{"title": "Artificial Olfactory Brain for Mixture Identification", "book": "Advances in Neural Information Processing Systems", "page_first": 1121, "page_last": 1128, "abstract": "The odor transduction process has a large time constant and is susceptible to various types of noise. Therefore, the olfactory code at the sensor/receptor level is in general a slow and highly variable indicator of the input odor in both natural and artificial situations. Insects overcome this problem by using a neuronal device in their Antennal Lobe (AL), which transforms the identity code of olfactory receptors to a spatio-temporal code. This transformation improves the decision of the Mushroom Bodies (MBs), the subsequent classifier, in both speed and accuracy.Here we propose a rate model based on two intrinsic mechanisms in the insect AL, namely integration and inhibition. Then we present a MB classifier model that resembles the sparse and random structure of insect MB. A local Hebbian learning procedure governs the plasticity in the model. These formulations not only help to understand the signal conditioning and classification methods of insect olfactory systems, but also can be leveraged in synthetic problems. Among them, we consider here the discrimination of odor mixtures from pure odors. We show on a set of records from metal-oxide gas sensors that the cascade of these two new models facilitates fast and accurate discrimination of even highly imbalanced mixtures from pure odors.", "full_text": "Arti\ufb01cial Olfactory Brain for Mixture Identi\ufb01cation\n\nMehmet K. Muezzinoglu1 Alexander Vergara1 Ramon Huerta1 Thomas Nowotny2\n\nNikolai F. Rulkov1 Heny D. I. Abarbanel1 Allen Selverston1 Mikhail I. Rabinovich1\n\n1 Institute for Nonlinear Science\nUniversity of California San Diego\n\n9500 Gilman Dr., La Jolla, CA, 92093-0402\n\n2 Centre for Computational Neuroscience and Robotics\n\nDepartment of Informatics, University of Sussex\n\nFalmer, Brighton, BN1 9QJ, UK\n\nAbstract\n\nThe odor transduction process has a large time constant and is susceptible to vari-\nous types of noise. Therefore, the olfactory code at the sensor/receptor level is in\ngeneral a slow and highly variable indicator of the input odor in both natural and\narti\ufb01cial situations. Insects overcome this problem by using a neuronal device in\ntheir Antennal Lobe (AL), which transforms the identity code of olfactory recep-\ntors to a spatio-temporal code. This transformation improves the decision of the\nMushroom Bodies (MBs), the subsequent classi\ufb01er, in both speed and accuracy.\nHere we propose a rate model based on two intrinsic mechanisms in the insect AL,\nnamely integration and inhibition. Then we present a MB classi\ufb01er model that re-\nsembles the sparse and random structure of insect MB. A local Hebbian learning\nprocedure governs the plasticity in the model. These formulations not only help to\nunderstand the signal conditioning and classi\ufb01cation methods of insect olfactory\nsystems, but also can be leveraged in synthetic problems. Among them, we con-\nsider here the discrimination of odor mixtures from pure odors. We show on a set\nof records from metal-oxide gas sensors that the cascade of these two new mod-\nels facilitates fast and accurate discrimination of even highly imbalanced mixtures\nfrom pure odors.\n\n1 Introduction\n\nOdor sensors are diverse in terms of their sensitivity to odor identity and concentrations. When\narranged in parallel arrays, they may provide a rich representation of the odor space. Biological\nolfactory systems owe the bulk of their success to employing a large number of olfactory receptor\nneurons (ORNs) of various phenotypes. However, chemo-diversity comes at the expense of two\npressing factors, namely response time and reproducibility, while fast and accurate processing of\nchemo-sensory information is vital for survival not only in natural, but also in many arti\ufb01cial situa-\ntions, including security applications.\n\nIdentifying and quantifying an odor accurately in a short time is an impressive characteristic of\ninsect olfaction. Given that there are approximately tens of thousands of ORNs sending slow and\nnoisy messages in parallel to downstream olfactory layers, in order to account for the observed\nrecognition performance, a computationally non-trivial process must be taking place along the insect\nolfactory pathway following the transduction. The two stations responsible for this processing are\nthe Antennal Lobe (AL) and the Mushroom Bodies (MBs). The former acts as a signal conditioning\n/ feature extraction device and the latter as an algebraic classi\ufb01er.