Neural coding and information theory: Grandmother cells v. distributed codes

Transcription

1 Neural coding and information theory: Grandmother cells v. distributed codes John Collins 1/20

2 Strengths of computers v. brains Computer Brain Accurate and fast computation Accurate and fast storage Doesn t get bored with repetitive tasks Recognizing people Reading handwriting Adaptive Avoids obstacles Invents computers Survives and reproduces 2/20

3 Summary Primer about neurons (Neural computation: Inspiration for new computational methods. ) E.g., FSA, ANN,... Issues local coding, distributed coding, grandmother cells Analyze computationally (large scale systems!) Analysis of data. Extreme detection bias See JCC + Dezhe Jin, Grandmother cells and the storage capacity of the human brain, Mental health warning: Not (yet) generally accepted! 3/20

4 Neuron Dendrite / dendritic tree: input Axon: output Connection: synapse, 1/several µm Dimensions (v. rough): Cell body: 10 µm Axon: diameter 0.1 to 20 µm, length: often several cm Several km of axon per mm 3 of brain Signals: Membrane potential Action potential: Spike propagates at 60 m/s Human brain: Neurons: neurons Synapses: Per neuron 10 4 ; total /20

5 Computation with action potentials Input: across synapses from other neurons; + and Membrane potential above threshold = action potential Active, non-linear Suitable for universal computational component 5/20

6 Neuron characterization Roughly: Neuron fires action potential when total input (in 10 ms): w j i y j is above threshold other cells j w i j is strength of synapse to i from j y j is (pulsed) signal on neuron j Signal propagation controlled by: connection topology, synaptic strengths Time scales: Processing (like CPU, but highly parallel,?> 10 6 GFLOPS?): Action potential: Width 1 ms; processing step 10 ms From stimulus to recognition: 200 ms Feedforward and re-entrant connectivity Programming and storage ( 10 6 GB): Synaptic plasticity: 1 s Synaptogenesis/deletion Adult neurogenesis (in some areas): 2 to 4 weeks 6/20

7 Computational task: Memory formation and retrieval E.g., face = (person ID or episode) = action. In < 300 ms Coding by neurons and synapses: activity state storage state Computational, quantitative, algorithmic analysis What is coded and stored? Data structure Efficiency, algorithms Slow and fast learning Large number of similar components Micro- v. macro-behavior Of course: component of bigger system 7/20

8 What is known and/or measured (Enormous amount of data!) Psychology: Behavior, etc Anatomical etc. = functional regions (e.g., hippocampus for memory) EEG: v. poor space resolution fmri: poor space resolution, v. poor time resolution... Extracellular and intracellular electrodes... Biochemistry, etc Not known: Overall view 8/20

9 Hierarchy of processing = retina lines,... objects,... Hierarchy: Points lines objects, etc Known: Direct meaning of many intermediate cells feedforward steps. But important feedback connections 9/20

10 Some responses of one neuron: From: Zigmond, Bloom, Landis, Roberts, & Squire Fundamental Neuroscience (Academic, 1999) p. 1351, from Bruce, Desimone, & Gross, J. Neurophysiol. 46, 369 (1981) 10/20

11 The debugger: Extracellular recordings electrode ~150 cells in range ~5 detected Factor K 30 more cells in range of electrode than detected Detected: Below threshold: spontaneous / background firing Above threshold for 1 stimulus: responsive Many silent cells. I.e., not reported in paper! 11/20

12 to 1). The grey lines show 99 ROC surrogate curves, testing iance to randomly selected groups of pictures (see Methods). As ted, these curves are close to the diagonal, having an area of t 0.5. None of the 99 surrogate curves had an area equal or larger the original ROC curve, implying that it is unlikely (P, 0.01) than the original ROC curve, implying that it is unlikely (P, 0.01) Catwoman that were not her (data not shown). Notably, the unit wa mainly localized between 300 and 600 ms after stimulus onset. selectively activated by the letter string Halle Berry. Such a invariant pattern of activation goes beyond common visual feature of the different stimuli. As with the previous unit, the responses wer mainly localized between 300 and 600 ms after stimulus onset Recent data: Halle Berry cell Figure 2 A single unit in the right anterior hippocampus that responds to letter string Halle Berry (picture no. 96). Such an invariant response cannot pictures of the actress Halle Berry (conventions as in Fig. 1). be attributed to common visual features of the stimuli. This unit also had a a c, Strikingly, this cell also responds to a drawing of her, to herself dressed very low baseline firing rate (0.06 spikes). The area under the red curve in c is as Catwoman (a recent movie in which she played the lead role) and to the [From: Quian Quiroga et al, Nature , 1102 (2005)] 2005 Nature Publishing Group 12/20

