A probabilistic approach to demixing odors

Journal name:
Nature Neuroscience
Year published:
Published online


The olfactory system faces a hard problem: on the basis of noisy information from olfactory receptor neurons (the neurons that transduce chemicals to neural activity), it must figure out which odors are present in the world. Odors almost never occur in isolation, and different odors excite overlapping populations of olfactory receptor neurons, so the central challenge of the olfactory system is to demix its input. Because of noise and the large number of possible odors, demixing is fundamentally a probabilistic inference task. We propose that the early olfactory system uses approximate Bayesian inference to solve it. The computations involve a dynamical loop between the olfactory bulb and the piriform cortex, with cortex explaining incoming activity from the olfactory receptor neurons in terms of a mixture of odors. The model is compatible with known anatomy and physiology, including pattern decorrelation, and it performs better than other models at demixing odors.

At a glance


  1. Circuit diagram.
    Figure 1: Circuit diagram.

    The olfactory receptor neurons (ORNs), which respond to volatile compounds in the air, are divided into different receptor types. All ORNs of the same receptor type project, via a glomerulus (which we do not model), onto a mitral cell. (Each of our mitral cells should be thought of as a 'meta-mitral' cell, since in the real circuit there are approximately 15 mitral cells for every glomerulus.) The mitral cells interact, via approximately reciprocal connections, with the granule cells (which are inhibitory and, in our network, outnumber the mitral cells by a factor of 3). The mitral cells also project, via the lateral olfactory tract, to the mean concentration cells in piriform cortex (labeled ). These are the cells that carry direct information about the distribution over concentration for odor j. They also provide feedback—essentially an estimate of the mean concentration—to the granule cells: when the odors are successfully inferred, the feedback signal cancels, via the inhibitory granule cells, the feedforward drive from the ORNs, and the mitral cells are pushed toward their baseline firing rates.

  2. Evolution of activity in the mean concentration cells (the ) when three odors are presented.
    Figure 2: Evolution of activity in the mean concentration cells (the ) when three odors are presented.

    The first three odors (blue) correspond to the presented odors; the remaining 637 (red) correspond to the odors that were not presented. All plots except that in e are on a log scale. (a) Template matching estimate, , 20 ms after odor onset. (b) Activity of the mean concentration cells 20 ms after odor onset. (c) Activity 50 ms after odor onset. (d) Activity 150 ms after odor onset. (e) Activity 150 ms after odor onsets, but on a linear, rather than a log, scale.

  3. Probability of odor presence and inferred concentration.
    Figure 3: Probability of odor presence and inferred concentration.

    (a) Probability that an odor is present given the inferred mean concentration, , computed by the network from 10,000 trials. (b) Inferred mean concentration ( ) versus true concentration (cj); error bars (shown only in the positive direction to reduce clutter) are s.d. On this scale, the inferred mean concentration is approximately proportional to (but slightly smaller than) the true concentration. (c) Same as b, but for concentrations between 0 and 3. Especially at low concentrations, our network underestimates the true concentration, with the underestimate larger when more odors are presented. This is due to the sparse prior on odors, which introduces a bias toward low inferred concentration. All three panels were constructed by performing a large number of simulations, each with a different olfactory scene; see Online Methods section “Determining the probability that an odor is present.” In b the average number of data points per bin was 37, 170 and 127 for 1, 3 and 5 presented odors, respectively, and in c the corresponding numbers were 14, 31 and 144.

  4. Activity in response to a single odor whose concentration is equal to 3, the mean concentration of present odors.
    Figure 4: Activity in response to a single odor whose concentration is equal to 3, the mean concentration of present odors.

    Top to bottom: activity of 8 ORN receptor types; activity of the 8 mitral cells that receive input from the ORNs in the top row, matched by color; activity of the 8 granule cells whose main input comes from the mitral cells in the second row, matched by color; activity of all 640 mean concentration cells in piriform cortex. ORNs: activity is the number of spikes in 50 ms. Other cells: activity is in arbitrary units (AU). The traces are an average over 10 trials. (a) The odor is known to the animal. The cyan line in the bottom panel corresponds to the presented odor (odor 1), the (barely visible) black lines correspond to all the other odors. (b) The odor is known to the animal, but the feedback from the mitral cells to piriform cortex is reduced by a factor of 100. Because there is almost no cortical activity, granule cells lose a large component of their excitatory input, and so have low activity—too low and indiscriminate to cancel mitral cell activity. (c) The odor is unknown to the animal. The cortex tries to explain the ORN activity with many odors at low concentration, resulting in indiscriminate granule cell activity and only partial cancellation of mitral cell activity. There is no cyan line, as the presented odor has not been learned.