\n\nOur motivation in this study is the potential for skillful feature extraction and classi\ufb01cation methods\nby insect olfactory systems in synthetic applications, which also deal with slow and noisy sensory\ndata. The particular problem we address is the discrimination of two-component odor mixtures from\n\n1\n\n\fOdor\n\n1\n\n2\n\n3\n\n.\n.\n.\n\n16\n\nMushroom\n\nBody\n\nClassifier\nModel\n\nOdor\nIdentity\n\nSensor\nArray\n\nDynamical\n\nAntennal Lobe Model\n\nSnapshot\n\nFigure 1: The considered biomimetic framework to identify whether an applied gas is a pure odor or\na mixture. The input is transduced by 16 parallel metal-oxide gas sensors of different type generating\nslow and noisy resistance time series. The signal conditioning in the antennal lobe is achieved by\nthe interaction of an excitatory Projection Neuron (PN) population (white nodes) with an inhibitory\nLocal Neurons (LNs, black nodes). The outcomes of AL processing is read from the PNs and\nclassi\ufb01ed in the Mushroom Body, which is trained by a local Hebbian rule.\n\npure odors in a three-class classi\ufb01cation setting. The problem is nontrivial when concentrations of\nmixture components are imbalanced. It becomes particularly challenging when the overall mixture\nconcentration is small. We treat the problem on two mixture datasets recorded from metal-oxide gas\nsensors (included in the supplementary material).\n\nWe propose in the next section a dynamical rate model mimicking the AL\u2019s signal conditioning\nfunction. By testing the model \ufb01rst with a generic Support Vector Machine (SVM) classi\ufb01er, we\nvalidate the substantial improvement that AL adds on the classi\ufb01catory value of raw sensory signal\n(Section 2). Then, we introduce a MB-like classi\ufb01er to substitute for the SVM and complete the\nbiomimetic framework, as outlined in Fig. 1. The model MB exploits the structural organization of\nthe insect MB. Its plasticity is adjusted by a local Hebbian learning procedure, which is gated by a\nbinary learning signal (Section 3). Some concluding remarks are given in Section 4.\n\nInsect Antennal Lobe Outline\n\n2 The Antennal Lobe\n2.1\nThe Antennal Lobe is a spatio-temporal encoder for ORN signals that include time in coding space.\nSome of its qualitative properties are apparent from the input-output perspective, without requiring\nmuch insight into its physiology. A direct analysis of spiking rates in raw ORN responses and in\nthe AL output [1] shows that in fruit \ufb02y AL maps ORN output to a low dimensional feature space\nwhile providing lower variability in responses to the same odor type (reducing within-class scatter)\nand longer average distance between responses for different odors (boosting between-class scatter).\nThese observations constitute suf\ufb01cient evidence that a realistic AL model should be sought within\nthe class of nonlinear \ufb01lters.\n\nAnother remarkable achievement of the AL shows itself in terms of recognition time. When sub-\njected to a constant odor concentration, the settling time of ORN activity is on the order of hundreds\nof milliseconds to seconds [3], whereas recognition is known to occur earlier [7]. This is a clear\nindicator that the AL makes extensive use of the ORN transient, since instantaneous activity is less\nodor-speci\ufb01c in transient than it is in during the steady state. To provide high accuracy under such a\ntemporal constraint, the classi\ufb01catory information during this period must be somehow accumulated,\nwhich means that AL has to be a dynamical system, utilizing memory.\n\nIt is the cooperation of these \ufb01ltering and memory mechanisms in the AL that expedites and consol-\nidates the decision made in the subsequent classi\ufb01er.\n\nStrong experimental evidence suggests that the insect AL representation of odors is a transient,\nyet reproducible, spatio-temporal encoding [8]. The AL is a dynamical network that is formed by\nthe coupling of an excitatory neuron population (projection neurons, PNs) with an inhibitory one\n\n2\n\n\f(local neurons, LNs). It receives input from glomeruli, junctions of synapses that group the ORNs\naccording to the receptor gene they express. The fruit \ufb02y has about 50 glomeruli as chemotopic\nclusters of synapses from nearly 50, 000 ORNs. There is no consensus on the functional role of this\nconvergence beyond serving as an input terminal to AL, which is certainly an active processing layer.