Elements of Olfactory Intelligence in Drosophila

The ability to make the world of odorants intelligible is a key capability of the Drosophila olfactory system that we shall call olfactory intelligence. We argue that olfactory intelligence does not only arise in the form of associative learning in the Mushroom Body, but can be seen throughout the first three stages of the early olfactory system: the Antenna, the Antennal Lobe and the Mushroom Body Calyx, where encoding and processing of odorants take places. Characterizing the structure and logic of the code underlying the spike trains accessing the memory in the Mushroom Body is a major challenge in neuroscience. To address this challenge and unveil the key elements of olfactory intelligence, we extensively model the function of the Drosophila early olfactory system from its intriguing connectome. We start by modeling the space of odorants using constructs of both semantic and syntactic information. Odorant semantics concerns the identity of odorants while odorant syntax pertains to their concentration amplitude. These odorant attributes are multiplicatively coupled in the process of olfactory transduction. To make the world of odorants intelligible, we establish that the Drosophila Antennal Lobe and Calyx largely reduce the concentration dependency of the odorant information from the confounding representation of the Antenna, and thereby disentangle the odorant semantic information from the odorant syntactic information. We also introduce a novel time and rank-based representation of Kenyon Cell (KC) outputs, called the marked first spike sequence code. We compare the cumulative inter-spike interval statistics of odorant semantics and introduce a novel distance measure for the accurate classification of odorant semantics. Computationally, these elements of olfactory intelligence are realized by a class ofdifferential divisive normalization processors (DNPs) modeling the feedback circuits in the Antennal Lobe facilitated by Local Neurons and in the Calyx by the Anterior Paired Lateral (APL) neuron. The marked first spike sequence code at the output of the DNP circuit of the Calyx provides a novel representation of the odorant semantics. The code reflects the amplitude ranking that drives the KCs in the time domain. Strikingly, the APL feedback not only removes the con- centration dependency of the KC outputs, but also increases the ranking distance between the marked first spike sequence codes representing different odorant identities. Thus, the rank-based representation supports accurate classification of odorant semantics. Abbreviations: Project Neurons (PNs), Kenyon Cells (KCs), Anterior Paired Lateral (APL) Neuron, Mushroom Body Output Neurons (MBONs).

odorant identity (semantics), odorant concentration (syntax), functional logic of the Drosophila early olfactory system, marked first spike sequence code. 1 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint 1 Introduction Drosophila olfactory circuits sense and process a wide range of information streams arising in many environmental niches [1]. The odorant spaces associated with these niches contain, among others, identifiable objects of interest. The early olfactory sensory system evolved to identify and characterize in detail the object features of their respective sensory world. But what is the structure and what are the identifiable objects in these spaces? To what extent are these objects similar and/or different? Formally characterizing the (i) objects of interest in the olfactory space of Drosophila’snatural sensory world, and the (ii) functional logic underlying the extraction of the object features, are major challenges in neuroscience. Central to our interests is the intelligent discrimination of odorant identity as an object of the olfactory world. It requires high accuracy in processing of possibly known and/or novel odorant mixtures encountered in novel settings/environments. Thus, in agreement with the broad outline in [2] we argue that taking the olfactory world to consist of intelligible odorant objects is an expression of intelligence and investigate how the Drosophila finds the olfactory world intelligible. 1.1 Overview of the Odorant Processing Pathways in the Drosophila EOS The three stages of the Early Olfactory System (EOS) of the fruit fly brain that we will be focussing on are the Antenna, the Antennal Lobe and the Mushroom Body Calyx. OSN 1 OSN 50 OSN 2 Receptor Type 2 OSN 1 OSN 50 OSN 2 Receptor Type 1 OSN 1 OSN 50 OSN 2 Receptor Type 3 OSN 1 OSN 50 OSN 2 Receptor Type 4 ANTENNA Channel 4 Channel 3 Channel 2 Channel 1 Figure 1: (top) Odorant mixture processing pathways of the Early Olfactory System of the fruit fly. (bottom) Structural pathways of the Early Olfactory System of the fruit fly. Only the right hand side of the EOS is shown. As shown in Figure 1(top), the complex odorant environment (see Figure 1(top, column 1)) is first sensed by the Olfactory Sensory Neurons (OSNs) hosted in olfactory sensilla that are located on the Antennae and Maxillary Palps (shown in Figure 1(top, column 2)) [3]. Olfactory transduction takes place on the dendrites of the OSNs, transforming the chemical odorant signal into an electrical signal in the form of action potentials [4]. 2 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint OSNs expressing the same olfactory receptor type (OR) project into an individual glomerulus of the Antennal Lobe (AL) (see Figure 1, top column 3) [5]. The dendrites of uniglomerular Projection Neurons (PNs) innervate a single glomerulus, receiving input from OSNs expressing a single OR- type. The PNs then project into the Mushroom Body Calyx and provide inputs to Kenyon Cells (KCs) [5]. In the Calyx, KC dendrites receive feedback from an Anterior Paired Lateral (APL) neuron that also receive inputs from all the KCs (see Figure 1, top column 4) [6, 7]. The odorant space model and the structural pathways of the Early Olfactory System of the fruit fly are schematically shown in Figure 1(bottom, columns 1, and 2 to 4), respectively. The ANTENNA circuit (Figure 1, bottom column 2) consists of parallel OSNs that are randomly distributed across the surface of the Maxillary Palp and Antenna. The OSNs are depicted in groups based on the olfactory receptors that they express. The OSNs provide input to the ANTENNAL LOBE (shown in Figure 1, bottom column 3). The axons of the OSNs expressing the same receptor type innervate the same glomerulus, a region with dense synaptic interaction between the axon terminals of OSNs, the dendrites of the PNs, and the local neurons (LNs). The olfactory signal, including the identity of pure and odorant mixtures is transformed by the ANTENNA and the ANTENNAL LOBE into and encoded as a code in the spike domain carried by the PNs. The PNs feed into Kenyon Cells (KCs) that are the primary outputs of the Calyx (see Figure 1, bottom column 4) and that project to the 15 Mushroom Body compartments where associative learning takes places [8]. Characterizing the code underlying the KC spike trains is a major challenge of elucidating the functional logic of associative learning. To address this challenge we closely follow the workflow, first described in [9], for discovering the functional logic of Drosophila brain circuits. 