Habituation As a Neural Algorithm for Online Odor Discrimination

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Submission. Direct PNAS Board. a is article This interest.y competing paper.y no the declare wrote authors S.N. The and S.D., Y.S., performed and S.N. and data; S.D., analyzed Y.S., Y.S. research; research; designed S.N. and S.D., Y.S., contributions: Author of across system in olfactory dishabituation The work (25). and scales mechanisms habituation time two multiple both (23, these facilitate itself how to bulb unclear tandem olfactory remains the it in and effects observed 24), the also cor- that are the body) suggests habituation in mushroom of evidence fly cells experimental the principal in However, and [KCs] (19). 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Fig. 1. Illustration of the fruit fly olfactory circuit and two habituation-related problems. (A) Cartoon illustration of the effects of short-term habituation. (B) Overview of the fruit fly olfaction circuit. For each input odor, ORNs each fire at some rate, denoted by gray shade. ORNs send feed-forward excitation to PNs of the same type. A single lateral inhibitory neuron (LN1) also receives feed-forward inputs from ORNs and then sends inhibition to PNs. The net firing rate of each PN is the summation of the excitation it received from its ORN minus the inhibition received from the LN1. The locus of habituation lies at the LN1 → PN synapse, and the weights of these synapses are shown via red line thickness. PNs then project to KCs, and each KC samples sparsely from a few PNs. KCs that receive a summed input above a threshold will output to a single inhibitory neuron, called APL. APL sends strong feed-back inhibition to the KCs, which silences about 95% of the lowest-firing KCs; the remaining 5% of highest-firing KCs form a “neural tag” for the odor. (C) Illustration of fine discrimination. Prior to habituation, three similar odors (sA, sB, and sC ) share overlapping neural tags. After habituation to odor sA, many of the KCs shared by all three odors stop firing. As a result, the differences between sB and sC are heightened leading to improved discrimination. (D) Illustration of foreground (mixture) discrimination. Before habituation, the neural tag of the odor mixture with 80% of odor s and 20% of odor s0 is similar to the neural tag of pure odor s. After habituation to s, the neural tag of the mixture resembles the tag for pure odor s0, since the s component of the mixture has been subtracted. KCs activated by odor s (blue); KCs activated by odor s’ (green).

is attractive to study because its anatomy and physiology, from ORN responds to almost every odor with a different activation level, and the receptor level to the mushroom body, have been relatively only a few ORNs respond highly to a given odor. well mapped (26–34), allowing us to interpret the effects of 2) In the second step, ORNs extend axons into structures called glomeruli in habituation on downstream odor coding, learning, and behavior. the antennae lobe, where they synapse onto dendrites of PNs. There are Short-term habituation has also been described in other systems, approximately 50 PN types, and ORNs of the same type send odor information to corresponding PNs of the same type. This step normalizes PN such as in mice, cats, and worms (35–38), and may follow similar responses such that the mean firing rate of PNs is nearly the same for all mechanisms. odors (47–50). In addition, PNs receive inhibition from lateral inhibitory Here, we follow experimentally derived mechanisms of short- neurons in the antennae lobe, including LN1 interneurons, which are term habituation in the fruit fly olfactory circuit to develop an involved in habituation, as described below. unsupervised algorithm (39) for enhancing odor discrimination. 3) In the third step, the dimensionality of the representation expands: The Our algorithm is based on the “negative image” model of habit- 50 PNs project to about 2,000 KCs in a structure called the mushroom uation (16, 40), in which a simple plasticity rule is used to store body. Each KC receives input from approximately six random PNs (30), an inhibitory image of a background odor signal, which is then and KCs respond by thresholding the sum of their PN inputs (26, 51, 52). Thus, KCs have a rectilinear threshold activation function, which helps subtracted from future inputs. Our model can replicate three suppress PN noise (53, 54). general features of habituation: stimulus adaptation (reduced 4) In the fourth step, each KC sends feed-forward excitation to a single responsiveness to neutral stimuli that do not have a learned or anterior paired lateral inhibitory neuron (APL) (55), which, in turn, sends innate valence associated with them), stimulus specificity (habitu- inhibitory feedback to each KC. As a result of this feedback loop, only ∼5% ation to one stimulus does not reduce responsiveness to other, of the most highly activated KCs fire for each odor in what is called a “win- distinct stimuli), and reversibility (dishabituation to the back- ner take all” computation (28, 29). Thus, an odor is finally encoded as a ground in case it becomes relevant). We also demonstrate the sparse point in a 2,000-dimensional space. We refer to the 5% of KCs that relevance of these features for computational problems, such fire for a given odor as the neural “tag” (the term used in neuroscience) or as online similarity search (41) and background subtraction (42, “hash” (the term used in computer science) for the odor. Because this circuit generates tags that are similarity preserving (41), tags for similar odors 43), using both neural and machine learning datasets. share more overlapping KCs than tags for different odors. 5) In the fifth step, KCs send feed-forward excitation to mushroom body Methods output neurons (MBONs) (31) that “decode” the input and drive behav- Basic Anatomy of the Fruit Fly Olfactory Circuit. Odors in the fruit fly olfactory ior. For example, there are MBONs involved in learning approach and circuit are encoded using five main steps (Fig. 1B). avoidance behavior. When an odor is paired with some reward or pun- 1) In the first step, ORNs are activated when odor molecules bind to specific ishment, the strength of synapses between KCs activated for the odor receptors. There are approximately 50 types of odorant receptors in the and downstream approach and avoidance MBONs are modified (32). fruit fly antennae, and a single ORN contains only one type of receptor. While there are many complexities in the decoding process still to be d Thus, an odor is initially encoded as a point in R+, where d = 50. The determined, it is generally accepted that it is easier to learn to associate coding of odors across the ORNs is combinatorial (44–46), such that every different behaviors to two different odors when the KCs activated for