\nIn the analogy we are building here (c.f. Fig. 1), the 16 arti\ufb01cial gas sensors actually correspond to\nglomeruli (rather than individual ORNs) so that the AL has direct access to sensor resistances.\n\nWe suggest that the two key principles underlying the AL\u2019s information processing are decorrelation\n(\ufb01ltering) and integration (memory), which can be uni\ufb01ed on a dynamical system. The \ufb01lter property\nprovides selectivity, while the integrator accumulates the re\ufb01ned information on trajectories. This\nsetting is capable of evaluating the transient portion of the sensory signal effectively.\n\nAn instantaneous value read from a receptor early in the transduction process is considered as im-\nmature, failing to convey a consistently high classi\ufb01catory value by its own. Nevertheless, the ORN\ntransient as an interval indeed offers unique features to expedite the classi\ufb01cation. In particular,\nthe novelty gained due to observing consecutive samples during the transient is on average greater\nthan the informational gain obtained during the steady-state. Hence, newly observed samples of the\nreceptor transients are likely to contribute to the cumulative classi\ufb01catory information base formed\nso far, whereas the informational entropy vanishes as the signal reaches the steady-state. As a device\nthat extracts and integrates odor-speci\ufb01c information in ORN signals, the AL provides an enriched\ntransient to the subsequent MB so that it can achieve accurate classi\ufb01cation early in the odor period.\n\nWe also note that there have been efforts, e.g., [9, 10] to illustrate the sharpening effect of inhibition\nin the olfactory system. However, to the best of our knowledge, the approach we present here is the\n\ufb01rst to formulate the temporal gain due to AL processing.\n2.2 The Model\nThe model AL is comprised of a population of PNs that project from the AL to downstream pro-\ncessing. The neural activity corresponding to the rate of action potential generation of the biological\nneurons is given by xi(t), i = 1, 2, ..., NE, for the NE neurons in the PN population. There are also\nNI interneurons or LNs whose activity is yi(t); i = 1, 2, ..., NI.\nThe rate of change in these activities is stimulated by a weighted sum over both populations and a\nset of input signals SE\ni (t) indicating the activity in the glomeruli stimulating the PNs and\nthe LNs, respectively. In addition, each population receives noise from the AL environment. Our\nformulation of these ideas is through a Wilson-Cowan-like population model [11]\n\ni (t) and SI\n\n= K E\ni\n\nwEI\n\nij yj(t) + gE\n\ninpSE\n\ni (t), i \u2208 1, . . . , NE,\n\n\u03b2E\ni\n\ndxi(t)\n\ndt\n\n\u03b2I\ni\n\ndyi(t)\n\ndt\n\nNI\n\nXj=1\n\n\u00b7 \u0398\uf8eb\n\uf8ed\u2212\ni \u00b7 \u0398\uf8eb\nXj=1\n\uf8ed\n\nNE\n\ni (t)\uf8f6\n\n\uf8f8 \u2212 xi(t) + \u00b5E\n\uf8f8 \u2212 yi(t) + \u00b5I\n\ni (t)\uf8f6\n\n= K I\n\nwIE\n\nij xj(t) + gI\n\ninpSI\n\ni (t), i \u2208 1, . . . , NI .\n\nThe superscripts E and I stand for excitatory and inhibitory populations. The matrix elements wXY\n,\nX, Y \u2208 {E, I} are time-independent weights quantifying the effect from units of type Y to units\ni (t) is the external input to i-th unit from a glomerulus (odor sensor) weighted by\nof type X. SX\ncoupling strength gX\nis an additive noise process and \u0398(\u00b7), the unit-ramp activation function:\n\u0398(u) = 0 for u < 0, and \u0398(u) = u, otherwise. The gains K E\ni are\ni , K I\n\ufb01xed for an individual unit but vary across PN and LN populations.\n\ni and time constants \u03b2E\n\ninp. \u00b5Y\n\ni , \u03b2I\n\nij\n\ni\n\nThe network topology is formed through a random process of Bernoulli type:\n\nwXY\n\nij = gY \u00b7(cid:26) 1 , with probability pXY\n\n0 , with probability 1 \u2212 pXY\n\nwhere gY is a \ufb01xed coupling strength. pXY is a design parameter to be chosen by us.\nEach unit, regardless of its type, accepts external input from exactly one sensor in the form of raw\nresistance time series. This sensor is assigned randomly among all 16 available sensors, ensuring\nthat all sensors are covered1.\n\n1It is assumed that NE + NI > 16.\n\n3\n\n\f15x 104\n\nTGS 2602\nTGS 2600\nTGS 2010\nTGS 2620\n\n20\n\n)\n\n\u2126\n\n(\n \n\ne\ns\nn\no\np\ns\ne\nr\n \nr\no\ns\nn\ne\nS\n\n10\n\n5\n\n0\n0\n\n \n\n40\n\n60\n\nTime (s)\n(a)\n\n \n\n12x 105\n\n10\n\n5\n7\n\n,\n.