  5. Performance of the model when detecting a known odor (target) against background odors.
    Figure 5: Performance of the model when detecting a known odor (target) against background odors.

    The target was present with probability 1/2. The y axis is the fraction of correct trials as a function of the number of odors present. Data are from our simulations, solid lines are least square fits, and dashed lines are fits to the experimental data of Rokni et al.2. Black: probability correct for all trials. Blue: probability correct for Go trials (trials containing the target). Red: probability correct for NoGo trials (trials not containing the target). For the Go and NoGo trials, each point corresponds to 500 simulations, with each simulation consisting of a randomly chosen set of odors. Error bars are s.e.m. assuming binomial statistics: error bars are ±(p(1 − p)/n)1/2, where p is the probability correct and n = 500 is the number of simulations per data point.

  6. Evolution of pattern correlations in our model.
    Figure 6: Evolution of pattern correlations in our model.

    (a) Pattern correlation matrices (Pearson correlation coefficients) for mitral cells at several time points. At time t = 0, before odor onset, activity is independent of odor; correlation coefficients are below 1 only because they were computed from a finite number of trials. In the early, 'bottom-up' phase (t = 40 ms), correlations reflect odor similarity. However, in the later, 'top-down' phase (t ≥ 80 ms), feedback from the cortex forces a return to baseline, which pushes correlations down slightly. Decorrelation occurs because of this shift, but only on average; there are many pairs that increase in correlation. Color indicates correlation coefficient. (b) Same data as in a, but plotted for all pairs of odors versus time. Color (black to red) indicates input pattern correlations (correlations among ORN responses); blue is average correlation. The average correlation after odor onset was statistically significantly different from that before odor onset (P < 10−6, two-sided t-test at −50 and 250 ms; n = 36, test statistic t = 5.7).

  7. Generalized ROC curves.
    Figure 7: Generalized ROC curves.

    Curves represent fraction of odors correctly identified (number of true positives (TP) versus number of false positives (FP) as the threshold varies); see text for details. In ac, colors indicate number of odors present; the labeling in b shows the mapping between color and number. (a) Our network. (b) Fisher's linear discriminant. (c) Template matching. (d) Average ROC curve, weighted by the probability that an odor is present, for the three methods.