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COMPUTER SCIENCES NEUROSCIENCE projection step, a rectilinear function is used to filter out noise in the KC Results responses. For each 1 ≤ i ≤ m, we set First, we provide an example of habituation and prove that, ( under our model, habituation weights converge to form a “nega- 0 yi if yi ≥ τo yi = [3] tive image” of a constant input. Second, we use habituation to 0 otherwise, address problem 1 (fine discrimination) and problem 2 (foreground discrimination) both empirically and analytically. Third, where τo is a small constant equal to the mean of the input vectors. Finally, we demonstrate applications of habituation for improving online the winner-take-all sparsification step sets the top 5% of the highest firing KCs to 1, and the remaining KCs are set to 0. This gives us a vector z ∈ similarity search. {0, 1}m, where An Example of Habituation and Stimulus Specificity. Fig. 2 shows an ( 0 0 1 if yj ∈ {d0.05me largest nonzero entries of y } example of how PN responses to repeated presentations of the zj = . [4] 0 otherwise same odor (odor A: acetic acid) change over time. Initially, PN firing rates for the odor are not suppressed, and the inhibitory Why is the first KC thresholding step needed, in addition to the second? synaptic weights between the LN1 and PNs are low. With time, The winner-take-all alone always allows about 5% (0.05m) of KCs to fire, these synaptic weights become stronger at different rates accord- even if the KCs are firing at very low rates (which, e.g., could occur when an ing to the firing rate for each PN, and this causes PN firing to odor is close to being habituated). In such a case, the activity of these KCs decrease (Fig. 2A). could drive approach or avoidance behavior, despite mostly encoding noise. Habituation is also stimulus specific (Fig. 2B). Before habitu- As a result, a minimum threshold (τ0) for firing is required to suppress KC noise; this is similar to the notion of a “firing threshold” for a neuron or the ation, about 50 (5% of the 1,000) KCs respond to odor A, but, “rectilinear threshold” of rectified linear units in artificial neural networks. after habituation, these KCs are almost entirely silenced. On the Thus, the tag of an input is a binary vector of length m, with up to 0.05m other hand, KCs remain responsive to a different odor (odor values as ones, and the rest as zeros. Equivalently, the tag can be repre- B: ethyl hexanoate) after habituation to odor A (Fig. 2B), sug- sented as a set of KC indices that are active for the odor: I(x) = {j:zj = 1}. gesting that habituation to one odor does not hamper responses We do not arbitrarily break ties, and thus, if there are ties in the KC firing to different odors. In addition, habituation is reversible, where rates, there may be slightly more ones in the vector. the circuit can dishabituate to one odor when it is not Neural tag similarity. The KC tag I(s) for an odor s is a set of indices (each observed, and then habituate to a different odor (SI Appendix, between 1 and m), corresponding to the KCs active for odor s. The similarity Fig. S2). between the tags of two odors s and s0 is defined as the Jaccard coefficient between I(s) and I(s0), |I(s) ∩ I(s0)| . |I(s) ∪ I(s0)| A The Jaccard coefficient is a widely used measure to gauge the similarity between two sets. Its value lies between 0 and 1, with 0 meaning that the two sets have nothing in common, and 1 meaning the two sets have identical items. Forming binary odor mixtures. Predicting ORN responses to an odor mixture remains a challenging problem, with evidence that ORNs for mixtures can respond both linearly (69, 70) and nonlinearly (71–73) with respect to the mixture’s individual components. We explore two models here to form mixtures. For the linear model, given two odors s and s0, the binary mixture is computed simply as s00 = ξs + (1 − ξ)s0, where ξ determines the concentra- B tion of each odor component. For experiments in this paper, we set ξ = 0.8 to explore regimes with a dominant background odor (s) in the mixture, and a low signal foreground (s0). For the nonlinear model, the binary mixture is computed as s00 = sξ + s0(1−ξ). For both models, s00 is normalized to have the same average firing rate as the single odors (45). Nearest neighbors analysis for online similarity search. For each of the 110 odors, we first compute a ground-truth list of the top N nearest neighbors for the odor. For odor s, this list is computed based on the Jaccard similarity between I(s) and the tag for each other odor. For a mixture, s00 = ξs + (1 − ξ)s0, we seek to determine how well the predicted nearest neighbors for s00 C after habituation to s overlap with the ground-truth nearest neighbors of pure s0. The overlap between two lists of N nearest neighbors is computed using the mean average precision (mAP) (74). The mAP measures the similarity between two ranked lists. Common items between the two lists are weighted by their ranks in the lists. Formally, assume there are Ntot items (odors), and let l1 and l2 be two ranked lists of N < Ntot of the items. Each list can contain items not present in the other list. The list l1 is the ground-truth list, and l2 is the predicted list whose similarity to l1 we wish to compute. Let Fig. 2. Changes in circuit activity due to habituation. (A) Over time l12 be the list of the Nk common items in l1 and l2, in the same order as they (x axis), the synaptic weights between the LN1 and activated PNs increase appear in l1. Finally, let r12(i) = the rank in l1 of the ith item in l12. Then, (y axis, left), and the corresponding PN firing rates decrease (y axis, right). The weights between the LN1 and all nonactivated PNs remain unchanged N Xk (green line at y = 0). There are 24 total PNs, and each curve corresponds to mAP(l1, l2) = (1/Nk) × i/r12(i). a different PN. (B) Before habituation, about 5% of the 1,000 KCs respond i=1 (vertical bar) to odor A. After habituation to A, only a few KCs respond for A. However, after habituation to odor A, KCs still respond to a different odor We compute the mAP over three values of N = {10, 20, 30} and report the B, suggesting that habituation is odor specific. (C) Left shows that odor A average. The mAP ranges from 0 (least similar) to 1 (most similar). We com- and odor B are relatively distinct odors with little overlap in their tags. Right pare the similarity of two lists using the mAP, as opposed to the Jaccard shows that, after habituation to odor A, a substantial number (44/50 = 88%) coefficient, because the former takes the rank of each nearest neighbor of KCs in original tag of odor B still respond to odor B after habituation to into account, as well. odor A. Odor A: acetic acid. Odor B: ethyl hexanoate.

