Input coding for neuro-electronic hybrid systems

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ARTICLE IN PRESSG ModelIO 3505 1–11

BioSystems xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

BioSystems

jo ur nal home p age: www.elsev ier .com/ locate /b iosystems

nput coding for neuro-electronic hybrid systems

ude Baby Georgec,∗, Grace Mathew Abrahamc, Katyayani Singhc, Shreya M. Ankolekarb,haradwaj Amrutura, Sujit Kumar Sikdarb

Department of Electrical Communications Engineering, IISC Bangalore, IndiaMolecular Biophysics Unit, IISC Bangalore, IndiaCenter for Nanoscience and Engineering, IISC Bangalore, India

r t i c l e i n f o

rticle history:eceived 2 April 2014eceived in revised form 31 July 2014ccepted 5 August 2014vailable online xxx

eywords:ultured neural networksSMemporal encodingeuro-electronic hybrid systems

a b s t r a c t

Liquid State Machines have been proposed as a framework to explore the computational properties ofneuro-electronic hybrid systems (Maass et al., 2002). Here the neuronal culture implements a recurrentnetwork and is followed by an array of linear discriminants implemented using perceptrons in electron-ics/software. Thus in this framework, it is desired that the outputs of the neuronal network, correspondingto different inputs, be linearly separable. Previous studies have demonstrated this by either using only asmall set of input stimulus patterns to the culture (Hafizovic et al., 2007), large number of input electrodes(Dockendorf et al., 2009) or by using complex schemes to post-process the outputs of the neuronal cultureprior to linear discriminance (Ortman et al., 2011). In this study we explore ways to temporally encodeinputs into stimulus patterns using a small set of electrodes such that the neuronal culture’s output canbe directly decoded by simple linear discriminants based on perceptrons. We demonstrate that network
can detect the timing and order of firing of inputs on multiple electrodes. Based on this, we demonstratethat the neuronal culture can be used as a kernel to transform inputs which are not linearly separablein a low dimensional space, into outputs in a high dimension where they are linearly separable. Thussimple linear discriminants can now be directly connected to outputs of the neuronal culture and allow
y fun

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for implementation of an

. Introduction

Cultures of dissociated neurons have been used as a paradigm totudy the computational properties of neural tissue. Such culturesan be interfaced to silicon computing systems via Micro Electroderrays and can thus provide a way to create hybrid computingystems (Dockendorf et al., 2009). Previous studies have reportedudimentary computational and learning capabilities of culturedetworks (Demarse and Dockendorf, 2005; Ruaro et al., 2005; Jimbot al., 1999; Marom and Shahaf, 2002). However, the computa-ional capabilities of such a culture generating complex patternsf activity have only been partially understood (Dockendorf et al.,009).

Liquid State Machines have been proposed as a framework to

Please cite this article in press as: George, J.B., et al., Input codhttp://dx.doi.org/10.1016/j.biosystems.2014.08.002

xplore the computational capabilities of such a system (Maasst al., 2002). These have been shown to be capable of doing univer-al computation. Several studies have shown the usability of this

∗ Corresponding author.E-mail addresses: [email protected] (J.B. George),

[email protected] (G.M. Abraham), [email protected]. Singh), [email protected] (B. Amrutur), [email protected] (S.K. Sikdar).

ttp://dx.doi.org/10.1016/j.biosystems.2014.08.002303-2647/© 2014 Published by Elsevier Ireland Ltd.

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ction for such a hybrid system.© 2014 Published by Elsevier Ireland Ltd.

framework using artificial neuronal networks to solve problems.The framework consists of two components, first is a dynamical sys-tem and the second is a readout unit. The dynamical system receivesinputs and computes a number of functions in a high dimensionalspace. This computation is such that the readout unit can outputthe desired function as a linear combination of the outputs of thedynamical system. In this scenario, the dynamical system must gen-erate outputs that are linearly separable. The readout units mustthen have a property of universal approximation so that given lin-early separable inputs, it must be capable of universal functionmapping.

Hence it is required that we have coding schemes such that weprovide designed inputs to the neuronal culture in form of stimu-lus patterns on which the network can work and generate outputsin form of changes in neuronal network activity that are linearlyseparable. We also need methods for output decoding to separatethe outputs from the culture to different classes.

Some studies were aimed at using this framework to develophybrid systems. Hafizovic et al. (2007) showed the linear separa-

ing for neuro-electronic hybrid systems. BioSystems (2014),

bility of outputs for two patterns. Dockendorf et al. (2009) havestudied the linear separability of output of a culture for simple inputpatterns. Ortman et al. (2011) have explored ways to create inputpatterns suitable for computation.