1.2 Semantic and Syntactic Odorant Information It is critical to realize that, fundamentally, two different types of information flows are present during the chemical to electrical signal transduction process. The first information flow is due to the chemical identity information of the odorant molecules obtained through a binding and dissociation process by the olfactory receptors expressed by OSNs. Each receptor type has a different binding and dissociation rate for each type of odorant molecules [10]. Since this type of information characterizes the identity of the odorant, we call it semantic information [11]. Semantic information relates to “meaning” [12]. An example of “semantics” in olfaction is the “smell of a rose” . Acetone might be perceived to be “aversive” or “attractive” . The second information flow is due to the concentration waveform of the odorant that determines its intensity. A stronger intensity typically indicates a stronger response of the OSN. We refer to the odorant concentration waveform as syntactic information [11]. Syntactic information (also known as Shannon information [12]) characterizes the concentration of the odorants of the biological environment. While Shannon information is rather well characterized, semantic information has been extremely difficult to formalize. Simply put, there is a dearth of research in modeling, characterizing and processing semantic information in neuroscience. A key observation regarding the very first stage of olfactory sensing is that, as we will show in Section 2.3, olfactory transduction in OSNs is a complex process where odorant semantic information and syntactic information are multiplicatively 3 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint coupled in individual OSNs. In other words, the early olfactory system of the fruit fly encodes the odorant object identity (semantic information) and the odorant concentration waveform (syntactic information) into a combinatorial neural code [10]. Therefore, the two attributes of an odorant must be untangled by the downstream circuit in order to recognize the identity of the odorant. This calls for i) explicitly modeling odorant stimuli in terms of their semantic and syntactic infor- mation content, and ii) exploring a new class of processors, called intelligent olfactory processors that process olfactory semantic information, as models of the early olfactory system of the fruit fly (exploring processors that extract, operate on and store semantic information flows), and, iii) formulating new representation of odorant semantics as inputs to the MB compartment circuits and supports a high degree of semantic specificity (i.e., separation between different odorant identities). Intelligent information processors operate on/store semantic information flows. As in traditional information theory, signal processing and control theory, olfactory syntactic information flows (con- centration waveforms) are processed by (syntactic) processors. In this article, we provide an approach to address these three elements of olfactory intelligence in the early olfactory system of the fruit fly. 1.3 Manuscript Organization In section 2 the functional logic of the Drosophila early olfactory system is presented. The odorant encoding machine modeling odorant processing in the EOS is introduced in Section 2.1. The modeling of the space of pure odorants is described in 2.2. The first element of olfactory intelligence appears at the sensory periphery of the EOS and is provided by the binding of pure odorants with receptors uniquely expressed by the antenna OSNs. The OSNs multiplicatively encode the semantic (odorant identity) and syntactic (odorant concentration) information that characterize odorant objects. The olfactory transduction process in the antenna is described in Section 2.3. The next element of olfactory intelligence is provided by the antennal lobe, a neuropil that extracts semantics and semantic timing events. Its function is covered in Section 2.4. The marked first spike sequence code provides the semantic information characterizing the odorant identity and the semantic timing to the MB. These information streams fully characterize the odorant objects that are presented to and encoded by the OSN receptors. The generation of the marked first spike sequence code is detailed in Section 2.5. In Section 3, we explore how the marked first spike sequence code generated through interaction between the KCs and APL feedback neuron can lead to a better classification of odorants in support of associative memory in the subsequent stages of the early olfactory system of the fruit fly brain. An overall discussion of the main elements of olfactory intelligence highlighted in the EOS of the Drosophila brain is presented in Section 4. 2 The Functional Logic of the Drosophila Early Olfactory System In this section, we describe an executable model of the Early Olfactory System (EOS) schematically outlined in Figure 1 (top: morphology, bottom: graph structural pathways) called the Odorant Encoding Machine (OEM). The circuit architecture of the OEM is shown in Figure 2. We will show how to (i) model odorants as objects characterized by the molecular level binding and the dissociation rates between odorants and OSN receptor-types, (ii) explore the morphological and 4 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint connectomic features of the EOS circuits, (iii) draw up executable EOS circuits with a class of canonical processors, and (iv) derive the functional logic of these circuits. 2.1 The Architecture of the Odorant Encoding Machine Modeling the EOS The circuit architecture of the OEM consists of a cascade of spatio-temporal differential divisive normalization processors (DNPs) [13] each modeling the graph structural pathways of the Antenna, Antennal Lobe (AL) and Calyx shown in Figure 1(bottom), and schematically depicted in Figure 2. Note that Figure 1 and Figure 2 taken together represent the 3 workflow modeling steps consisting of (i) the 3D exploration and visualization of fruit fly brain morphology datasets, (ii) the abstraction of the graph structure of the connectome and (iii) the creation of executable circuits. The fourth step, the interactive exploration of the functional logic of executable circuits, is one of the main goals pursued here. OTP OTP OSN Axon Terminal OSN Axon Terminal Pre-LN PN PN Post-iLN Post-eLN Post-eLN Post-iLN KC Dendrtite KC Dendrite APL KC KC PN to KC Synapses Antennal Lobe Calyx Antenna Natural Odorant Scene OSN OSNCo-Receptor Channel Active Receptor Co-Receptor Channel Active Receptor Glomerulus N Glomerulus 1 Odorant 1 Odorant 2 Odorant N Odorant Mixture Figure 2: The architecture of the Odorant Encoding Machine (OEM) modeling the early olfactory system of the fruit fly. Note that in Figure 2, (i) pure odorants are modeled as objects in the Natural Odorant Space; (ii) all odorants in a mixture are sensed and encoded by a molecular Odorant Transduction Process (OTP) in the Antenna OSNs - the OTP circuit is modeled as a DNP; (iii) 3 types of local neurons in the Antennal Lobe block, the Presynaptic Local Neurons (Pre-LNs), the Postsynaptic excitatory LNs (Post-eLNs) and the Postsynaptic inhibitory LNs (Post-iLNs), are modeled as 3 types of DNPs. (iv) the Calyx features an expansion of Projection Neuron (PN) to KC connectivity, a DNP circuit consisting of the KC dendrites, KC biological spike generators and the APL spatio-temporal feedback neuron. The rest of Section 2 is organized as follows. A model of the space of odorants (sketched in Figure 2(column 1)) that explicitly takes into account the semantic and syntactic information is described in detail in Section 2.2. Olfactory transduction in the Antenna (see Figure 2, column 2) and Maxillary Palps (not shown) is modeled with DNPs in Section 2.3. The glomerular structure of the Antennal Lobe (AL) is modeled as multiple processing channels in Section 2.4 (see Figure 2, column 3). In addition, local neurons (LNs) in AL facilitate local processing in and between glomeluri. In Section 2.4, we model the local processing using 3 DNPs to extract, respectively, the semantic information and the semantic ON and OFF timing events. In Section 2.5, we model the 5 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint APL feedback as a DNP (see Figure 2, column 4) that further reduces the dependence of the KC spiking response to odorant syntactic information, and transforms the semantic information into a first spike sequence code. 2.2 Modeling the Space of Pure Odorants The proposed odorant space model is not defined by the (largely intractable) chemical structure of the odorants [14, 15]. Rather, it is described by the interaction between odorants and olfactory receptors as a pair of tensors. The tensor pair determines what types of sensors (olfactory receptors) will be activated by a certain odorant, and the level