{"title": "Efficient and Robust Spiking Neural Circuit for Navigation Inspired by Echolocating Bats", "book": "Advances in Neural Information Processing Systems", "page_first": 938, "page_last": 946, "abstract": "We demonstrate a spiking neural circuit for azimuth angle detection inspired by the echolocation circuits of the Horseshoe bat Rhinolophus ferrumequinum and utilize it to devise a model for navigation and target tracking, capturing several key aspects of information transmission in biology. Our network, using only a simple local-information based sensor implementing the cardioid angular gain function, operates at biological spike rate of 10 Hz. The network tracks large angular targets (60 degrees) within 1 sec with a 10% RMS error. We study the navigational ability of our model for foraging and target localization tasks in a forest of obstacles and show that our network requires less than 200X spike-triggered decisions, while suffering only a 1% loss in performance compared to a proportional-integral-derivative controller, in the presence of 50% additive noise. Superior performance can be obtained at a higher average spike rate of 100 Hz and 1000 Hz, but even the accelerated networks requires 20X and 10X lesser decisions respectively, demonstrating the superior computational efficiency of bio-inspired information processing systems.", "full_text": "Ef\ufb01cient and Robust Spiking Neural Circuit for\n\nNavigation Inspired by Echolocating Bats\n\nPulkit Tandon, Yash H. Malviya\n\nIndian Institute of Technology, Bombay\n\npulkit1495,yashmalviya94@gmail.com\n\nBipin Rajendran\n\nNew Jersey Institute of Technology\n\nbipin@njit.edu\n\nAbstract\n\nWe demonstrate a spiking neural circuit for azimuth angle detection inspired by\nthe echolocation circuits of the Horseshoe bat Rhinolophus ferrumequinum and\nutilize it to devise a model for navigation and target tracking, capturing several key\naspects of information transmission in biology. Our network, using only a simple\nlocal-information based sensor implementing the cardioid angular gain function,\noperates at biological spike rate of approximately 10 Hz. The network tracks large\nangular targets (60\u25e6) within 1 sec with a 10% RMS error. We study the navigational\nability of our model for foraging and target localization tasks in a forest of obstacles\nand show that it requires less than 200X spike-triggered decisions, while suffering\nless than 1% loss in performance compared to a proportional-integral-derivative\ncontroller, in the presence of 50% additive noise. Superior performance can be\nobtained at a higher average spike rate of 100 Hz and 1000 Hz, but even the acceler-\nated networks require 20X and 10X lesser decisions respectively, demonstrating the\nsuperior computational ef\ufb01ciency of bio-inspired information processing systems.\n\n1\n\nIntroduction\n\nOne of the most remarkable engineering marvels of nature is the ability of many species such as\nbats, toothed whales and dolphins to navigate and identify preys and predators by echolocation, i.e.,\nemit sounds with complex characteristics, and use neural circuits to discern the location, velocity\nand features of obstacles or targets based on the echo of the signal. Echolocation problem can be\nsub-divided into estimating range, height and azimuth angle of objects in the environment. These\ncoordinates are resolved by the bat using separate mechanisms and networks [1, 2]. While the bat\u2019s\nheight detection capability is obtained through the unique structure of its ear that creates patterns\nof interference in the spectrum of incoming echoes [3], the coordinates of range and azimuth are\nestimated using specialized neural networks [1, 2].\nArti\ufb01cial neural networks are of great engineering interest, as they are suitable for a wide variety\nof autonomous data analytics applications [4]. In spite of their impressive successes in solving\ncomplex cognitive tasks [5], the commonly used neuronal and synaptic models today do not capture\nthe most crucial aspects of the animal brain where neuronal signals are encoded and transmitted as\nspikes or action potentials and the synaptic strength which encodes memory and other computational\ncapabilities is adjusted autonomously based on the time of spikes [6, 7]. Spiking neural networks\n(SNNs) are believed to be computationally more ef\ufb01cient than their second-generation counterparts[8].