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dx.doi.org/10.1016/j.biosystems.2014.08.002


http://www.sciencedirect.com/science/journal/03032647

http://www.elsevier.com/locate/biosystems

mailto:[email protected]






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Table 1List of abbreviations.

i Index used for input electrodej Index used for input patternk Index used for kth trial of input patternr Number of electrodes used for stimulationIj jth input patternXj

kkth presentation of Input j

sMjk

Spike Indicator for electrode M for kth presentation of Input j

Ojk

Output of perceptron j for kth presentation of Input jWj Weight vector for perceptron j

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ARTICLEIO 3505 1–11

J.B. George et al. / BioS

In this study we explore the possibility of computing with hip-ocampal neuronal cultures. We need to have an input codingcheme to provide inputs to the culture. Hafizovic et al. (2007) havesed two electrodes for a sequence of activations. Dockendorf et al.2009) have shown results of stimulating one electrode at a time ofll electrodes available to them. Ortman et al. (2011) have selectedandom subsets of available electrodes for stimulation. However,he number of distinct patterns that can be obtained in this way isimited. Furthermore, it is not clear how an input variable woulde mapped to these stimulation patterns in a straightforward man-er. In this study we show a simpler scheme for encoding inputs tohe culture. We show that linearly separable output patterns cane created by using a fixed subset of electrodes by varying the timet which an electrode is stimulated with respect to others. In effect,e show that temporal code is an effective way to encode inputs

or the culture. Interestingly, relative-time based code have beenhown to encode for various sensory inputs in biological systemsHaddad et al., 2013; Hallock and Dilorenzo, 2006; Victor, 2005).

We also need an output decoding scheme to identify specificutput patterns. Since outputs are expected to be linearly separa-le, we expect that the decoder must rely on this property and notse complex decoding schemes. Ortman et al. (2011) used an SVMfter transforming the outputs of the culture using a kernel to clas-ify output patterns. In this case the decoders try to transform theutput patterns so that they become linearly separable. In such acenario, it is not clear if the outputs of the culture are linearly sepa-able. Dockendorf et al. (2009) used templates for the time functionf output patterns that were then compared based on euclideanistance. We show that with appropriate input coding, the neu-onal culture can generate outputs that can be decoded by simplerchemes. We show that a feature like the occurrence of a spike atn electrode can be used as a measure of culture output which areinearly separable. This is demonstrated using perceptrons. Sinceerceptrons can only learn to separate between linearly separa-le inputs, success of this scheme would imply linear separabilityf culture outputs. Biological neurons equipped with Spike-Timingependant plasticity(STDP) learning mechanisms have been showno perform the task done by a perceptron (Legenstein et al., 2005).tudies with artificial neuronal networks within the framework ofiquid State Machine (LSM) have also shown the usability of percep-rons for arbitrary function mapping. Also, perceptrons offer a muchimpler hardware implementation compared to other methods ands more suitable for parallel implementation. This would allow cre-ting real-time systems capable of processing and distinguishing aarge number of output patterns.

Properties of the input spatio-temporal patterns that allow theetwork to compute have not been discussed in the literature. It

s also not clear if and how stimulations at different electrodesnteract to generate different outputs. In this study we examinehe properties of inputs that allows the network to identify rela-ions among them. We show that the interaction between differentnputs can cause a change in output of the culture. This demon-trates that cultures can combine different inputs to generateeaningful neuronal output rather than output being a superposi-

ion of responses to stimuli at the different electrodes.

. Materials and methods

.1. Neuronal culture and long term maintenance

Neuronal culture growth and maintenance was done similar to


he procedures described by Potter and Demarse (2001).Dissociated neuronal cell cultures were prepared by papain

igestion of whole hippocampus of 0–2 day old rat pups. 120 chan-el Micro-Electrode Arrays (MEA) from MultiChannel Systemsˆ©

td Time delay between stimulation of two electrodespj

MProbability of occurrence of spike at electrode M for input pattern j

for reusing, were soaked overnight with Tergazyme detergent(Sigma–Aldrich, USA), thoroughly rinsed with MilliQ water andallowed to dry under laminar hood, sterilized with 70% ethanol andUV light. Sterilized MEA were coated with 0.05% (w/v) polyethylen-imine solution in borate buffer, rinsed thoroughly with MilliQ waterallowed to dry and kept under laminar hood until cell seeding.

