nips nips2009 nips2009-200 knowledge-graph by maker-knowledge-mining

200 nips-2009-Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)

Source: pdf

Author: Tao Hu, Anthony Leonardo, Dmitri B. Chklovskii

Abstract: One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. Reconstructing a large neural circuit using such a “brute force” approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron’s voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. To reconstruct these synaptic connections from the recorded voltage we apply a decoding algorithm recently developed for compressive sensing. Compared to the brute force approach, our method promises significant time savings that grow with the size of the circuit. We use computer simulations to find optimal stimulation parameters and explore the feasibility of our reconstruction method under realistic experimental conditions including noise and non-linear synaptic integration. Multineuronal stimulation allows reconstructing synaptic connectivity just from the spiking activity of post-synaptic neurons, even when sub-threshold voltage is unavailable. By using calcium indicators, voltage-sensitive dyes, or multi-electrode arrays one could monitor activity of multiple postsynaptic neurons simultaneously, thus mapping their synaptic inputs in parallel, potentially reconstructing a complete neural circuit. 1 In tro d uc tio n Understanding information processing in neural circuits requires systematic characterization of synaptic connectivity [1, 2]. The most direct way to measure synapses between a pair of neurons is to stimulate potentially pre-synaptic neuron while recording intra-cellularly from the potentially post-synaptic neuron [3-8]. This method can be scaled to reconstruct multiple synaptic connections onto one neuron by combining intracellular recordings from the postsynaptic neuron with photo-activation of pre-synaptic neurons using glutamate uncaging [913] or channelrhodopsin [14, 15], or with multi-electrode arrays [16, 17]. Neurons are sequentially stimulated to fire action potentials by scanning a laser beam (or electrode voltage) over a brain slice, while synaptic weights are measured by recording post-synaptic voltage. Although sequential excitation of single potentially pre-synaptic neurons could reveal connectivity, such a “brute force” approach is inefficient because the connectivity among neurons is sparse. Even among nearby neurons in the cerebral cortex, the probability of connection is only about ten percent [3-8]. Connection probability decays rapidly with the 1 distance between neurons and falls below one percent on the scale of a cortical column [3, 8]. Thus, most single-neuron stimulation trials would result in zero response making the brute force approach slow, especially for larger circuits. Another drawback of the brute force approach is that single-neuron stimulation cannot be combined efficiently with methods allowing parallel recording of neural activity, such as calcium imaging [18-22], voltage-sensitive dyes [23-25] or multi-electrode arrays [17, 26]. As these techniques do not reliably measure sub-threshold potential but report only spiking activity, they would reveal only the strongest connections that can drive a neuron to fire [2730]. Therefore, such combination would reveal only a small fraction of the circuit. We propose to circumvent the above limitations of the brute force approach by stimulating multiple potentially pre-synaptic neurons simultaneously and reconstructing individual connections by using a recently developed method called compressive sensing (CS) [31-35]. In each trial, we stimulate F neurons randomly chosen out of N potentially pre-synaptic neurons and measure post-synaptic activity. Although each measurement yields only a combined response to stimulated neurons, if synaptic inputs sum linearly in a post-synaptic neuron, one can reconstruct the weights of individual connections by using an optimization algorithm. Moreover, if the synaptic connections are sparse, i.e. only K << N potentially pre-synaptic neurons make synaptic connections onto a post-synaptic neuron, the required number of trials M ~ K log(N/K), which is much less than N [31-35]. The proposed method can be used even if only spiking activity is available. Because multiple neurons are driven to fire simultaneously, if several of them synapse on the post-synaptic neuron, they can induce one or more spikes in that neuron. As quantized spike counts carry less information than analog sub-threshold voltage recordings, reconstruction requires a larger number of trials. Yet, the method can be used to reconstruct a complete feedforward circuit from spike recordings. Reconstructing neural circuit with multi-neuronal excitation may be compared with mapping retinal ganglion cell receptive fields. Typically, photoreceptors are stimulated by white-noise checkerboard stimulus and the receptive field is obtained by Reverse Correlation (RC) in case of sub-threshold measurements or Spike-Triggered Average (STA) of the stimulus [36, 37]. Although CS may use the same stimulation protocol, for a limited number of trials, the reconstruction quality is superior to RC or STA. 2 Ma pp i ng sy na pti c inp ut s o nto o n e ne uro n We start by formalizing the problem of mapping synaptic connections from a population of N potentially pre-synaptic neurons onto a single neuron, as exemplified by granule cells synapsing onto a Purkinje cell (Figure 1a). Our experimental protocol can be illustrated using linear algebra formalism, Figure 1b. We represent synaptic weights as components of a column vector x, where zeros represent non-existing connections. Each row in the stimulation matrix A represents a trial, ones indicating neurons driven to spike once and zeros indicating non-spiking neurons. The number of rows in the stimulation matrix A is equal to the number of trials M. The column vector y represents M measurements of membrane voltage obtained by an intra-cellular recording from the post-synaptic neuron: y = Ax. (1) In order to recover individual synaptic weights, Eq. (1) must be solved for x. RC (or STA) solution to this problem is x = (ATA)-1AT y, which minimizes (y-Ax)2 if M>N. In the case M << N for a sparse circuit. In this section we search computationally for the minimum number of trials required for exact reconstruction as a function of the number of non-zero synaptic weights K out of N potentially pre-synaptic neurons. First, note that the number of trials depends on the number of stimulated neurons F. If F = 1 we revert to the brute force approach and the number of measurements is N, while for F = N, the measurements are redundant and no finite number suffices. As the minimum number of measurements is expected to scale as K logN, there must be an optimal F which makes each measurement most informative about x. To determine the optimal number of stimulated neurons F for given K and N, we search for the minimum number of trials M, which allows a perfect reconstruction of the synaptic connectivity x. For each F, we generate 50 synaptic weight vectors and attempt reconstruction from sequentially increasing numbers of trials. The value of M, at which all 50 recoveries are successful (up to computer round-off error), estimates the number of trial needed for reconstruction with probability higher than 98%. By repeating this procedure 50 times for each F, we estimate the mean and standard deviation of M. We find that, for given N and K, the minimum number of trials, M, as a function of the number of stimulated neurons, F, has a shallow minimum. As K decreases, the minimum shifts towards larger F because more neurons should be stimulated simultaneously for sparser x. For the explored range of simulation parameters, the minimum is located close to 0.1N. Next, we set F = 0.1N and explore how the minimum number of measurements required for exact reconstruction depends on K and N. Results of the simulations following the recipe described above are shown in Figure 3a. As expected, when x is sparse, M grows approximately linearly with K (Figure 3b), and logarithmically with N (Figure 3c). N = 1000 180 25 160 20 140 120 15 100 10 80 5 150 250 400 650 1000 Number of potential connections (N) K = 30 220 200 (a) 200 220 Number of measurements (M) 30 Number of measurements (M) Number of actual connections (K) Number of necessary measurements (M) (b) 180 160 140 120 100 80 5 10 15 20 25 30 Number of actual connections (K) 210 (c) 200 190 180 170 160 150 140 130 120 2 10 10 3 Number of potential connections (N) Figure 3: a) Minimum number of measurements M required for reconstruction as a function of the number of actual synapses, K, and the number of potential synapses, N. b) For given N, we find M ~ K. c) For given K, we find M ~ logN (note semi-logarithmic scale in c). 4 R o b ust nes s o f re con st r uc t io n s t o noi se a n d v io la tio n o f si m pli fy in g a ss umpt io n s To make our simulation more realistic we now take into account three possible sources of noise: 1) In reality, post-synaptic voltage on a given synapse varies from trial to trial [4, 5, 46-52], an effect we call synaptic noise. Such noise detrimentally affects reconstructions because each row of A is multiplied by a different instantiation of vector x. 2) Stimulation of neurons may be imprecise exciting a slightly different subset of neurons than intended and/or firing intended neurons multiple times. We call this effect stimulation noise. Such noise detrimentally affects reconstructions because, in its presence, the actual measurement matrix A is different from the one used for recovery. 3) A synapse may fail to release neurotransmitter with some probability. Naturally, in the presence of noise, reconstructions cannot be exact. We quantify the 4 reconstruction x − xr l2 = error ∑ N i =1 by the normalized x − xr l2–error l2 / xl , where 2 ( xi − xri ) 2 . We plot normalized reconstruction error in brute force approach (M = N = 500 trials) as a function of noise, as well as CS and RC reconstruction errors (M = 200, 600 trials), Figure 4. 