Available online at www.sciencedirect.com ScienceDirect The role of adaptation in neural coding 1,3 2,3 Alison I Weber and Adrienne L Fairhall The concept of ‘neural coding’ supposes that neural firing can identify aspects of high-dimensional time-varying neural patterns in some sense represent some external correlate, dynamics—such as the instantaneous firing rate of aneuron or whether sensory, motor, or structural knowledge about the set of neurons—and map them onto inputs (or motor outputs). world. While the implied existence of a one-to-one mapping The power of this approach is that it can tell us which between external referents and neural firing has been useful, particular properties of the inputs or outputs are explicitly the prevalence of adaptation challenges this. Adaptation represented in neural activity. It can further allow one to provides neural responses with dynamics on timescales that evaluate how the relationship between the external world and range from milliseconds up to many seconds. These timescales activity changes, for example, as a function of learning. If a are highly relevant for sensory experience in the natural world, neuron or population exhibits a response to a particular in which local statistical properties of inputs change stimulus, that response is said to adapt if after time or upon continuously, and are additionally altered by active sensing. subsequent presentations, the response decreases. Here, we Adaptation has a number of consequences for coding: it will use a broader definition of the term ‘adaptation’, to creates short-term history dependence; it engenders complex describe a wide variety of phenomena whichare characterized feature selectivity that is time-varying; and it can serve to by history-dependence or context-dependence in neural enhance information representation in dynamic environments. response properties [2,3,4 ]; most generally, it is used to Considering how to best incorporate adaptation into neural refer to a change inthe entire suite of steady-state responses of models exposes a fundamental dichotomy in approaches to a neuron after a change in stimulus statistics or context. Thus, the description of neural systems: ones that take an explicitly adaptation is defined within the neural coding concept but is ‘coding’ perspective versus ones that describe the system’s also a sign of complexity of the coding metaphor, implying dynamics. Here we discuss the pros and cons of different that ‘the neural code’ depends on history and context. approaches to the modeling of adaptive dynamics. Neurons and neural circuits are dynamic on a continuum of Addresses timescales, undergoing continuous changes in cellular prop- 1 Graduate Program in Neuroscience, University of Washington, erties such as excitability due to the dynamics of ion channels United States 2 and synaptic properties such as vesicle availability with time- Department of Physiology and Biophysics and Computational Neuroscience Center, University of Washington, United States scales of history dependence ranging from milliseconds to 3 UW Institute for Neuroengineering, United States seconds [5,6]. Response properties evaluated at the single neuron level are further influenced by network level dynam- Corresponding author: Fairhall, Adrienne L ([email protected]) ics. Typically, experiments exploring adaptation have probed the system in two or more different and distinct states. After Current Opinion in Neurobiology 2019, 58:135–140 abruptly changing the value of a stimulus, or the statistical ensemble from which stimulus samples are drawn, one can This review comes from a themed issue on Computational neuroscience track the response of the system as the system relaxes into its new state in order to characterize how firing rates change; or fit Edited by Brent Doi ron and Ma´ te´ Lengyel models for the coding properties of the system in its new For a complete overview see the Issue and the Editorial ‘adapted’ state, Figure 1. Despite this typical experimental Available online 27th September 2019 design, however, natural environments are continuously https://doi.org/10.1016/j.conb.2019.09.013 changing, and the underlying neural dynamics responsible 0959-4388/ã 2019 Elsevier Ltd. All rights reserved. for both temporal relaxation and steady-state characteriza- tions of adaptation are always in play as the nervous system is continually driven by ongoing changes in the environment. In light of these ongoing processes, what does it mean for a neuron to adapt? How might one think about adaptation The notion of a neural code pervades neuroscience. In its in the absence of a natural separation of timescales most direct interpretation, the firing of a neuron or a neuronal between ‘response’ and ‘adaptation’? How does our population is interpreted as signaling the presence and understanding of adaptation depend on the models we strength of an external stimulus or a motor output. It is of employ? As the field moves beyond single neuron record- course evident that the idea of coding is an approximation [1 ]. ings and isolated stimulus presentations to situations, in A