of activation will be jointly governed by the identity and the concentration waveform of the odorant. More precisely, the overall activation of the sensors is determined by the value of the odorant-receptor binding rate modulated by the odorant concentration profile. Figure 3: Modeling the space of pure odorants. In what follows, we explicitly and separately model the semantics and syntax of pure odorants [10, 11]. As depicted in Figure 3, the odorant semantics are modeled as a pair of tensors ( b, d), where b, d denote the 3-dimensional tensor of binding and dissociation rates, respectively. Here, a tensor is simply seen as a generalization of vectors and matrices into multidimensional arrays. In 3D these tensors are a function of, respectively, the odorant identity, the olfactory receptor type and the index of the OSN that expresses the receptor type. Therefore, each entry of b represents the binding rate of odorant o interacting with olfactory receptor r expressed by OSN n, where o∈1,···,O , r∈1,···,R and n = 1,···,N , and O is the the number of odorants, R is the number of olfactory receptor types and N is the number of OSNs that express a specific receptor type (see Figure 3). d is similarly constructed (see Figure 3). The odorant syntax is modeled as a temporal signal, characterized by its odorant concentration waveform. Even though this signal has no bandwidth limitation as the natural odorant concentra- tion can widely fluctuate in high velocity odorant plumes, the odorant transduction process acts as a low-pass filter that limits the bandwidth of the concentration waveform [16]. This aligns well with the key objective of olfaction, that is to extract the identity, or semantics of the odorant and not its syntax. Existing recordings of OSN responses [17, 18] have been used to estimate the affinity [10], i.e., the ratio between binding and dissociation rates. However, no recordings are currently available for individually extracting the binding and dissociation rates. New experiments for identifying the odorant-receptor dissociation rates are in order. In sum, the olfactory objects of the odorant space are explicitly described by both their identity (odorant semantics) and their concentration amplitude (odorant syntax). 6 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint 2.3 Olfactory Transduction in the Antenna Multiplicatively Couples Odorant Semantic and Syntactic Information In the first stage of olfactory processing, odorant molecules bind to olfactory receptors expressed by each OSN residing on the Antennae and Maxillary Pulps, and thereby starting the olfactory transduction process. The spikes generated by the OSNs are transmitted to the Antennal Lobe. The olfactory transduction, and, the spike generation and transmission run largely in parallel among OSNs. Recent discovery of ephaptic coupling, however, suggests that there are additional lateral interaction between OSNs whose dendrites are housed in the same sensillum [19]. Our model currently does not account for interactions between OSNs. Figure 4: Olfactory transduction process. (left) The molecular machinery of odorant transduction. A cartoon of a sensillum that houses an OSN. Odorant molecules enter through the sensillum pores into sensillum lymph, to be transported to the membrane of OSN dendrites by odorant binding proteins (OBPs) [20]. The binding of odorant molecules to ORs starts a transduction cascade that opens ion channels located on the OSN dendrites. The transduction current then induces the OSNs to generate action potentials. Adapted from [21]. (right) Schematic diagram of the Olfactory Transduction Process for a set O of odorant mixture components, o ∈ O pure odorant. The OTP has 3 stages. In the first stage, also known as the active receptor model, each odorant mixture component is processed by a peri-receptor process followed by a feedback controlled receptor binding process that depends on the receptor binding of the other odorant components. The output of the bounded receptor generator is then fed into the second stage, the co-receptor channel model, that generates the transduction current. Finally, a biophysical spike generator model converts the transduction current into a spike train. The Olfactory Transduction Process (OTP) model shown in Figure 4 consists of 3 stages. The first stage is the Peri-Receptor Process block modeling the interaction between odorants and the olfactory sensilla before the odorant-receptor binding takes place. This process reduces the rapid fluctuations of the odorant concentration waveform and enhances the response to concentration gradients [16]. The second stage shown in Figure 4 is the binding process. At any point in time, the number of bound receptors depends on the amplitude of the concentration waveform of the odorant (syntax), and, the binding rate as well as the dissociation rate between the odorant and the olfactory receptors (semantics). The semantic and syntactic information of the odorant are multiplicatively coupled during the binding process [10]. Note that it is not possible to separate the two information streams from the spikes generated by a single OSN, as two different odorants with different concentration waveforms may evoke the same OSN spike response. Thus, without the entangling of the two types of information streams across the population of OSNs, odorants cannot be identified. This is similar to sensing light intensity reflected by an object with a Lambertian surface, which depends on both the luminous intensity and the reflectance of the surface material [22]. The third stage shown in Figure 4 is the co-receptor channel that models the opening of transduction 7 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint ion channels by the total bound receptors. The opening of the ion channels is also controlled by a feedback mediated calcium concentration. Finally, the transduction current shown in Figure 4 is encoded by a biophysical spike generator (BSG) into the spike domain. Concluding Section 2.2 and Section 2.3, objects of the odorant space are characterized by the odorant-receptor binding rate ( b) and dissociation rate ( d), and the odorant concentration wave- form amplitude (u(t)). • (b, d) defines the odorant object identity (semantic information), while the concentration waveformu(t) carries syntactic (Shannon) information. • The odorant stimulus is multiplicatively encoded as (receptor ( r), odorant (o), neuron (n)) ([b]ron·u(t), [d]ron), r = 1, 2,...,R,o= 1, 2,...,O,n = 1, 2,...,N. Since the semantic and the syntactic information are multiplicatively coupled, they can not be separated from the response generated by a single OSN. 2.4 The Antennal Lobe Extracts Semantics and Semantic Timing Events The Antennal Lobe (AL) consists of some 50 glomeruli. Each glomerulus is the target of OSNs that express a single olfactory receptor type. Uniglomeruli projection neurons (uPNs) also exclusively arborize in only a single glomerulus. For example, in Figure 5(top left), we show the DL3 and VA3 glomeruli. For the DL3 glomerulus, the at4B OSNs (cyan) expressing Or65a project from the antennal lobe into the glomerulus, and provide inputs to DL3 uPN (magenta), and the synapses are shown in pink. For the VA3 glomerulus, the ab9 OSNs (light green) expressing Or67b synapse onto the VA3 PN (yellow). In addition to this feedforward connection within each glomerulus, a complex network of Local Neurons (LNs) also arborize in varying number of glomeruli to facilitate local and global feedback processing within and between glomeruli [23]. In Figure 5(A), we show an instance of a LN (in transparent light green) that innervates all glomeruli. In [23], we have characterized the interaction of LNs with OSNs and PNs in each glomerulus, showing a diverse range of patterns. Some LNs receive feedforward inputs from OSNs and feedback inputs from PNs while providing feedback to both. Others may have a subset of these connections. While the uPNs receive dedicated inputs only from a single type of OSNs, LNs enables crosstalk between them, and therefore the outputs of the AL carried by PNs are the result of inter-glomerular processing. However, the connections of LNs are too complex to be used directly in revealing their individual functions. To go beyond the connectome, our first step is to postulate the overall functionality of the different classes of LNs based on the connectivity features observed in the connectome. Building on the 2D encoding model of OSN transduction [10], we introduced in [11] a new class of biophysical models termed differential Divisive Normalization Processors (differential DNPs). They are designed explicitly to extract odorant semantic information from olfactory signals carried by OSNs. These models are functionally related to the (convolutional) DNPs previously developed for the fly early visual system to model spatio-temporal feedforward and/or feedback control [13]. 