4 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1915252117 Shen et al. 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I w s (s tetg of tags )—the w − .Assume *. s ) n thus and , IAppendix, SI Then . w and ) + w s ∈ denote d d I R w 24 = 50 = (s w For 0 d 0 ; * 0 s < is ), 0 ee eso httilt fsmlrooscnb better be can odors similar s odors. of the of triplets one to that habituating 1). after (Problem show discriminated Odors Similar we of Here, Separation the Enhances Habituation ilgclmcaim,t efr akrudsbrcinin subtraction (SI background from data imaging perform derived streaming we algorithm, to Finally, habituation mechanisms, odor S4). biological simple Fig. this Appendix , used (SI also (Methods), trends mixtures similar form repeated to observed model We and nonlinear 4B). a (Fig. with analysis habituation this before the similarity and their habituation than after odor mixture the of of tag tag sim- the The between mixtures. corresponding ilarity their and odors of pairs ∼6,000 compo- detect. minor the allowed (s to odor nent the habituation of Thus, component similarity). dominant the Jaccard (96% overlap strongly mixture, the of to tag habituated then We similarity). 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COMPUTER SCIENCES NEUROSCIENCE AB

Fig. 3. Habituation and fine discrimination. (A) Odors sA, sB and sC are highly correlated with each other. Shaded circles illustrate ORN firing rates. (B)(Left) Before habituation to odor sA, the tags for odors sB and sC highly overlap. (Right) After habituation to odor sA, overlap between the tags of odors sB and sC decreased. Odor sA: dimethyl sulfide. Odor sB: acetone. Odor sC : 2-butanone. (C) Firing rates of PNs for each odor before and after habituation to odor sA. After habituation, PNs that respond highly to odor sA are mostly silent for all three odors, while some activity of other PNs remains intact for odors sB and sC .(D) Comparing Jaccard similarity between odors sB and sC before and after habituation to odor sA, for all odor triplets (sA, sB, sC ) with pairwise correlation r > 0.80. After habituation, the overlap between the tags of odors sB and sC generally decreases, making them easier to discriminate.