Wistar rats were decapitated, according to approved protocolsby the ‘Animal Ethics and Welfare Committee’ of Indian Institute ofScience, Bangalore, India, and these were followed in all the exper-iments. The brain was removed, chilled with frozen phosphatebuffer saline (PBS), and the hippocampus was micro-dissectedunder sterile conditions. Papain solution was prepared accordingto Segal et al. (1998) and aliquoted into 1.5 ml and stored at −20 ◦C,and thawed at 37 ◦C just before use. Hippocampus was digestedin 2 ml papain solution for 20 min at 37 ◦C stirring manually. Thepapain solution was aspirated and the pieces were triturated threetimes, three passes each with 1 ml of medium, using a P-1000 Pipet-man. 50 000–200 000 cells were plated in a 20 �l droplet coveringthe 2.4 mm × 2.4 mm electrode region of the 120MEA200/30iR-Ti (Multichannel Systems, Germany), forming a dense monolayer.The MEA’s were coated with laminin and incubated for 1/2 h justbefore seeding. The dishes were flooded with 1 ml of mediumafter the cells had adhered to the substrate (45 min), and storedwith ethylene-propylene membrane lids (MEA-MEM membranes,ALA Scientific Instruments Inc., USA in a 65% RH incubator at 37 ◦C, 5%CO2. The medium, adapted from (Jimbo et al., 1999), was Dulbecco’smodified Eagle’s medium (DMEM, Irvine Scientific) with 10% FBSserum (Gibco) and was stored in the incubator to equilibrate the pHand temperature before feeding. We used antibiotic/antimycoticdrugs to control contamination. Feedings consisted of 50% mediumreplacement twice per week. The medium was used with glial con-ditioning (ara-C) after 7 days.

The culture dish was placed in a separate incubator which main-tained an ambient of 5% CO2 at 37 ◦C while doing recordings andstimulations. Fig. 1 shows the activity recorded from the cultureafter 25 days in vitro.

2.2. Recording and stimulation

We used MEA-2100 System from MultiChannel Systems,Germanyˆ© for recording from and stimulating the cultures grownon the MEA. The hardware was used to record signals from 120channels simultaneously at 50 kHz and to generate stimulus pulsesat all electrodes under software control. There is a Digital SignalProcessor in the interface which was used for real time analysis ofthe electrophysiological signals.

2.3. Processing and control


Table 1.The data was acquired from the device using MATLAB. Spike

detection was done on the acquired data for further processing. This

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Fig. 1. Neuronal culture activity after DIV25. Each box represents the electric

equired filtering the data, artefact suppression and appropriatehresholding. This was done on-line either using MATLAB or then board DSP system depending on the experiment. For filtering,e either used on board hardware configured as high pass filter

r used SALPA algorithm on computer as described by Wagenaarnd Potter (2002). The threshold for each electrode was estimateds 5× standard deviation (estimated using median values) and waspplied on the absolute value of the signal.

For electrical stimulation, we chose the parameters which haveeen shown to be effective in previous studies (Wagenaar et al.,004). For each stimulus we used a bi-phasic voltage pulse of ampli-ude 500 mV and a pulse width of 500 � s in each phase.

.4. Input coding

We used temporal coding as a method to generate various inputatterns to stimulate the culture. For this purpose, we selected a


xed set of 8 electrodes for stimulation. The time of firing of eachlectrode was then determined based on the input value for thatlectrode. In this way, different input value combinations resultedn different input patterns. Input pattern P with r electrodes was

vity from an electrode in the MEA. Scale bar: y-axis, 200 � V; x-axis, 1000 ms.

then defined as a sequence of firing of the input electrodes withsome time delay between each stimulation.

Ij =

⎡⎢⎢⎢⎣

t1

t2

· · ·tr

⎤⎥⎥⎥⎦ (1)

where ti indicates the time of firing for input electrode i for the jthinput pattern. This time is an offset from the start of presentationof the stimulus.

Iji = tdJji (2)

Here Jj is the input vector that is to be encoded for the culture.


The time of firing of each electrode w.r.t a fixed time is an integermultiple of a time delay td ms which can be varied from 0.5 ms to1sec in steps of 20 � s.

Fig. 3 shows some sample stimulation patterns.

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ig. 2. System to study input coding and output decoding: here temporaly coded stiecoding schemes.

.5. Output decoding

Let the output patterns be defined as follows.

jk =

⎡⎢⎢⎢⎢⎣

s1jk

s2jk

· · ·s120j

k

⎤⎥⎥⎥⎥⎦ (3)

jk

is the output pattern for the culture for the kth presentation

f input pattern j. Here sMjk

is the spike occurrence indicator for

lectrode M and is defined as sMjk

= 1 if at least one spike occursn the time window 5ms to 100ms after the jth input pattern isresented to the culture kth time.


