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The Benefits of Noise in Neural Systems

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The Benefits of Noise in Neural Systems PERSPECTIVES diverged from the statistical physics dis- OPINION course3–6,16–20. As a result, an abstract model is chosen and stochastic resonance is said to The benefits of noise in neural be observed with respect to an output of the model if its statistical signal processing per- systems: bridging theory and formance improves according to an arbitrary metric as various levels of stochastic noise are added6. This approach tends to neglect experiment the biological appropriateness of key factors such as the signal, the noise, the model and Mark D. McDonnell and Lawrence M. Ward the neural processing role of the system. The characteristics of the system’s processing21–23 Abstract | Although typically assumed to degrade performance, random (for example, encoding, transforming, fluctuations, or noise, can sometimes improve information processing in feedback inhibition, coincidence detection non-linear systems. One such form of ‘stochastic facilitation’, stochastic and gain control) should inform the choice resonance, has been observed to enhance processing both in theoretical models of models and metrics to help to ensure that of neural systems and in experimental neuroscience. However, the two any theoretical enhancement of performance does convey true benefits in biological terms. approaches have yet to be fully reconciled. Understanding the diverse roles of Systemic failure to consider biological noise in neural computation will require the design of experiments based on new appropriateness and broader definitions of theory and models, into which biologically appropriate experimental detail feeds stochastic resonance highlights the impor- back at various levels of abstraction. tance of two-way dialogue between theoreti- cians and experimentalists. Stochastic noise There is substantially increased interest in resonance is observed when the presence is ubiquitous in neural systems1,2,24 and its the sources and impact of stochastic biologi- of additive noise allows the input signal to potential roles in facilitating information cal noise in the nervous system, stemming be detected based on a calculation of the processing deserve greater attention. both from new experimental methods for output signal-to-noise ratio from the spec- For progress to be achieved in this field, identifying it and from a growing body of tral content (power spectral density) of the however, the dichotomous approaches of modelling work demonstrating its functional response. Typically, the signal-to-noise ratio researchers with different backgrounds must consequences. Recent reviews have defined exhibits a single peak as the power of the be reconciled using a common approach. noise in terms of variability that results from noise is varied. By the mid 1990s, however, One obstacle has been historical semantic “random or unpredictable fluctuations and the concept had spread to many other scien- baggage, and we believe it is timely to advo- disturbances”1, and they describe stochastic tific fields and the definition had broadened cate using a new term, stochastic facilitation resonance as one example of the potential considerably6. (FIG. 1b), as a descriptor for all research into benefits of noise1,2. Here, we take a closer The last decade has seen a growing body the constructive roles of biologically relevant look at the divergence between experimen- of experimental and biologically detailed noise in the nervous system, including tal and theoretical approaches to studying modelling work on stochastic resonance stochastic resonance — see below and FIG. 2. stochastic resonance. We propose a unify- in the neurosciences7–15, but we are of the We also propose a unified framework ing framework that reconciles these two opinion that because these approaches typi- for studying stochastic facilitation in future approaches and advocate the use of the term cally focus on classical stochastic resonance, experimental and modelling approaches. ‘stochastic facilitation’ to describe all biologi- they have not yet been fully reconciled with This framework emphasizes the importance cally relevant noise benefits in the nervous advances in theoretical work. Increased of beginning every study with a concrete system, including stochastic resonance. understanding of the functional roles of The term ‘stochastic resonance’ was noise in in vivo neural information pro- introduced in the early 1980s in the statisti- cessing will require new experiments to be we believe it is timely to cal physics community3–5. Within this field, developed in close conjunction with new the term has a very specific definition — in theoretical approaches. Although these new advocate using a new term, this article it is referred