\n.\n.\n,\n\n1\n=\n\ni\n \n \n \n \n)\nt\n(\nx\n\ni\n\n8\n\n6\n\n4\n\n2\n\n0\n\n80\n\n100\n\n0\n\n0.5\n\n1.5\n\n2\n\n1\n\nTime (s)\n(b)\n\nFigure 2: (a) A record from Dataset 1, where 100ppm acetaldehyde was applied to the sensor array\nfor 0 \u2264 t \u2264 100s. Offsets are removed from the time-series. Curve labels indicate the sensor types.\n(b) Activity of NE = 75 excitatory PN units of the sample AL model in response to the (time-scaled\nversion of) record shown on panel (a). The conductances are selected as (gE, gI ) = (10\u22126, 9 \u00b7 10\u22126)\nand other parameters as given in text. Bar indicates the odor period.\n\ni , K I\n\nFor the mixture identi\ufb01cation problem of this study, we consider a network with NE = NI = 75 and\ninp = 10\u22122. The probabilities used in the generative Bernoulli process are \ufb01xed at pIE =\ngE\ninp = gI\npEI = 0.5. The synaptic conductances gE and gI are optimized for the particular classi\ufb01cation\ninstance through the brute force search described below. The gains K E\nj and the time-scales\nj , i = 1, . . . , NE, j = 1, . . . , NI are drawn independently from exponential distributions\n\u03b2E\ni , \u03b2I\nwith \u03bbK = 7.5 and \u03bb\u03b2 = 0.5, respectively. Following construction, the initial condition of each\nunit is taken as zero and \u00b5 is taken as a white noise process with variance 10\u22124 independently\nfor each unit. We perform the simulation of the 150-dimensional Wilson-Cowan dynamics by 5/6\nRunge-Kutta integration with variable step size where the error tolerance is set to 10\u221215.\nAlthough the considered network structure can accommodate limit cycles and strange attractors, the\nselected range of parameters yield a \ufb01xed point behavior. We con\ufb01rm this in all simulations with the\nselected parameter values, both during and after the sensory input (odor) period (see Fig. 2(b)).\n2.3 Validation\nWe consider the activity in PN population as the only piece of information regarding the input odor\nthat is passed on to higher-order layers of the olfactory system. Access to this activity by those\nlayers can be modeled as instantaneous sampling of a selected brief window of temporal behavior\nof PNs [7]. Therefore, the recognition system in our model utilizes such snapshots from the spiking\nactivity in the excitatory population xi(t). A snapshot is passed as the feature vector to the classi\ufb01er;\nit is comprised of an NE-dimensional \ufb01xed vector taken as a sample from the states x1, . . . , xNE at\na particular time ts.\n2.3.1 Dataset\nThe model is driven by responses recorded from 16 metal-oxide gas sensors in parallel. We have\nmade 80 recordings and grouped them into two sets based on vapor concentration: records for\n100ppm vapor in Dataset 1 and 50ppm in Dataset 2. Each dataset contains 40 records from three\nclasses: 10 pure acetaldehyde, 10 pure toluene, and 20 mixture records. The mixture class con-\ntains records from imbalanced acetaldehyde-toluene mixtures with 96%-4%, 98%-2%, 2%-98%,\nand 4%-96% partial concentrations, \ufb01ve from each. Hence, we have two instances of the mixture\nidenti\ufb01cation problem in the form of three-class classi\ufb01cation. See the supplementary material for\ndetails on measurement process.\n\nWe removed the offset from each sensor record and scaled the odor period to 1s. This was done\nby mapping the odor period, which has \ufb01xed length of 100s in the original records, to 1s by re-\nindexing the time series. These one-second long raw time series, included in the supplementary\nmaterial, constitute the pool of raw inputs to be applied to the AL network during the time interval\n0.5 \u2264 t \u2264 1.5s. The input is set to zero outside of this odor period. See Fig. 2 for a sample record\nand the AL network\u2019s response to it. Note that, although we apply the network to pre-recorded data\nin simulations, the general scheme is causal, thus can be applied in real-time.\n\n4\n\n\f100\n\n)\n\n%\n\n(\n \ne\nt\na\nr\n \ns\ns\ne\nc\nc\nu\nS\n\n80\n\n60\n\n40\n\n \n\nwithout AL network\nwith optimized AL network\n\n \n\n20\n0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5\n\nSnapshot time ts (s)\n\n100\n\n)\n\n%\n\n(\n \ne\nt\na\nr\n \ns\ns\ne\nc\nc\nu\nS\n\n80\n\n60\n\n40\n\n(a)\n\n \n\n without AL network using SVM\n with optimized AL network using SVM\n with optimized AL network using MB\n\n \n\n20\n0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5\n\nSnapshot time ts (s)\n\n(c)\n\ns\n5\n\n.