys. Rev. Lett. 79, 325–328 (1997). 8. Dowling, J. P. & Milburn, G. J. Phil. Trans. R. Soc. Lond. A 361, 1655–1674 (2003). code depends on the ensemble of sounds to be encoded; a code that is most efficient for one set of sounds is not necessarily most efficient for another. Why should the most efficient code depend on the stimulus ensemble? The basic intuition is straightforward. Suppose I ask you to describe individual sounds produced by different musical instruments, but I limit your vocabulary to only four words (of your choosing). If you know that the instruments are used in a rock band (that is, they are chosen from the rock ensemble), you might choose a code consisting of the words ‘guitar’, ‘bass’, ‘drums’, ‘keyboard’; but if the instruments are used in a classical orchestra (the classical ensemble), you might choose instead ‘woodwind’, ‘brass’, ‘percussion’, ‘string’. So, the choice of the most efficient code depends on what is being described. The depen (...truncated)