\nBat\u2019s echolocation behavior has two distinct attributes \u2013 prey catching and random foraging. It is\nbelieved that an \u2018azimuth echolocation network\u2019 in the bat\u2019s brain plays a major role in helping it to\nforage randomly as it enables obstacle detection and avoidance, while a \u2018range detection network\u2019\nhelps in modulating the sonar vocalizations of the bat which enable better detection, tracking and\ncatching of prey [1, 2]. In this paper, we focus on the relatively simple azimuth detection network of\nthe greater horseshoe bat to develop a SNN for object tracking and navigation.\n\n30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain.\n\n\fFigure 1: Schematic diagram of the navigation system based on a spiking neural network (SNN) for\nazimuth detection, inspired by bat echolocation. The two input sensors (mimicking the ears), encode\nincoming sound signals as spike arrival rates which is used by the SNN to generate output spikes that\ncontrols the head aim. Spikes from the top channel induces an anti-clockwise turn, and the bottom\nchannel induces a clockwise turn. Thus, the head-aim is directed towards maximum intensity. We\nuse small-head approximation (i.e., Rl = Rr, \u03b1l = \u03c0/2 \u2212 \u03b8 and \u03b1r = \u03c0/2 + \u03b8).\n\n2 System Design\n\nWe now discuss the broad overview of the design of our azimuth detection network and the navigation\nsystem, and the organization of the paper. The functioning of our echolocation based navigation\nmodel can be divided into \ufb01ve major parts. Figure 1 illustrates these parts along with a model of the\ntracking head and the object to be detected. Firstly, we assume that all objects in the environment\nemit sound isotropically in all our simulations. This mimics the echo signal, and is assumed to be\nof the same magnitude for simplicity. Let the intensity of an arbitrary source be denoted as Is. We\nassume that the intensity decays in accordance with an inverse square dependence on the distance\nfrom the source. Hence, the intensity at the ears (sensors) at a distance Rl and Rr will be given as\n\nIl =\n\nIs\nR2\nl\n\nIr =\n\nIs\nR2\nr\n\n(1)\n\nThe emitted sound travels through the environment where it is corrupted with noise and falls on the\nreceivers (bat\u2019s ears). In our model, the two receivers are positioned symmetric to the head aim,\n180\u25e6 apart. Like most mammals, we rely on sound signal received at the two receivers to determine\nazimuth information [1]. By distinguishing the sound signals received at the two receivers, the\nnetwork formulates a direction for the potential obstacle or target that is emitting the signal.\nIn our model, we use a cardioid angular gain function as input sensor, described in detail in Section 3.\nWe \ufb01lter incoming sound signals using the cardioid, which are then translated to spike domain and\nforwarded to the azimuth detection network. The SNN we design (Section 4) is inspired by several\nstudies that have identi\ufb01ed the different neurons that are part of the bat\u2019s azimuth detection network\nand how they are inter-connected [1], [2]. We have critically analyzed the internal functioning of this\nbiological network and identi\ufb01ed components that enable the network to function effectively.\nThe spiking neural network that processes the input sound signals generates an output spike train\nwhich determines the direction in which the head-aim of our arti\ufb01cial bat should turn to avoid\nobstacles or track targets. The details of this dynamics are discussed in Section 5. We evaluate the\nperformance of our system in the presence of ambient noise by adding slowly varying noise signals\nto the input (section 6). The simulation results are discussed in Section 7, and the performance of the\nmodel evaluated in Section 8, before summarizing our conclusions.