8 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint Here, they are reformulated to operate in the temporal and spatio-temporal domains relevant to olfaction. We advanced temporal differential DNPs for single-channel AL circuits and spatio-temporal differ- ential DNPs for multi-channel AL circuits, incorporating three types of local neurons that shape information flow within the AL: (i) pre-synaptic pan-glomerular inhibitory local neurons (Pre-LNs), (ii) post-synaptic uni-glomerular excitatory local neurons (Post-eLNs), and (iii) post-synaptic uni- glomerular inhibitory local neurons (Post-iLNs). For single-channel AL circuits modeled as 3 parallel temporal differential DNPs (see Figure 5(B) within each glomerulus dashed box), we found that the divisive normalization mediated by the Pre-LN plays a central role in enhancing the concentration-invariance of the PN responses, which we interpret as a first step toward extracting odorant semantics. In parallel, the transient PN responses show a stronger correlation with the concentration contrast. Post-eLN excitation and Post-iLN inhibition selectively enhance transient PN responses at stimulus onset and offset, a response feature we refer to as contrast boosting. These dynamics strongly amplify the contrast of PN transients relative to OSN responses, allowing precise signaling of odorant semantic timing information. Scaling from single-channel to multi-channel AL circuits (see Figure 5(B)), concentration-invariant PN population responses can be achieved across all channels. We hypothesized that this invariant PN activity corresponds to a reconstruction of the odorant semantics in the form of the odorant affinity rate vector as the element-wise ratio between binding and dissociation rates defined in the model of odorant space in Section 2.2. In Figure 6, we show the responses of OSNs and PNs to different pure odorants and mixtures at different concentrations and mixture ratios. We note that the steady-state OSN responses (Figure 6, middle column) are clearly dependent on the odorant concentrations, whereas such dependence is largely removed in the PN responses (Figure 6, right column). This demonstrates that the spatio-temporal differential DNP along the Pre-LN pathway is critical for the recovery of the odorant semantics at the level of PNs (see Figure 5(C4)). At the same time, the contrast-boosted transient components of PN responses encode ON and OFF timing events associated with changes in odorant semantics across all channels (see Fig- ure 5(C2,C3)). Together, the multi-channel AL circuits disentangle the confounded semantic and syntactic information streams at the output of the Antenna, and encode both the identity and the timing information of the odorant objects into the PN output spike trains (see Figure 5(C6)) In summary, the functional logic of the AL is that of an ON-OFF odorant object identity recov- ery processor, robustly extracting odorant semantics as well as the precise temporal structure of semantic changes [11]. 2.5 The Mushroom Body Calyx Maps Semantics into a First Spike Sequence Code The Mushroom Body Calyx largely consists of the axons of the uniglomerular PNs, dendrites of the Kenyon Cells and the multi-input multi-output APL neuron (see Figure 7(A)). PN axons terminals (Figure 7(A) in yellow, blue and magenta) form large boutons in the Calyx, with numerous presynaptic sites providing inputs to many KCs and the APL neuron. Akin to the OSN axon terminals, PN boutons also receive feedback from the APL neuron. Synapses around a PN bouton 9 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint Tim e [sec] 0 200[ppm ] Acetone Concentraion Waveform 5 10 15 1 59b 23 Channel Index Post- eLN to PN Synaptic Current 5 10 15 1 59b 23 Channel Index Post- iLN to PN Synaptic Current 5 10 15 5 10 15 1 59b 23 Channel Index OSN Axon- Term inal to PN Synaptic Current 0 5 10 Synaptic Current [ A] 0 200[ppm ] Acetone Concentraion Waveform 5 10 15 5 10 15 Tim e [sec] Or2a Or7a Or9a Or10a Or19a Or22a Or23a Or35a Or43a Or43b Or47a Or47b Or49b Or59b Or65a Or67a Or67c Or82a Or85a Or85b Or85f Or88a Or98aChannel Index Multi- Channel PN PSTH 0 20 40 60 80 100 120 140 PN PSTH [Hz] OSN to Post-eLN Synapse OSN Axon T erminal OSN Axon T erminal OSN to Post-iLN Synapse Post-iLN Post-iLN to PN Synapse Post-eLN Pre-LN OSN PN OSN-to-PreLN Synapse OSN-to-PreLN Synapse OSN to PN Synapse OSN to PN Synapse Post-eLN to PN Synapse OSN to Post-eLN Synapse OSN to Post-iLN Synapse Post-iLN Post-iLN to PN Synapse Post-eLN OSN PN Post-eLN to PN Synapse VA3 Glomerulus DL3 Glomerulus Other Glomeruli A B C1 C2 C3 C4 C5 C6 Figure 5: (A) Morphology of a small number of neurons in the AL of the fruit fly brain and (B) a multi- channel AL model architecture. Two glomeruli are shown: DL3 glomerulus with OSNs in cyan and uPN in magenta, VA3 glomerulus with OSNs in light green and uPN in yellow. Synapses are shown in light pink. A Pre-LN is shown in transparent green across the Antennal Lobe. The multi-channel AL model architecture has the same color code for each block. (bottom) an evaluation of the input/output relationship of the AL model architecture. (C1,C5) Acetone staircase odorant concentration waveform recorded in [24]. (C2) Post-eLN to PN synaptic currents. Different hues of red indicate strengths of synaptic current, with strongest due to the Post-eLN receiving input from the Or59b OSN indicated in dark red. (C3) Post-iLN to PN synaptic currents. Different hues of blue indicate strengths of synaptic current, with strongest due to the Post-iLN receiving input from the Or59b OSN indicated in dark blue. (C4) OSN Axon-Terminal to PN synaptic current shown as a heatmap. Different hues of grey indicate strengths of synaptic current. Refer to the colorbar for scale. (C5) Multi-channel PN PSTH, with synaptic current of ON/OFF pathways along Or59b/DM4 channel shown as red and blue arrows, respectively. Figure adapted from [11]. 10 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint Pure Odorants Odorant Mixtures A1 A2 B1 B2 B3 Figure 6: OSN and PN responses to different pure odorants and odorant mixtures. (A) Pure odorants: (A1) Furfural, (A2) 1-Butanol. (B) Odorant mixtures: (B1) Furfural : 1-Butanol = 2 : 1, (B2) Furfural : 1-Butanol = 1 : 1, (B3) Furfural : 1-Butanol = 1 : 2. First column: The affinity of the pure odorant or odorant mixture for each olfactory receptor-type, sorted in descending order. Second column: The responses of OSNs when the EOS is presented the pure odorant or odorant mixture. For each pure odorant, 4 different constant concentrations are included: 200ppm, 150ppm, 100ppm and 50 ppm. The steady state OSN responses for each odorant concentration are sorted in descending order. For odorant mixtures, 4 different concentrations of Furfural are used while the ratio of the two odorants are always kept the same. Third column: The responses of the PNs sorted in descending order. form what is collectively called a microglomerulus [25]. Each of the KCs, on the other hand, forms several discrete dendritic claws (Figure 7(A) in turquoise). Each claw is typically associated with a single PN bouton. On average, each KC has 6 to 7 claws, connecting to the same number of different PNs. Thus, with a total of ∼2,000 KCs and ∼50 types of uPNs, the olfactory signal represented by the PNs undergoes an expansive transformation. In addition to PN boutons and KC dendrites, an APL neuron (Figure 7(A) in red) covers the entire Mushroom Body, including the Calyx. It receives inputs from almost all PN boutons and all KCs, and also provides them with feedback. We map the Calyx circuit into a circuit model, whose schematic diagram is shown in Figure 7(B). Note that the color code in the circuit diagram is consistent with the color code in the visualization of the morphology. For simplicity, the PN inputs are linearly summed [26]. We notice that the summed PN inputs are still concentration dependent, as shown in Figure 7(C and D, column 1). We model the APL to KCs feedback circuit as a DNP, as shown in Figure 7(B). This DNP largely 11 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint reduces the concentration dependency at the KC dendritic output, demonstrated in Figure 7(C1 and C3, column 2). In contrast, by silencing the APL neuron and thereby removing the feedback of the Calyx circuit, the KC dendritic output no longer exhibits sparseness. Neither is it diverse across different odorants (see Figure 7(C2 and C4)). Additional DNPs modeling the interaction between PN boutons and the APL neuron can be simi- larly constructed. We omit them here for simplicity. After the connectivity driving the APL feedback, we simply merge the first spike of each of the KC responses to form a first spike sequence code, as shown in Figure 7(C,D column 3). This code reflects the ordered strength of the concentration-invariant KCs dendritic output. Code utilizing ordered strength of a population of neurons has also been observed in the Antenna and Antennal Lobe [28, 29, 30, 31, 32], as well as in the piriform cortex of vertebrates [33], and proposed for modeling circuits in the visual system [34, 35]. Note that the cumulative inter-spike interval of the first spike sequence code, shown in Figure 7(C1 and C3, column 4), is highly conserved for different concentrations of the same odorant, but diverse for different odorants. This diversity, however, is largely reduced by the absence of the APL neuron feedback (see Figure 7(C2 and C4, column 4)). For a comparison between the Calyx circuit with and without APL neuron feedback for all odorants tested, see Supplementary Figure S1. The expansion from the PNs to KCs and the readout of the ordered strength is a simple yet effective strategy for extracting features of the PN output vector. Moreover, the readout of the KC code by the downstream MBON is similarly kept simple. MBONs receive inputs from all KCs that project to the corresponding compartment. The code can be generally applied on different flies even though the connection between PNs and KCs are considered random and differs among different flies. 12 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint KC Dendrtite KC Dendrite APL PN KC PN KC PN-to-KC Synapse PN-to-KC Synapse PN PN-to-KC Synapse KC-to-APL Synapse KC-to-APL Synapse APL-to-KC Synapse APL-to-KC Synapse 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 100Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 250 500Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 100 200Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 500Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 100Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 100 200Event Count 0 200 400 600 800 1000 Rank of KC 0 100 Dendritic Input Strength 0 200 400 600 800 1000 Rank of KC 0.0 0.5 1.0Dendritic Output 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Tim e (m s) First Spike Sequence 0.0 2.5 5.0 7.5 10.0 12.5 15.0 Tim e (m s) 0 100 200Event Count BA Pure Odorants Odorant Mixtures C1 C2 C3 C4 D1 D2 D3 Figure 7: (A) Schematic morphology of a small subset of neurons in the Calyx. (red) APL, (turquoise) KCs, (other colors) PNs. (B) Schematic diagram of the Calyx circuit with spatio-temporal APL feedback. APL feedback facilitates the extraction of odorant semantic information by normalizing KC responses and by reducing odorant concentration dependence of the KC dendritic output [27]. (C1-C4) Response in the Calyx circuit to different pure odorants. (C1) Furfural, (C2) Furfural with APL feedback silenced, (C3) 1-Butanol, (C4) 1-Butanol with APL feedback silenced. For each pure odorant, 4 different constant concentrations are included: 200ppm, 150ppm, 100ppm and 50 ppm. (D1-D3) Response in the Calyx circuit to odorant mixtures. (D1) Furfural : 1-Butanol = 2 : 1, (D2) Furfural : 1-Butanol = 1 : 1, (D3) Furfural : 1-Butanol = 1 : 2. For odorant mixtures, 4 different concentrations of Furfural are used while the ratio of the two odorants are always kept the same. (1st column) Ranking of KC dendritic inputs. (2nd column) Ranking of KC dendritic outputs. (3rd column) Odorant semantics encoded in the time domain across the population of KCs. The first spikes of each of the active KCs in response to each odorant are collected onto a single row for each of the odorant concentration amplitude values. (4th column) Cumulative inter-spike interval of the first spike sequence. 13 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint 3 Odorant Semantics Classification The outputs of the KCs feed directly into the associative memory circuits of the Mushroom Body compartments. There, the integrated processing of the odorant semantics carried by the KCs and the sensory semantics carried by the Dopaminergic neurons (DANs) underlies the associative learning process. Olfaction is a highly effective sensory modality that helps the fly associate with non-olfactory semantics, such as an electric shock and a taste of sugar. Furthermore, sensory semantics such as starvation or cold can also be recalled by the odorant semantics alone. To support associative learning mechanism in the MB compartments, the MB must be able to distinguish currently experiencing odorant semantics from the stored semantics [36]. Here, we incorporate ranking information as marks into the first spike sequence code. The marks provide the ranking information of the KC neurons that generated the first spikes in the sequence. In order to classify the marked first spike sequence code generated in response to pure odorants we employ a distance measure based on the ranking information carried by the marks of first spike sequence code. Note that, typical rank correlation coefficients due to Kemeny-Snell [37] or Emond-Mason [38] are not sensitive to a mutual swap of KC ranks at different positions. For example, swapping the 1st and 10th, and swapping the 11th and 20th items result in the same rank correlation with respect to the original, unswapped rank sequence. In the KC (first spike sequence) responses, the higher-ranked KCs are clearly more important than the lower-ranked KCs that do not spike. Therefore, we use a weighted rank correlation measure [39] when defining the distance between two first spike sequence codes (see Appendix for details). If two rankings are identical, then the distance is 0. If two rankings are exactly the reverse of each other, the distance is 1. A distance of 0.5 suggests that the correlation coefficient between the two sequences is 0. We ask if the identity of an odorant (semantics) represented in the marks of the first spike sequence code, when stored in the MB associative memory, can be recalled by the same odorant but not others. As an example, in Figure 8(A1), we consider acetone as the associated odorant and compute the distance of the marks of the marked first spike sequence code of acetone with that of the other 103 odorants. The distance between two odorants is calculated as the minimum distance across all pairs of concentrations. The histogram of the evaluated distances is shown in blue. We also computed the maximum distance between first spike sequence codes from responses to acetone of different concentrations. This is indicated by the blue vertical line. Two cases are considered in Figure 8(A1): with/without APL feedback. On top of Figure 8(A1) (with APL) we can see that acetone can be largely differentiated