Population coding/vector Coding Distributed representing 群体编码 / 向量编码 / 分布式表征

Transcription

1 Neural coding

2 Population coding/vector Coding Distributed representing 群体编码 / 向量编码 / 分布式表征

3 Theory:Single Cells as Feature Detector 外界世界的信息 ( 甚至运动输出和复杂的认知过程 ) 的编码可以由单个神经元来完成的 Running-out-of-neurons problem? 人的大脑神经细胞数目有限, 如何表达无限可能的外界信息和内部思维状态

4 Population Coding Theory Information is represented by pools of neurons The Independent-Coding Hypothesis Each neuron contributes to the pool independently The vote of each neuron gives a population vector The Coordinated-Coding Hypothesis The relationships among the neurons in a population is an important part of the signal. The signal cannot be decoded without considering spike synchrony, oscillations, or some other relationship among the neurons in the population. 4

5 How is a stimulus encoded by neural activities? (Do you remember the tuning curve?) The discussion to this point has focused on information carried by single neurons, but information is typically encoded by neuronal populations Encoding by the most active neuron sounds reasonably if there is no noise, but it does not work in practice because of large fluctuations in neural activities. Basically many nervous systems use large numbers of neurons to encode information..

6 Independent Code The biggest advantage of Population code is the ability to average out noises in individual neurons if they are independent. Consider how we can encode a single number 1 use rate code with a single neuron 2 use many identical coding neurons and average to reduce noise (muscle stretch receptor e.g.) 3 use a position code with receptive fields tuned to different values (cortex)

7 Position Coding This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision. For a population of unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in grid cells that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision.

8 Distributed (population) coding Miguel A. L. Nicolelis 2003, Nature Reviews Neuroscience 8

9 Population coding in the cercal system of cricket by a small number of neurons Crickets have two projections sticking out their posterior end: cerci. Each cercus is covered with small innervated hairs. Thousands of these primary sensory neurons send axons to a set of interneurons that relay the sensory information to the rest of the cricket s nervous system. No single interneuron of the cercal system responds to all wind directions, and multiple interneurons respond to any given wind direction.

10 Tuning curves for the four low-velocity interneurons of the cricket cercal system plotted as a function of the wind direction. r max 40 Hz. Wind speed is constant. (Theunissen and Miller 1991) At low wind velocities, information about wind direction is encoded by just four interneurons. The tuning curve for interneuron a:

11 Decoding the cercal system by employing the close relationship between the representation of wind direction and a Cartesian coordinate system. This vector is known as the population vector, and the associated decoding method is called the vector method. (Dayan and Abbott 2001)

12 Example - Population coding in V4 Pasupathy, Connor (2002)

13 Gaussian-like Tuning is supporting the Population Position Coding x i If the Gaussian tuning is too narrow, the network becomes a look up table, in which a unit gives a non zero signal only if the input x exactly matches its center x i : the network cannot generalize and becomes a simple memory. 13

14 Population Position Coding For a population of unimodal tuning curves, i.e. with a single peak, the precision typically scales linearly with the number of neurons. Hence, for half the precision, half as many neurons are required. In contrast, when the tuning curves have multiple peaks, as in grid cells that represent space, the precision of the population can scale exponentially with the number of neurons. This greatly reduces the number of neurons required for the same precision.

15 Sparse Code

16 Sparse Coding The sparse code is when each item is encoded by the strong activation of a relatively small set of neurons. For each item to be encoded, this is a different subset of all available neurons.

17 神经元发放率呈长尾分布

18 Sparse Coding Algorithms Given a potentially large set of input patterns, sparse coding algorithms (e.g. Sparse Autoencoder) attempt to automatically find a small number of representative patterns which, when combined in the right proportions, reproduce the original input patterns. The sparse coding for the input then consists of those representative patterns. For example, the very large set of English sentences can be encoded by a small number of symbols (i.e. letters, numbers, punctuation, and spaces) combined in a particular order for a particular sentence, and so a sparse coding for English would be those symbols.

