Seemingly Redundant Modules Enhance Robust Odor Learning in Fruit Flies

Thank you for constructive comments. We have revised the manuscript as follows：

1. Dual use of the symbol and explanations of $t_{jk}^X$ and $t_{kl}^{LN}$

We appreciate your careful observations to help us clarify ambiguities in the model description, particularly regarding notation consistency, which is critical for reader comprehension and strengthens the rigor and readability of our work.

We fully acknowledge that the dual use of the symbol X (to denote both layer and input) has introduced confusion. To address this, we will:

(1) Revise notation for clarity:

Introduce a distinct symbol for input (e.g., I) to replace X in the context of input data description.

(2) Add notation table for readability:

Explicitly define all symbols in a dedicated notation table at the beginning of the model section, specifying whether each denotes a layer, input, parameter, or variable, as well as its related meaning. Especially, $t_{kl}^{LN}$ in Eqs. 2 denotes the $l_{th}$ spike time of the $k_{th}$ local neuron (LN), while $t_{jk}^X$ in Eqs. 3 represents the $k_{th}$ spike time of the $j_{th}$ neuron in the $X_{th}$ layer. To standardize variable usage, we will revise $t_{jk}^X$ to $t_{jl}^X$. We further recheck all equations and text ensuring consistency with the revised notation, and add contextual cues when symbols first appear in each section to reinforce their meaning. These changes will eliminate notation overlap and make the model description more accessible.

2.More precise description of spiking threshold

Thank you for the question, which helps us clarify the rationale behind key modeling choices and enhance the precision of our description. We apologize for the ambiguity in using "slightly." To quantify this: the spiking threshold of mushroom body output neurons (MBONs) was set to 1.5 times the threshold of projection neurons (PNs) and kenyon cells (KCs). This range was determined based on the ratios of neurons and connection structure of the circuit:

(1) The highly convergent architecture from KCs to MBONs (KCs: MBONs $\approx$ 2000:1).

(2) Fully connected between KCs and MBONs.

A higher threshold of MBONs prevents excessive spiking which integrates signals from thousands of upstream KCs. We will revise the text to explicitly state this quantitative range.

3. Consideration of the learning site

The restriction of plasticity to a single set of weights (specifically, the synapses from the hidden layer to the readout layer) was guided by both biological plausibility and task-specific functionality:

(1) Biological relevance: In many neural circuits (e.g., olfactory or visual pathways), plasticity is often concentrated at "output interfaces" where signals are integrated for behavioral relevance, rather than being distributed uniformly across all synapses. This aligns with experimental observations that plasticity in downstream projection neurons is critical for forming task-specific representations.

(2) Functional necessity: Our task required the model to map hidden layer activity (encoding sensory features) to a categorical readout (e.g., odor discrimination). Pilot simulations showed that restricting plasticity to hidden-to-readout synapses was sufficient to achieve robust performance, while allowing plasticity in upstream layers introduced unnecessary complexity (e.g., unstable feature encoding) without improving results.

We will add these details to the Methods section, including a brief summary of control simulations that validated this choice (e.g., showing that plasticity in other weight sets did not enhance performance but increased computational cost).

These revisions will make our modeling decisions more transparent and grounded, strengthening the rigor of our work. We appreciate your guidance in refining these critical details.

4. Explanation of Figure 3

We appreciate your observation that the claim about LI inducing larger differences in population firing rates and patterns was not sufficiently clear in the current presentation. To address this, we will enhance the figure and its accompanying text in two ways:

(1) Additional commentary: We will add detailed descriptions of key features in Figure 3 (e.g., specific time windows where firing rate divergence is most prominent, and qualitative differences in pattern clustering between LI and control conditions).

(2) Quantitative analysis: We will try to include more quantitative metrics to make statistical comparisons of firing profile of distinct odors. These metrics will be reported in the text and summarized in a new panel or table within Figure 3, after surveying more research.

5. Explanation of Figure 4

We apologize for not clearly defining the "Low," "Medium," and "High" conditions (differentiated by blue shades) in Figure 4. To clarify, these reflect varying strengths of the respective mechanisms, achieved by systematically adjusting relevant synaptic weights across three levels: $w_{LN \rightarrow PN}$ in Eq. 2 for LI and $w_{\text{self},X}$ in Eqs. 3 for SFA. For both mechanisms, "Low," "Medium," and "High" correspond to increasing weights in an approximate 1:2:3 ratio.