  1. Su, C.-Y., Menuz, K. & Carlson, J.R. Olfactory perception: receptors, cells, and circuits. Cell 139, 4559 (2009).
  2. Rokni, D., Hemmelder, V., Kapoor, V. & Murthy, V.N. An olfactory cocktail party: figure-ground segregation of odorants in rodents. Nat. Neurosci. 17, 12251232 (2014).
  3. Malnic, B., Hirono, J., Sato, T. & Buck, L.B. Combinatorial receptor codes for odors. Cell 96, 713723 (1999).
  4. Pouget, A., Beck, J.M., Ma, W.J. & Latham, P.E. Probabilistic brains: knowns and unknowns. Nat. Neurosci. 16, 11701178 (2013).
  5. Li, Z. A model of olfactory adaptation and sensitivity enhancement in the olfactory bulb. Biol. Cybern. 62, 349361 (1990).
  6. Hendin, O., Horn, D. & Tsodyks, M.V. Associative memory and segmentation in an oscillatory neural model of the olfactory bulb. J. Comput. Neurosci. 5, 157169 (1998).
  7. Li, Z. & Hertz, J. Odour recognition and segmentation by a model olfactory bulb and cortex. Network 11, 83102 (2000).
  8. Hopfield, J.J. Olfactory computation and object perception. Proc. Natl. Acad. Sci. USA 88, 64626466 (1991).
  9. Hendin, O., Horn, D. & Hopfield, J.J. Decomposition of a mixture of signals in a model of the olfactory bulb. Proc. Natl. Acad. Sci. USA 91, 59425946 (1994).
  10. Connelly, T., Savigner, A. & Ma, M. Spontaneous and sensory-evoked activity in mouse olfactory sensory neurons with defined odorant receptors. J. Neurophysiol. 110, 5562 (2013).
  11. Beck, J., Heller, K. & Pouget, A. Complex inference in neural circuits with probabilistic population codes and topic models. in Advances in Neural Information Processing Systems 25 (Curran Associates, 2012).
  12. Grabska-Barwińska, A., Beck, J., Pouget, A. & Latham, P. Demixing odors – fast inference in olfaction. in Advances in Neural Information Processing Systems 26 (Curran Associates, 2013).
  13. Egger, V., Svoboda, K. & Mainen, Z.F. Mechanisms of lateral inhibition in the olfactory bulb: efficiency and modulation of spike-evoked calcium influx into granule cells. J. Neurosci. 23, 75517558 (2003).
  14. Weiss, Y., Simoncelli, E.P. & Adelson, E.H. Motion illusions as optimal percepts. Nat. Neurosci. 5, 598604 (2002).
  15. Shepherd, G. (ed.) The Synaptic Organization of the Brain 5th edn. (Oxford Univ. Press, 2004).
  16. Fukunaga, I., Berning, M., Kollo, M., Schmaltz, A. & Schaefer, A.T. Two distinct channels of olfactory bulb output. Neuron 75, 320329 (2012).
  17. Igarashi, K.M. et al. Parallel mitral and tufted cell pathways route distinct odor information to different targets in the olfactory cortex. J. Neurosci. 32, 79707985 (2012).
  18. Spors, H. et al. Illuminating vertebrate olfactory processing. J. Neurosci. 32, 1410214108 (2012).
  19. Koulakov, A.A. & Rinberg, D. Sparse incomplete representations: a potential role of olfactory granule cells. Neuron 72, 124136 (2011).
  20. Fuentes, R.A., Aguilar, M.I., Aylwin, M.L. & Maldonado, P.E. Neuronal activity of mitral-tufted cells in awake rats during passive and active odorant stimulation. J. Neurophysiol. 100, 422430 (2008).
  21. Cury, K.M. & Uchida, N. Robust odor coding via inhalation-coupled transient activity in the mammalian olfactory bulb. Neuron 68, 570585 (2010).
  22. Shusterman, R., Smear, M.C., Koulakov, A.A. & Rinberg, D. Precise olfactory responses tile the sniff cycle. Nat. Neurosci. 14, 10391044 (2011).
  23. Gschwend, O. et al. Neuronal pattern separation in the olfactory bulb improves odor discrimination learning. Nat. Neurosci. 18, 14741482 (2015).
  24. Moulton, D. Electrical activity in the olfactory system of rabbits with indwelling electrodes. in Wenner-Gren Center International Symposium Series vol. 1, 7184 (Pergamon, 1963).
  25. Otazu, G.H., Chae, H., Davis, M.B. & Albeanu, D.F. Cortical feedback decorrelates olfactory bulb output in awake mice. Neuron 86, 14611477 (2015).
  26. Jinks, A. & Laing, D.G. A limit in the processing of components in odour mixtures. Perception 28, 395404 (1999).
  27. Mathis, A., Rokni, D., Kapoor, V., Bethge, M. & Murthy, V.N. Reading out olfactory receptors: Feedforward circuits detect odors in mixtures without demixing. Neuron 91, 11101123 (2016).
  28. Friedrich, R.W. & Laurent, G. Dynamic optimization of odor representations by slow temporal patterning of mitral cell activity. Science 291, 889894 (2001).
  29. Gschwend, O., Beroud, J. & Carleton, A. Encoding odorant identity by spiking packets of rate-invariant neurons in awake mice. PLoS One 7, e30155 (2012).
  30. Uchida, N. & Mainen, Z.F. Speed and accuracy of olfactory discrimination in the rat. Nat. Neurosci. 6, 12241229 (2003).
  31. Shen, K., Tootoonian, S. & Laurent, G. Encoding of mixtures in a simple olfactory system. Neuron 80, 12461262 (2013).
  32. Luo, S.X., Axel, R. & Abbott, L.F. Generating sparse and selective third-order responses in the olfactory system of the fly. Proc. Natl. Acad. Sci. USA 107, 1071310718 (2010).