\n\n1\n=\n\ns\n\nt\n \nt\n\na\n\n \n)\n\n%\n\n(\n \ne\n\nt\n\na\nR\n \ns\ns\ne\nc\nc\nu\nS\n\n.\n\ns\n5\n1\n=\n\ns\n\nt\n \nt\n\na\n\n \n)\n\n%\n\n(\n \n\nt\n\ne\na\nR\n \ns\ns\ne\nc\nc\nu\nS\n\n100\n\n98\n\n96\n\n94\n1\n\nx 10\u22125\n\n \n\n0.5\ngI\n\nMax 99.7%\n\nat (1e\u22126,9e\u22126)\n\n \n\nNo connectivity\n\n0\n\n0.5\ngE\n\nx 10\u22125\n\n0\n\n1\n\n(b)\n\n99\n\n98\n\n97\n\n96\n\n95\n\nMax 95.5%\n\nat (6e\u22126,9e\u22126)\n\n100\n\n90\n\n80\n1\n\n \n\n95\n\n90\n\nx 10\u22125\n\n \n\n0.5\ngI\n\n0\n\n1\n\n(d)\n\nNo connectivity\n\n0\n\n0.5\ngE\n\nx 10\u22125\n\n85\n\nFigure 3: (a) Estimated correct classi\ufb01cation pro\ufb01le versus snapshot time ts during the normalized\nodor period for Dataset 1. The red curve is the classi\ufb01cation pro\ufb01le due to the proposed AL network,\nwhich has the \ufb01xed sample topology with (gE, gI ) = (10\u22126, 9 \u00b7 10\u22126). The black baseline pro\ufb01le is\nobtained by discarding AL and directly classifying snapshots from raw sensor responses by SVM.\n(b) Correct classi\ufb01cation rates extracted by a sweep through gE, gI using Dataset 1. Panels (c) & (d)\nshow the results for Dataset 2, where the best pair is determined as (gE, gI ) = (6 \u00b7 10\u22126, 9 \u00b7 10\u22126).\n\n2.3.2 Adjustment of AL Network and Performance Evaluation\nTo reveal the signal conditioning performance of the stand-alone AL model, we \ufb01rst interface it\nwith an established classi\ufb01er. We use a Support Vector Machine (SVM) classi\ufb01er with linear kernel\nto map the snapshots from PN activity to odor identity. This choice is due to the parameter-free\ndesign that rules out the possibility of over-\ufb01tting. The classi\ufb01er is realized by the publicly available\nsoftware LibSVM [2].\n\nDue to the wide diversity of PNs and LNs in terms of their time scales \u03b2 and gains K, the perfor-\nmance of the network is highly sensitive to the agreement between the outcome of the generative\nprocess and the choice of parameters gE and gI. Therefore, it is not possible to give a one-size-\n\ufb01ts-all value for these. Instead, we have generated one sample network topology via the Bernoulli\nprocess described above and customized gE and gI for it on each problem. For reproducibility, this\ntopology is provided in the supplementary material. Comparable results can be obtained with other\ntopologies but possibly with different gE, gI values than the ones reported below.\nThe validation is carried out in the following way: First we set the classi\ufb01cation problem (i.e.,\nselect Dataset 1 or 2) and \ufb01x gE = gI = 0 (suppress the connectivity). We present each record\nin the dataset to the network and then log the network response from excitatory population in the\nform of NE simultaneous time series (see Fig. 2). Then, at each percentile of the odor period\nk=0, we take a snapshot from each NE-dimensional time series and label it\nts \u2208 {0.5 + k/100}100\nby the odor identity (pure acetaldehyde, pure toluene, or mixture). We use randomly selected 80%\nof the resulting data in training the SVM classi\ufb01er and keep the remaining 20% for testing it. We\nrecord the rate of correct classi\ufb01cation on the test data. The train-test stage is repeated 1000 times\nwith different random splits of labelled data. The average correct classi\ufb01cation rate is assigned as\nthe performance of the AL model at that ts. The classi\ufb01cation pro\ufb01le versus time is extracted when\nthe ts sweep through the odor period is complete.\nTo maximize the performance over conductances gE and gI, we further perform a sweep through\na range of these parameters by repeating the above procedure for each combination of gE, gI. Fig-\n\n5\n\n\fure 3 (a) shows the classi\ufb01cation pro\ufb01le for the best pair encountered along the parameter sweep\nk=0. This pair is determined as the one maximizing classi\ufb01cation success rate\ngE, gI \u2208 {k/100}100\nwhen samples from the end of odor period is used ts = 1.5. Note that these optimum values are\nproblem-speci\ufb01c. For the two instances considered in this work, we mark them by the peaks of the\nsurfaces in Fig. 3 (b) and (d).