Neural Circuits for Fast Poisson Compressed Sensing in the Olfactory Bulb

Abstract

Within a single sniff, the mammalian olfactory system can decode the identity and concentration of odorants wafted on turbulent plumes of air. Yet, it must do so given access only to the noisy, dimensionally-reduced representation of the odor world provided by olfactory receptor neurons. As a result, the olfactory system must solve a compressed sensing problem, relying on the fact that only a handful of the millions of possible odorants are present in a given scene. Inspired by this principle, past works have proposed normative compressed sensing models for olfactory decoding. However, these models have not captured the unique anatomy and physiology of the olfactory bulb, nor have they shown that sensing can be achieved within the 100-millisecond timescale of a single sniff. Here, we propose a rate-based Poisson compressed sensing circuit model for the olfactory bulb. This model maps onto the neuron classes of the olfactory bulb, and recapitulates salient features of their connectivity and physiology. For circuit sizes comparable to the human olfactory bulb, we show that this model can accurately detect tens of odors within the timescale of a single sniff. We also show that this model can perform Bayesian posterior sampling for accurate uncertainty estimation. Fast inference is possible only if the geometry of the neural code is chosen to match receptor properties, yielding a distributed neural code that is not axis-aligned to individual odor identities. Our results illustrate how normative modeling can help us map function onto specific neural circuits to generate new hypotheses.

Figure G.1:

A. Fraction of odors correctly detected within 100 ms (left), 200 ms (center), and 1 s (right) after odor onset as a function of the number of odors present, with $n_{\text{odor}}=500$ possible odors, for models with one-to-one, naïvely distributed, and geometry-aware codes. B. As in $\mathbf{A}$, but for $n_{\text{odor}}=1000$. This matches Fig. 3B. C, D, E. As in $\mathbf{A}$, but for $n_{\text{odor}}=2000,4000$, or 8000 possible odorants, respectively. Shaded patches show ±1.96 SEM over realizations throughout.

Figure G.2:

A. Heatmap with overlaid smoothed contours of the fraction of odors correctly detected as a function of number of present odors and time window out of a panel of $n_{\text{odor}}=500$ possible odors for models with one-to-one (left), naïvely distributed (center), and geometry-aware (right) codes. B. As in $\mathbf{A}$, but for $n_{\text{odor}}=1000$. This matches Fig. 3B. C, D, E. As in A, but for $n_{\text{odor}}=2000,4000$, or 8000 possible odorants, respectively.

Figure G.3:

Fast uncertainty estimation using Langevin sampling of the posterior, showing estimates for individual odorants. Here, we use a simple concentration estimation task in which 5 randomly-selected ‘low’ odorants out of a panel of 1000 appear at concentration 10 at time 0 s, and then a further 5 randomly-selected ‘high’ odorants appear at concentration 40 at time 1 s. A. Smoothed timeseries of instantaneous concentration estimates for low, high, and background odorants, for models with one-to-one (top), naïvely distributed (middle), and geometry-aware (bottom) codes. Background odorant estimates are shown as mean ± standard deviation over odorants. Dashed lines show true concentrations over time. B. Cumulative estimates of concentration mean for low (top) and high (bottom) odorants after the onset of the low odorants for one-to-one, naïvely distributed, and geometry-aware codes. Black lines indicate baseline estimates of the posterior mean. Thick colored lines indicate means over odorants, while thin lines show traces for individual odorants. C. As in $\mathbf{B}$, but for the estimated variance. D. As in $\mathbf{B}$, but after the onset of high odorants. E. As in $\mathbf{C}$, but after the onset of high odorants. See Appendix G for details of our numerical methods.