13 Distributed v. Local ( Grandmother-Cell ) Representations Distributed representation: overlapping firing between categories GM categorizer: Exclusive firing of groups of cells between categories 13/20

14 Examples for distributed coding v. grandmother cells GM cell responds to small fraction of stimuli: Halle-Berry cell Seeing her face, her name Memory for wedding The wedding couple, parents,... Distributed-code cell responds to many more stimuli: Female face All female film star, any bride,... Beard Any bearded person 14/20

15 But: Distributed representation: overlapping firing between categories Reality: GM cells (if they exist at all) need distributed input/output: Raw input Processed input Output G... Therefore GM categorizer is actually 15/20

16 Basic memory cell model: Possible sub-system Input GM mem. cells Output Learning: activate synapses to/from unallocated/new memory cell Memory cells : GM-like cells. (Expect huge number.) Inhibitory interneurons to improve performance Advantages/features: Sparse binary (distributed) input. (Feature detectors?) = One-trial learning, unimportant interference = Recall: partial stimulus can activate memory Maximally efficient in use of synapses. (Information storage) 16/20

17 Why not GM cells? Textbooks say: Representationally hopelessly inefficient; impossible But this argument incorrect for memory storage Properties. E.g.: How often responsive? 5% 1/10 5 How many cells? 0.2% > 99% = We link to data on sample: General method of analyzing sample of neuronal responses Deduce population fractions and sparsities Implications 17/20

18 2-population analysis Data: cells, 93.9 images 132 responsive cells 51 respond to 1 image (of 93.9) 81 respond to 2. Avg Rest non-face (silent) Model: f D = 0.2% Distrib. Sparsity a = 4% f GM GM-like Repertoire R Rest Silent Non-responsive 43 GM cells: 43 = 1 R f GM ( ) R 10 5 f GM I.e., up to 10 5 categories for classic GM cells Many more for memory cells à la BMW 18/20

19 Analysis by experimental group Single population, single sparsity Less incisive analysis: less informative observables Fit sparsity 0.23% to 0.54% Actually poor fit, with compromise between two populations Contrast our fit: Few at 4% sparsity plus many GM cells at 10 5 [Waydo et al., J. Neurosci. 26, (2006)] 19/20

20 Summary and outlook New: Deduction of two classes of cell (in hippocampus etc) Image processors : relatively frequently firing. 0.2% of cells Memory cells : Ultra-sparsely firing. > 99% of cells Extreme bias against detection of memory cells. Memories/components 10 5 or more. Removed textbook arguments against local memory cells (Generalized) GM cells for recognition and memories can be efficient General method for analysis of data with multiple cell populations, to compensate extreme detection bias against GM-like cells Future: Physics of detection Extend to other data. Anatomy Predictions for mechanisms and algorithms Build explicit models Bigger picture 20/20

21 Appendix

22 References Hopfield model and developments: Distributed memory, attractor states: J.J. Hopfield, Neural Networks and Physical Systems with Emergent Collective Computational Abilities, Proc. Natl. Acad. Sci. 79, (1982) J.J. Hopfield, Local, grandmother-cell (GM) model for memory: E.B. Baum, J. Moody, and F. Wilczek, Internal representations for associative memory, Biol. Cybern. 59, (1988) Our paper: J. Collins & D.-Z. Jin, Grandmother cells and the storage capacity of the human brain, Ver. 2 Recent data (Halle-Berry cell, etc), and the experimentalists analysis: R. Quian Quiroga, L. Reddy, G. Kreiman, C. Koch, and I. Fried, Invariant visual representation by single neurons in the human brain, Nature 435, (2005) S. Waydo, A. Kraskov, R Quian Quiroga, I. Fried, and C. Koch, Sparse Representation in the Human Medial Temporal Lobe, J. Neurosci. 26, (2006) And references therein