.5.1. Using a perceptronA perceptron is a simple processing element which does a

eighted sum of its inputs and generates a binary (1/0) output if

ig. 3. Temporal coding for stimulation of few electrodes. The examples show two 8 dimas applied at 5 ms wrt the reference time.

re applied to 8 electrodes and spiking activity on the array is analysed using output

the sum is greater than a threshold value. It can be described by thefollowing expression.

Ojk=

{1 Wj · Xj

k − Threshold > 0

0 otherwise(4)

Here Ojk

is defined as the output of the perceptron j with a weightvector Wj for the kth presentation of input pattern j.

The weight vector describes a hyperplane which separates theset of outputs the perceptron is trained to decode from the rest ofthe outputs. The procedure to do this is described below. In everyexperiment a set of m different input patterns are presented to theculture n times and the responses are collected. The output vec-tor for each input pattern for very trial Oj

kis formed as described

above. For every input pattern Ij, we train a perceptron to find a

weight vector Wj to detect the output vector Ojk

from the reset ofthe outputs Ol

k, l /= j. These set of weights are learned using the per-

ceptron training algorithm, the delta rule (Widrow and Hoff, 1960).The delta rule is described briefly below.


For each perceptron, the set of outputs are divided in to twoclasses C1 and C0 where C1 corresponds to the set of outputs corre-sponding to the input pattern the perceptron is required to identifyand C0 is the set which the perceptron is trained to reject. So, the

ensional input vectors encoded to a stimulation pattern with td = 5 ms. The pattern

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erceptron output as defined by Eq. (4) has to be 1 for C1 and 0therwise. This can be achieved by initializing the weight vectoro a random value and rotating it slightly for every error in theutput using the algorithm shown. In short, for every error in clas-ification, the weight vector is rotated towards the vector whichs wrongly classified. This rotation is achieved by adding the mis-lassified vector to the weight vector. After sufficient number ofterations(maxIter), the weight vector settles down to a value which

inimizes the error in classification. We use a value of 1000 foraxIter.

lgorithm 1. The delta rule1: procedure GetWeightVector2: Xj

k← Culture outputs for n trials of m patterns

3: Classjk← C1/C0 as required for perceptron

4: init:5: Wj← 06: i ← maxIter7: loop:8: for all Xj

k, k ∈ Training Set do

9: Calculate Ojk

10: if (Classjk== C1 AND Oj

k== 0) OR (Classj

k== C0 AND Oj

k== 1) then

11: Wj ← Wj + Xjk

12: i ← i − 1.13: if i = =0 then returen Wj

14: goto loop.

The decoder is an array of parallel perceptrons that can berained to distinguish between each input from the rest of thenputs or a set of inputs from the remaining ones.

Fig. 2 shows the various blocks involved in the above discussion.

. Experiments

The following section describes the experiments to investigatehe coding schemes and properties of the culture so that is can besed as a reservoir for computation in a LSM model.

.1. Experimental procedure

Each experiment consists of two parts

.1.1. Selecting a set of electrodes for stimulationEach of the 120 electrodes was stimulated in a random order

ith an inter pulse delay of 1 s. This was repeated 3 times. For eachlectrode that was stimulated, the number of electrodes at whichhere was a response within 100 ms was counted. 8 electrodeshich evoked maximum response in the network were selected

or further experiments.

.1.2. Applying stimulation protocols and collecting responsesA stimulation pattern is defined as a sequence of firing of r elec-

rodes with a delay between them. An infinite number of suchatterns are possible if we allow any delay value. For a particu-

ar experiment we fixed the inter pulse delay between the firing oflectrodes as td ms. A stimulation protocol consisted of a set of suchtimulation patterns.

.2. Protocols used

Protocol 1 Stimulus patterns with two(r =2) electrodes per pat-tern

For each pattern two electrodes were taken and stimulatedwith a time delay of td ms between them. 56 such patterns are


possible with a set of 8 electrodes. Multiple experiments withvalues for td set at [50 10 5 2 ms 0.5 ms . . .] were performed.

The goal of this protocol was to investigate if stimulus at differ-ent electrodes interact and if so under what condition. Different

PRESSs xxx (2014) xxx–xxx 5

pairings allow the study of interaction between different set ofelectrodes and different time delays allows us to investigate therequirements for such interaction.• Protocol 2 Stimulus patterns with eight electrodes(r =8) per pat-

tern.For each pattern 8 electrodes were stimulated with a time delay

td of 5 ms. Out of the 40320(8!) such possible patterns we ran-domly selected 20 patterns and created 20 more patterns whichhave a sequence of firing reverse of the former set. Thus we havea set of 40 patterns with 8 electrodes firing in random order.