2 0.9 Normalized reconstruction error ||x-x|| /||x|| 1 r 2 For each noise source, the reconstruction error of the brute force approach can be achieved with 60% fewer trials by CS method for the above parameters (Figure 4). For the same number of trials, RC method performs worse. Naturally, the reconstruction error decreases with the number of trials. The reconstruction error is most sensitive to stimulation noise and least sensitive to synaptic noise. 1 (a) 1 (b) 0.9 0.8 (c) 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 0.7 RC: M=200 RC: M=600 Brute force method: M=500 CS: M=200 CS: M=600 0.6 0.5 0 0.05 0.1 0.15 Synaptic noise level 0.2 0.25 0 0.05 0.1 0.15 Stimulation noise level 0.2 0.25 0 0 0.05 0.1 0.15 0.2 0.25 Synaptic failure probability Figure 4: Impact of noise on the reconstruction quality for N = 500, K = 30, F = 50. a) Recovery error due to trial-to-trial variation in synaptic weight. The response y is calculated using the synaptic connectivity x perturbed by an additive Gaussian noise. The noise level is given by the coefficient of variation of synaptic weight. b) Recovery error due to stimulation noise. The matrix A used for recovery is obtained from the binary matrix used to calculate the measurement vector y by shifting, in each row, a fraction of ones specified by the noise level to random positions. c) Recovery error due to synaptic failures. The detrimental effect of the stimulation noise on the reconstruction can be eliminated by monitoring spiking activity of potentially pre-synaptic neurons. By using calcium imaging [18-22], voltage-sensitive dyes [23] or multi-electrode arrays [17, 26] one could record the actual stimulation matrix. Because most random matrices satisfy the reconstruction requirements [31, 34, 35], the actual stimulation matrix can be used for a successful recovery instead of the intended one. If neuronal activity can be monitored reliably, experiments can be done in a different mode altogether. Instead of stimulating designated neurons with high fidelity by using highly localized and intense light, one could stimulate all neurons with low probability. Random firing events can be detected and used in the recovery process. The light intensity can be tuned to stimulate the optimal number of neurons per trial. Next, we explore the sensitivity of the proposed reconstruction method to the violation of simplifying assumptions. First, whereas our simulation assumes that the actual number of connections, K, is known, in reality, connectivity sparseness is known a priori only approximately. Will this affect reconstruction results? In principle, CS does not require prior knowledge of K for reconstruction [31, 34, 35]. For the CoSaMP algorithm, however, it is important to provide value K larger than the actual value (Figure 5a). Then, the algorithm will find all the actual synaptic weights plus some extra non-zero weights, negligibly small when compared to actual ones. Thus, one can provide the algorithm with the value of K safely larger than the actual one and then threshold the reconstruction result according to the synaptic noise level. Second, whereas we assumed a linear summation of inputs [53], synaptic integration may be 2 non-linear [54]. We model non-linearity by setting y = yl + α yl , where yl represents linearly summed synaptic inputs. Results of simulations (Figure 5b) show that although nonlinearity can significantly degrade CS reconstruction quality, it still performs better than RC. 5 (b) 0.45 0.4 Actual K = 30 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 10 20 30 40 50 60 Normalized reconstruction error ||x-x||2/||x|| r 2 Normalized reconstrcution error ||x-x||2/||x|| r 2 (a) 0.9 0.8 0.7 CS RC 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.15-0.12-0.09-0.06-0.03 0 0.03 0.06 0.09 0.12 0.15 Relative strength of the non-linear term α × mean(y ) K fed to CoSaMP l Figure 5: Sensitivity of reconstruction error to the violation of simplifying assumptions for N = 500, K = 30, M = 200, F = 50. a) The quality of the reconstruction is not affected if the CoSaMP algorithm is fed with the value of K larger than actual. b) Reconstruction error computed in 100 realizations for each value of the quadratic term relative to the linear term. 5 Ma pp i ng sy na pti c inp ut s o nto a n e uro na l po pu la tio n Until now, we considered reconstruction of synaptic inputs onto one neuron using subthreshold measurements of its membrane potential. In this section, we apply CS to reconstructing synaptic connections onto a population of potentially post-synaptic neurons. Because in CS the choice of stimulated neurons is non-adaptive, by recording from all potentially post-synaptic neurons in response to one sequence of trials one can reconstruct a complete feedforward network (Figure 6). (a) x p(y=1) A Normalized reconstruction error ||x/||x||2−xr/||xr||2||2 y (b) (c) 100 (d) 500 700 900 1100 Number of spikes 1 STA CS 0.8 0.6 0.4 0.2 0 1000 0 300 3000 5000 7000 9000 Number of trials (M) Ax Figure 6: Mapping of a complete feedforward network. a) Each post-synaptic neuron (red) receives synapses from a sparse subset of potentially pre-synaptic neurons (blue). b) Linear algebra representation of the experimental protocol. c) Probability of firing as a function of synaptic current. d) Comparison of CS and STA reconstruction error using spike trains for N = 500, K = 30 and F = 50. Although attractive, such parallelization raises several issues. First, patching a large number of neurons is unrealistic and, therefore, monitoring membrane potential requires using different methods, such as calcium imaging [18-22], voltage sensitive dyes [23-25] or multielectrode arrays [17, 26]. As these methods can report reliably only spiking activity, the measurement is not analog but discrete. Depending on the strength of summed synaptic inputs compared to the firing threshold, the postsynaptic neuron may be silent, fire once or multiple times. As a result, the measured response y is quantized by the integer number of spikes. Such quantized measurements are less informative than analog measurements of the sub-threshold membrane potential. In the extreme case of only two quantization levels, spike or no spike, each measurement contains only 1 bit of information. Therefore, to achieve reasonable reconstruction quality using quantized measurements, a larger number of trials M>>N is required. We simulate circuit reconstruction from spike recordings in silico as follows. First, we draw synaptic weights from an experimentally motivated distribution. Second, we generate a 6 random stimulation matrix and calculate the product Ax. Third, we linear half-wave rectify this product and use the result as the instantaneous firing rate for the Poisson spike generator (Figure 6c). We used a rectifying threshold that results in 10% of spiking trials as typically observed in experiments. Fourth, we reconstruct synaptic weights using STA and CS and compare the results with the generated weights. We calculated mean error over 100 realizations of the simulation protocol (Figure 6d). Due to the non-linear spike generating procedure, x can be recovered only up to a scaling factor. We propose to calibrate x with a few brute-force measurements of synaptic weights. Thus, in calculating the reconstruction error using l2 norm, we normalize both the generated and recovered synaptic weights. Such definition is equivalent to the angular error, which is often used to evaluate the performance of STA in mapping receptive field [37, 55]. Why is CS superior to STA for a given number of trials (Figure 6d)? Note that spikeless trials, which typically constitute a majority, also carry information about connectivity. While STA discards these trials, CS takes them into account. In particular, CoSaMP starts with the STA solution as zeroth iteration and improves on it by using the results of all trials and the sparseness prior. 6 D i s c uss ion We have demonstrated that sparse feedforward networks can be reconstructed by stimulating multiple potentially pre-synaptic neurons simultaneously and monitoring either subthreshold or spiking response of potentially post-synaptic neurons. When sub-threshold voltage is recorded, significantly fewer measurements are required than in the brute force approach. Although our method is sensitive to noise (with stimulation noise worse than synapse noise), it is no less robust than the brute force approach or RC. The proposed reconstruction method can also recover inputs onto a neuron from spike counts, albeit with more trials than from sub-threshold potential measurements. This is particularly useful when intra-cellular recordings are not feasible and only spiking can be detected reliably, for example, when mapping synaptic inputs onto multiple neurons in parallel. For a given number of trials, our method yields smaller error than STA. The proposed reconstruction method assumes linear summation of synaptic inputs (both excitatory and inhibitory) and is sensitive to non-linearity of synaptic integration. Therefore, it is most useful for studying connections onto neurons, in which synaptic integration is close to linear. On the other hand, multi-neuron stimulation is closer than single-neuron stimulation to the intrinsic activity in the live brain and can be used to study synaptic integration under realistic conditions. In contrast to circuit reconstruction using intrinsic neuronal activity [56, 57], our method relies on extrinsic stimulation of neurons. Can our method use intrinsic neuronal activity instead? We see two major drawbacks of such approach. First, activity of non-monitored presynaptic neurons may significantly distort reconstruction results. Thus, successful reconstruction would require monitoring all active pre-synaptic neurons, which is rather challenging. Second, reliable reconstruction is possible only when the activity of presynaptic neurons is uncorrelated. Yet, their activity may be correlated, for example, due to common input. We thank Ashok Veeraraghavan for introducing us to CS, Anthony Leonardo for making a retina dataset available for the analysis, Lou Scheffer and Hong Young Noh for commenting on the manuscript and anonymous reviewers for helpful suggestions. References [1] Luo, L., Callaway, E.M. & Svoboda, K. (2008) Genetic dissection of neural circuits. Neuron 57(5):634-660. [2] Helmstaedter, M., Briggman, K.L. & Denk, W. (2008) 3D structural imaging of the brain with photons and electrons. Current opinion in neurobiology 18(6):633-641. [3] Holmgren, C., Harkany, T., Svennenfors, B. & Zilberter, Y. (2003) Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. Journal of Physiology 551:139-153. [4] Markram, H. (1997) A network of tufted layer 5 pyramidal neurons. Cerebral Cortex 7(6):523-533. 