Seemingly Redundant Modules Enhance Robust Odor Learning in Fruit Flies
Authors: HaiYang Li
Liao Yu
Qiang Yu
Yunliang Zang
Venue: NeurIPS 2025 poster ()
Keywords: olfactory representations; lateral inhibition；spike frequency adaptation;pattern classification；spiking neural networks
Primary area: neuroscience_and_cognitive_science

Abstract: Biological circuits have evolved to incorporate multiple modules that perform similar functions. In the fly olfactory circuit, both lateral inhibition (LI) and neuronal spike frequency adaptation (SFA) are thought to enhance pattern separation for odor learning. However, it remains unclear whether these mechanisms play redundant or distinct roles in this process. In this study, we present a computational model of the fly olfactory circuit to investigate odor discrimination under varying noise conditions that simulate complex environments. Our results show that LI primarily enhances odor discrimination in low‑ and medium‑noise scenarios, but this benefit diminishes and may reverse under higher‑noise conditions. In contrast, SFA consistently improves discrimination across all noise levels. LI is preferentially engaged in low‑ and medium‑noise environments, whereas SFA dominates in high‑noise settings. When combined, these two sparsification mechanisms enable optimal discrimination performance.  This work demonstrates that seemingly redundant modules in biological circuits can, in fact, be essential for achieving optimal learning in complex contexts.