23 the diagonal, with an area close to 1. In Fig. 1c we show the ROC curve for all seven pictures of Jennifer Aniston (red trace, with an area equal to 1). The grey lines show 99 ROC surrogate curves, testing invariance to randomly selected groups of pictures (see Methods). As expected, these curves are close to the diagonal, having an area of about 0.5. None of the 99 surrogate curves had an area equal or larger than the original ROC curve, implying that it is unlikely (P, 0.01) unit was also activated by several pictures of Halle Berry dressed as Catwoman, her character in a recent film, but not by other images of Catwoman that were not her (data not shown). Notably, the unit was selectively activated by the letter string Halle Berry. Such an invariant pattern of activation goes beyond common visual features of the different stimuli. As with the previous unit, the responses were mainly localized between 300 and 600 ms after stimulus onset. Recent data: More from the Halle Berry cell [From: Quian Quiroga et al, Nature 435, 1102 (2005)]

24 How to measure distributed v. GM? Sparsity α of cell: fraction of stimuli it responds to. Often small One cell: Sample of p stimuli, n responses: P (n, cell i ) = α n i (1 α i ) p n p! n! (p n)! (pα i) n e pα i 1 n! Sample of cells, with sample of p stimuli: P (n p) = 1 0 dα D(α) α n (1 α) p n p! n! (p n)! 1 0 dα D(α) (pα) n e pα 1 n! = E.g.: GM population: α 1/R, e.g., 10 5 Distributed population, e.g., α several%

25 Quian Quiroga et al. method detected cells: Total 2000 cells Extracellular electrodes, sensitive to many cells; improved spike-sorting (Us: Multiply cells by K 30 for silent cell correction) I.e., cells in range of electrodes Measurements: Screening session (find responsive cells) 93.9 different images (familiar people, etc) = trials Testing session (selectivity) Different views

26 Sample of images and cells (screening sessions) Data [QQ et al, Nature 435, 1102 (2005)] cells, 93.9 images 132 responsive cells 51 respond to 1 image (of 93.9) 81 respond to 2. Avg Rest non-responsive or non-detected Model: 3 fractions: f D Distrib. Sparsity a f GM GM-like Repertoire R Rest Silent Non-responsive Distributed rep. cells: Poisson response distribution Fit: sparsity a = 4% = 91 cells f D = 91/(60 000) 0.2%(!) Rest (> 99%) of cells: GM or silent = 43 detected GM cells

27 2-population analysis: GM-cell part Data: cells, 93.9 images 132 responsive cells 51 respond to 1 image (of 93.9) 81 respond to 2. Avg Rest non-face (silent) Model: f D = 0.2% Distrib. Sparsity a = 4% f GM GM-like Repertoire R Rest Silent Non-responsive 43 GM cells: 43 = 1 R f GM ( ) R 10 5 f GM I.e., up to 10 5 categories for classic GM cells Many more for memory cells à la BMW

28 Information in stimuli Telephone numbers: Input Arbitrary stimulus Storage 1000 remembered Info. current state 10 digits = 34 bits Info. stored 1000 ( ) bits (with associations) Neurons in GM rep possible stimuli 1000 recognized stimuli Neurons in distributed rep. 100 Synapses 1000 ( ) synapses

29 Naive estimate of bias in cell detection for earlier data E.g., Abbott, Rolls & Tovee (1996): 14 face-responsive neurons, 20 face stimuli, monkeys Our first fit to 2005 human data, blindly applied, postdicts detected GM cells D Popn. frac. QQ (2005) ART (1996) 5% K GM f GM 99% detected frac. det. # det. frac. det. # 4.5% K = 0.15% % = 0.08% K 14 GM# 93.9 f GM 20 = 0.07% K f GM 4400 K = 0.015% 2 ART (1996): two... cells showed grandmother -like responses In prediction of bias, value of f GM and number of extra very-silent cells cancel Cell-number ratios indt. of K and f GM