7 [5] Markram, H., Lubke, J., Frotscher, M., Roth, A. & Sakmann, B. (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. Journal of Physiology 500(2):409-440. [6] Thomson, A.M. & Bannister, A.P. (2003) Interlaminar connections in the neocortex. Cerebral Cortex 13(1):5-14. [7] Thomson, A.M., West, D.C., Wang, Y. & Bannister, A.P. (2002) Synaptic connections and small circuits involving excitatory and inhibitory neurons in layers 2-5 of adult rat and cat neocortex: triple intracellular recordings and biocytin labelling in vitro. Cerebral Cortex 12(9):936-953. [8] Song, S., Sjostrom, P.J., Reigl, M., Nelson, S. & Chklovskii, D.B. (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. Plos Biology 3(3):e68. [9] Callaway, E.M. & Katz, L.C. (1993) Photostimulation using caged glutamate reveals functional circuitry in living brain slices. Proceedings of the National Academy of Sciences of the United States of America 90(16):7661-7665. [10] Dantzker, J.L. & Callaway, E.M. (2000) Laminar sources of synaptic input to cortical inhibitory interneurons and pyramidal neurons. Nature Neuroscience 3(7):701-707. [11] Shepherd, G.M. & Svoboda, K. (2005) Laminar and columnar organization of ascending excitatory projections to layer 2/3 pyramidal neurons in rat barrel cortex. Journal of Neuroscience 25(24):5670-5679. [12] Nikolenko, V., Poskanzer, K.E. & Yuste, R. (2007) Two-photon photostimulation and imaging of neural circuits. Nature Methods 4(11):943-950. [13] Shoham, S., O'connor, D.H., Sarkisov, D.V. & Wang, S.S. (2005) Rapid neurotransmitter uncaging in spatially defined patterns. Nature Methods 2(11):837-843. [14] Gradinaru, V., Thompson, K.R., Zhang, F., Mogri, M., Kay, K., Schneider, M.B. & Deisseroth, K. (2007) Targeting and readout strategies for fast optical neural control in vitro and in vivo. Journal of Neuroscience 27(52):14231-14238. [15] Petreanu, L., Huber, D., Sobczyk, A. & Svoboda, K. (2007) Channelrhodopsin-2-assisted circuit mapping of long-range callosal projections. Nature Neuroscience 10(5):663-668. [16] Na, L., Watson, B.O., Maclean, J.N., Yuste, R. & Shepard, K.L. (2008) A 256×256 CMOS Microelectrode Array for Extracellular Neural Stimulation of Acute Brain Slices. Solid-State Circuits Conference, 2008. ISSCC 2008. Digest of Technical Papers. IEEE International. [17] Fujisawa, S., Amarasingham, A., Harrison, M.T. & Buzsaki, G. (2008) Behavior-dependent shortterm assembly dynamics in the medial prefrontal cortex. Nature Neuroscience 11(7):823-833. [18] Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D. & Yuste, R. (2004) Synfire chains and cortical songs: temporal modules of cortical activity. Science 304(5670):559-564. [19] Ohki, K., Chung, S., Ch'ng, Y.H., Kara, P. & Reid, R.C. (2005) Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433(7026):597-603. [20] Stosiek, C., Garaschuk, O., Holthoff, K. & Konnerth, A. (2003) In vivo two-photon calcium imaging of neuronal networks. Proceedings of the National Academy of Sciences of the United States of America 100(12):7319-7324. [21] Svoboda, K., Denk, W., Kleinfeld, D. & Tank, D.W. (1997) In vivo dendritic calcium dynamics in neocortical pyramidal neurons. Nature 385(6612):161-165. [22] Sasaki, T., Minamisawa, G., Takahashi, N., Matsuki, N. & Ikegaya, Y. (2009) Reverse optical trawling for synaptic connections in situ. Journal of Neurophysiology 102(1):636-643. [23] Zecevic, D., Djurisic, M., Cohen, L.B., Antic, S., Wachowiak, M., Falk, C.X. & Zochowski, M.R. (2003) Imaging nervous system activity with voltage-sensitive dyes. Current Protocols in Neuroscience Chapter 6:Unit 6.17. [24] Cacciatore, T.W., Brodfuehrer, P.D., Gonzalez, J.E., Jiang, T., Adams, S.R., Tsien, R.Y., Kristan, W.B., Jr. & Kleinfeld, D. (1999) Identification of neural circuits by imaging coherent electrical activity with FRET-based dyes. Neuron 23(3):449-459. [25] Taylor, A.L., Cottrell, G.W., Kleinfeld, D. & Kristan, W.B., Jr. (2003) Imaging reveals synaptic targets of a swim-terminating neuron in the leech CNS. Journal of Neuroscience 23(36):11402-11410. [26] Hutzler, M., Lambacher, A., Eversmann, B., Jenkner, M., Thewes, R. & Fromherz, P. (2006) High-resolution multitransistor array recording of electrical field potentials in cultured brain slices. Journal of Neurophysiology 96(3):1638-1645. [27] Egger, V., Feldmeyer, D. & Sakmann, B. (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nature Neuroscience 2(12):1098-1105. [28] Feldmeyer, D., Egger, V., Lubke, J. & Sakmann, B. (1999) Reliable synaptic connections between pairs of excitatory layer 4 neurones within a single 'barrel' of developing rat somatosensory cortex. Journal of Physiology 521:169-190. [29] Peterlin, Z.A., Kozloski, J., Mao, B.Q., Tsiola, A. & Yuste, R. (2000) Optical probing of neuronal circuits with calcium indicators. Proceedings of the National Academy of Sciences of the United States of America 97(7):3619-3624. 8 [30] Thomson, A.M., Deuchars, J. & West, D.C. (1993) Large, deep layer pyramid-pyramid single axon EPSPs in slices of rat motor cortex display paired pulse and frequency-dependent depression, mediated presynaptically and self-facilitation, mediated postsynaptically. Journal of Neurophysiology 70(6):2354-2369. [31] Baraniuk, R.G. (2007) Compressive sensing. Ieee Signal Processing Magazine 24(4):118-120. [32] Candes, E.J. (2008) Compressed Sensing. Twenty-Second Annual Conference on Neural Information Processing Systems, Tutorials. [33] Candes, E.J., Romberg, J.K. & Tao, T. (2006) Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics 59(8):1207-1223. [34] Candes, E.J. & Tao, T. (2006) Near-optimal signal recovery from random projections: Universal encoding strategies? Ieee Transactions on Information Theory 52(12):5406-5425. [35] Donoho, D.L. (2006) Compressed sensing. Ieee Transactions on Information Theory 52(4):12891306. [36] Ringach, D. & Shapley, R. (2004) Reverse Correlation in Neurophysiology. Cognitive Science 28:147-166. [37] Schwartz, O., Pillow, J.W., Rust, N.C. & Simoncelli, E.P. (2006) Spike-triggered neural characterization. Journal of Vision 6(4):484-507. [38] Candes, E.J. & Tao, T. (2005) Decoding by linear programming. Ieee Transactions on Information Theory 51(12):4203-4215. [39] Needell, D. & Vershynin, R. (2009) Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. Foundations of Computational Mathematics 9(3):317-334. [40] Tropp, J.A. & Gilbert, A.C. (2007) Signal recovery from random measurements via orthogonal matching pursuit. Ieee Transactions on Information Theory 53(12):4655-4666. [41] Dai, W. & Milenkovic, O. (2009) Subspace Pursuit for Compressive Sensing Signal Reconstruction. Ieee Transactions on Information Theory 55(5):2230-2249. [42] Needell, D. & Tropp, J.A. (2009) CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis 26(3):301-321. [43] Varshney, L.R., Sjostrom, P.J. & Chklovskii, D.B. (2006) Optimal information storage in noisy synapses under resource constraints. Neuron 52(3):409-423. [44] Brunel, N., Hakim, V., Isope, P., Nadal, J.P. & Barbour, B. (2004) Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell. Neuron 43(5):745-757. [45] Napoletani, D. & Sauer, T.D. (2008) Reconstructing the topology of sparsely connected dynamical networks. Physical Review E 77(2):026103. [46] Allen, C. & Stevens, C.F. (1994) An evaluation of causes for unreliability of synaptic transmission. Proceedings of the National Academy of Sciences of the United States of America 91(22):10380-10383. [47] Hessler, N.A., Shirke, A.M. & Malinow, R. (1993) The probability of transmitter release at a mammalian central synapse. Nature 366(6455):569-572. [48] Isope, P. & Barbour, B. (2002) Properties of unitary granule cell-->Purkinje cell synapses in adult rat cerebellar slices. Journal of Neuroscience 22(22):9668-9678. [49] Mason, A., Nicoll, A. & Stratford, K. (1991) Synaptic transmission between individual pyramidal neurons of the rat visual cortex in vitro. Journal of Neuroscience 11(1):72-84. [50] Raastad, M., Storm, J.F. & Andersen, P. (1992) Putative Single Quantum and Single Fibre Excitatory Postsynaptic Currents Show Similar Amplitude Range and Variability in Rat Hippocampal Slices. European Journal of Neuroscience 4(1):113-117. [51] Rosenmund, C., Clements, J.D. & Westbrook, G.L. (1993) Nonuniform probability of glutamate release at a hippocampal synapse. Science 262(5134):754-757. [52] Sayer, R.J., Friedlander, M.J. & Redman, S.J. (1990) The time course and amplitude of EPSPs evoked at synapses between pairs of CA3/CA1 neurons in the hippocampal slice. Journal of Neuroscience 10(3):826-836. [53] Cash, S. & Yuste, R. (1999) Linear summation of excitatory inputs by CA1 pyramidal neurons. Neuron 22(2):383-394. [54] Polsky, A., Mel, B.W. & Schiller, J. (2004) Computational subunits in thin dendrites of pyramidal cells. Nature Neuroscience 7(6):621-627. [55] Paninski, L. (2003) Convergence properties of three spike-triggered analysis techniques. Network: Computation in Neural Systems 14(3):437-464. [56] Okatan, M., Wilson, M.A. & Brown, E.N. (2005) Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Computation 17(9):1927-1961. [57] Timme, M. (2007) Revealing network connectivity from response dynamics. Physical Review Letters 98(22):224101. 9