from the other odorants by the proposed distance measure, except for 2-butanone, whose affinity profile is largely the sane as the one of acetone for the 23 odorant receptors model we used here. This exception may be dropped when the full spectrum of 50 odorant receptors is available. When the APL neuron is silenced, the rank distances produced by the circuit with APL feedback present (shown at the bottom of Figure 8(A1)) are closer to 0.5, indicating that the APL neuron decreases the correlation between the first spike sequence codes of different pure odorants. Figures 8(A2-A4) show similar observations of the shift of the distance measures towards 0.5. In fact, this can be observed for almost all odorants (see Supplementary Figure S2). Figure 8(B) shows an aggregation of the distances between all pairs of different odorants. We can see a clear shift in the distribution of pairwise distances when APL feedback is present in the Calyx circuit model. By shifting the distance measure between the first spike sequence codes for different odorants toward 14 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint 0.5, less classification error will be made by bounding the distance range of different concentrations for the same odorant. This suggests the circuit with APL feedback potentially leads to a better classification of the first spike sequence codes, and therefore, the underlying odorant semantics. Figure 8: Role of APL feedback in shaping distances between the first spike sequence codes. (A1) Histograms of distances between the first spike sequence code of acetone and the other 103 odorants. The minimum distance between two odorants across all concentration pairs is defined in appendix A. Blue vertical line indicates the maximum distance between first spike sequence codes responding to acetone of different concentration levels. Top is from KC responses of a Calyx model with APL feedback. Bottom is from KC responses of a Calyx model without APL feedback. (A2-A4) Same as A1 but for octanoic acid, ethyl butyrate and 1-butanol, respectively. (B) Histogram of distance measures between the first spike sequence codes of all pairs of two odorants. Distances calculated from KC responses (blue) of a Calyx model with APL feedback and (orange) without APL feedback. The result shown here suggests that the marked first spike sequence code is a strong candidate for the representation of odorant semantics at the output of the MB Calyx. Across all pairs of odorants simulated, the error rate of making an incorrect decision using a global threshold across all odorants is only 0.61%. Thanks to the APL feedback, this error rate can still be kept low when more odorants are considered. Compared to a binary code with activated KCs labeled as 1 and 0 otherwise [40, 41], rank-based distance measure can further differentiate the code as different ranking can be placed on the same set of activated KCs. Yet, the marked first spike sequence code can naturally carry such rank information without further effort for extracting the ranking. In Figure 7, we have argued that the feedback from the APL neuron is capable to largely normalize the range of KC outputs across different concentrations, leading to a more “standard” output from inputs with a varying range. This evaluation is, to a degree, similar to the evaluation of the Pre-LN feedback in the AL in Figure 5, as both feedback circuits are extracting odorant semantics. 15 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint In contrast, the classification of the marked KC first spike sequence codes provides a novel way of evaluating the effectiveness of the (large scale MIMO) APL feedback neuron in the Calyx circuit. The rank-based distance measure allows for the comparison between the extracted semantics, a key aspect of olfactory intelligence. The evaluation of the effectiveness of the APL feedback neuron through the rank-based distance measure between the ranks of the KC outputs highlights the key role played by the APL neuron as part of an intelligent olfactory processor involved in associative learning. 4 Discussion We have extensively argued in [27] that, traditional applications of methods of information theory, signal processing and control theory to odor signal processing is lacking the notion of “meaning” or semantics. Shannon himself did not address the challenges of formalizing the concept of semantic information, arguing that “a bit is a bit” and there is no meaning associated with “bits’ [12]’ . In olfaction, different odorant identity and concentration pairs can lead to the same OSN spike train response [42]. To make the world of odorants intelligiable, we explicitly modeled odorant stimuli by theoretically and computationally characterizing their object identity (“semantic information” or “semantics”), and concentration waveform (“syntactic information” or “syntax”) [10]. Under this model, semantic information is time-independent and is characterized by a tensor, reflecting the fact that odorant object identity is encoded collectively with spatially-distributed sensors. Odorant syntax, on the other hand, are time-varying and embedded in the individual sensor responses. This forms a baseline relating odorant space with the representation of semantic and syntactic information at the first 3 stages of early olfactory processing: the Antenna, Antennal Lobe and MB Calix circuits. Key questions that early olfactory systems must address are (i) how to disentangle the odorant semantic information from the odorant syntactic information, and (ii) how to classify odorant identity (semantics). To address these questions, we introduced a class of differential Divisive Normalization Processors (DNPs) for modeling the AN, AL and MB Calyx circuits. DNPs are temporal and spatio-temporal processing building blocks described by non-linear differential equations with largely stable temporal and spatio-temporal feedback loops. Differential DNPs provide a generalization of divisive normalization models previously considered in experimental settings [43]. A key first element of olfactory intelligence in the Drosophila is the binding of odorant objects to receptors expressed in the OSNs. The odorant semantics and syntax are multiplicatively coupled during the process of olfactory transduction by the OSNs in the Antenna. For odorant objects encoded by the spatially-distributed receptors expressed by the OSNs, the spatio-temporal DNPs employed in the AL and the Calyx largely reduce the concentration depen- dency and extract the semantic information from the confounding representation of the Antenna. The DNP circuit in the Calyx, involving a PN-KC expansion circuit and APL feedback circuit, underlies a novel representation of the odorant semantics as a first spike sequence code. The code reflects the amplitude ranking that drives the KCs in the time domain. Strikingly, the APL feedback not only removes the concentration dependency of the KC outputs, but also increases the ranking distance between the marked first spike sequence codes representing different odorant identities. Thus, the rank-based representation supports accurate classification of odorant semantics. 