\n\n3\n\nInput and Receiver Modeling\n\nThe bat has two ears to record the incoming signal and like most mammals relies on them for\nidentifying the differences at these two sensors to detect azimuth information [1]. These differences\ncould either be in the time of arrival or intensity of signal detected at the two ears. Since the bat\u2019s\nhead is small (and the ears are only about 1\u2212 2 cm apart) the interaural time difference (ITD), de\ufb01ned\nas the time difference of echo arrival at the two ears, is very small [9]. Hence, the bat relies on\nmeasurement of the interaural level difference (ILD), also known as interaural intensity difference\n\n2\n\nAUDIO SOURCE NOISE SENSOR 1 LEFT EAR SENSOR 2 RIGHT EAR NETWORK 8-Neurons DYNAMICS SPATIAL PARAMETERS f(\ud835\udf3d,\ud835\udc79\ud835\udc93) SPATIAL PARAMETERS f(\ud835\udf3d,\ud835\udc79\ud835\udc8d) SPIKES \ud835\udc85\ud835\udf3d\ud835\udc85\ud835\udc95=\ud835\udc88(\ud835\udc7a\ud835\udc91\ud835\udc8a\ud835\udc8c\ud835\udc86\ud835\udc94) \ud835\udc85\ud835\udf3d \ud835\udc85\ud835\udf3d \ud835\udf3d HEAD AIM LEFT EAR RIGHT EAR Rl AUDIO SOURCE HEAD Rr \ud835\udf36\ud835\udc8d \ud835\udf36\ud835\udc93 \f(a)\n\n(b)\n\nFigure 2: a) The Interaural Level Difference, de\ufb01ned as relative intensity of input signals received at\nthe two sensors in the bat is strongly correlated with the azimuth deviation between the sound source\nand the head aim. Adapted from [9]. b) In our model, sensitivity of the sensor (in dB) as a function\nof the angle with source obeys cardioid dependence (readily available in commercial sensors).\n\n(IID) for azimuth angle detection. As shown in Figure 2a, the ILD signal detected by the ears is a\nstrong function of the azimuth angle; our network is engineered to mimic this characteristic feature.\nIn most animals, the intensity of the signal detected by the ear depends on the angle between the ear\nand the source; this arises due to the directionality of the ear. To model this feature of the receiver, we\nuse a simple cardioid based receiver gain function as shown in Figure 2b, which is the most common\ngain characteristic of audio sensors available in the market. Hence, if \u03b1r/l is the angle between the\nsource and the normal to the right/left ear, the detected intensity is given as\n\nId,r/l = Ir/l \u00d7 10\u22121+cos(\u03b1r/l)\n\n(2)\n\nWe model the output of the receiver as a spike stream, whose inter-arrival rate, \u03bb encodes this \ufb01ltered\nintensity information\n\n\u03bbr/l = kId,r/l\n\n(3)\n\nwhere k is a proportionality constant chosen to ensure a desired average spiking rate in the network.\nWe chose two different encoding schemes for our network. In the uniform signal encoding scheme,\nthe inter-arrival time of the spikes at the output of the receiver is a constant and equal to 1/\u03bb. In the\nPoisson signal encoding scheme, we assume that the spikes are generated according to a Poisson\nprocess with an inter-arrival rate equal to \u03bb. Poisson source represents a more realistic version of\nan echo signal observed in biological settings. In order to update the sound intensity space seen by\nthe bat as it moves, we sample the received sound intensity (Id,r/l) for a duration of 300 ms at every\n450 ms. The fallow 150 ms between the sampling periods allows the bat to process received signals,\nand reduces interference between consecutive samples.\n\n4 Spiking Neural Network Model\n\nFigure 3a shows our azimuth detection SNN inspired by the bat. It consists of 16 sub-networks whose\nspike outputs are summed up to generate the network output. In each sub-network, Antroventral\nCochlear Nucleus (AVCN) neurons receive the input signal translated to spike domain from the\nfront-end receiver as modeled above and deliver it to Lateral Superior Olive (LSO) neurons. Except\nfor the synaptic weights from AVCN layer to LSO layer, the 16 sub-networks are identical. The left\nLSO neuron further projects excitatory synapses to the right Dorsal Nucleus of Lateral Lemniscus\n(DNLL) neuron and to the right Inferior Colliculus (IC) neuron and inhibitory synapses to the left\nDNLL and IC neurons. Additionally, inhibitory synapses connect the DNLL neurons to both IC\nneurons which also inhibit each other. The AVCN and IC neurons trigger navigational decisions.\nMinor variations in the spike patterns at the input of multi-layered spiking neural networks could result\nin vastly divergent spiking behaviors at the output due to the rich variations in synaptic dynamics.