We have added a detailed legend to Figure 4 and expanded the text in the Results section to explicitly describe these parameter manipulations, ensuring the relationship between the lines and the underlying mechanism strength is clear.

7.Corrections to minor points

(1) improves discrimination/ learning for discriminating odors

We fully agree that the original description in the abstract ("LI improves discrimination") is overly broad and fails to emphasize the key mechanism we demonstrate—specifically, that LI acts on the learning process underlying odor discrimination. We have modified the Abstract to clarify the core contribution of LI mechanism.

(2) Noise types

We acknowledge that the justification for assuming a normal distribution in odor noise was not sufficiently clear in the manuscript. This choice aligns with established conventions in olfactory modeling—widely adopted in Drosophila olfactory studies (e.g., [Cit 2]) and broader sensory neuroscience. This consistency enables direct comparison with existing models, supporting cumulative insights into how noise influences odor discrimination learning. We recognize that biological noise may deviate from strict normality in more real olfactory systems (e.g., due to stochasticity in receptor activation or neural firing). However, our choice prioritized tractability and comparability, which we now realize needed explicit explanation. To address this, we will add a brief discussion in the Methods section acknowledging this assumption, its alignment with previous literature, and explore non-normal noise distributions (e.g., OU process and power law noises) to further validate the generality of our findings.

(3) Inconsistency and explanation in notation

We apologize for the oversight in using both $\tau_{\mathrm{trace}\_\mathrm{LN}}$ and $\tau_{\mathrm{trace}\_\mathrm{ln}}$ to refer to the same parameter (the time constant of the local neuron voltage trace). To resolve this, we have standardized the notation throughout the manuscript to $\tau_{\mathrm{trace}\_\mathrm{LN}}$ (using uppercase "LN" to match the full term "Local Neuron" as defined in the text). This revision ensures consistency with our naming convention for other neuron-type-specific parameters and eliminates any potential confusion. The bold dot in Eqs. 3 and 8 denotes the inner product. To avoid confusion, we have added an explicit note in the text immediately preceding these equations, specifying that "the bold dot (•) represents the inner product operation between the respective vectors." This clarification ensures consistency with standard mathematical notation and aligns with the conventions used elsewhere in the manuscript.

We appreciate your attention to this detail, which enhances the clarity and rigor of our notation.

(4) References to the Figure 2

We apologize for failing to reference Figure 2 in the main text. To address this, we have added explicit citations to Figure 2 at relevant positions in the Results section. This revision ensures that the figure is properly integrated with the textual analysis, enhancing the coherence of the manuscript.

We appreciate your attention to this detail, which helps strengthen the clarity of our presentation.

(5) Color in the Table 1

We sincerely apologize for the errors and omissions.

1. Regarding the accuracy labeling: We have corrected the color of the first row, left column and right column, to accurately reflect the Base and SFA model’s performance level.

2. Concerning the color coding: We have added a note below the table specifying, “Color coding indicates performance levels: magenta denotes the best performance, purple denotes intermediate performance, and blue denotes the poorest performance. These revisions enhance the accuracy and clarity of Table 1. We appreciate your careful review, which helps improve the rigor of our presentation.

Thank you for your constructive comments. We have reflected on the content as follows:

1. Consideration of Flexible PN-to-KC connections

We thank the reviewer for highlighting this important point and appreciate the insights drawn from relevant empirical and theoretical work.

We agree that the potential structure and trainability of PN-to-KC connections—supported by studies such as those by Krotov and colleagues (on performance gains from training sparse matrices via backpropagation) and Koulakov and colleagues (on shared low-dimensional structure)—are critical to consider. In the current model, we opted for fixed PN-to-KC connections to isolate and rigorously assess the contributions of other circuit mechanisms (e.g., lateral inhibition, adaptation) to pattern recognition, providing a baseline for structural advantages.