16 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint The natural representation of semantics accessing the associative memory circuit lies in the spike domain. Time is an intrinsic variable of the concentration waveform, but not of the odorant object identity. As the temporal variability of the concentration waveform is largely removed from the extracted semantics, spike timing in the first spike sequence code represents the odorant semantic information. The order of the first spikes in the time domain across the population of KCs reflects the ranking order of the amplitude at negligible complexity. This supports a low complexity rapid readout of the semantic information at the KC-MBON synapses where associative memory is assumed to reside. The feedback circuits in the early olfactory system discussed here are instrumental in extracting odorant identity information (semantics) from the confounding odorant syntactic information (con- centration) as well as in boosting the accuracy in classifying odorant semantics. Feedback circuits are extremely common in the fruit fly brain across modalities [44, 45]. However, current models of fly circuits mainly focus on the on using syntactic information models and largely ignore the processing of semantic information given the, abounding number of, feedback circuits in higher brain neuropils. Feedback circuits based on large scale MIMO neurons, such as the APL neuron, call for novel methods of end-to-end evaluation/classification. We put forth here a novel method of evaluating the effectiveness of the APL feedback neuron based on information carried by the marked first spike sequence code of the input Calyx circuit. This is a rather simple methodology given that ranking is in the amplitude domain, by itself, NP-complete. This opens up a new research direction in feedback control/processing of semantic information. Another set of important questions in olfactory intelligence arises in dealing with odorant mixtures. As previously observed in many olfactory systems, odorant mixtures can be perceived as configural or elemental [46, 47, 48], and receptor binding of odorant mixtures is more complex than in simple linear model [49, 50, 51]. In addition, olfactory processing already starts with ephaptic coupling between the OSN axons [19, 52, 53]. This has important implications on the processing of odorant semantics. Under what conditions would an odorant mixture considered as a new odor, and when would it be possible to identify the odorants composing a mixture? These questions apply when the mixture is associated with a single odorant object. An odorant mixture also arises when multiple objects are presented at the same time. This is similar to the cocktail party problem in audition, as the task of the olfactory system is to recognize a particular odorant or mixture from a background of odorant mixtures. How can odorant semantics be defined and how does odorant syntax play a role in recognizing these separate objects? What is the condition that an odorant can be overshadowed by a mixture of odorants? The answer may lie in a more in-depth modeling of the space odorant mixture semantics and syntax as well as the feedback circuits that operate on semantic information in higher neuropils of the fruit fly brain. 17 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint

[1] Richard Benton. Drosophila olfaction: past, present and future. Proceedings of the Royal Society B, 289(1989):20222054, 2022. [2] Brian C. Smith. The Promise of Artificial Intelligence. The MIT Press, 2019. [3] Fernando Martin, Tamara Boto, Carolina Gomez-Diaz, and Esther Alcorta. Elements of olfac- tory reception in adult drosophila melanogaster. The Anatomical Record, 296(9):1477–1488, 2013. [4] Joerg Fleischer, Pablo Pregitzer, Heinz Breer, and J¨ urgen Krieger. Access to the odor world: olfactory receptors and their role for signal transduction in insects. Cellular and Molecular Life Sciences, 75(3):485–508, February 2018. [5] Nicolas Y. Masse, Glenn C. Turner, and Gregory S.X.E. Jefferis. Olfactory information pro- cessing in drosophila. Current Biology, 19(16):R700–R713, 2009. [6] Xu Liu and Ronald L Davis. The GABAergic anterior paired lateral neuron suppresses and is suppressed by olfactory learning. Nature Neuroscience, 12(1):53–59, January 2009. [7] Maria Papadopoulou, Stijn Cassenaer, Thomas Nowotny, and Gilles Laurent. Normalization for sparse encoding of odors by a wide-field interneuron. Science, 332(6030):721–725, 2011. [8] Yoshinori Aso, Daisuke Hattori, Yang Yu, Rebecca M. Johnston, Nirmala A. Iyer, Teri T.B. Ngo, Heather Dionne, L. F. Abbott, Richard Axel, Hiromu Tanimoto, and Gerald M. Rubin. The neuronal architecture of the mushroom body provides a logic for associative learning. eLife, 3:e04577, 2014. [9] Aurel A. Lazar, Tingkai Liu, Mehmet Kerem Turkcan, and Yiyin Zhou. Accelerating with flybrainlab the discovery of the functional logic of the Drosophila brain in the connectomic and synaptomic era. eLife, 10:e62362, feb 2021. [10] Aurel A. Lazar and Chung-Heng Yeh. A molecular odorant transduction model and the com- plexity of spatio-temporal encoding in the Drosophila antenna. PLOS Computational Biology, 16(4):e1007751, 4 2020. [11] Aurel A. Lazar, Tingkai Liu, and Chung-Heng Yeh. The functional logic of odor information processing in the drosophila antennal lobe. PLOS Computational Biology, 19(4):1–33, 04 2023. doi: 10.1371/journal.pcbi.1011043. [12] Claude E. Shannon. A mathematical theory of communication. The Bell System Technical Journal, 27(3), July 1948. [13] Aurel A. Lazar, Nikul H. Ukani, and Yiyin Zhou. Sparse identification of contrast gain control in the fruit fly photoreceptor and amacrine cell layer. The Journal of Mathematical Neuro- science, 10(1):3, 2020. doi: 10.1186/s13408-020-0080-5. [14] Josefina del M´ armol, Mackenzie A. Yedlin, and Vanessa Ruta. The structural basis of odorant recognition in insect olfactory receptors. Nature, 597(7874):126–131, 9 2021. 18 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint [15] Ngoc Tran, Daniel Kepple, Sergey Shuvaev, and Alexei Koulakov. DeepNose: Using artificial neural networks to represent the space of odorants. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 6305–6314. PMLR, 09–15 Jun 2019. [16] Anmo J. Kim, Aurel A. Lazar, and Yevgeniy B. Slutskiy. System identification of drosophila olfactory sensory neurons. Journal of computational neuroscience , 30(1):143–161, 2011. [17] Elissa a Hallem and John R Carlson. Coding of odors by a receptor repertoire.Cell, 125(1):143– 60, April 2006. [18] Daniel M¨ unch and C. Giovanni Galizia. DoOR 2.0 - comprehensive mapping of drosophila melanogaster odorant responses. Scientific Reports, 6:21841, 2 2016. [19] Chih-Ying Su, Karen Menuz, Johannes Reisert, and John R. Carlson. Non-synaptic inhibition between grouped neurons in an olfactory circuit. Nature, 492(7427):66–71, 2012. [20] Nikki K Larter, Jennifer S Sun, and John R Carlson. Organization and function of Drosophila odorant binding proteins. eLife, 5:e20242, nov 2016. [21] Nath´ alia F. Brito, Monica F. Moreira, and Ana C.A. Melo. A look inside odorant-binding proteins in insect chemoreception. Journal of Insect Physiology, 95:51–65, 2016. [22] Berthold K.P. Horn. Robot Vision. The MIT Press, 1986. [23] Aurel A. Lazar, Mehmet Kerem Turkcan, and Yiyin Zhou. A programmable ontology en- compassing the functional logic of the drosophila brain. Frontiers in Neuroinformatics , 16, 2022. [24] Anmo J. Kim, Aurel A. Lazar, and Yevgeniy B. Slutskiy. Projection neurons in drosophila antennal lobes signal the acceleration of odor concentrations. eLife, page e06651, 2015. [25] Kouji Yasuyama, Ian A. Meinertzhagen, and Friedrich-Wilhelm Sch¨ urmann. Synaptic orga- nization of the mushroom body calyx in drosophila melanogaster. Journal of Comparative Neurology, 445(3):211–226, 2002. [26] Eyal Gruntman and Glenn C Turner. Integration of the olfactory code across dendritic claws of single mushroom body neurons. Nature neuroscience, 16(12):1821–9, 12 2013. [27] Aurel A. Lazar, Tingkai Liu, Chung-Heng Yeh, and Yiyin Zhou. Modeling and characterization of pure and odorant mixture processing in the Drosophila mushroom body calyx. Frontiers in Physiology: Invertebrate Physiology, 15, 2024. [28] Rafi Haddad, Anne Lanjuin, Linda Madisen, Hongkui Zeng, Venkatesh N Murthy, and Naoshige Uchida. Olfactory cortical neurons read out a relative time code in the olfactory bulb. Nature Neuroscience, 16(7):949–957, 2013. [29] Christopher D. Wilson, Gabriela O. Serrano, Alexei A. Koulakov, and Dmitry Rinberg. A primacy code for odor identity. Nature Communications, 8(1):1477, 2017. [30] David Zwicker. Primacy coding facilitates effective odor discrimination when receptor sensi- tivities are tuned. PLOS Computational Biology , 15(7):1–22, 07 2019. 