\nTo avoid this, we use 16 clone networks which are identical except for the weights of synapse from\nAVCN layer to LSO layer (which are incremented linearly for each clone). These clones operate in\n\n3\n\n\f(a)\n\n(b)\n\nFigure 3: (a) Our azimuth detection SNN consists of 16 sub-networks whose spike outputs are\nsummed up to generate the network output. Except for the synaptic weights from AVCN layer to\nLSO layer, sub-networks are identical (see Supplementary Materials). Higher spike rate at the left\ninput results in higher output spike rate of neurons N1 and N8. (b) Top panel shows normalized\nresponse of the SNN with impulses presented to input neuron N1 at t = 50 ms and N2 at t = 150 ms.\nBottom panel shows that the output spike rate difference of our SNN mimics that in Figure 2a.\n\nparallel and the output spike stream of the left and right IC neurons are merged for the 16 clones,\ngenerating the net output spike train of the network.\nWe use the adaptive exponential integrate and \ufb01re model for all our neurons as they can exhibit\ndifferent kinds of spiking behavior seen in biological neurons [10]. All the neurons implemented in\nour model are regular spiking (RS), except the IC layer neurons which are chattering neurons (CH).\nCH neurons aggregate the input variations over a period and then produce brisk spikes for a \ufb01xed\nduration, thereby improving accuracy. The weights for the various excitatory and inhibitory synapses\nhave been derived by parameter space exploration. The selected values enable the network to operate\nfor the range of spike frequencies considered and allows spike responses to propagate through the\ndepth of the network (All simulation parameters are listed in Supplementary Materials).\nAn exemplary behavior of the network corresponding to short impulses received by AVCNleft at\nt = 50 ms and by AVCNright at t = 150 ms is shown in Figure 3b. If \u03bbright of a particular sound input\nis higher than \u03bbleft, the right AVCN neuron will have a higher spiking rate than its left counterpart.\nThis in turn induces a higher spiking rate in the right LSO neuron, while at the same time suppressing\nthe spikes in left LSO neuron. Thereafter, the LSO neurons excite spikes in the opposite DNLL and\nIC neurons, while suppressing any spikes on the DNLL and IC neurons on its side. Consequently, an\ninput signal with higher \u03bbright will produce a higher spike rate at the left IC neuron.\nIt has been proposed that the latter layers enable extraction of useful information by correlating\nthe past input signals with the current input signals [11]. The LSO neuron that sends excitatory\nsignals to an IC neuron also inhibits the DNLL neuron which suppresses IC neuron. Inhibition\nof DNLL neuron lasts for a few seconds even after the input signal stops. Consequently, for a\nshort period, the IC neuron receives reduced inhibition. Lack of inhibition changes the network\u2019s\nresponse to future input signals. Hence, depending on the recent history of signals received, the\noutput spike difference may vary for the same instantaneous input, thus enabling the network to\nexhibit proportional-integral-derivative controller like behavior. Figure 4 highlights this feature.\n\n4\n\n\f(a)\n\n(b)\n\n(c)\n\nFigure 4: Spike response of the network (blue) depends not only on the variations in the present input\n(red) but also on its past history, akin to a proportional-integral-derivative controller. Input spike\ntrains are fed to neurons N1 and N2. Choosing the input spikes in (a) as reference, in (b) second half\nof the input pattern is modi\ufb01ed, whereas in (c) \ufb01rst half of the input pattern is modi\ufb01ed.\n\n5 Head-Rotation Dynamics\n\nThe difference in the spike rate of the two output neurons generated by the network indicates angular\ndeviation between the head-aim and the object detected (Figure 3b). In order to orient the tracking-\nhead in the direction of maximum sound intensity, the head-aim is rotated by a pre-speci\ufb01ed angle\nfor every spike, de\ufb01ned as the Angle of Rotation (AoR). AoR is a function of the operating spike\nfrequency of the network and the nature of input source coding (Poisson/Uniform). It is an engineered\nparameter obtained by minimizing RMS error during constant angle tracking. We have provided AoR\nvalues for a range of SNN frequency operation also ensuring that AoR chosen can be achieved by\ncommercial motors (Details in Supplementary Materials).