We fully endorse the suggestion to explore these ideas further. In future work, we plan to: (1) incorporate trainable PN-to-KC connections using approaches like backpropagation (as in Krotov et al.); (2) test the impact of imposing low-dimensional structure (consistent with Koulakov et al.’s findings); and (3) investigate coupling between olfactory input statistics and PN-to-KC connection statistics. These extensions will clarify how such structural features modulate the circuit’s performance, complementing our current findings and deepening understanding of the fly olfactory system’s computational principles.

We believe these experiments will add significant depth to our analysis, and we thank the reviewer for encouraging this important direction.

2. The necessity of using spiking neural network

We appreciate your question regarding the necessity of using Spiking Neural Networks (SNNs) in this study compared to conventional non-spiking models. While SNNs may require significant computational resources, we believe their use is crucial for the following reasons, particularly given our focus on the fly olfactory circuit:

(1) Biological Plausibility: SNNs are inherently better suited to simulate the biological characteristics of neurons, such as membrane potential dynamics, threshold-based firing, spike generation, and post-spike reset. These features are fundamental to how real neurons, including those in the fly, process information. This closer adherence to biological reality allows our model to more accurately reflect the actual working principles of fly neurons.

(2) Temporal Processing in Olfaction: Olfactory processing is an inherently temporal process. Odor signals unfold over time, and the neural circuit's responses exhibit complex temporal dynamics. SNNs are event-driven, with information encoded and transmitted through the timing of spikes. This allows them to naturally capture and simulate these dynamic processes, such as membrane potential accumulation and decay, and changes in neuronal firing rates. In contrast, non-spiking models typically rely on continuous activation functions, which cannot capture these discrete, time-dependent neuronal behaviors. This gives SNNs a distinct advantage in explaining biological mechanisms.

Modeling of Specific Mechanisms (LI and SFA): The mechanisms we primarily investigate, LI and SFA, are intrinsically linked to neuronal spiking activity and membrane potential dynamics. SNNs enable us to implement and analyze these mechanisms in a way that is much closer to biological reality. This allows for a more faithful representation of how these processes might operate in the actual fly brain.

In summary, despite the higher computational resource demands, SNNs offer a superior framework for modeling the fly olfactory circuit compared to traditional non-spiking models. They excel at embodying and capturing the biological characteristics of neurons, especially their time-dependent dynamics and learning processes, which are critical for understanding the complexities of biological olfaction.

3. the ethological roles of LI and SFA

Thank you sincerely for this valuable suggestion, which has prompted us to reflect deeply on the ethological significance of our findings. We fully recognize the importance of exploring the distinct roles of these two subcircuits in natural behavioral contexts, and we are committed to approaching this with the utmost rigor and dedication.

We plan to delve into an extensive review of relevant literature—including studies on insect ethology, olfactory-mediated behaviors, and neural circuit function—to synthesize existing knowledge and contextualize our results. This process will involve careful consideration of how the functional differences we observed might map onto sensorimotor control such as foraging, predator avoidance, or conspecific communication.

We are determined to refine our understanding through ongoing critical thinking and iterative analysis, and we aim to incorporate these insights into an expanded discussion that clarifies the potential ethological relevance of each subcircuit. Rest assured, we will spare no effort in strengthening this aspect of the work, as we share your commitment to ensuring the depth and validity of our conclusions.

Thank you again for pushing us to explore this important dimension.

Thank you for this valuable feedback, which points out crucial areas for improving our analysis depth. We fully acknowledge the shortcomings in the current representation analysis and will address them comprehensively. It is a pity that we didn't make the model structure sufficiently clear. We built a feedforward network model. We will improve this in our manuscript.

1. The combined effect and noise adaptability of LI and SFA

We fully agree that the need to elaborate on the combined effect of mechanisms in the circuit—key aspects we aim to address comprehensively. To clarify the combined effect of lateral inhibition (LI) and spike-frequency adaptation (SFA), we supplement comparative analyses in the table across three conditions: LI alone, SFA alone, and their co-activation. Our results clearly demonstrate that the co-activation of LI and SFA enables the fly olfactory circuit to achieve more efficient and robust odor discrimination, showcasing a synergistic effect.