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 org Abstract One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. [sent-4, score-0.769]

2 Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. [sent-5, score-0.89]

3 Instead, we propose to measure a post-synaptic neuron’s voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. [sent-7, score-0.273]

4 To reconstruct these synaptic connections from the recorded voltage we apply a decoding algorithm recently developed for compressive sensing. [sent-8, score-0.856]

5 We use computer simulations to find optimal stimulation parameters and explore the feasibility of our reconstruction method under realistic experimental conditions including noise and non-linear synaptic integration. [sent-10, score-1.084]

6 Multineuronal stimulation allows reconstructing synaptic connectivity just from the spiking activity of post-synaptic neurons, even when sub-threshold voltage is unavailable. [sent-11, score-1.229]

7 By using calcium indicators, voltage-sensitive dyes, or multi-electrode arrays one could monitor activity of multiple postsynaptic neurons simultaneously, thus mapping their synaptic inputs in parallel, potentially reconstructing a complete neural circuit. [sent-12, score-1.315]

8 1 In tro d uc tio n Understanding information processing in neural circuits requires systematic characterization of synaptic connectivity [1, 2]. [sent-13, score-0.713]

9 The most direct way to measure synapses between a pair of neurons is to stimulate potentially pre-synaptic neuron while recording intra-cellularly from the potentially post-synaptic neuron [3-8]. [sent-14, score-0.955]

10 Neurons are sequentially stimulated to fire action potentials by scanning a laser beam (or electrode voltage) over a brain slice, while synaptic weights are measured by recording post-synaptic voltage. [sent-16, score-0.731]

11 Although sequential excitation of single potentially pre-synaptic neurons could reveal connectivity, such a “brute force” approach is inefficient because the connectivity among neurons is sparse. [sent-17, score-0.803]

12 Even among nearby neurons in the cerebral cortex, the probability of connection is only about ten percent [3-8]. [sent-18, score-0.343]

13 Connection probability decays rapidly with the 1 distance between neurons and falls below one percent on the scale of a cortical column [3, 8]. [sent-19, score-0.302]

14 Thus, most single-neuron stimulation trials would result in zero response making the brute force approach slow, especially for larger circuits. [sent-20, score-0.583]

15 Another drawback of the brute force approach is that single-neuron stimulation cannot be combined efficiently with methods allowing parallel recording of neural activity, such as calcium imaging [18-22], voltage-sensitive dyes [23-25] or multi-electrode arrays [17, 26]. [sent-21, score-0.793]

16 As these techniques do not reliably measure sub-threshold potential but report only spiking activity, they would reveal only the strongest connections that can drive a neuron to fire [2730]. [sent-22, score-0.424]