\nIn a biological system, not every spike will necessarily cause a head turn as information transmission\nthrough the neuromuscular junction is stochastic in nature. To model this, we specify that an AoR\nturn is executed according to a probability model given as\n\n\u02d9\u03b8 = [(sl \u2212 sr)pi \u2212 (rl \u2212 rr)pj] AoR\n\n(4)\nwhere sl,r is 1 if spike is issued in left (or right) IC neuron and 0 otherwise and rl,r is 1 if a spike is\nissued in left (or right) AVCN neurons. pi and pj are Bernoulli random variables (with mean values\n(cid:104)pi(cid:105) = 0.5 and (cid:104)pj(cid:105) = 0.0005) denoting the probability that an output and input spike causes a turn\nrespectively. The direction and amplitude of the turn is naturally encoded in the spike rates of output\nand input neurons. The sign of rl \u2212 rr is opposite to sl \u2212 sr as a higher spike rate in right (or left)\nAVCN layer implies higher spike rate in left (or right) IC layer and hence they should have same\ncausal effect on head aim. We have assigned our \u2018arti\ufb01cial bat\u2019 a \ufb01xed speed of 15 mph (6.8 m/s)\nconsistent with biologically observed bat speeds [12].\n\n6 Noise Modeling\n\nIn order to study the impact of realistic noisy environments on the performance of our network, we\nincorporate noise in our simulations by adding a slowly varying component to the source sound\nIntensity, Is. Hence, (3) is modi\ufb01ed as\n\n(5)\nwhere n is obtained by low-pass \ufb01ltering uniform noise. Also note that for Poisson input source\nencoding, since we are sampling a random signal for a \ufb01xed duration, large variations in the stimulus\nspike count is possible for the same values of input intensity. We will study the effect of the above\nadditive uniform noise for both encoding schemes.\n\n\u03bbr/l = k(Id,r/l + n)\n\n7 Simulation Results\n\nWe \ufb01rst show our system\u2019s response to a stair-case input, i.e., the source is moving along a circle with\nthe \u2018bat\u2019 \ufb01xed at the center, but free to turn along the central axis (Figure 5). It can be seen that the\nnetwork performs reasonably well in tracking the moving source within a second.\n\n5\n\n\fFigure 5: Response of the azimuth tracking network for time varying staircase input for Poisson input\nencoding at 10 Hz operating frequency.\n\nWe now study the step response of our SNN based azimuth tracking system for both uniform and\nPoisson source encoding schemes at various operating frequencies of the network, with and without\nadditive noise (Figure 6). To quantify the performance of our system, we report the following two\nmetrics: (a) Time of Arrival (ToA) which is the \ufb01rst time when the head aim comes within 5% of\ntarget head aim (source angle); and (b) RMS error in head aim measured in the interval [ToA, 4.5 s].\nAt t = 0, the network starts tracking a stationary source placed at \u221260\u25e6; the ToA is \u223c 1 s in all cases,\neven in the presence of 50% additive noise. The trajectories for 1 kHz Poisson encoding is superior to\nthat corresponding to its low frequency counterpart. At low frequencies, there are not enough spikes\nto distinguish between small changes in angles as the receiver\u2019s sampling period is only 300 ms. It\nis possible to tune the system to have much better RMS error by increasing the sampling period\nor decreasing AoR, but at the cost of larger ToA. Our design parameters are chosen to mimic the\nbiologically observed ToA while minimizing the RMS error [13]. We observed that uniform source\nencoding performs better than Poisson encoding in terms of average jitter after ToA, as there is no\nsampling noise present in former.\n\n(a) Poisson source 10 Hz\n\n(b) Poisson source 1 kHz\n\n(c) Uniform source 1 kHz\n\n(d) Poisson source 10 Hz, 50% noise (e) Poisson source 1 kHz, 50% noise (f) Uniform source 1kHz,50% noise\nFigure 6: Step response of our SNN based azimuth tracking system, for \ufb01ve different exemplary\ntracks for different input signal encoding schemes, network frequencies and input noise levels. At\nt = 0, the network starts tracking a stationary source placed at \u221260\u25e6. The time taken to reach within\n5% of the target angle, denoted as Time of Arrival (ToA), is \u223c 1 s for all cases.