2. The potential for higher inhibition

We appreciate for your careful observation—these points are critical for clarifying the consistency of our results and the dynamics of inhibition levels, and we the address them as follows:

(1) Resolving the apparent discrepancy between the table and high-noise plots

(2) the potential for higher inhibition

To directly test the hypothesis of whether "even higher inhibition can lead to better performance", we have supplemented our experiments by testing higher inhibition levels beyond the previously maximal values. Our extended experimental results reveal that the relationship between performance and inhibition level is more complex than a simple monotonic increase:

1. In some cases, increasing the inhibition level can indeed lead to further improvements in accuracy. For example, as noise intensity is 0.15, a significant increase in inhibition strength resulted in an increase in accuracy of approximately 4.3%.

2. However, this improvement does not always occur. For example, for the LI model, under no-noise(0) and high-noise(0.3) intensity, even a significant increase in inhibition strength resulted in nearly unchanged accuracy, with performance tending to plateau. This suggests that under these conditions, the contribution of the LI mechanism to performance reaches saturation after a certain inhibition level. For the SFA model, in medium-to-low noise(0 to 0.1) intensity, its effect also did not significantly change with increasing inhibition strength, and performance similarly tended to plateau.

These results suggest the existence of an optimal inhibition threshold. Crucially, this threshold is dynamic and dependent on factors such as the noise level, as evidenced by the observation that performance saturation occurs under different noise conditions for different models.Once the inhibition strength exceeds this threshold, its beneficial effect on performance diminishes and saturates, and the performance curve tends to flatten.

In summary, initial observation was based on a specific range of parameters we set. Through extended experiments, we found a more complex, non-linear relationship between inhibition level and model performance, typically showing a saturation or plateauing of performance after reaching a certain strength.

3.Robustness analysis of parameters

We sincerely appreciate your attention to the rigor of our experiments and the robustness of our conclusions. We recognize that the choice of parameters could impact the simulation results. To mitigate this, we will conduct parameter robustness analysis.

We primarily investigated the influence of the following key hyperparameters: random seed, learning rate, and batch size. In all these experiments, we strictly ensured that all other conditions remained identical except for the parameter being tested. Our analysis yielded the following results:

(1) Random Seed: Under different noise intensities, the variations in pattern recognition accuracy caused by different random seeds typically ranged between 0.1% and 1.3%. This indicates that the model's performance is very insensitive to the initial random state.

(2) Learning Rate: When the learning rate was varied from 0.5 to 2 times its original value, the different settings resulted in accuracy changes ranging between 0.1% and 1.6%. This suggests that within a reasonable range, variations in the learning rate have a limited impact on the final performance.

(3) Batch Size: When the batch size was varied from 0.5 to 2 times its original value, the different settings led to accuracy differences generally less than 3%. Specifically, smaller batch sizes showed differences less than 1%, while larger batch sizes showed differences less than 3%. This indicates good robustness of our model to the choice of batch size.

Crucially, these parameter variations did not alter our conclusions regarding the roles of LI and SFA mechanisms. Under all tested conditions, we consistently observed that the LI model performed optimally at low noise intensities, while the SFA model performed optimally at high noise intensities. This critical relative performance ranking remained consistent across all parameter combinations.

Therefore, although there might be some noise and non-monotonic trends in the simulation results, our extensive parameter robustness analysis strongly demonstrates that the core behavior and main findings of our model are highly robust and not merely artifacts of specific parameter choices. These experiments provide a solid foundation for our understanding of this SNN model's behavior. We are committed to incorporating these improvements to strengthen the support for our conclusions and elevate the overall quality of the study.

4.time-averaged MBON

We appreciate the reviewer's insightful observation. While the MBON output is indeed time-averaged for final decision-making, the temporal dynamics and precise spiking patterns in the preceding layers are critically important for forming effective and discriminative representations that ultimately lead to better classification.

From a learning perspective, our use of BPTT explicitly leverages these temporal differences. The weight updates are computed through full temporal unrolling, meaning that the precise timing and sequence of spikes, as well as the membrane potential trajectories throughout the simulation, directly affect these gradient computations. This allows the network to optimize for and utilize temporal features for better pattern separation.