  33. Druckmann, S., Hu, T. & Chklovskii, D.B. A mechanistic model of early sensory processing based on subtracting sparse representations. in Advances in Neural Information Processing Systems 25, 19791987 (Curran Associates, 2012).
  34. Tootoonian, S. & Lengyel, M. A dual algorithm for olfactory computation in the locust brain. In Advances in Neural Information Processing Systems 27, 22762284 (Curran Associates, 2014).
  35. Baird, B. Nonlinear dynamics of pattern formation and pattern recognition in rabbit olfactory bulb. Physica 22D, 150175 (1986).
  36. Erdi, P., Gröbler, T., Barna, G. & Kaski, K. Dynamics of the olfactory bulb: bifurcations, learning, and memory. Biol. Cybern. 69, 5766 (1993).
  37. Freeman, W.J. Nonlinear dynamics of paleocortex manifested in the olfactory EEG. Biol. Cybern. 35, 2137 (1979).
  38. Freeman, W.J. EEG analysis gives model of neuronal template-matching mechanism for sensory search with olfactory bulb. Biol. Cybern. 35, 221234 (1979).
  39. Li, Z. & Hopfield, J.J. Modeling the olfactory bulb and its neural oscillatory processings. Biol. Cybern. 61, 379392 (1989).
  40. Yao, Y. & Freeman, W.J. Model of biological pattern recognition with spatially chaotic dynamics. Neural Netw. 3, 153170 (1990).
  41. Hendin, O., Horn, D. & Tsodyks, M.V. The role of inhibition in an associative memory model of the olfactory bulb. J. Comput. Neurosci. 4, 173182 (1997).
  42. Brody, C.D. & Hopfield, J.J. Simple networks for spike-timing-based computation, with application to olfactory processing. Neuron 37, 843852 (2003).
  43. Polese, D., Martinelli, E., Marco, S., Di Natale, C. & Gutierrez-Galvez, A. Understanding odor information segregation in the olfactory bulb by means of mitral and tufted cells. PLoS One 9, e109716 (2014).
  44. Arevian, A.C., Kapoor, V. & Urban, N.N. Activity-dependent gating of lateral inhibition in the mouse olfactory bulb. Nat. Neurosci. 11, 8087 (2008).
  45. Cleland, T.A. Early transformations in odor representation. Trends Neurosci. 33, 130139 (2010).
  46. Cleland, T.A. & Linster, C. On-center/inhibitory-surround decorrelation via intraglomerular inhibition in the olfactory bulb glomerular layer. Front. Integr. Neurosci. 6, 5 (2012).
  47. Wiechert, M.T., Judkewitz, B., Riecke, H. & Friedrich, R.W. Mechanisms of pattern decorrelation by recurrent neuronal circuits. Nat. Neurosci. 13, 10031010 (2010).
  48. Hopfield, J.J. Odor space and olfactory processing: collective algorithms and neural implementation. Proc. Natl. Acad. Sci. USA 96, 1250612511 (1999).
  49. Kato, H.K., Chu, M.W., Isaacson, J.S. & Komiyama, T. Dynamic sensory representations in the olfactory bulb: modulation by wakefulness and experience. Neuron 76, 962975 (2012).
  50. Zhaoping, L. Olfactory object recognition, segmentation, adaptation, target seeking, and discrimination by the network of the olfactory bulb and cortex: computational model and experimental data. Curr. Opin. Behav. Sci. 11, 3039 (2016).
  51. Firestein, S. & Werblin, F. Odor-induced membrane currents in vertebrate-olfactory receptor neurons. Science 244, 7982 (1989).
  52. Wachowiak, M. & Cohen, L.B. Representation of odorants by receptor neuron input to the mouse olfactory bulb. Neuron 32, 723735 (2001).
  53. Bozza, T., Feinstein, P., Zheng, C. & Mombaerts, P. Odorant receptor expression defines functional units in the mouse olfactory system. J. Neurosci. 22, 30333043 (2002).
  54. Grosmaitre, X., Vassalli, A., Mombaerts, P., Shepherd, G.M. & Ma, M. Odorant responses of olfactory sensory neurons expressing the odorant receptor MOR23: a patch clamp analysis in gene-targeted mice. Proc. Natl. Acad. Sci. USA 103, 19701975 (2006).
  55. Mitchell, T. & Beauchamp, J. Bayesian variable selection in linear regression. J. Am. Stat. Assoc. 83, 10231032 (1988).
  56. Wainwright, M.J. & Jordan, M.I. Graphical Models, Exponential Families, and Variational Inference, Foundations and Trends Machine Learning (Now Publishers, 2008).

Download references

Author information

  1. These authors contributed equally to the work.

    • Alexandre Pouget &
    • Peter E Latham


  1. Gatsby Computational Neuroscience Unit, University College London, London, UK.

    • Agnieszka Grabska-Barwińska,
    • Alexandre Pouget &
    • Peter E Latham
  2. Google DeepMind, London, UK.

    • Agnieszka Grabska-Barwińska
  3. CNRS, Gipsa-lab, Grenoble, France.

    • Simon Barthelmé
  4. Department of Neurobiology, Duke University Medical School, Durham, North Carolina, USA.

    • Jeff Beck
  5. Champalimaud Centre for the Unknown, Lisbon, Portugal.

    • Zachary F Mainen
  6. Department of Basic Neuroscience, University of Geneva, Geneva, Switzerland.

    • Alexandre Pouget
  7. Department of Brain and Cognitive Sciences, University of Rochester, Rochester, New York, USA.

    • Alexandre Pouget


A.G.-B., Z.F.M., A.P. and P.E.L conceived the project. A.G.-B., S.B., J.B., A.P. and P.E.L. developed the theory. A.G.-B., S.B., A.P. and P.E.L. wrote the manuscript. A.G.-B. performed the simulations.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

Additional data