The goal of this protocol was to investigate if longer stimuluspatterns where all electrodes fire in different sequences can bedistinguished by the network.• Protocol 3 Inputs from a 3 dimensional space

An input space of 3 dimensions is defined with each dimensiontaking value from set {1,2,3}. Each dimension of the input wasmapped to an electrode. For a particular input [x1, x2, x3], thetime of firing of the input was defined as td * xi where td = 3 ms.There are 27 such possible inputs out of which 15 can be mappedto unique stimulus patterns.

This experiment was designed to demonstrate the use of inputcoding and output decoding schemes for a particular problem.

For each experiment, appropriate stimulus sequence was gen-erated using the defined coding scheme. Voltage pulses were thengenerated corresponding to these stimulus patterns using the DAC’sin MEA2100 system and the DSP. Stimulation patterns were pre-sented to the culture in a random order with an inter pattern delayof tp ms. For every experiment each pattern was presented 45 timesin a random order. Inter pattern delay values were 250 ms, 500 ms,and 1 s. The responses from 120 electrodes were recorded, filteredand spikes detected (The data from the 8 stimulating electrodeswere blanked out.). The output vector corresponding to each pre-sentation of the pattern was formed as described in the Methodssection. An array of preceptrons were then trained to be used as out-put decoders. A fraction (about 0.8) of the available samples is usedfor training the preceptron and the rest were used for testing. Forexample, in protocol 1, we have trained 56 perceptron decoders toidentify the 56 input patterns. For each perceptron, 35 out of 45patterns of output (called class C1) corresponding to the desiredinput and 55*35 of the other patterns (class C0) corresponding toother inputs are used for training the perceptron. The remainingpatterns are used for testing the decoders.

4. Results

The following section describes the various results obtainedfrom the preceding experiments.

4.1. Wide variety of patterns

Using the temporal coding scheme, unique patterns of responsescould be evoked from the culture for different patterns of inputstimuli. We estimated the probability of spike occurrence pj

M atelectrode ‘M’ in response to stimulus pattern j as


This output response is shown in Fig. 4 with varying shades ofred for some input patterns (8 out of 56) corresponding to protocol1 for an experiment on a culture (darkest corresponds to pj

M= 1 and

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Fig. 4. A variety of output patterns were observed with temporal coding scheme for inputs on 8 electrodes with protocol 1. The figure shows 8 out of 56 output patternsobserved when using protocol 1. Each dot represents an electrode. The intensity of the dot shows the probability that a spike is detected on that electrode. These patternsa g tem

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re representative of the typical patterns of spiking probability observed when usin

ightest to pjM = 0). These kind of patterns are typical for a healthy

ulture.1

.2. Response of the neuronal culture is modulated by the ordernd timing of input pulses

The network response to a stimulus depends on the electrodestimulated and the relative timing of their firing. Fig. 5 shows theetwork response for some of the stimulus patterns applied usingrotocol 1. Each column corresponds to a pair of electrodes beingtimulated with different time delays. Each row corresponds to aarticular time delay between the stimulation of these electrodes.he set of outputs corresponding to each pattern of inputs is dis-inguishable from the rest as seen from the results in Table 2. It cane seen that the probability of observing a spike at an electrode is

ndeed modulated by the input electrodes that are stimulated, theequence in which they are stimulated and the timing of the stimu-us. Results obtained for protocol 2 also showed a similar behaviouror a longer sequence.

.3. Dependency on the time delay between stimuli

The effect of interaction between the inputs depend on the timeelay between the stimuli. While using protocol 1 we found thathen the two stimuli were separated by a large time interval say 50s, the total response of the culture was independent of the order

n which they fire. The set of electrodes that show a spike responseas essentially the union of electrodes that show a response for

timulation at the two input electrodes independently. But as thesetimulus pulses were brought closer together, the responses tendedo be different. They became separable showing that the inputs


nteract to produce different outputs. The time interval at whichhis was observed varied with cultures and was in the range of.5–2 ms.

1 A culture which showed spontaneous activity in at-least 80 of 120 electrodesnd stimulation of 8 electrodes evoked a response at more than 20 other electrodes

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poral coding scheme.