17 We propose to circumvent the above limitations of the brute force approach by stimulating multiple potentially pre-synaptic neurons simultaneously and reconstructing individual connections by using a recently developed method called compressive sensing (CS) [31-35]. [sent-24, score-0.941]

18 In each trial, we stimulate F neurons randomly chosen out of N potentially pre-synaptic neurons and measure post-synaptic activity. [sent-25, score-0.728]

19 Although each measurement yields only a combined response to stimulated neurons, if synaptic inputs sum linearly in a post-synaptic neuron, one can reconstruct the weights of individual connections by using an optimization algorithm. [sent-26, score-0.87]

20 only K << N potentially pre-synaptic neurons make synaptic connections onto a post-synaptic neuron, the required number of trials M ~ K log(N/K), which is much less than N [31-35]. [sent-29, score-1.178]

21 Because multiple neurons are driven to fire simultaneously, if several of them synapse on the post-synaptic neuron, they can induce one or more spikes in that neuron. [sent-31, score-0.415]

22 As quantized spike counts carry less information than analog sub-threshold voltage recordings, reconstruction requires a larger number of trials. [sent-32, score-0.527]

23 Although CS may use the same stimulation protocol, for a limited number of trials, the reconstruction quality is superior to RC or STA. [sent-36, score-0.485]

24 2 Ma pp i ng sy na pti c inp ut s o nto o n e ne uro n We start by formalizing the problem of mapping synaptic connections from a population of N potentially pre-synaptic neurons onto a single neuron, as exemplified by granule cells synapsing onto a Purkinje cell (Figure 1a). [sent-37, score-1.314]

25 We represent synaptic weights as components of a column vector x, where zeros represent non-existing connections. [sent-39, score-0.51]

26 Each row in the stimulation matrix A represents a trial, ones indicating neurons driven to spike once and zeros indicating non-spiking neurons. [sent-40, score-0.606]

27 The number of rows in the stimulation matrix A is equal to the number of trials M. [sent-41, score-0.344]

28 The column vector y represents M measurements of membrane voltage obtained by an intra-cellular recording from the post-synaptic neuron: y = Ax. [sent-42, score-0.344]

29 (1) In order to recover individual synaptic weights, Eq. [sent-43, score-0.51]

30 In this section we search computationally for the minimum number of trials required for exact reconstruction as a function of the number of non-zero synaptic weights K out of N potentially pre-synaptic neurons. [sent-47, score-0.966]

31 First, note that the number of trials depends on the number of stimulated neurons F. [sent-48, score-0.525]

32 If F = 1 we revert to the brute force approach and the number of measurements is N, while for F = N, the measurements are redundant and no finite number suffices. [sent-49, score-0.425]

33 To determine the optimal number of stimulated neurons F for given K and N, we search for the minimum number of trials M, which allows a perfect reconstruction of the synaptic connectivity x. [sent-51, score-1.387]

34 For each F, we generate 50 synaptic weight vectors and attempt reconstruction from sequentially increasing numbers of trials. [sent-52, score-0.772]

35 The value of M, at which all 50 recoveries are successful (up to computer round-off error), estimates the number of trial needed for reconstruction with probability higher than 98%. [sent-53, score-0.262]

36 As K decreases, the minimum shifts towards larger F because more neurons should be stimulated simultaneously for sparser x. [sent-56, score-0.404]

37 1N and explore how the minimum number of measurements required for exact reconstruction depends on K and N. [sent-60, score-0.355]

38 2) Stimulation of neurons may be imprecise exciting a slightly different subset of neurons than intended and/or firing intended neurons multiple times. [sent-68, score-0.991]

39 We quantify the 4 reconstruction x − xr l2 = error ∑ N i =1 by the normalized x − xr l2–error l2 / xl , where 2 ( xi − xri ) 2 . [sent-73, score-0.33]

40 We plot normalized reconstruction error in brute force approach (M = N = 500 trials) as a function of noise, as well as CS and RC reconstruction errors (M = 200, 600 trials), Figure 4. [sent-74, score-0.763]

41 9 Normalized reconstruction error ||x-x|| /||x|| 1 r 2 For each noise source, the reconstruction error of the brute force approach can be achieved with 60% fewer trials by CS method for the above parameters (Figure 4). [sent-76, score-0.933]

42 Naturally, the reconstruction error decreases with the number of trials. [sent-78, score-0.262]

43 The reconstruction error is most sensitive to stimulation noise and least sensitive to synaptic noise. [sent-79, score-1.044]

44 25 Synaptic failure probability Figure 4: Impact of noise on the reconstruction quality for N = 500, K = 30, F = 50. [sent-121, score-0.311]

45 a) Recovery error due to trial-to-trial variation in synaptic weight. [sent-122, score-0.51]

46 The response y is calculated using the synaptic connectivity x perturbed by an additive Gaussian noise. [sent-123, score-0.6]

47 The noise level is given by the coefficient of variation of synaptic weight. [sent-124, score-0.559]

48 The detrimental effect of the stimulation noise on the reconstruction can be eliminated by monitoring spiking activity of potentially pre-synaptic neurons. [sent-128, score-0.838]

49 By using calcium imaging [18-22], voltage-sensitive dyes [23] or multi-electrode arrays [17, 26] one could record the actual stimulation matrix. [sent-129, score-0.545]

50 Because most random matrices satisfy the reconstruction requirements [31, 34, 35], the actual stimulation matrix can be used for a successful recovery instead of the intended one. [sent-130, score-0.601]

51 Instead of stimulating designated neurons with high fidelity by using highly localized and intense light, one could stimulate all neurons with low probability. [sent-132, score-0.719]

52 The light intensity can be tuned to stimulate the optimal number of neurons per trial. [sent-134, score-0.353]

53 Next, we explore the sensitivity of the proposed reconstruction method to the violation of simplifying assumptions. [sent-135, score-0.262]

54 In principle, CS does not require prior knowledge of K for reconstruction [31, 34, 35]. [sent-138, score-0.262]

55 Then, the algorithm will find all the actual synaptic weights plus some extra non-zero weights, negligibly small when compared to actual ones. [sent-140, score-0.652]

56 Thus, one can provide the algorithm with the value of K safely larger than the actual one and then threshold the reconstruction result according to the synaptic noise level. [sent-141, score-0.872]

57 Second, whereas we assumed a linear summation of inputs [53], synaptic integration may be 2 non-linear [54]. [sent-142, score-0.563]

58 We model non-linearity by setting y = yl + α yl , where yl represents linearly summed synaptic inputs. [sent-143, score-0.51]

59 Results of simulations (Figure 5b) show that although nonlinearity can significantly degrade CS reconstruction quality, it still performs better than RC. [sent-144, score-0.3]

60 05 0 10 20 30 40 50 60 Normalized reconstruction error ||x-x||2/||x|| r 2 Normalized reconstrcution error ||x-x||2/||x|| r 2 (a) 0. [sent-154, score-0.262]

61 5 Ma pp i ng sy na pti c inp ut s o nto a n e uro na l po pu la tio n Until now, we considered reconstruction of synaptic inputs onto one neuron using subthreshold measurements of its membrane potential. [sent-176, score-1.438]

62 In this section, we apply CS to reconstructing synaptic connections onto a population of potentially post-synaptic neurons. [sent-177, score-0.851]

63 Because in CS the choice of stimulated neurons is non-adaptive, by recording from all potentially post-synaptic neurons in response to one sequence of trials one can reconstruct a complete feedforward network (Figure 6). [sent-178, score-1.054]

64 a) Each post-synaptic neuron (red) receives synapses from a sparse subset of potentially pre-synaptic neurons (blue). [sent-184, score-0.614]