\n\nDataset 1 induces an easier instance of the identi\ufb01cation problem toward the end of odor period,\nwhich can be resolved reasonably well using raw sensor data at the steady state. Therefore, the gain\nover baseline due to AL processing is not so signi\ufb01cant in later portions of the odor period for Dataset\n1. Also observe from panels (b) and (d) that, when dealing with Dataset 1, the conductance values are\nless decisive than they are for Dataset 2. Again, this is because the former is an easier problem when\nthe sensors reach the steady-state at ts = 1.5s, where almost all conductance within the swept range\nensures > 95% performance. The relative dif\ufb01culty of the problem in Dataset 2 manifests itself as\nthe \ufb02uctuations in the baseline performance. We see in Fig. 3(c) that there are actually periods early\nin the period where the raw sensor data can be fairly indicative of the class information; however, it\nis not possible to predict these intervals in advance. It should also be noted that some of these peaks\nin baseline performance, at least the very \ufb01rst one near ts = 0.55s, are artifacts (due to classi\ufb01cation\nof pure noise) since we know that there is hardly any vapor in the measurement chamber during that\nperiod (see Fig. 2(a) and other records in supplementary material). In any case, in both problems,\nthe suggested AL dynamics (with adjusted parameters) contributes substantially to the classi\ufb01cation\nperformance during the transient of the sensory signal. This makes early decisions of the classi\ufb01er\nsubstantially and consistently more accurate with respect to the baseline classi\ufb01cation.\n\nHaving established the contribution of the AL network to classi\ufb01cation, our goal in the remainder\nof the paper is to replace the unbiased SVM classi\ufb01er by a biologically plausible MB model, while\npreserving the performance gain seen in Fig. 3.\n3 Mushroom Body Classi\ufb01er\nThe MBs of insects employ a large number of identical small intrinsic cells, the so-called Kenyon\ncells, and fewer output neurons in the MB lobes. It has been observed that, unlike in the AL, the\nactivity in the KCs is very sparse, both across the population and for individual cells over time. The-\noretical work suggests that a large number of cells with sparse activity enables ef\ufb01cient classi\ufb01cation\nwith random connectivity [4]. The power of this architecture lies in its versatility: The connectivity\nis not optimized for any speci\ufb01c task and can, therefore, accommodate a variety of input types.\n3.1 The Model\nThe insect MB consists of four crucial elements (see Fig. 4): i) a nonlinear expansion from the\nAL representation at the \ufb01nal stage, x, that resembles the connectivity from the Antennal Lobe to\nthe MBs, ii) a gain control in the MB to achieve a uniform level of sparse activity the KCs, y, iii)\na classi\ufb01cation phase, where the connections from the KCs to the output neurons, z, are modi\ufb01ed\naccording to a Hebbian learning rule, and iv) a learning signal that determines when and which\noutput neuron\u2019s synapses are reinforced.\n\nIt has been shown in locusts that the activity patterns in the AL are practically discretized by a\nperiodic feedforward inhibition onto the MB calyces and that the activity levels in KCs are very\nlow [7]. Based on the observed discrete and sparse activity pattern in insect MB, we choose to\nrepresent KC units as simple algebraic McCulloch-Pitts \u2018neurons.\u2019 The neural activity values taken\n\ni=1 cjixi \u2212 \u03b8KC(cid:17) j =\n\nby this neural model are binary (0 = no spike and 1 = spike): \u00b5j = \u03a6(cid:16)PNE\n\n1, 2, ..., NKC. The vector x is the representation of the odor that is received as a snapshot from the\nexcitatory PN units of AL model. The components of the vector x = (x1, x2, ..., xNE ) are the direct\nvalues obtained by integration of the ODE of the AL model described above. The KC layer vector \u00b5\nis NKC dimensional. cij \u2208 {0, 1} are the components of the connectivity matrix which is NE \u00d7NKC\nin size. The \ufb01ring threshold \u03b8KC is integer number and \u03a6(\u00b7) is the Heaviside function.\nThe connectivity matrix [cji] is determined randomly by an independent Bernoulli process. Since\nthe degree of connectivity from the input neurons to the KC neurons did not appear to be critical for\nthe performance of the system, we made it uniform by setting the connection probability as pc = 0.1.\nIt, nevertheless, seems advisable to ensure in the construction that the input-to-KC layer mapping is\nbijective to avoid loss of information. We performed this check during network construction. All\nother parameters of the KC layer are then assigned admissible values uniformly randomly and \ufb01xed.