19 稀疏编码

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21 Selectivity emerging: Simple Cell Carve out a subspace in high dimensional space Hubel and Wiesel, 1962

22 Brain Algorithm for pattern separation Locality sensitive hashing LSH: compute random projections of the input data that is, to multiply the input feature vector by a random matrix A neural algorithm for a fundamental computing problem Science 2017

23 Some neurons participate in several ensembles? Visual stimuli recruit intrinsically generated cortical ensembles Rafael Yuste and colleagues PNAS 2014

24 层级编码 Organizing principles of real time memory encoding: neural clique assemblies and universal neural codes Trends in Neurosci 2006 Joe Tsien and colleageus

25 Sparseness is layer specific

26 Differential Computation of Layer 2/3 and Layer 5 Layer 2/3 for pattern separation and Layer 5 for hierarchical organization Firing rate is higher in layer 5, dense code, suitable for rate code/burst code

27 Two fundamental Cognitive Architectures of Human minds Abstract Space and Tree How to Grow a Mind: Statistics, Structure, and Abstraction. Tenenbaum, J. B., Kemp, C., Griffiths, T. L., and Goodman, N. D. (2011). Science 331 (6022),

28 Speculation: Different Function of different cortical layers Layer 2/3 -- Sparse coding Uniform distribution in abstract space Locality Sensitive Hashing mostly for recognition? Layer 5/6 -- Tree like structure PCA like? mostly for association?

29 Two parallel Streams of Processing?

30 Population coding coordinated coding When we study population coding, we must consider whether individual neurons act independently, or whether correlations between different neurons carry additional information. Early work suggested that correlation between spike trains can only reduce, and never increase, the total mutual information present in the two spike trains about a stimulus feature. However, this was later demonstrated to be incorrect. Correlation structure can increase information content if noise and signal correlations are of opposite sign.

31 Sychrony Code Synchronous firing of two or more neurons is one mechanism for conveying information in a population correlation code. Will be discussed under temporal coding

32 Temporal Coding

33 Temporal coding: When precise spike timing or high-frequency firingrate fluctuations are found to carry information, the neural code is often identified as a temporal code. Temporal codes employ those features of the spiking activity that cannot be described by the firing rate. For example, time to first spike after the stimulus onset, characteristics based on the second and higher statistical moments of the ISI probability distribution, spike randomness, or precisely timed groups of spikes (temporal patterns) are candidates for temporal codes.

34 Temporal code can represent information about stimulus Example: Auditory System: coincidence Used to encode specific temporal feature for very brief stimuli exactly when did the stimulus occur. For very brief stimuli, a neuron's maximum firing rate may not be fast enough to produce more than a single spike. Due to the density of information about the abbreviated stimulus contained in this single spike, it would seem that the timing of the spike itself would have to convey more information than simply the average frequency of action potentials over a given period of time. This model is especially important for sound localization, which occurs within the brain on the order of milliseconds.

35 Sound localization in barn owl Spike must have temporal precision on the order of us. Accuracy 1 degree Temporal precision <5us

36 How to convert such precise temporal code to downstream rate code? The decoding cue: the time difference between a sound reaches the two ears (the order of 0.1ms). Coincidence detector: the neuron will only be active when the inputs from two ears are received simultaneously.

37 Jeffress model (Jeffress, 1948)

38 Remarkably enough, such a coincidence detector circuit was found four decades later by Carr and Konishi (1990) in the nucleus laminaris of the barn owl. It gives, however, no indication of how the precision of a few microseconds is finally achieved. Temporal precision is less than 5μs even though the membrane time constant and synaptic time constant are in the range of microseconds. How is it reached within this circuit? Interaural intensity differences (for high frequency sounds (wavelength smaller than the head) Interaural phase differences (for low frequency sounds) Delay tuning in barn owl auditory system

39 Temporal code can represent information other than temporally related features about stimulus Latency to first spike code: Retina encode visual information in the latency time between stimulus onset and first action potential, also called latency to first spike. This type of temporal coding has been shown also in the auditory and somato-sensory system. The main drawback of such a coding scheme is its sensitivity to intrinsic neuronal fluctuations.

40 Correlation Code (Synchrony Code) The correlation coding model of neuronal firing claims that correlations between action potentials, or "spikes", within a spike train may carry additional information above and beyond the simple timing of the spikes. Correlations can also carry information not present in the average firing rate of two pairs of neurons. A good example of this exists in the pentobarbital-anesthetized marmoset auditory cortex, in which a pure tone causes an increase in the number of correlated spikes, but not an increase in the mean firing rate, of pairs of neurons. [55]

41 Temporal code can represent information about stimulus identity Auditory and Olfactory System: Stimulus fluctuation is slow Frees up a lot of temporal bandwidth for temporal code. e.g. Groups of neurons may synchronize in response to a stimulus. The temporal component of the pattern elicited by each tastant may be used to determine its identity (e.g., the difference between two bitter tastants, such as quinine and denatonium). In this way, both rate coding and temporal coding may be used in the gustatory system rate for basic tastant type, temporal for more specific differentiation.