Figure G.4:

Langevin sampling of the posterior using sparse non-negative distributed codes. Here, we use a simple concentration estimation task in which 5 randomly-selected ‘low’ odors out of a panel of 500 appear at concentration 10 at time 0 s, and then a further 5 randomly-selected ‘high’ odors appear at concentration 40 at time 1 s. This figure replicates Fig. 4, except that the code is distributed using a sparse non-negative random matrix rather than an orthogonal matrix. Smoothed timeseries of instantaneous concentration estimates for low, high, and background odors, for models with one-to-one (top), naïvely distributed (middle), and geometry-aware (bottom) codes. Background odor estimates are shown as mean ± standard deviation over odors. Dashed lines show true odor concentrations over time. B. Cumulative estimates of odor concentration mean for low (top) and high (bottom) odors after the onset of the low odors for one-to-one, naïvely distributed, and geometry-aware codes. Black lines indicate baseline estimates of the posterior mean. Thick lines indicate means over odors, and thin lines individual odors. C. As in $\mathbf{B}$, but for the estimated variance. D. As in $\mathbf{B}$, but after the onset of high odors. E. As in $\mathbf{C}$, but after the onset of high odors. See Appendix G for details of our numerical methods.

Figure 1:

Circuit architecture of the mammalian olfactory bulb. A. Outline of the anatomy of OB circuits. B. Fit of the responses of 228 OSN glomerular responses to a panel of 32 odorants. (Gray line, response of single glomeruli, Blue line, Fitted average response.) See Appendix F for details of how these data were collected. C. Affinity matrix generated from the data-driven model ensemble. For illustrative purposes, we use only 30 receptors and 100 odorants; in simulations we use 300 receptors to roughly match humans [45], and 1000 or more odorants.

Figure 2:

State-dependent inhibition of mitral cells. A. Upon stimulation, mitral cells exhibit a transient burst of activity followed by relaxation to a plateau. Darker color indicates stronger stimulation. B. In the circuit for Poisson CS we propose (blue line), the inhibition due to the activation of a second mitral cell $\left(M{C}_B\right)$ is gated by the activity of the cell we are recording from $\left(M{C}_A\right)$, as observed experimentally by Arevian et al. [95] in their Fig. 2D. This state-dependent gating does not occur in a circuit derived from a Gaussian noise model (orange line). Rates are normalized to the maximal stimulation of the principal cell. Dashed line indicates the unity line. C. Strength of inhibition as a function of time and of stimulation intensity; c.f. [95] Fig. 3B.

Figure 3:

Fast detection of many odorants. A. Fraction of odorants correctly detected within 100 ms (left), 200 ms (center), and 1 s (right) after odorant onset as a function of the number of odorants present, for models with one-to-one, naïvely distributed, and geometry-aware codes. Here, we consider a repertoire of 1000 possible odorants. B. Heatmap with overlaid smoothed contours of correct detection fraction as a function of number of present odorants and time window for models with one-to-one (left), naïvely distributed (center), and geometry-aware (right) codes. As in A, a repertoire of 1000 possible odorants is used. C. Threshold number of odorants for which half can be correctly detected as a function of total repertoire size within 100 ms (left), 200 ms (center), and 1 s (right) after odorant onset. See also Supp. Figs. G.1 and G.2 for versions of panels $\mathbf{A}$ and $\mathbf{B}$ with varying repertoire sizes, from which the capacities shown here are derived. See Appendix G for details of our numerical methods. Shaded patches show ±1.96 SEM over realizations throughout.

Figure 4:

Fast uncertainty estimation using Langevin sampling of the posterior. Here, we use a simple concentration estimation task in which 5 randomly-selected ‘low’ odorants out of a panel of 1000 appear at concentration 10 at time 0 s, and then a further 5 randomly-selected ‘high’ odorants appear at concentration 40 at time 1 s. A. Smoothed timeseries of instantaneous concentration estimates for low, high, and background odorants, for models with one-to-one (top), naïvely distributed (middle), and geometry-aware (bottom) codes. Background odorant estimates are shown as mean ± standard deviation over odorants. Dashed lines show true concentrations over time. B. Cumulative estimates of concentration mean for low (top) and high (bottom) odorants after the onset of the low odorants for one-to-one, naïvely distributed, and geometry-aware codes. Black lines indicate baseline estimates of the posterior mean. Thick colored lines indicate means over odorants. C. As in $\mathbf{B}$, but for the estimated variance. D. As in $\mathbf{B}$, but after the onset of high odorants. E. As in $\mathbf{C}$, but after the onset of high odorants. See Appendix G for details of our numerical methods, and for individual-odor traces.