Beyond the algorithmic aspect, even if only an average is taken at the MBON, the pattern of accumulated activity (i.e., the spike count pattern) in the preceding layers is fundamentally shaped by these intricate temporal dynamics. Therefore, while the temporal dynamics are not directly 'read out' as a sequence by the MBON, the differences they create in the underlying activity patterns are ultimately reflected in the MBON's averaged membrane potential.

In essence, the temporal structure in the earlier layers is not merely incidental; it is fundamental to generating the highly separated and robust representations that ultimately contribute to the high classification accuracy observed at the time-averaged MBON output.

5.Sparsity

To address the sparsity analysis gap, we will further supplement our study with a systematic investigation of coding sparsity induced by LI alone, SFA alone, and their co-activation. Specifically, we will:

(1) Quantify Sparsity: Calculate sparsity metrics (e.g., the proportion of non - zero neural responses, or the distribution of neural activation magnitudes) under different conditions (with LI only, SFA only, both LI and SFA, and neither). This will help us clearly define how each mechanism, and their combination, influences the sparsity of the neural code.

(2) Test the Sparsity - Based Hypothesis: We will directly test the hypothesis that the effectiveness of LI and SFA in odor discrimination (or relevant tasks) can be explained by coding sparsity. This involves correlating changes in sparsity metrics with changes in task performance (such as accuracy, robustness to noise). If a strong correlation is found, we can determine the extent to which sparsity mediates the effects of LI and SFA; if not, we will explore other potential mechanisms (e.g., temporal coding features, population - level coordination) that work alongside or instead of sparsity.

By conducting these analyses, we aim to provide a more nuanced and mechanistic understanding of how LI and SFA contribute to neural coding in the olfactory circuit. We believe these additions will significantly enhance the clarity of the underlying mechanisms and better align our study with the high standards of neural computation research.

6.Inconsistency and inadequate explanation of notations

We are sorry for the inconsistency and inadequate explanation of notations. We have clarified more details and have added more discussions to improve the readability.

1. Input Data $X_{i,j}$ represents the $j_{th}$ element of $i_{th}$ class odor, we revise it as $X_{i,j}$.

2. we revise $X_i^k = \max(X_i^k, 0)$ as $\tilde{X}_i^k = \max(X_i^k, 0)$.

3. Page 3, 2nd paragraph, “...reduced by the value of the value of the threshold.” We revise it as “...reduced by the value of the threshold.”

4. Page 3, bottom, “the synaptic weights $w_{LN \rightarrow PN}$, representing the connection from LNs to PNs, are always negative”.

We appreciate the reviewer's positive feedback and rigorous attention, especially regarding the dynamics introduced by the inhibitory mechanism in Equation (2). We regret that the temporal integration in the trace variable $T_k^{\text{LN}}(t)$ may have led to the interpretation of recurrent dynamics.

The fundamental distinction between a feedforward neural network and a recurrent neural network (RNN) lies in the presence or absence of explicit feedback loops in the network's connectivity.

Let us recall Equation (2) in the context of our network's information flow:

$$I_{\text{lat},j}^{\text{PN}}(t) = \sum_k w_{\text{LN}\to\text{PN},jk} T_k^{\text{LN}}(t)$$ $$\tau_{\text{traceLn}} \frac{dT_k^{\text{LN}}(t)}{dt} = -T_k^{\text{LN}}(t) + S_k^{\text{LN}}(t)$$ $$S_k^{\text{LN}}(t) = \sum_l \delta(t - t_{kl}^{\text{LN}})$$

Here's a detailed explanation of each component and why it supports a feedforward classification:

• $S_k^{\text{LN}}(t)$: This term represents the spike train of the $k$-th Local Neuron (LN), driven by inputs from upstream layers (ORNs). Crucially, there are no connections from Projection Neurons (PNs) back to Local Neurons (LNs). The absence of feedback from PNs to LNs is a defining feature of a feedforward design.

• $T_k^{\text{LN}}(t)$: This inhibitory trace variable for the $k$-th LN integrates its own recent spiking activity $S_k^{\text{LN}}(t)$ and decays over time. While this introduces temporal dynamics (a form of "memory" of the LN's own past activity), it is internal to the LN's output pathway. This is akin to a synaptic filter or intrinsic neuronal adaptation—common in spiking neuron models—which does not make the overall network recurrent as long as the connectivity remains unidirectional.