\n\n6\n\n\fCalyx\u00b5\n\n[ c   ]\n\nji\n\nAntennal Lobe PNs\n\nx\n\nOutput Nodes\n\nz\n\n[ w   ]\n\nlj\n\nPure\n\nToluene\n\nPure\n\nAcetaldehyde\n\nMixture\n\nAcetaldehyde\n\n+\n\nToluene\n\nFigure 4: Suggested MB model for\nclassifying the AL output. The \ufb01rst layer\nof connections from AL to calyx are set\nrandomly and \ufb01xed. The plasticity of the\noutput layer is due to a binary learning\nsignal that rewards the weights of output\nunits responding to the correct stimulus.\n\nj=1 wlj \u00b7 \u00b5j \u2212 \u03b8LB(cid:17),\n\nPitts neurons: zl = \u03a6(cid:16)PNKC\n\nAlthough the basic system described so far implements the divergent (and static) input layer ob-\nserved in insect calyx, it is very unstable against \ufb02uctuations in the total number of active input\nneurons due to the divergence of connectivity. This is an obstacle for inducing sparse activity at KC\nlevel. One mechanism suggested to remove this instability is gain control by feedforward inhibition.\nFor our purposes, we impose a number nKC of simultaneously active KCs, and admit the \ufb01ring of\nonly the top nKC = NKC/5 neurons that receive the most excitation in the \ufb01rst layer.\nThe fan-in stage of projections from the KCs to the extrinsic MB cells in the MB lobes is the\nhypothesized locus of learning. In our model, the output units in the MB lobes are again McCulloch-\nl = 1, 2, ..., NLB. Here, the index LB denotes the\nMB lobes. The output vector z of the MB lobes has dimension NLB (equals 3 in our problem) and\n\u03b8LB is the threshold for the decision neurons in the MB lobes. The NLB \u00d7 NKC connectivity matrix\nwlj has integer entries. Similar to the above-mentioned gain control, we allow only the decision\nneuron that receives the highest synaptic input to \ufb01re. These synaptic strengths wlj are subject to\nchanges during learning according to a Hebbian type plasticity rule described next.\n3.2 Training\nThe hypothesis of locating reinforcement learning in mushroom bodies goes back to Montague and\ncollaborators [6]. Every odor class is associated with an output neuron of the MB, so there are three\noutput nodes \ufb01ring for either pure toluene, pure acetaldehyde, or mixture type of input. The plas-\nticity rule is applied on the connectivity matrix W , whose entries are randomly and independently\ninitialized within [0, 10]. The exact initial distribution of weights have no signi\ufb01cant impact on the\nresulting performance nor on the learning speed.\n\n\u2113\n\nDuring learning, the inputs are presented to the system in an arbitrary order. The entries of the\nconnectivity matrix at the time of the nth input are denoted by wlj(n). When the next training input\nwith label \u2113 is applied, then the weight w\u2113j is updated by the rule w\u2113j(n + 1) = H (z\u2113, \u00b5j, w\u2113j(n)),\nwhere H(z, \u00b5, w) = w + 1 when z = 1, \u00b5 = 1; and 0, otherwise. This learning rule strenghtens\na synaptic connection with probability p+ if presynaptic activity is accompanied by postsynaptic\nactivity. To facilitate learning during the training phase, the \u2018correct\u2019 output neuron \u2113 is forced to\n\ufb01re for an input with label \u2113, while the rest are kept silent. This is provided by pulling down the\nthreshold \u03b8LB\n, unless neuron \u2113 is already \ufb01ring for such input. Learning is terminated when the\nperformance (correct classi\ufb01cation rate) converges.\n3.3 Validation\nUsing Dataset 2, we applied the proposed MB model with NKC = 10, 000 KCs at the output of\nthe sample AL topology having the same parameters reported in Section 2. For p+ = p\u2212 = 1,\nwe trained the output layer of MB using the labelled AL outputs sampled at 10 points in the odor\nperiod. The mean correct classi\ufb01cation rate over 20 splits of the labelled snapshots (\ufb01ve-fold cross-\nvalidation) are shown in Fig.3(c) as blue dots. With respect to the red curve on the same panel, which\nwas obtained by the (maximum-margin) SVM classi\ufb01er, a slight reduction in the generalization\ncapability is visible. Nevertheless, the MB classi\ufb01er in its current form still exploits the superior\njob of AL over baseline classi\ufb01cation during transient, while mimicking two essential features of\nthe biological MB, namely sparsity in KC-layer and incremental local learning in MB lobes. The\nimplementation details and parameters of the MB model are provided in the supplementary material.