65 c) Probability of firing as a function of synaptic current. [sent-186, score-0.595]

66 d) Comparison of CS and STA reconstruction error using spike trains for N = 500, K = 30 and F = 50. [sent-187, score-0.343]

67 First, patching a large number of neurons is unrealistic and, therefore, monitoring membrane potential requires using different methods, such as calcium imaging [18-22], voltage sensitive dyes [23-25] or multielectrode arrays [17, 26]. [sent-189, score-0.821]

68 Depending on the strength of summed synaptic inputs compared to the firing threshold, the postsynaptic neuron may be silent, fire once or multiple times. [sent-191, score-0.91]

69 Such quantized measurements are less informative than analog measurements of the sub-threshold membrane potential. [sent-193, score-0.289]

70 Therefore, to achieve reasonable reconstruction quality using quantized measurements, a larger number of trials M>>N is required. [sent-195, score-0.431]

71 We simulate circuit reconstruction from spike recordings in silico as follows. [sent-196, score-0.444]

72 First, we draw synaptic weights from an experimentally motivated distribution. [sent-197, score-0.51]

73 Fourth, we reconstruct synaptic weights using STA and CS and compare the results with the generated weights. [sent-201, score-0.553]

74 We propose to calibrate x with a few brute-force measurements of synaptic weights. [sent-204, score-0.603]

75 Thus, in calculating the reconstruction error using l2 norm, we normalize both the generated and recovered synaptic weights. [sent-205, score-0.772]

76 6 D i s c uss ion We have demonstrated that sparse feedforward networks can be reconstructed by stimulating multiple potentially pre-synaptic neurons simultaneously and monitoring either subthreshold or spiking response of potentially post-synaptic neurons. [sent-211, score-0.702]

77 When sub-threshold voltage is recorded, significantly fewer measurements are required than in the brute force approach. [sent-212, score-0.506]

78 Although our method is sensitive to noise (with stimulation noise worse than synapse noise), it is no less robust than the brute force approach or RC. [sent-213, score-0.614]

79 The proposed reconstruction method can also recover inputs onto a neuron from spike counts, albeit with more trials than from sub-threshold potential measurements. [sent-214, score-0.72]

80 This is particularly useful when intra-cellular recordings are not feasible and only spiking can be detected reliably, for example, when mapping synaptic inputs onto multiple neurons in parallel. [sent-215, score-1.036]

81 The proposed reconstruction method assumes linear summation of synaptic inputs (both excitatory and inhibitory) and is sensitive to non-linearity of synaptic integration. [sent-217, score-1.399]

82 Therefore, it is most useful for studying connections onto neurons, in which synaptic integration is close to linear. [sent-218, score-0.682]

83 On the other hand, multi-neuron stimulation is closer than single-neuron stimulation to the intrinsic activity in the live brain and can be used to study synaptic integration under realistic conditions. [sent-219, score-1.048]

84 In contrast to circuit reconstruction using intrinsic neuronal activity [56, 57], our method relies on extrinsic stimulation of neurons. [sent-220, score-0.676]

85 First, activity of non-monitored presynaptic neurons may significantly distort reconstruction results. [sent-223, score-0.694]

86 Thus, successful reconstruction would require monitoring all active pre-synaptic neurons, which is rather challenging. [sent-224, score-0.319]

87 Second, reliable reconstruction is possible only when the activity of presynaptic neurons is uncorrelated. [sent-225, score-0.656]

88 (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. [sent-254, score-0.902]

89 (2002) Synaptic connections and small circuits involving excitatory and inhibitory neurons in layers 2-5 of adult rat and cat neocortex: triple intracellular recordings and biocytin labelling in vitro. [sent-269, score-0.714]

90 (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. [sent-278, score-0.6]

91 (2000) Laminar sources of synaptic input to cortical inhibitory interneurons and pyramidal neurons. [sent-290, score-0.632]

92 (2005) Laminar and columnar organization of ascending excitatory projections to layer 2/3 pyramidal neurons in rat barrel cortex. [sent-295, score-0.665]

93 (2009) Reverse optical trawling for synaptic connections in situ. [sent-385, score-0.636]

94 (2003) Imaging reveals synaptic targets of a swim-terminating neuron in the leech CNS. [sent-425, score-0.667]

95 (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. [sent-438, score-0.956]

96 (1999) Reliable synaptic connections between pairs of excitatory layer 4 neurones within a single 'barrel' of developing rat somatosensory cortex. [sent-444, score-0.843]

97 (2004) Optimal information storage and the distribution of synaptic weights: perceptron versus Purkinje cell. [sent-537, score-0.51]

98 (1994) An evaluation of causes for unreliability of synaptic transmission. [sent-547, score-0.51]

99 (1991) Synaptic transmission between individual pyramidal neurons of the rat visual cortex in vitro. [sent-563, score-0.57]

100 (1990) The time course and amplitude of EPSPs evoked at synapses between pairs of CA3/CA1 neurons in the hippocampal slice. [sent-584, score-0.428]

similar papers computed by tfidf model

tfidf for this paper:

wordName wordTfidf (topN-words)

[('synaptic', 0.51), ('neurons', 0.302), ('reconstruction', 0.262), ('stimulation', 0.223), ('cs', 0.18), ('neuron', 0.157), ('brute', 0.152), ('voltage', 0.136), ('connections', 0.126), ('sta', 0.122), ('pyramidal', 0.122), ('trials', 0.121), ('rat', 0.11), ('stimulated', 0.102), ('reconstructing', 0.096), ('calcium', 0.095), ('measurements', 0.093), ('activity', 0.092), ('connectivity', 0.09), ('rc', 0.088), ('force', 0.087), ('firing', 0.085), ('yuste', 0.085), ('spiking', 0.082), ('synapses', 0.082), ('spike', 0.081), ('potentially', 0.073), ('neuroscience', 0.073), ('circuits', 0.069), ('imaging', 0.069), ('svoboda', 0.068), ('recovery', 0.065), ('excitatory', 0.064), ('stimulating', 0.064), ('cosamp', 0.064), ('recording', 0.06), ('dyes', 0.059), ('fire', 0.059), ('circuit', 0.058), ('monitoring', 0.057), ('membrane', 0.055), ('synapse', 0.054), ('inputs', 0.053), ('actual', 0.051), ('stimulate', 0.051), ('feedforward', 0.051), ('callaway', 0.051), ('chklovskii', 0.051), ('glutamate', 0.051), ('kleinfeld', 0.051), ('sakmann', 0.051), ('noise', 0.049), ('arrays', 0.048), ('quantized', 0.048), ('onto', 0.046), ('postsynaptic', 0.046), ('hippocampal', 0.044), ('purkinje', 0.044), ('tio', 0.044), ('thomson', 0.044), ('physiology', 0.044), ('tao', 0.044), ('recordings', 0.043), ('reconstruct', 0.043), ('compressive', 0.041), ('na', 0.041), ('cerebral', 0.041), ('neuronal', 0.041), ('find', 0.04), ('candes', 0.039), ('significantly', 0.038), ('america', 0.037), ('united', 0.036), ('measurement', 0.036), ('cortex', 0.036), ('io', 0.036), ('excitation', 0.036), ('release', 0.034), ('xr', 0.034), ('bannister', 0.034), ('barbour', 0.034), ('barrel', 0.034), ('detrimentally', 0.034), ('egger', 0.034), ('feldmeyer', 0.034), ('granule', 0.034), ('ikegaya', 0.034), ('inp', 0.034), ('isope', 0.034), ('kristan', 0.034), ('logn', 0.034), ('lubke', 0.034), ('nto', 0.034), ('photostimulation', 0.034), ('pti', 0.034), ('sjostrom', 0.034), ('tufted', 0.034), ('uncaging', 0.034), ('uro', 0.034), ('layer', 0.033)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.99999875 200 nips-2009-Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)