4.4. Linearly separable outputs

An array of perceptrons were trained to recognize different out-put patterns. A perceptron was said to be able to correctly classifya pattern if it detected more than 80% of patterns for the trainedinput and rejected more than 80% of the false inputs. The train-ing was repeated for every experiment. Thus a single perceptronwas expected to differentiate between a pattern caused by a singleinput against those generated by the rest of the inputs. The num-ber of such perceptrons for a set of input patterns gave the numberof separable patterns for the experiment. Fig. 6 shows the selec-tive response of perceptrons to trained patterns. Here we can seethat the average response of the perceptron for the output pat-tern it is trained to decode is positive while it is negative for otherpatterns. This means that the hyperplane encoded by the percep-tron separates the response to one of the input patterns from therest. The trained perceptrons are able to do this with accuracy fora number of cases. The details are shown in Table 2. This showsthat a simple measure like occurrence of a spike at an electrodehas a linear separable property in the high dimensional output.Fig. 7 shows the confusion matrix for a typical case while usingprotocol 1 with 56 input patterns. 56 decoders were trained todetect each class of output pattern. It can be seen that except fora few cases, the number of false positives and false negatives arelow.

4.5. Linearly non separable points in 3 dimensions are separatedin 120 dimensions

In experiments with protocol 3, it can be seen that inputs thatwere not linearly separable in low dimensions were separatedby simple decoders in high dimensions. Fig. 8 shows the variouspoints in input space. It can be seen that all points are not linearlyseparable from others. However the output of the culture corre-


sponding to these inputs are linearly separable. This demonstratesthat cultured neural networks can be used for projection of lowdimensional data to high dimensions where they can be linearlyseparated.

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Fig. 5. Network response depends on the pair of inputs stimulated and the relative timing between them. This figure shows a few of the samples. Here, each column

c et of 8{ }

b Each dp terns

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f

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orresponds to an electrode pair shown in the top of the column chosen from the s

etween the stimulation of these electrodes as labelled on the left side of the row.

robability of a spike at that electrode for the stimulus pattern. Different activity pat

. Discussion

.1. Temporal code can be used to encode information to the


ulture

Consider two electrodes A and B. We apply stimulus patternsuch that there are conditions where A fires before B and B fires

able 2esults of classification tasks: Ti indicates different trials for a protocol on different culturifferent trials.

Number of cultures Number of patterns Mean

Protocol 1 7 56 54

Protocol 2 4 40 38

Protocol 3 2 15 13

a Trials are selected based on the response of the culture to stimulus inputs. Culturesurther experiments.

electrodes A, B, C, D, E . Each row corresponds to a particular order and timing

ot corresponds to an electrode and the intensity of the color is proportional to thecan be observed on the electrodes for various combination of sequences and timing.

before A. With our definition of output response, for the abovetwo orderings, if the network response were just a superposition ofresponse due to A and response due to B the two outputs must be


the same. The set of electrodes having a ’1’ would be the union ofelectrodes with a ’1’ when A and B are stimulated independently.However, we find that these two sequences produce linearly sep-arable outputs from the culture if the stimulus is within 2 ms. This

es. Mean separability is the mean number of separable patterns for a protocol over

separability Separability in selected trialsa

T1 T2 T3 T4 T5

56 55 53 55 5340 40 36 38 3612 12 13 15 13

that evoke reasonable activity on stimulation of input electrodes are selected for

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Fig. 6. Trained perceptrons give a selective response to a particular input pattern using protocol 1. Each box corresponds to a different perceptron. Each bar shows an averageresponse of the perceptron on all trials (45) of a particular pattern. It can be seen that the perceptron shows a positive response to the input pattern it is trained to detectwhile showing a negative response to others.Thresholding allows us to decide whether

arbitrary. It is the average of Wj · Xkj ∀ k. Since X is a binary vector and we compare the res

such that the outputs always lie within the range of a 16-bit integer which is suitable for

Fig. 7. Confusion matrix for an experiment using protocol 1: The experiment has56 input patterns and 56 decoders are trained to identify a single class of output.Each entry in the matrix indicates the fraction of times the perceptron reports iden-tt

doofleb

dfiliaa

electrodes (Ortman et al., 2011) as inputs to the culture. In both

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ification of a pattern and is colored as per the color bar to right. It can be seen thathe probability of false positives and false negatives are low for most of the cases.

emonstrates that different inputs can interact to produce distinctutputs. The interaction and linear separability of patterns dependsn the time difference of stimuli at input electrodes. If they occururther apart in time, the generated patterns are similar and notinearly separable. This shows that temporal code can be used toncode information for the network and network can computeased on the time of arrival of different inputs.