to as classical sto- approaches should be liberated from the stochastic facilitation, as a chastic resonance. In this paradigm, the classical description of stochastic resonance, descriptor for all research presence of a weak periodic input to a non- it is important that they are constrained by into the constructive roles of linear dynamical system cannot be inferred biologically appropriate modelling. from the response of the system in the Theoretical work on stochastic resonance, biologically relevant noise in the absence of noise (FIG. 1a). Classical stochastic whether classical or otherwise, has rarely nervous system NATURE REVIEWS | NEUROSCIENCE VOLUME 12 | JULY 2011 | 415 © 2011 Macmillan Publishers Limited. All rights reserved PERSPECTIVES and precise hypothesis regarding the com- anticipate that an increased intersection Why ‘stochastic facilitation’? putational role of a specific neural system, between theoretical ideas and experimental There are several reasons why we advocate thus encouraging divergence from classical approaches will lead to substantial progress the term stochastic facilitation. First, the stochastic resonance and simultaneously in understanding the constructive roles of term stochastic resonance is problematic in embracing biological appropriateness. We stochastic noise in the brain. several ways. Pinpointing which phenomena C %NCUUKECNUVQEJCUVKETGUQPCPEG 5KIPCNCPFPQKUG /QFGNUCPFTKICPFFCVCCESWKUKVKQP 5KIPCNRTQEGUUKPI IGPGTCVKQPCPFEQPVTQNU 5OCNN # Ũ# nUWDVJTGUJQNFo 5 0 0 0QPNKPGCT 25& UKIPCN F[PCOKECN #0 U[UVGO 1WVRWV (TGSWGPE[ UKIPCN #5 0 504 #0 4 9JKVGPQKUG #FFKVKXG 50 RQYGT )CWUUKCP YJKVGPQKUG 0QKUGRQYGT D 5VQEJCUVKEHCEKNKVCKQPHTCOGYQTM 5VQEJCUVKEHCEKNKVCVKQP 5KIPCNCPFPQKUGIGPGTCVKQP /QFGNCPFTKICPFFCVCCESWKUKVKQP &CVCRTQEGUUKPICPF J[RQVJGUKU CPFEQPVTQNU 5VGRUCPF J[RQVJGUKUCUUGUUOGPV 5VGR 5VGR 5VGRUCPF 5RGEKȮE PGWTCNU[UVGO 4GNGXCPV #URGEKȮEDKQNQIKECNN[ 4GNGXCPV UKIPCN QWVRWV 2TQEGUUKPIQHFCVCCESWKTGF CRRTQRTKCVGUQWTEGQHPQKUG UKIPCN CPFECNEWNCVKQPQH KPCURGEKȮEPGWTCNU[UVGO CRRTQRTKCVGOGVTKEUEJQUGP RTQXKFGUCDGVVGTOGEJCPKUO DCUGFQPVJGJ[RQVJGUKU HQTCEQORWVCVKQPVJCPVJG 4GNGXCPV 'PFQIGPQWU UCOGU[UVGOKPVJGCDUGPEG PQKUG PQKUGUQWTEG QHPQKUG EQPVTQNU Figure 1 | Classical Stochastic resonance versus stochastic facilita- the experimental material or model are chosen (step 3). Once the input tion. a | The necessary conditions for classical stochastic resonance5. A signals and noise (or its suppression) that are selected in step 3 are intro- weak periodic signal is assumed to be an input to a non-linear dynamical duced into the experimental rig or simulation0CVWT ofG4G theXKGYU model,^0GWT theQUEKGPEG relevant system, such that its presence cannot be inferred from the response of the output data are acquired (step 4) and processed (step 5). Finally, the hypoth- system in the absence of noise. In many cases, the signal is labelled as ‘sub- esis from step 1 is assessed based on step 5 (step 6). In many past studies of threshold’. Classical stochastic resonance is said to be observed when noise neural-system stochastic resonance, these steps have been followed in a allows the input signal to be detected statistically, with the quality of that different sequence. Typically, the neural system was chosen for study and detection measured by output signal-to-noise ratio (SNR), based on the performance was measured by output SNR, as a function of noise power spectral content (power spectral density (PSD)) of the response4. Typically, — which requires the signal to be periodic. Often the output was defined the SNR exhibits a single peak as the power of the noise is varied. Non- solely in terms of the times of action potentials, and the SNR was based on classical variations of stochastic resonance have discarded the require- the output PSD of the resulting stochastic point process. Rather than first ments of periodic signals and SNR6, and weak subthreshold signals have stating a hypothesis regarding a computational role, the choice of SNR as a been shown to be unnecessary for a simple network of neurons89. metric imposed an implied hypothesis; that the computational role of the b | A six-step scheme for studying stochastic facilitation in neural systems. neural system is to produce a sequence of action potentials when a sinusoi- First, a hypothesis concerning the positive role of stochastic biological noise dal input current at a specific frequency is introduced into the system and in facilitating signal processing or a computational task of a specified neural to produce a statistically distinct pattern of action potentials when it is system is stated (step 1). Next, a neural preparation — or mathematical or absent. Moreover, the full computation, which is to determine if the noisy computational model — that can be stimulated by inputs relevant to the periodic signal is
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