Author: Tao Hu, Anthony Leonardo, Dmitri B. Chklovskii

2 0.29780984 121 nips-2009-Know Thy Neighbour: A Normative Theory of Synaptic Depression

Author: Jean-pascal Pfister, Peter Dayan, Máté Lengyel

Abstract: Synapses exhibit an extraordinary degree of short-term malleability, with release probabilities and effective synaptic strengths changing markedly over multiple timescales. From the perspective of a ﬁxed computational operation in a network, this seems like a most unacceptable degree of added variability. We suggest an alternative theory according to which short-term synaptic plasticity plays a normatively-justiﬁable role. This theory starts from the commonplace observation that the spiking of a neuron is an incomplete, digital, report of the analog quantity that contains all the critical information, namely its membrane potential. We suggest that a synapse solves the inverse problem of estimating the pre-synaptic membrane potential from the spikes it receives, acting as a recursive ﬁlter. We show that the dynamics of short-term synaptic depression closely resemble those required for optimal ﬁltering, and that they indeed support high quality estimation. Under this account, the local postsynaptic potential and the level of synaptic resources track the (scaled) mean and variance of the estimated presynaptic membrane potential. We make experimentally testable predictions for how the statistics of subthreshold membrane potential ﬂuctuations and the form of spiking non-linearity should be related to the properties of short-term plasticity in any particular cell type. 1

3 0.25034526 99 nips-2009-Functional network reorganization in motor cortex can be explained by reward-modulated Hebbian learning

Author: Steven Chase, Andrew Schwartz, Wolfgang Maass, Robert A. Legenstein

Abstract: The control of neuroprosthetic devices from the activity of motor cortex neurons beneﬁts from learning effects where the function of these neurons is adapted to the control task. It was recently shown that tuning properties of neurons in monkey motor cortex are adapted selectively in order to compensate for an erroneous interpretation of their activity. In particular, it was shown that the tuning curves of those neurons whose preferred directions had been misinterpreted changed more than those of other neurons. In this article, we show that the experimentally observed self-tuning properties of the system can be explained on the basis of a simple learning rule. This learning rule utilizes neuronal noise for exploration and performs Hebbian weight updates that are modulated by a global reward signal. In contrast to most previously proposed reward-modulated Hebbian learning rules, this rule does not require extraneous knowledge about what is noise and what is signal. The learning rule is able to optimize the performance of the model system within biologically realistic periods of time and under high noise levels. When the neuronal noise is ﬁtted to experimental data, the model produces learning effects similar to those found in monkey experiments.

4 0.24405544 52 nips-2009-Code-specific policy gradient rules for spiking neurons

Author: Henning Sprekeler, Guillaume Hennequin, Wulfram Gerstner

Abstract: Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning rules emerge from a policy gradient approach depending on which features of the spike trains are assumed to inﬂuence the reward signals, i.e., depending on which neural code is in effect. We use the framework of Williams (1992) to derive learning rules for arbitrary neural codes. For illustration, we present policy-gradient rules for three different example codes - a spike count code, a spike timing code and the most general “full spike train” code - and test them on simple model problems. In addition to classical synaptic learning, we derive learning rules for intrinsic parameters that control the excitability of the neuron. The spike count learning rule has structural similarities with established Bienenstock-Cooper-Munro rules. If the distribution of the relevant spike train features belongs to the natural exponential family, the learning rules have a characteristic shape that raises interesting prediction problems. 1

5 0.24204291 162 nips-2009-Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling

Author: Lei Shi, Thomas L. Griffiths

Abstract: The goal of perception is to infer the hidden states in the hierarchical process by which sensory data are generated. Human behavior is consistent with the optimal statistical solution to this problem in many tasks, including cue combination and orientation detection. Understanding the neural mechanisms underlying this behavior is of particular importance, since probabilistic computations are notoriously challenging. Here we propose a simple mechanism for Bayesian inference which involves averaging over a few feature detection neurons which ﬁre at a rate determined by their similarity to a sensory stimulus. This mechanism is based on a Monte Carlo method known as importance sampling, commonly used in computer science and statistics. Moreover, a simple extension to recursive importance sampling can be used to perform hierarchical Bayesian inference. We identify a scheme for implementing importance sampling with spiking neurons, and show that this scheme can account for human behavior in cue combination and the oblique effect. 1

6 0.17183952 19 nips-2009-A joint maximum-entropy model for binary neural population patterns and continuous signals

7 0.15258661 183 nips-2009-Optimal context separation of spiking haptic signals by second-order somatosensory neurons

8 0.14464439 210 nips-2009-STDP enables spiking neurons to detect hidden causes of their inputs

9 0.12783226 165 nips-2009-Noise Characterization, Modeling, and Reduction for In Vivo Neural Recording

10 0.11391543 164 nips-2009-No evidence for active sparsification in the visual cortex

11 0.11357724 157 nips-2009-Multi-Label Prediction via Compressed Sensing

12 0.1053246 167 nips-2009-Non-Parametric Bayesian Dictionary Learning for Sparse Image Representations

13 0.10498799 43 nips-2009-Bayesian estimation of orientation preference maps

14 0.10267469 62 nips-2009-Correlation Coefficients are Insufficient for Analyzing Spike Count Dependencies

15 0.092634752 231 nips-2009-Statistical Models of Linear and Nonlinear Contextual Interactions in Early Visual Processing

16 0.090823472 13 nips-2009-A Neural Implementation of the Kalman Filter

17 0.080489911 228 nips-2009-Speeding up Magnetic Resonance Image Acquisition by Bayesian Multi-Slice Adaptive Compressed Sensing

18 0.075420983 38 nips-2009-Augmenting Feature-driven fMRI Analyses: Semi-supervised learning and resting state activity

19 0.069694288 163 nips-2009-Neurometric function analysis of population codes

20 0.068508469 145 nips-2009-Manifold Embeddings for Model-Based Reinforcement Learning under Partial Observability

similar papers computed by lsi model

lsi for this paper:

topicId topicWeight

[(0, -0.157), (1, -0.262), (2, 0.346), (3, 0.227), (4, 0.059), (5, -0.026), (6, -0.122), (7, -0.03), (8, 0.056), (9, 0.062), (10, -0.019), (11, -0.022), (12, 0.024), (13, 0.019), (14, -0.103), (15, 0.079), (16, -0.044), (17, -0.06), (18, 0.041), (19, -0.001), (20, 0.007), (21, -0.011), (22, 0.102), (23, 0.107), (24, 0.052), (25, 0.054), (26, -0.044), (27, -0.133), (28, -0.01), (29, 0.018), (30, -0.147), (31, 0.009), (32, 0.118), (33, -0.043), (34, 0.007), (35, -0.051), (36, 0.071), (37, 0.007), (38, 0.159), (39, -0.078), (40, 0.069), (41, -0.038), (42, 0.041), (43, 0.008), (44, -0.055), (45, 0.016), (46, 0.06), (47, -0.035), (48, -0.012), (49, 0.016)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.98455924 200 nips-2009-Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)

Author: Tao Hu, Anthony Leonardo, Dmitri B. Chklovskii

2 0.84765989 121 nips-2009-Know Thy Neighbour: A Normative Theory of Synaptic Depression

Author: Jean-pascal Pfister, Peter Dayan, Máté Lengyel

3 0.81496722 99 nips-2009-Functional network reorganization in motor cortex can be explained by reward-modulated Hebbian learning

Author: Steven Chase, Andrew Schwartz, Wolfgang Maass, Robert A. Legenstein

4 0.66348439 210 nips-2009-STDP enables spiking neurons to detect hidden causes of their inputs