We determine the change in probability of spike at an electrodeue to pairing as follows. Let pM

A , pMB , pM

AB, pMBA be the probability of

ring of electrode ‘M’ to stimulus at electrodes A only, B only, A fol-owed by B in 0.5 ms and B followed by A in 0.5 ms. Then the change


n probability of firing at ‘M’ due to pairing is �pMAB = pM

A + pMB − pM

ABnd �pM

BA = pMA + pM

B − pMBA. The collection of these values is shown

s a histogram in Fig. 9. The X axis corresponds to the amount

the input pattern belongs to the class it is trained to detect. The scale on y axis isult with a threshold, Wj can be arbitrarily scaled (we typically scale this to a range

real-time implementation.)

of change and Y axis the number of electrodes that show such achange. It can be seen that most of the electrodes show a smallchange. But there are electrodes that show a change in probabil-ity of 1. This means that these electrodes did not show a responsewhen input sites A and B were stimulated independently. How-ever when these stimulations were paired, they started showing aresponse. Similarly there are electrodes that show a change of −1.This means that they showed a response when A and B were stim-ulated independently but their spiking activity was suppressed onpairing.

Similarly we find the change in probability of firing of an elec-trode due to change in order of stimulus as �pM = pM

AB − pMBA. The

collection of these values is shown as a histogram in Fig. 10. It canbe seen that the order of firing changes the probability of spikingat output electrodes. Some electrodes show an increase in prob-ability of firing when the order is reversed while others show adecrease. Interestingly, there are electrodes which do not show aspike response when inputs are fired in a particular order but showspikes when the order is reversed (those which show a change inprobability of 1 and −1). Thus we can conclude that pairing of elec-trodes and the order of pairing allows the system to distinguishbetween the cases. This effect depends on the timing of the stimulusas shown before.

5.2. Input coding scheme allows direct mapping of inputvariables to electrode stimulation

This study shows that temporal coding may be used as a schemeto interact with cultured neurons. Direct mapping of input variablesto the firing of electrodes can be achieved with this scheme whileusing a fixed set of electrodes.

Previous studies have used either stimulation of a single elec-trode (Dockendorf et al., 2009) or random patterns using available


the cases a mapping function would be required to map the inputsto stimulation patterns. It is not clear how this would be achieved.One solution would be to assign a pattern to every possible value of

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ig. 8. Points in three dimensional space that are not linearly separable. Coordinate

nput. But this would require a look-up table to store this associa-ion and a decoder to look-up the right pattern based on the inputs.emporal coding scheme allows a simple mapping for inputs. Weave shown that sequence and time delay of stimulation pattern


hus achieved can be used as input patterns to the culture.Table 3 shows a comparison of the proposed coding scheme with

elected previous results reported in the literature. It can be seen

ig. 9. Histogram of change in probability of firing of different electrodes when twolectrodes A and B were paired when compared to a superposition of activity of And B (shows only probabilities >0.2).

ome of the points are indicated. Input coding scheme used these coordinates.

that the input coding scheme taking into account the time delaysfor interaction allows us to encode a larger number of patterns tothe culture while using fewer electrodes.


5.3. Linear separability

This property allows the culture to be used expand the space ofthe inputs thus allowing us to differentiate easily between different

Fig. 10. Histogram of change in probability of firing of different electrodes when twoelectrodes A and B were fired in different sequences A followed by B vs B followedby A (shows only probabilities >0.2).

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Table 3Comparison of input coding scheme with existing reports. nE, number of electrodes.

nE Basis of patterngeneration

Total numberof patterns

Hafizovic et al. (2007) 2 Sequence of firing 2Dockendorf et al. (2009) 60 Stimulate an electrode 60Ortman et al. (2011) 60 Random

spatio-temporalpattern

16/100

pptrtepttbte

5

bipStcpctbowcT

bS(

Table 4Comparison of output decoding scheme with existing reports. nE, number of elec-trodes; nP, number of patterns.

Output definition nE/nP Total patterns

Hafizovic et al. (2007) Spatio-temporal pattern 128/128 2Dockendorf et al. (2009) Spatio-temporal pattern 59/944 60

Fp

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This work 8 Spatio-temporalpattern on input

50

oints on the input space. We can expect that if a culture is able toroduce sufficiently distinct outputs for different input patterns,hen in a decoding scheme where output feature used is the occur-ence of a spike, they would be linearly separable. If we look athe output vectors under this scheme, each output is a vector withntries 1/0 for its various coordinates. In the high dimensional out-ut space, the points corresponding to these vectors would lie onhe corners of a cube. If there were a single distinct output pat-ern corresponding to every input, they would be linearly separableased on the geometry. Due to variability in outputs, each input pat-ern is mapped to a set of corners of this hypercube. We can stillxpect a reasonable linear separation for different input patterns.