\n\nWe expect RMS error to increase with decrease in operation frequency and increase in percentage\nchannel noise. Figure 7a clearly shows this behavior for uniform source encoding. With no additive\nnoise (pink label), the RMS error decreases with increase in frequency. Although RMS error remains\nalmost constant with varying noise level for 10 Hz (in terms of median error and variance in error),\nit clearly increases for 1 kHz case. This can be attributed to the fact that since our \u2018arti\ufb01cial bat\u2019\nmoves whenever a spike occurs, at lower frequency, the network itself \ufb01lters the noise by using it\u2019s\nslowly varying nature and averaging it. At higher frequencies, this averaging effect is reduced making\n\n6\n\n\f(a) RMS error, Uniform source encoding\n\n(b) RMS error, Poisson source encoding\n\nFigure 7: a) RMS error in head aim for Uniform source encoding measured after the ToA during\ntracking a constant target angle in response to varying noise levels. At zero noise, increasing the\nfrequency improves performance due to \ufb01ne-grained decisions. However, in the presence of additive\nnoise, increasing the frequency worsens the RMS error, as more error-prone decisions are likely. b)\nRMS error with Poisson source encoding: at zero noise, an increase in operation frequency reduces\nthe RMS error but compared to Figure 7a, the performance even at 1 kHz is unaffected by noise.\n\nthe trajectory more susceptible to noise. A trade-off can be seen for 50% noise (red label), where\naddition of noise is more dominating and hence the system performs worse when operated at higher\nfrequencies. Figure 7b reports the frequency dependence of the RMS error for the Poisson encoding\nscheme. Performance improves with increase in operation frequency as before, but the effect of added\nnoise is negligible even at 50% additive noise, showing that this scheme is more noise resilient. It\nshould however be noted that performance of Poisson is at best equal to that of uniform encoding.\n\n8 Performance Evaluation\n\nTo test the navigational ef\ufb01ciency of our design, we test its ability to track down targets while avoiding\nobstacles on its path in a 2D arena (120 \u00d7 120 m). The target and obstacles are modeled as a point\nsources which emit \ufb01xed intensity sound signals. Net detected intensity due to these sources is\ncalculated as a linear superposition of all the intensities by modifying (2) as\n\nId =\n\n\u00d7 10\u22121+cos(\u03b1t) +\n\nIt\nR2\nt\n\n\u00d7 10\u22121+cos(\u03c0+\u03b1o)\n\nIo\nR2\no\n\n(6)\n\n(cid:88)\n\nt\n\n(cid:88)\n\no\n\nwhere subscript t refers to targets and o to obstacles. Choosing the effective angle of the obstacles as\n\u03c0 + \u03b1o has the effect of steering the \u2018bat\u2019 180\u25e6 away from the obstacles. There are approximately 10\nobstacles for every target in the arena placed at random locations.\nNeurobiological studies have identi\ufb01ed a range detection network which determines the modulation\nof bat\u2019s voice signal depending on the distance to its prey [1]. Our model does not include it; we\nreplace the process of the bat generating sound signals and receiving echoes after re\ufb02ection from\nsurrounding objects, by the targets and obstacles themselves emitting sound signals isotropically. It\nis known that the bat can differentiate between prey and obstacles by detecting slight differences in\ntheir echoes [14]. This ability is aided by specialized neural networks in bat\u2019s nervous system. Since\nour \u2018arti\ufb01cial bat\u2019 employs a network which detects azimuth information, we model it arti\ufb01cially.\nTo benchmark the ef\ufb01ciency of our SNN based navigation model, we compare it with the performance\nof a particle that obeys standard second-order PID control system dynamics governed by the equation\n\nd2(\u03b8 \u2212 \u03b8t)\n\ndt2\n\nd(\u03b8 \u2212 \u03b8t)\n\ndt\n\n+ k1\n\n+ k2(\u03b8 \u2212 \u03b8t) = 0\n\n(7)\n\nThe particle calculates a target angle \u03b8t, which is chosen to be the angle at which the net detected\nintensity calculated using (6) is a maximum. This calculation is performed periodically (every 450 ms,\nSNN sampling period). The above PID controller thus tries to steer the instantaneous angle of the\nparticle \u03b8 towards the desired target angle. The parameters k1 and k2 (Refer Supplementary material)\nhave been chosen to match the rise-time and overshoot characteristics of the SNN-model.