\n\n7\n\n\f4 Conclusions\nWe have presented a complete odor identi\ufb01cation scheme based on the key principles of insect\nolfaction, and demonstrated its validity in discriminating mixtures of odors from pure odors using\nactual records from metal-oxide gas sensors.\n\nThe bulk of the observed performance is due to the AL, which is a dynamical feature extractor for\nslow and noisy chemo-sensory time series. The cooperation of integration (accumulation) mecha-\nnism and sharpening \ufb01lter enabled by inhibition leave an almost linearly separable problem for the\nsubsequent classi\ufb01er. The proposed signal conditioning scheme can be considered as a mathematical\nimage of reservior computing [5]. For this simpli\ufb01ed classi\ufb01cation task, we have also suggested a\nbio-inspired MB classi\ufb01er with local Hebbian plasticity. By exploiting the dynamical nature of the\nAL stage and the sparsity in MB representation, the overall model provides an explanation for the\nhigh speed and accuracy of odor identi\ufb01cation in insect olfactory processing.\n\nFor future study, we envision an improvement on the MB classi\ufb01cation performance, which has been\nexplored here to be slightly worse than linear SVM. We think that this can be done without compro-\nmising biological plausibility, by imposing mild constraints on the KC-level generative process.\n\nThe mixture identi\ufb01cation problem investigated here is in general more dif\ufb01cult than the traditional\nproblem of discriminating pure odors, since the mixture class can be made arbitrarily close to the\npure odor classes. The classi\ufb01cation performance attained here is promising for other mixture-\nrelated problems that are among the hardest in the \ufb01eld of arti\ufb01cial olfaction.\n\nAcknowledgments\nThis work was supported by the MURI grant ONR N00014-07-1-0741.\nReferences\n\n[1] V. Bhandawat, S. R. Olsen, N. W. Gouwens, M. L. Schlief, and R. I. Wilson. Sensory processing in the\ndrosphila antennal lobe increases reliability and separability of ensemble odor representations. Nature\nNeuroscience, 10:1474\u20131482, 2007.\n\n[2] C.C. Chang and C. J. Lin. LibSVM - A library for support vector machines, v2.85, 2007.\n[3] M de Bruyne, P. J. Clyne, and J. R. Carlson. Odor coding in a model olfactory organ: The Drosophila\n\nmaxillary palp. Journal of Neuroscience, 11:4520\u20134532, 1999.\n\n[4] R. Huerta, T. Nowotny, M. Garcia-Sanchez, H. D. I. Abarbanel, and M. I. Rabinovich. Learning classi\ufb01-\n\ncation in the olfactory system of insects. Neural Computation, 16:1601\u20131640, 2004.\n\n[5] W. Maass, T. Natschlaeger, and H. Markram. Real-time computing without stable states: A new frame-\n\nwork for neural computation based on perturbations. Neural Computation, 14:2531\u20132560, 2002.\n\n[6] P. R. Montague, P. Dayan, C. Person, and T. J. Sejnowski. Bee foraging in uncertain environments using\n\npredictive Hebbian learning. Nature, 337:725\u2013728, 1995.\n\n[7] J. Perez-Orive, O. Mazor, G. C. Turner, S. Cassenaer, R. I. Wilson, and G. Laurent. Oscillations and\n\nsparsening of odor representations in the mushroom body. Science, 297:359\u2013365, 2002.\n\n[8] M. I. Rabinovich, R. Huerta, and G. Laurent. Transient dynamics for neural processing. Science, 321:48\u2013\n\n50, 2008.\n\n[9] B. Raman and R. Gutierrez-Osuna. Chemosensory processing in a spiking model of the olfactory bulb:\nChemotopic convergence and center surround inhibition. In L. K. Saul, Y. Weiss, and L. Bottou, editors,\nNIPS 17, pages 1105\u20131112. MIT Press, Cambridge, MA, 2005.\n\n[10] M. Schmuker and G. Schneider. Processing and classi\ufb01cation of chemical data inspired by insect olfac-\n\ntion. Proc. Nat. Acad. Sci., 104:20285\u201320289, 2007.\n\n[11] H. R. Wilson and J. D. Cowan. A mathematical theory of the functional dynamics of cortical and thalamic\n\nnervous tissue. Kybernetik, 13:55\u201380, 1973.\n\n8\n\n\f", "award": [], "sourceid": 968, "authors": [{"given_name": "Mehmet", "family_name": "Muezzinoglu", "institution": null}, {"given_name": "Alexander", "family_name": "Vergara", "institution": null}, {"given_name": "Ramon", "family_name": "Huerta", "institution": null}, {"given_name": "Thomas", "family_name": "Nowotny", "institution": null}, {"given_name": "Nikolai", "family_name": "Rulkov", "institution": null}, {"given_name": "Henry", "family_name": "Abarbanel", "institution": null}, {"given_name": "Allen", "family_name": "Selverston", "institution": null}, {"given_name": "Mikhail", "family_name": "Rabinovich", "institution": null}]}