42 Temporal Code can be internally generated A theory of perception --- the temporal binding. Unfortunated not-proven yet. This model assumes that neural synchrony with precision in the millisecond range is crucial for object representation, response selection, attention and sensorimotor integration It defines dynamic functional relations between neurons in distributed sensorimotor networks, i.e., neurons that respond to the same sensory object may fire in temporal synchrony (Engel, Fries and Singer 2001)

43 Coordinated Temporal Coding Synchrony and oscillations A theory of perception --- the temporal binding. Unfortunated not-proven yet. This model assumes that neural synchrony with precision in the millisecond range is crucial for object representation, response selection, attention and sensorimotor integration It defines dynamic functional relations between neurons in distributed sensorimotor networks, i.e., neurons that respond to the same sensory object may fire in temporal synchrony (Engel, Fries and Singer 2001)

44 An example: bistability Bistability: Two interpretations are possible of this figure (Engel, Fries and Singer 2001)

45 In this case, the temporal binding model predicts that neurons should dynamically switch between assemblies and, hence, that temporal correlations should differ for the two perceptual states Four visual cortical neurons with receptive fields over these four image components: the grouping which changes from one precept to another. (Engel, Fries and Singer 2001)

46 Neurons 1 & 2 should synchronize if the respective contours are apart of the one background face; and for neurons 3 & 4 for the candlestick. When the image is segmented into two opposing faces, the temporal coalition switches to synchrony between 1-3 and 2-4 respectively (Engel, Fries and Singer 2001)

47 Phase of firing code Place cells in rat hippocampal pyramidal cells 1 mv 200 ms Two types of theta: I and II (Skaggs et al. 1996) Examples of raw and filtered EEG. Filter bandpass: Hz (A); 6-10 Hz (B)

48 Place fields of place cells 1. Finding place cells by O Keefe and Dostrovsky (1971) 2. Finding theta phase precession by O Keefe and Recce (1993)

49 Theta phase precession in hippocampal pyramidal cells Sequential information processing perhaps 0 o /360 o phase 270 o phase (Huxter, Burgess, and O Keefe 2003)

50 Theta phase precession in a place cell (Huxter, Burgess, and O Keefe 2003)

51 Theta phase precession in a place cell Theta rhythm 7-12 Hz. The spikes of the place cell gradually and monotonically advances to earlier phase relative to hippocampal theta rhythm as the rat traverses along the cell s place field (Mehta, Lee and Wilson 2002)

52 节律 ( 时钟 ) 和抑制性神经元有关 Multiple inhibitory cell types for different time-scales Remember that brain has multiple oscillatory rthythms PV 20ms gamma oscillation (>40Hz) SOM 100 ms (alpha/beta Hz) Neurogliform 1s (Delta/Theta 1Hz-4Hz)

53 Divisions of Identified Parvalbumin-Expressing Basket Cells during Working Memory- Guided Decision Making S (16) pdf Individual PV+ Basket Cells Are Differently Recruited or Inhibited during Sequential Episodes of the Delayed Cue-Matching-to-Place Task 抑制性神经元还可以表示任务中不同的时段

54 大脑采取多时钟同步通讯方式 大脑中存在 hub 脑区 (rich-club), 这些脑区的时钟比较慢 ( 通常是内部状态, 如情绪相关脑区 ) 其他脑区变化比较快, 尤其是管感知的脑区 Brain has hub areas Local circuits has hub neurons, and they participate in slow rhythms 局部神经环路也存在 hub (rich-club) 这些神经元存在低频同步放电, 其他神经元受脑节律影响较小 脑节律可能是脑之间通讯的主要机制 大脑采用多个时钟, 不同脑区, 不同任务的时钟频率不同, 时钟的同步方式很灵活 Dwelling quietly in the rich club: brain network determinants of slow cortical fluctuations Leonardo L. Gollo, Andrew Zalesky, R. Matthew Hutchison, Martijn van den Heuvel, Michael Breakspear Uniting functional network topology and oscillations in the fronto-parietal single unit network of behaving primates Benjamin Dann, Jonathan A Michaels, Stefan Schaffelhofer, Hansjörg Scherberger Elife 2016

55 Dynamic Routing Algorithm: Capsule Model by Hinton: So far represented by a simple vector length. Possible Improvements: Routing Consensus is achieved in an iterative fashion through slow rhythms by hubs neurons These neurons control information exchange of other non-hub neurons

56 Key points: 1. Topographic maps in cortex 2. Tuning curve 3. Spike-train statistics 4. Dynamic Routing in the Brain