Analysis of mixture representations posthabituation. Our empir- tains 80% of s. However, after habituation, this overlap ical results are supported by theoretical results. Recall that the decreased (median mAP = 0.19 ± 0.16), and, instead, the mix- mixture s00 = ξs + (1 − ξ)s0. Detecting the minor component of ture shares almost the same nearest neighbors as odor s0 (median a mixture depends on the concentrations of the two components mAP = 0.84 ± 0.22; Fig. 4C). These results suggest that, after (determined by ξ) and the values of α (habituation rate) and β habituation, the representation assigned for the mixture allows (dishabituation rate). When the concentration of the habituated the retrieval of nearest neighbors that are relevant to pure odor odor s within the mixture surpasses a threshold, KC responses to s0, even though s0 represents only a small component of the the mixture are suppressed. input. In SI Appendix, we discuss additional applications where Lemma 2: If ξ ≥ α/(α + β) and online similarity searches may be beneficial. α + β Discussion ksk , ks0k ≤ · τ , ∞ ∞ cβ o We developed and analyzed an online unsupervised learning algorithm for short-term odor habituation based on the “neg- then I (s00; s) = ∅, where I (s00; s) is the tag associated with s00 after ative image” mechanism in the fruit fly olfactory circuit (16, habituation to s. 40). Our model can replicate three important aspects of habit- Proof: See SI Appendix, Lemma S1. uation: decreased activity to repeated, neutral stimulus; stimu- On the other hand, the tag for the mixture resembles the tag lus specificity; and reversibility (dishabituation). The algorithm for the unhabituated component when ξ < α/(α + β), which is demonstrates how habituation can filter out background signals, 83% for α = 0.05, β = 0.01. See SI Appendix, Lemma S3. making it easier to discriminate between similar odors and detect novel components in odor mixtures, even if these components Application to Online Similarity Search. The two problems above have relatively low concentration. Our results are consistent with exemplify why only encoding the change of an input with respect previous experimental studies of habituation and potentially lay to data observed in the recent past may better highlight out- out a framework for understanding the effects of habituation liers or novel components of the input in streaming data. We use on downstream sensory coding, behavior, and cognition in other this motivation to present a twist on the classic similarity search systems and species (24, 82, 83). problem (76–81) (SI Appendix). A critical component of the habituation algorithm is the use We calculated the tags I (s) and I (s0) of two odors, and of rectilinear thresholding by KCs, which filters noise prior to the tags of their mixture I (s00) and I (s00; s) before and after the “winner take all” calculation. After habituating to odor A, habituation, respectively. We then calculated the top N nearest there will likely still be small nonzero PN activity in response neighbors for each tag (Methods). Before habituation, I (s00) and to A. Without a rectilinear function, this noise will persist I (s) share a large portion of nearest neighbors (median mAP = in the KCs, and may not be eliminated by APL because the 0.81 ± 0.08, over all pairs s, s0), as expected since s00 con- winner-take-all mechanism adapts the amount of feed-back

6 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1915252117 Shen et al. 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COMPUTER SCIENCES NEUROSCIENCE neuroscience (39, 95–97). Speciﬁcally, these insights may be Data Availability applicable for deep learning (98) [e.g., to enhance attention- Code for the habituation algorithms is available at GitHub, https:// modulated artiﬁcial neural networks (99, 100)], for online sim- github.com/aspen-shen/Habituation-as-a-neural-algorithm-for- ilarity search problems, and in electronic noses for event-based online-odor-discrimination. smell processing. Moreover, recent theoretical work has argued that deep neural networks particularly excel in overcoming real- ACKNOWLEDGMENTS. We thank Mani Ramaswami, Jaiyam Sharma, and world “nuisances”, that is, task-irrelevant variation in inputs such Shyam Srinivasan for helpful discussions and comments on the manuscript. S.N. was supported by the Pew Charitable Trusts, the National Institutes as translations, rotations, and deformations (101, 102). Habitua- of Health under Awards 1R01DC017695 and 1UF1NS111692, and funding tion may further support this advance by reducing background from the Simons Center for Quantitative Biology at Cold Spring Harbor nuisances. Laboratory. Y.S. was supported by a Swartz Foundation Fellowship.

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