\nIn order to compare performance under noisy conditions we add 50% slow varying noise to the sound\nsignal emitted by targets and obstacles as explained in Section 6. We simulate the trajectory for\n\n7\n\n\f18 s (40 sampling periods of the bat) and report the number of successful cases where the particle\n\u2018reached\u2019 the target without \u2018running\u2019 into any obstacles (i.e., particle-target separation was less than\n2 m and particle-obstacle separation was always more than 2 m). Table 1 summarizes the results\nfor these scenarios - the SNN model operating at 1000 Hz has signi\ufb01cantly higher % Success and\ncomparable average success time, though the PID particle is highly ef\ufb01cient in avoiding obstacles.\n\nTable 1: Performance Validation Results\n\n% Success\n\nAvg. success time (sec)\n\n% No-collision\n\n% Obstacle\n\nSNN 1 kHz\n\n68\n2.4\n29.6\n6.27\n\nSNN 100 Hz\n\n66.2\n3.6\n30.2\n6.66\n\nSNN 10 Hz\n\n28.4\n21.6\n50\n6.68\n\nPID\n29.13\n60.86\n\n10\n5.08\n\nTo compare the computational effort of these approaches, we de\ufb01ne \u2018number of decisions\u2019 as number\nof changes made in head aim while navigating. The SNN model utilizes 220X times less number of\ndecisions while suffering < 1% decrease in % Success and a 31.5% increase in average success time\nas compared to PID particle. Our network when operated at 100Hz (1000Hz) still retains its ef\ufb01ciency\nin terms of decision making as it incurs 20 (10) times lesser decisions respectively, as compared to\nthe PID particle while achieving much higher % Success. A closer look at the trajectories traced by\nthe bat and the PID particle shows that the PID particle has a tendency to get stuck in local maxima\nof sound intensity space, explaining why it shows high % No-collision but poor foraging (Figure 8b).\n\n(a)\n\n(b)\n\nFigure 8: a) At 50% slowly-varying additive noise, our network requires up to 220x lesser spike-\ntriggered decisions, while suffering less than 1% loss in performance compared to a PID control\nalgorithm. Superior performance can be obtained at a higher spike rate of \u223c 100 Hz and \u223c 1000 Hz,\nbut even the accelerated networks requires 20x and 10x lesser decisions respectively (a decision\ncorresponds to a change in the head aim). b) Exemplary tracks traced by the SNN (blue) and the PID\nparticle (black) in a forest of obstacles (red dots) with sparse targets (green dots).\n\n9 Conclusion\n\nWe have devised an azimuth detection spiking neural network for navigation and target tracking,\ninspired by the echolocating bat. Our network can track large angular targets (60\u25e6) within 1 sec\nwith a 10% mean RMS error, capturing the main features of observed biological behavior. Our\nnetwork performance is highly resilient to additive noise in the input and exhibits ef\ufb01cient decision\nmaking while navigating and tracking targets in a forest of obstacles. Our SNN based model that\nmimics several aspects of information processing of biology requires less than 200X decisions while\nsuffering < 1% loss in performance, compared to a standard proportional-integral-derivative based\ncontrol. We thus demonstrate that appropriately engineered neural information processing systems\ncan outperform conventional control algorithms in real-life noisy environments.\n\nAcknowledgments\n\nThis research was supported in part by the CAMPUSENSE project grant from CISCO Systems Inc.\n\n8\n\n\fReferences\n[1] C. F. Moss and S. R. Sinha. Neurobiology of echolocation in bats. 13(6):751\u20138, 2003.\n\n[2] N. Suga. Biosonar and neural computation in bats. 262(6):60\u20138, 1990.\n\n[3] Ferragamo M. J. Simmons J. A. Wotton J. M., Haresign T. Sound source elevation and external\near cues in\ufb02uence the discrimination of spectral notches by the big brown bat, Eptesicus fuscus.\n100(3):1764\u201376, 1996.\n\n[4] Y. Bengio Y. LeCun and G. Hinton. 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