Seemingly Redundant Modules Enhance Robust Odor Learning in Fruit Flies
Haiyang Li"
Liao Yu² Qiang Yu Yunliang Zang
Acaddmy of Medical Engineering and Translational Medicine, Tianjin University, Tianjin, China School of Mathematical Sciences, Beihang University, Beijing, China Schooo of Artificial Intelligence, Tianjin University, Tianjin, China *Xiamen Intretech Inc, Xiamen, Fujian, China haiyangli@tji edu. edu. cn yuliao yuliao_16Qbuaa edu. yuqiangatju edu. edu. cn yunliangzangee edu. en
Abstract
Biological circuits have evolved incorporate multiple modules that perform similar functions. In the fly olfactory circuit, both lateral inhibition (LI) and neuronal spike frequency adaptation (SFA) are thought enhance pattern sepa- ration for odor learning. However, it remains unclear whether these mechanisms play redundant or distinct roles this process. this study, we present a com- putational model of the fly olfactory circuit to investigate odor discrimination under varying noise conditions that simulate complex environments. Our results show that LI primarily enhances odor discrimination in low- and medium-noise scenarios, but this benefit diminishes and may reverse under higher-noise condi- tions. In contrast, SFA consistently improves discrimination across all noise levels. LI is preferentially engaged low- and medium-noii environments, whereas SFA dominates in high-noise settings. When combined, these two sparsification mechanisms enable optimal discrimination performance. This work demonstrates that seemingly redundant modules in biological circuits can, in fact, be essential for achieving optimal learning in complex contexts. The code is available at: https: / //ggtgitttb..... www.gi...............ee. hoom/LLOcean//ly-- btttp:///gthin
Introduction
Biological redundancy is commonly observed in the brain, where different regions, pathways, or mechanisms can perform similar functions 4 Different motifs of biological redundancy may exist; for instance, different modules may have evolved to fulfill similar roles, ensuring robust neural functions under pathological conditions (18). Alternatively, these mechanisms may be required to achieve near-optimal learning in more complex environments. Comparative analyses of the roles of putatively redundant modules in learning
clarify how the brain adapts and, in turn, inform theories that guide neuromorphic design 9 [0]. For instance, core computational features of the fly olfactory circuit have motivated the Loy architecture [Л], which enhances task decoupling and parameter efficiency.
The fly olfactory system, canonical cerebellum-lin like circuit, is a tractable model for dissecting neural computation owing its relative simplicity and well-characterized anatomy and function
Equal contribution.
Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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[8.18]. Two motifs lateral inhibition (LI) and spike-frequenn adaptation (SFA) are prominent in the mushroom body and related circuits and both are known to shape neuronal responses [19 21. LI is mediated by inhibitory interneurons that constrain the spatial spread of excitation and sharpen population representations [22 SFA reflects spike-triggered neuronal adaptation currents that accumulate during sustained stimulation, producing a progressive reduction in firing rate and emphasizing stimulus onsets and changes 25).
Prior work has extensively characterized the roles of LI and STA in neural information processing. LI drives competition and winner-take-all dynamics [26]. increases population sparseness 227] enhances
input contrast
[28), and decorrelates activity patterns (29), it also facilitates subtractive or divisive gain modulation and strengthens regularization [30]. SFA functions as a nonlinear high-pass filter
31, promoting intensity-invarian coding [32]. encoding changes in input statistics [33]. sparsifying
temporal responses, and forming short-term memory with non-stored retrieval (distinct from synaptic
memory) 255
Although the roles Lf and SFA in sparsifying neuronal responses are well documented, their relative under naturalistic conditions-rematee less well characterized. Both mechanisms are expected to transform odor inputs into spatially and temporally sparse codes, attenuate noise, and enhance pattern separation (3438) 38 (Figure D. However, how they shape noisy odor representations and support discrimination learning across different noise regimes is not well understood. From an Al perspective, designing noise-robust classifiers is a classical challenge; elucidating how a fly learns to classify noisy odors may inform the development of robust, biologically inspired algorithms [39]
contributions to
In this work, we developed a fly olfactory circuit model investigate the roles of LI and SFA in odor discrimination tasks under varying noise conditions that simulate complex environments. Our main finding is that LI enhances learning performance in low- and medium-noise conditions. but this benefit gradually diminishes and may reverse when odors become noisier. In contrast, SFA consistently improves odor learning regardless of noise levels. LI tends be more effective in low- and medium-noie environments, while SFA shows superior performance under high-noise conditions. When combined, the enhancement effects of these two mechanisms can be added up to achieve the optimal performance. These results suggest that seemingly redundant modules may be selectively recruited to optimize learning under different noisy conditions.
2 Method Overview
We developed a spiking neural network model of the fly olfactory circuit. The input layer consists of 50 olfactory receptor neurons (ORNs) that transduce odor stimuli into spikes. Each ORN projects to corresponding projection neuron (PN), yielding 50 PNs. We also included local interneurons (LNs), which receive excitatory input from ORNs and provide lateral inhibition onto PNs. PN activity is relayed to 2,000 Kenyon cells (KCs) the mushroom body; each KC samples inputs from approximately six PNs on average. Finally, KCs converge onto mushroom body output neurons (MBONs), which serve as readout units; in our task configuration, each MBON corresponds to an odor class being learned 40
The fly olfactory pathway exhibits three canonical features that critical for discrimination 42 large expansion (PN + KC), sparse connectivity, and sparse coding. Here, we focus on the role of spatiotemporally sparse spike coding, which conventional ANN models cannot capture; other architectural and connectivity parameters were constrained to experimentally observed values.
A schematic of the network and its putative role in odor discrimination is shown in Figure D After the KC stage, the sparsification mechanisms can transform odor responses in ways that facilitate odor discrimination. For example, they may preserve the original inter-class separability while increasing intra-class compactness (top), increase inter-class separation while keeping intra-class compactness unchanged (middle), simultaneously achieve high intra-class compactness and improved inter-class separability (bottom). Regardless of the specific transformation, these changes are supposed to enhance the decision boundaries for odor discrimination.
Synaptic plasticity was restricted to the KC-MBON connections; all other synapses were fixed. Details of the training procedure and plasticity rule are provided in the Learning Algorithm section. dection
2