Author: Bernhard Nessler, Michael Pfeiffer, Wolfgang Maass

Abstract: The principles by which spiking neurons contribute to the astounding computational power of generic cortical microcircuits, and how spike-timing-dependent plasticity (STDP) of synaptic weights could generate and maintain this computational function, are unknown. We show here that STDP, in conjunction with a stochastic soft winner-take-all (WTA) circuit, induces spiking neurons to generate through their synaptic weights implicit internal models for subclasses (or “causes”) of the high-dimensional spike patterns of hundreds of pre-synaptic neurons. Hence these neurons will ﬁre after learning whenever the current input best matches their internal model. The resulting computational function of soft WTA circuits, a common network motif of cortical microcircuits, could therefore be a drastic dimensionality reduction of information streams, together with the autonomous creation of internal models for the probability distributions of their input patterns. We show that the autonomous generation and maintenance of this computational function can be explained on the basis of rigorous mathematical principles. In particular, we show that STDP is able to approximate a stochastic online Expectation-Maximization (EM) algorithm for modeling the input data. A corresponding result is shown for Hebbian learning in artiﬁcial neural networks. 1

5 0.66073269 162 nips-2009-Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling

Author: Lei Shi, Thomas L. Griffiths

6 0.63293678 52 nips-2009-Code-specific policy gradient rules for spiking neurons

7 0.61314684 165 nips-2009-Noise Characterization, Modeling, and Reduction for In Vivo Neural Recording

8 0.60483444 13 nips-2009-A Neural Implementation of the Kalman Filter

9 0.53027576 183 nips-2009-Optimal context separation of spiking haptic signals by second-order somatosensory neurons

10 0.43133014 19 nips-2009-A joint maximum-entropy model for binary neural population patterns and continuous signals

11 0.42236903 62 nips-2009-Correlation Coefficients are Insufficient for Analyzing Spike Count Dependencies

12 0.37765819 203 nips-2009-Replacing supervised classification learning by Slow Feature Analysis in spiking neural networks

13 0.35382622 164 nips-2009-No evidence for active sparsification in the visual cortex

14 0.33352926 36 nips-2009-Asymptotic Analysis of MAP Estimation via the Replica Method and Compressed Sensing

15 0.31686917 185 nips-2009-Orthogonal Matching Pursuit From Noisy Random Measurements: A New Analysis

16 0.28444329 231 nips-2009-Statistical Models of Linear and Nonlinear Contextual Interactions in Early Visual Processing

17 0.28419358 228 nips-2009-Speeding up Magnetic Resonance Image Acquisition by Bayesian Multi-Slice Adaptive Compressed Sensing

18 0.28389254 43 nips-2009-Bayesian estimation of orientation preference maps

19 0.28124255 167 nips-2009-Non-Parametric Bayesian Dictionary Learning for Sparse Image Representations

20 0.28007111 157 nips-2009-Multi-Label Prediction via Compressed Sensing

similar papers computed by lda model

lda for this paper:

topicId topicWeight

[(7, 0.023), (24, 0.022), (25, 0.044), (35, 0.028), (36, 0.034), (39, 0.033), (44, 0.016), (58, 0.07), (62, 0.014), (71, 0.02), (81, 0.533), (86, 0.046), (91, 0.017)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.94463599 200 nips-2009-Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)

Author: Tao Hu, Anthony Leonardo, Dmitri B. Chklovskii

2 0.72770661 140 nips-2009-Linearly constrained Bayesian matrix factorization for blind source separation

Author: Mikkel Schmidt

Abstract: We present a general Bayesian approach to probabilistic matrix factorization subject to linear constraints. The approach is based on a Gaussian observation model and Gaussian priors with bilinear equality and inequality constraints. We present an efﬁcient Markov chain Monte Carlo inference procedure based on Gibbs sampling. Special cases of the proposed model are Bayesian formulations of nonnegative matrix factorization and factor analysis. The method is evaluated on a blind source separation problem. We demonstrate that our algorithm can be used to extract meaningful and interpretable features that are remarkably different from features extracted using existing related matrix factorization techniques.

3 0.6649639 75 nips-2009-Efficient Large-Scale Distributed Training of Conditional Maximum Entropy Models

Author: Ryan Mcdonald, Mehryar Mohri, Nathan Silberman, Dan Walker, Gideon S. Mann

Abstract: Training conditional maximum entropy models on massive data sets requires signiﬁcant computational resources. We examine three common distributed training methods for conditional maxent: a distributed gradient computation method, a majority vote method, and a mixture weight method. We analyze and compare the CPU and network time complexity of each of these methods and present a theoretical analysis of conditional maxent models, including a study of the convergence of the mixture weight method, the most resource-efﬁcient technique. We also report the results of large-scale experiments comparing these three methods which demonstrate the beneﬁts of the mixture weight method: this method consumes less resources, while achieving a performance comparable to that of standard approaches.

4 0.58735353 141 nips-2009-Local Rules for Global MAP: When Do They Work ?

Author: Kyomin Jung, Pushmeet Kohli, Devavrat Shah

Abstract: We consider the question of computing Maximum A Posteriori (MAP) assignment in an arbitrary pair-wise Markov Random Field (MRF). We present a randomized iterative algorithm based on simple local updates. The algorithm, starting with an arbitrary initial assignment, updates it in each iteration by ﬁrst, picking a random node, then selecting an (appropriately chosen) random local neighborhood and optimizing over this local neighborhood. Somewhat surprisingly, we show that this algorithm ﬁnds a near optimal assignment within n log 2 n iterations with high probability for any n node pair-wise MRF with geometry (i.e. MRF graph with polynomial growth) with the approximation error depending on (in a reasonable manner) the geometric growth rate of the graph and the average radius of the local neighborhood – this allows for a graceful tradeoff between the complexity of the algorithm and the approximation error. Through extensive simulations, we show that our algorithm ﬁnds extremely good approximate solutions for various kinds of MRFs with geometry.

5 0.47193807 99 nips-2009-Functional network reorganization in motor cortex can be explained by reward-modulated Hebbian learning

Author: Steven Chase, Andrew Schwartz, Wolfgang Maass, Robert A. Legenstein

6 0.42456779 121 nips-2009-Know Thy Neighbour: A Normative Theory of Synaptic Depression

7 0.41540587 162 nips-2009-Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling

8 0.40726787 210 nips-2009-STDP enables spiking neurons to detect hidden causes of their inputs

9 0.38240483 13 nips-2009-A Neural Implementation of the Kalman Filter

10 0.3767125 17 nips-2009-A Sparse Non-Parametric Approach for Single Channel Separation of Known Sounds

11 0.35565782 19 nips-2009-A joint maximum-entropy model for binary neural population patterns and continuous signals

12 0.3262144 62 nips-2009-Correlation Coefficients are Insufficient for Analyzing Spike Count Dependencies

13 0.32587034 41 nips-2009-Bayesian Source Localization with the Multivariate Laplace Prior

14 0.3148984 70 nips-2009-Discriminative Network Models of Schizophrenia

15 0.31187686 52 nips-2009-Code-specific policy gradient rules for spiking neurons

16 0.31047279 228 nips-2009-Speeding up Magnetic Resonance Image Acquisition by Bayesian Multi-Slice Adaptive Compressed Sensing

17 0.29950932 164 nips-2009-No evidence for active sparsification in the visual cortex

18 0.29875872 183 nips-2009-Optimal context separation of spiking haptic signals by second-order somatosensory neurons

19 0.29768759 168 nips-2009-Non-stationary continuous dynamic Bayesian networks

20 0.29595438 155 nips-2009-Modelling Relational Data using Bayesian Clustered Tensor Factorization