.4. Simple decoders

The perceptrons used have 120 inputs from the culture and aias input. Hence the number of parameters for each perceptron

s 121. In a similar problem, Ortman et al. (2011) have used 944arameters for each classifier (59 inputs, 16 time bins) when usingVM as a method of classification. Dockendorf et al. (2009) usedemplates of activity on each electrode for classification. These werereated from smoothed peri-stimulus histogram in a time windowost stimulus. In this case too, the number of parameters for eachlassifier would be 944 (59 inputs and 16 time bins). Compared tohese results, we demonstrate linear separability with fewer num-er of parameters which is achievable due to the linear separabilityf a simple feature like occurrence of spike in high dimensionshen compared to a spatio-temporal pattern on using temporal

ode for inputs. A comparison with previous results is shown inable 4.


It has been previously shown that an array of perceptrons cane used to do universal function approximation (Auer et al., 2008).uch results have been demonstrated in artificial neural networksMaass et al., 2002). We have shown that such methods can be

ig. 11. A simple network structure which can modulate the proability of firing of neurrobability of firing of n4 and n5 depends on the order of activation of n1 and n2

Ortman et al. (2011) Spatio-temporal pattern 59/944 16This work Spatial pattern 120/120 50

applied to cultured networks too with the proposed temporal cod-ing for inputs and defining outputs based on occurrence of spikes.

5.5. Arbitrary function mapping

Since the temporally coded inputs are linearly separable usingperceptrons, the culture can be used as a reservoir to do universalfunction mapping. With these experiments we show that wheninputs are applied at a relative time to each other, the response ofthe culture with reference to the time of input can be used to decodeall information about the input. Simulation studies using artificialneural networks have shown the feasibility of such a property forsolving problems (Grando et al., 2010).

5.6. Real time implementation

The decoding scheme used in these experiments use simpleperceptrons which have a simpler hardware implementation com-pared to other proposed schemes. A large array of perceptrons canbe easily implemented and can thus do parallel decoding for vari-ous output patterns. Several previous works have shown hardwareimplementations for such systems. We have also implemented thedecoders on a DSP chip which implements an array of 2048 suchdecoders and run in real time. In this implementation, perceptronoutputs are calculated once the outputs for a stimulus pattern iscollected for a predefined time window.

5.7. How does the network achieve the ability to distinguishbetween temporally coded inputs?

Although it is difficult to determine how the network achievesdifferent firing patterns for time coded inputs, a guess can be madeabout the basic scheme in which randomly connected neurons gen-


erate different spatio-temporal patterns. Excitatory and inhibitoryconnections along with different propagation delays can achievethe task of firing or not firing a neuron based on the sequence ofarrival of inputs. The following is a simplified notion of the network

ons based on timing of inputs. Inhibitory connections are shown in red. Here, the

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onnections with different delays as described by Szatmry andzhikevich (2010) allowing the network to modulate its dynamics.ig. 11 shows a situation where this is achieved. The probability ofring of neurons depends on the sequence of activation of inputs.onsider the probability of firing of readout neurons n4 and n5. n4ould have a higher probability of firing if n1 is activated before2 whereas n5 has a higher probability of firing if n2 is activatedefore n1.

.8. Limitations

This scheme exploits the fact that the order of firing with timeifferences in the range of 0.5–3 ms generates linearly separableutputs. However, it is not clear how the inputs spread over a longerime scale or range could be encoded. This does not explore theossible short term or long term memory properties that could beresent in the network.

. Conclusion

In this paper, we have shown that temporal coding can be useds a coding scheme to encode inputs to a cultured neural net-ork that is formed randomly which can then act as a Liquid Stateachine. We have shown that stimulus at different stimulation

ites can interact to affect the output of the neuronal network. Theime scales at which such interactions take place have been deter-

ined. We have shown that this scheme allows us to use simpleecoders at the output of the culture. With this coding scheme,e have demonstrated that the network can be used as a Liquid

tate Machine for some problem solving.Thus, this coding scheme allows us to interact with the cultured

euronal networks. This can be used to translate various prob-ems for the neuronal culture. It can also be used as an effective


ay to probe the state of the network.We have a large number ofnput patterns to generate different outputs from the network. This

ould allow us to study the change in the properties of the networkver time. This would be a more effective way when compared to

PRESSs xxx (2014) xxx–xxx 11

analyzing the spontaneous activity of the network for the changessince we have a very defined time of stimulus and a very simpledescription of the response which shows a wide variety. Thus wecan explore the effects of training and plasticity on the network.

Acknowledgments

We would like to thank Mohan Raghavan for multiple discuss-ions about the neuronal networks. This work was supported byDepartment of Electronics and Information Technology, Ministryof Communications and Information Technology, Government ofIndia.

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Input coding for neuro-electronic hybrid systems