• $I_{\text{lat},j}^{\text{PN}}(t)$: This is the lateral inhibition current received by the $j$-th PN, calculated as a weighted sum of the inhibitory traces $T_k^{\text{LN}}(t)$ from LNs. This current flows strictly unidirectionally from LNs to PNs.

The overall information flow in our model is: Input (ORNs) → LNs → PNs → KCs→ Readout. The temporal dynamics in Equation (2) are a feature of the feedforward inhibitory pathway (ORN-LN-PN), enabling LNs to exert a sustained inhibitory effect on PNs based on their own recent activity.

Therefore, despite the presence of internal temporal dynamics within the LN trace variable, the absence of any feedback connections at the network level means our architecture remains a feedforward neural network.

In addition, we have also updated our response to reviewer qgpQ.

Thank you for constructive comments. We have revised the manuscript as follows：

1.Fly olfactory network VS unstructured network

We fully agree that comparing our proposed fly olfactory network architecture with unstructured networks of comparable size is essential to rigorously validate the claim that its efficiency in odor discrimination can partly stem from inherent structural properties. To address this, we supplement our analysis with systematic comparisons between our model and appropriately sized feedforward network. These comparisons are be conducted under strictly controlled conditions, ensuring consistency with the task settings used for our model, which includes but not limited to number of neurons, noise intensity and learning rate. It is worth remembering that fly olfactory network features fixed sparse connectivity of ORNs-PNs and PNs-KCs. We find that the fly olfactory circuit outperforms the unstructured networks.

(1) Fly neural network vs. fully connected feedforward network We first built a fully connected feedforward network with only readout layer connection weights learnable; all other weights are fixed/non-learnable. Notably, when learning 1,000 classes of odors, the fly olfactory network without any mechanism (Base-model) achieved discrimination accuracy 91% in Figure 2, and the fully connected only reached 45%. This significant performance disparity (91% vs. 45%) clearly indicates that the sparse connectivity of ORNs-PNs and PNs-KCs within the fly olfactory network confer an overwhelming advantage in odor discrimination.

(2) Fly neural network vs. sparse connectivity of feedforward network To further investigate the role of distinct fixed sparse connectivity in the fly olfactory network, we performed two additional control experiments:1) fully connected ORNs-PNs but sparse connected PNs-KCs, this architecture achieved optimal accuracy only 80%. 2) sparse connected ORNs-PNs but fully connected PNs-KCs, this architecture achieved optimal accuracy only 82%. These results strongly support that sparse connectivity of fly olfactory circuit architecture is crucial for learning in the fly neural network.

2.The combined effect and noise-induced switching of LI and SFA

We fully agree that the need to elaborate on the combined effect and noise adaptability of mechanisms in the circuit—key aspects we aim to address comprehensively.

(1) Combined effect To clarify the combined effect of lateral inhibition (LI) and spike-frequency adaptation (SFA), we supplement comparative analyses in the table across three conditions: LI alone, SFA alone, and their co-activation. Our results clearly demonstrate that the co-activation of LI and SFA enables the fly olfactory circuit to achieve more efficient and robust odor discrimination, showcasing a synergistic effect.

(2) Noise-induced switching The switching between these two mechanisms is indeed a challenging and exploratory part. We will aim to further investigate their triggering conditions and regulatory mechanisms after conducting more extensive literature research. For contextual cues of noise levels, we will examine the circuit’s ability to encode noise-related statistics (e.g., input variance), and link these noise signatures to adaptive switching in LI and SFA—for example, whether high noise amplifies SFA to preserve signal continuity while weakening LI to suppress irrelevant activity, and vice versa for low noise. Moreover, we also want to explore further whether switching occurs as a discrete transition or a graded adjustment, and how it optimizes circuit performance across dynamic inputs. These analyses will deepen our understanding of how LI and SFA interact as a coordinated system, rather than isolated processes, to enable robust function across variable environments.