19 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint [31] Edmund Chong, Monica Moroni, Christopher Wilson, Shy Shoham, Stefano Panzeri, and Dmitry Rinberg. Manipulating synthetic optogenetic odors reveals the coding logic of olfactory perception. Science, 368(6497):eaba2357, 2020. [32] Alexander Egea-Weiss, Alpha Renner, Christoph J. Kleineidam, and Paul Szyszka. High pre- cision of spike timing across olfactory receptor neurons allows rapid odor coding in drosophila. iScience, 4:76–83, 2018. [33] Kevin A. Bolding and Kevin M. Franks. Recurrent cortical circuits implement concentration- invariant odor coding. Science, 361(6407):eaat6904, 2018. [34] Rufin Van Rullen and Simon J. Thorpe. Rate Coding Versus Temporal Order Coding: What the Retinal Ganglion Cells Tell the Visual Cortex. Neural Computation, 13(6):1255–1283, 06 2001. [35] Tim Gollisch and Markus Meister. Rapid neural coding in the retina with relative spike latencies. Science, 319(5866):1108–1111, 2008. [36] Andrew C. Lin, Alexei M. Bygrave, Alix De Calignon, Tzumin Lee, and Gero Miesenb¨ ock. Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination. Nature Neuroscience, 17(4):559–568, 2014. [37] J.G. Kemeny and Snell J.L. Mathematical Models in the Social Sciences, chapter 2. Preference rankings an axiomatic approach, pages 9–23. The MIT Press, Cambridge, MA, 1962. [38] Edward J. Emond and David W. Mason. A new rank correlation coefficient with application to the consensus ranking problem. Journal of Multi-Criteria Decision Analysis, 11(1):17–28, 2002. [39] Antonella Plaia, Simona Buscemi, and Mariangela Sciandra. Consensus among preference rankings: a new weighted correlation coefficient for linear and weak orderings. Advances in Data Analysis and Classification , 15(4):1015–1037, December 2021. [40] James E M Bennett, Andrew Philippides, and Thomas Nowotny. Learning with reinforcement prediction errors in a model of the drosophila mushroom body. Nature Communications, 12(1):2569, May 2021. [41] Evripidis Gkanias, Li Yan McCurdy, Michael N Nitabach, and Barbara Webb. An incen- tive circuit for memory dynamics in the mushroom body of Drosophila melanogaster. eLife, 11:e75611, apr 2022. [42] A. A. Lazar and Y. B. Slutskiy. Identifying dendritic processing in drosophila osns. In Com- putational and Systems Neuroscience Meeting (COSYNE 2012) , February 2012. [43] Matteo Carandini and David J. Heeger. Normalization as a canonical neural computation. Nature Reviews Neuroscience, 13(1):51–62, 1 2012. [44] Aurel A. Lazar and Yiyin Zhou. Divisive normalization processors in the early visual system of the drosophila brain. Biological Cybernetics, 117(6):411–431, 2023. [45] Louis K Scheffer, C Shan Xu, Michal Januszewski, Zhiyuan Lu, Shin-ya Takemura, Kenneth J Hayworth, Gary B Huang, Kazunori Shinomiya, Jeremy Maitlin-Shepard, Stuart Berg, et al. A connectome and analysis of the adult Drosophila central brain. eLife, 9:e57443, 9 2020. 20 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint [46] James D Howard and Jay A Gottfried. Configural and elemental coding of natural odor mixture components in the human brain. Neuron, 84(4):857–869, November 2014. [47] Pramit Bandyopadhyay and Silke Sachse. Mixing things up! — how odor blends are processed in drosophila. Current Opinion in Insect Science , 59, 2023. [48] Matthias Durrieu, Antoine Wystrach, Patrick Arrufat, Martin Giurfa, and Guillaume Isabel. Fruit flies can learn non-elemental olfactory discriminations. Proceedings of the Royal Society B: Biological Sciences, 287(1938):20201234, 2020. [49] Jean-Pierre Rospars, Petr Lansky, Michel Chaput, and Patricia Duchamp-Viret. Competi- tive and noncompetitive odorant interactions in the early neural coding of odorant mixtures. Journal of Neuroscience, 28(10):2659–2666, 2008. [50] Vijay Singh, Nicolle R. Murphy, Vijay Balasubramanian, and Joel D. Mainland. Competitive binding predicts nonlinear responses of olfactory receptors to complex mixtures. Proceedings of the National Academy of Sciences of the United States of America, 116(19):9598–9603, 2019. [51] Gautam Reddy, Joseph D. Zak, Massimo Vergassola, and Venkatesh N. Murthy. Antagonism in olfactory receptor neurons and its implications for the perception of odor mixtures. eLife, 7:1–23, 2018. [52] Shiuan-Tze Wu, Jen-Yung Chen, Vanessa Martin, Renny Ng, Ye Zhang, Dhruv Grover, Ralph J. Greenspan, Johnatan Aljadeff, and Chih-Ying Su. Valence opponency in peripheral olfactory processing. Proceedings of the National Academy of Sciences, 119(5):e2120134119, 2022. [53] Mario Pannunzi and Thomas Nowotny. Non-synaptic interactions between olfactory receptor neurons, a possible key feature of odor processing in flies. PLOS Computational Biology , 17(12):e1009583, dec 2021. [54] Jos´ e Luis Garc´ ıa-Lapresta and David P´ erez-Rom´ an. Consensus measures generated by weighted kemeny distances on weak orders. In 2010 10th International Conference on In- telligent Systems Design and Applications , pages 463–468, 2010. Acknowledgments The results reported here were presented in part at the Workshop on the Functional Logic of Neural Circuits: Diamonds in the Rough, San Juan, Puerto Rico, February 28, 2024, at the Computational Neuroscience Meeting, CNS*24, July 20-24, 2024, Natal, Brazil, at the Symposium on Informers: Computational and Organizational Insights from the Insect Nervous System, Entomology 2024, Phoenix, AZ, November 10-13, 2024, and at the Workshop on the Nature of Intelligence, Bridging Animal and Artificial Intelligence , 4–5 September 2025, University of Sheffield, UK. The research reported here was supported, in part, by the National Science Foundation under grant #2024607 and grant #2400687. 21 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint A A Brief Definition of the Distance Measure of the First Spike Sequence Codes The distance between two first spike sequence codes is defined as a weighted rank correlation coefficient [39] using the ranking of KC outputs marked by the first spike sequence codes. Consider a set of m KCs whose times to first spike in response to odorant A is listed as the set {tA 1,tA 2,···,tA m}, wheretA j is the first spike time of the j-th KC. Let πbe a permutation of the index set (1, 2,...,m). By applying πon the KC index set, we obtain {tA π(1),tA π(2),···,tA π(m)}. We now construct a pair of matrices with a permutation πin response to odorant A as A+π=    a+ 11 π a+ 12 π ···a+ 1m π a+ 21 π a+ 22 π ···a+ 2m π .. . . . . ... . . . a+ m1 π a+ m2 π···a+ mm π    , A−π=    a− 11 π a− 12 π ···a− 1m π a− 21 π a− 22 π ···a− 2m π .. . . . . ... . . . a− m1 π a− m2 π···a− mm π    , (1) where a+ ij π=    1 if tA π(i)≤tA π(j) 0 if i =j −1 iftA π(i)>t A π(j) ,a− ij π=    1 if tA π(i)<t A π(j) 0 if i =j −1 iftA π(i)≥tA π(j) . (2) Note that the only difference between a+ ij πanda− ij πis whether 1 or−1, respectively, is assigned to the tied spike times. We now define the permutation πA that maps the KC index set into non-decreasing first spike time sequence tA πA(1)≤tA πA(2)≤···≤tA πA(m). We denote the set of first spike time KC responses to odorantB as{tB 1,tB 2,···,tB m}. The permutationπB maps the KC index set into the non-decreasing first spike time tB πB(1)≤tB πB(2)≤···≤tB πB(m). The weighted correlation coefficient between the first spike sequences in response to odorants A and B is defined as τw x (A,B ) = m∑ i<j ( a+ ij πA b+ ij πA +a+ ij πB b+ ij πB +a− ij πA b− ij πA +a− ij πB b− ij πB ) 2c (3) where w = [w1,w 2,···,wm−1] is a non-increasing weighting vector, and wi is the weight given to position i in the ranking, and, c = 2∑m−1 i=1 (m−i)wi is the maximum weighted Kemeny distance [54]. The normalized distance between the KC responses to odorants A and B amounts to dw(A,B ) = 1−τw x (A,B ) 2 , (4) and takes values in [0, 1]. dw(A,B ) = 0 indicates that the two first spike sequence ordering are the same. dw(A,B ) = 1 indicates the exact reverse order between the responses to A and B. dw(A,B ) = 0.5 will result in a correlation of 0, thus making the responses toA andB uncorrelated. In Section 3, we chosewi = 0.95i−1,i = 1, 2,···,m−1 and further normalize the weights such that m−1∑ i=1 wi = 1. 22 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted January 5, 2026. ; https://doi.org/10.64898/2026.01.05.697602doi: bioRxiv preprint