neural system is a highly interconnected nonlinear dynam- which population recordings are made during natural ical system that receives and computes upon multiple com- stimulation and behavior, it is worth revisiting adaptation plex inputs. The coding paradigm rests on the idea that one in view of emerging model characterizations. www.sciencedirect.com Current Opinion in Neurobiology 2019, 58:135–140 136 Computational neuroscience Figure 1 This can serve to allow a relatively larger response at the onset of a novel stimulus. Adaptation also refers to a linear-nonlinear models change in the steady-state responses properties of a neuron or network following a change in the stimulus ensemble. For example, the spike-triggering features or tuning curve of a neuron might change after a change in stimulus statistics or context. In response to a contrast change, early sensory areas have been shown to adjust both the temporal feature that drives responses and the generalized linear models associated nonlinear input-output function (Figure 1). This adjustment often occurs such that the dynamic range of the responses is matched to the range of inputs, a phenomenon known as gain scaling [3], regarded as a signature of efficient coding This canonical computation of the nervous system occurs throughout early [4 ,7,8] and higher order [9] sensory areas, as well as in circuits that perform multisensory integration [10], motor control [11], and economic decision making [12]. subunit models The multiplicity of cellular dynamical timescales leads to multiple timescales of firing rate adaptation [13,14]. A signature of these multiple timescales is that adaptation toa stepchangeinstimulusoftendoes notoccurwitha fixed time constant, but with a time constant that scales with the frequency of change in the stimulus. When driven with continuously varying stimuli such as sine waves, these responses have been found to be compactly described by a rate responsetothestimulus that haspowerlaw properties [14,15], or acts like fractional differentiation applied to the input [14,16]. In the case of cortical neurons, this transfor- deep neural networks mation serves to decorrelate output, which may improve coding efficiency of the system [15]. Using models to probe adaptation How can one model adaptation? There are two main Current Opinion in Neurobiology classes of models in sensory neuroscience. One may try to develop dynamical models of a system, approximate Statistical models of neural responses. dynamical equations for neural activity r(t) that may be Linear-nonlinear cascade models consist of a linear filtering step driven by external variables s(t), generically: followed by a static nonlinear transformation. LN models are commonly used to probe response properties of a system in two dr different states and often reveal stimulus-dependent changes in both ¼ Fðr; sÞ ð1Þ the linear filter and nonlinearity that best characterize responses. dt Generalized linear models incorporate dependence on spike history into a linear-nonlinear framework and can capture several adaptive The function F represents a general nonlinear, possibly properties. Subunit models consist of multiple converging LN components and have successfully described response properties at multidimensional, set of dynamical equations, such as the many stages of the visual system. Deep neural networks comprised Hodgkin-Huxley equations driven by a current input. Alter- many layers of cascaded linear-nonlinear computations and are natively, statistical models evaluate and express the correlative defined by a large number of parameters. Deep neural networks have relationships between the firing of a neuron or population, r(t), the ability to capture a wide array of observed phenomena, but often at the current time t, and external variables stðtÞ in a time lack interpretability in terms of mechanism. window extending over a window of time t relative to t, r ðtÞ ¼ f ðstðtÞÞ ð2Þ What is adaptation and what roles might it serve? for some functional form f. Classically, adaptation refers to a gradual reduction in a neuron’s firing rate following stimulus onset or following a While at some level equivalent, the first class of models change in the stimulus, as in spike frequency adaptation. aims to explicitly capture dynamical mechanisms while the Current Opinion in Neurobiology 2019, 58:135–140 www.sciencedirect.com Adaptation in neural coding Weber and Fairhall 137 second is often thought of as defining ‘coding’. Examples of channel or synaptic dynamics, but rather an understand- Eq. (2) include simple, phenomenological models such as ing of how the components of the LN model description linear-nonlinear (LN) models [17 ]. Typically, fitting such arise from the underlying neural dynamics [29,30,31]. models under changing stimulus conditions reveals changes in a neuron’s response properties (Figure 1) A key property of overt adaptation mechanisms is that [18–21]. A general way to capture such adaptive effects response properties are modulated by the history of activity is to extend Eq. (2) to incorporate parameters u describing of the system.