3.Different types of noise

Considering different types of noise will help better understand the robustness of the olfactory circuit mechanism we study across different noise environments and provide a more comprehensive evaluation of its functional characteristics. This extension will enhance the generalizability of our findings and address the important consideration of noise diversity in the olfactory system. To address the concern about different types of noise, we supplement our study by incorporating noise generated by Ornstein-Uhlenbeck process (OU noise), mimicing the temporal correlations in odor. By generating odor samples with OU noise following similar logic as the Gaussian noise (i.e., adding appropriate noise terms to the prototype odor and applying necessary clipping for physiological plausibility), we systematically explore how the odor discrimination performance of the model is affected.

The results indicate a remarkable consistency in model performance under Gaussian and OU noise. Specifically, when the noise intensity (as measured by the average change in PN firing rate) is equivalent, the performance of all three models exhibited highly similar perturbation effects. The accuracy difference between models under these two noise types was consistently around 1%, demonstrating that the specific type of common biological noise does not significantly alter the overall pattern recognition accuracy. Crucially, the relative efficacy of the adaptive mechanisms remained consistent: LI consistently showed the best performance at low noise intensities, while SFA proved most effective at higher noise intensities, regardless of whether the noise was Gaussian or OU noise . This confirms that the functional benefits of these mechanisms are robust across these common noise types.

4.Biologically plausible algorithm for learning

We fully agree that the choice of learning algorithm and its biological plausibility are critical considerations, and we appreciate the reviewer's insightful comment regarding Backpropagation Through Time (BPTT). While BPTT is indeed not considered biologically plausible, our primary objective in this study was to rigorously evaluate the inherent efficiency and structural advantages of the proposed fly olfactory circuit architecture in pattern recognition. We chose BPTT for the following key reasons:

(1) Performance Benchmark: BPTT serves as a powerful and highly effective learning algorithm that allows the network architecture to achieve its maximal potential performance under ideal learning conditions. By using such an optimal learner, we can confidently demonstrate the capabilities of the specific biological architecture (e.g., fixed sparse PN-KC connections, lateral inhibition, adaptation mechanisms) without the confounding limitations that might arise from less powerful, albeit more biologically plausible, learning rules. It effectively provides an upper bound on what the architecture can achieve.

(2) Decoupling structure and learning: Our focus was to isolate and investigate the impact of the circuit's structural properties on pattern recognition. Employing BPTT enabled us to decouple the effectiveness of the architecture itself from the complexities and current limitations of biologically plausible learning rules (like STDP). This approach allowed us to clearly attribute the observed performance gains to the circuit's unique structural design.

We acknowledge the immense importance of developing and employing biologically plausible learning rules. Our current work, by establishing the strong performance of the fly olfactory circuit architecture under optimal learning conditions, lays a crucial foundation. Future work will naturally extend this by exploring how these structural advantages can be leveraged by more biologically realistic learning mechanisms, such as various forms of STDP or three-factor learning rules, to achieve similar levels of performance.

5.Minibatch optimization

(1) The influence of minibatch optimization on the reported results

We conducted control experiments with varying batch sizes showed minimal absolute accuracy differences (<3% vs. default) within the tested range. Critically, batch size did not alter the relative efficacy of mechanisms: LI outperformed SFA and the Base model in low noise, while SFA prevailed in high noise. These results confirm the robustness of our performance findings and conclusions to reasonable batch size variations.

(2) The implementation in-vivo

Notably, minibatch optimization—a strategy for efficient ANN training—has no direct biological equivalent in olfactory or general neural circuits. However, analogous group-based biological processes may serve similar functions: in the olfactory bulb, mitral/tufted cells integrate inputs from multiple ORNs in spatiotemporally organized groups (resembling minibatches) to refine representations and optimize odor coding; synaptic plasticity like STDP may act at the population level, with subset activation enabling implicit batch-like adaptive updates. These processes are not identical to artificial minibatch methods, but exploring such parallels contextualizes our model. We will expand the discussion to clarify these connections, highlight limitations in mapping ANN techniques to in vivo mechanisms, and outline future research directions.

In summary, we appreciate this opportunity to delve deeper into these aspects. The planned analyses and expanded discussions will not only clarify the impact of minibatch optimization on our results but also better situate our computational model within the realm of biological plausibility.