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plastic
ORNS
PNs/LNs
KCs
MBONS
b
Buse-model
ORNE
PNS
Odoss
Class A Class B
Ll-model
.Ns
ORNE
PNs
Class C
SFA-model
INo
ORN
PNS
Figure Schematic the fly olfactory circuit model. Odor inputs are sensed and encoded by ORNs. After passing through the ORNs, odor-triggered spikes in PNs can be shaped by two factors: LI caused by LNs and SFA by inherent adaptation currents. Neuronal spikes in KCs may subsequently show different variation patterns to favor odor discrimination in MBONs.
Input Data. We adapted the odor- dioo-discrimination dataset from 43 For each odor class we define prototype ORN response vector I, E 50 Its components are independently sampled from uniform distribution: 4., U(0, 1) for j .,, 50. An individual sample from class i, denoted ((a) is generated by adding an additive noise vector the prototype: ((k) I, + Y()), where every component of the noise vector (k) E 1550 is independently sampled from a zero-mean Gaussian distribution, yj (0, o2 ). In accordance with the non-negativity of ORN firing rates, we applied element- clipping so that I!a
All neurons were modeled as leaky integrate-and-Ne (LIF)) units with a soft reset. The membrane potential of neuron in the layer X evolves according to:
Neuron Model.
(V)(()) dt -
(t)
I imput. (t) + I +
X.X SPA, (t) + I. (t)
Where TXX is the membrane time constant. Tix 1 (t) denotes the input current to neuron j in layer X, arising from odor-evoked stimulation or synaptic drive from presynaptic neurons; Ip constant bias that sets a baseline drive (used primarily in PNs and LNs to provide small excitatory input); IX (t), (t) a ppike-triggered adaptation current that depends on the neuron's recent spiking history and typically exerts net inhibitory effect; and IY,, (4) is the lateral inhibitory current from LNs onto PNs, scaled by LN spiking activity.
In the model, a spike emitted when V/x((t (t) reaches the threshold ViX Upon spiking, the membrane potential undergoes soft reset: Vxx(t*)
V (t) V.X. For simplicity, we used the same membrane time constant and threshold across layers (T Tm, V. Vin), except in the readout (MBON) layer, where the threshold was set to 1.5 times higher. Given the dense KC - MBON connectivity, this higher threshold mitigates excessive spiking driven by the convergence of inputs from thousands of KCs.
LI Mechanism. LI onto PNs is mediated by LNs and modeled as an inhibitory current driven by an exponentially decaying trace of LN spiking. The inhibitory current onto PN
IPN (t)
Σ
WLN-PPN T
T
(2)
3

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Where WLN-PNNjk S 0 are inhibitory synaptic weights, and 7% xt (t) is the spike- triggered trace of LN k that integrates recent activity and decays over time:
(t) - (t) + (t)
Tirace_ di
(3)
(t) - Σ 8(1 -()
with Tirce LN the decay time constant, S (t) the spike train of LN and 1 the I-th spike time. To compensate for the added inhibition and maintain comparable PN firing rates across conditions, we apply a modest increase in PN input drive when LI enabled.
SFA Mechanism. SFA was implemented in PNs, LNs, and KCs as an inhibitory, spike-triggered current driven by an exponentially decaying state variable. For neuron j in layer X,
(t) w AT(t)) (t)
(5)
dA (t) - (1) (1)
X SIA
(6)
dt
(t)= Σ 5(t - (,,))
where AI (t) integrates the recent spiking history and decays with time constant X USPA S 0 sets
the strength (sign) the inhibitory adaptation current; SI (t) is the spike train of neuron j (Dirac delta representation), and 3.1 denotes the I-th spike time.
To maintain comparable firing rates across conditions when SFA is enabled, we applied small positive bias current to PNs and LNs.
Learning Algorithm. our model, classification based on the average membrane potential of the MBONs over a fixed evaluation window rather than spike counts. Membrane potentials vary more smoothly than discrete spike trains and thus provide a more stable signal for gradient-basee The complete training procedure is outlined in Algorithm I
optimization 44 45
Algorithm Simplified SNN Training with Adaptive Mechanisms for Olfactory Tasks
1: Input: Training dataset Duain- Learnable weights WKC-MBBN. Non-leamable parameters P.
2: for epoch 1, 2, ..., num_ num_epochs do
3: for each batch (Abatch; Ybatch) Dunin do
4: Phase 1: Temporal Forward Simulation
5: Initialize all SNN states Ho. Set Hhist = []. num_steps' 1 do 1 = Input(Zhachh Step)
6: for step f
7:
b Get input current SNN forward pass and state update
8:
H |+1 F(4, H,, P)
9:
Record MBON membrane potentials in Haist- end for
11:
Phase 2: Backpropagation and Weight Update
12:
Younch nHHnis)
Process MBON output Cross-Entropp Loss
13:
loss L(Yraacho Ybatch)
14:
loss. bossbbackward)
b Perform Backpropagation Through Time
15:
Optimizer.stepO
b Update WKC--MBON
16:
end for
17:
end for
For input sample i, we recorded each MBON's membrane potential the evaluation window [t., tz] and computed its time average. Let NMBON be the number of MBONs. The mean potential for MBON and the corresponding vector across MBONs are
V m.i
Vy(t) dt,
Vm, E B NAmoN
to - to Se.

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We convert Vm,s to class probabilities using a softmax function and train the network with cross-entropy loss:
v¹ softmax V miily
(9)
NABON
L
Σ vs log(r))
(10)
Where yi is the one-hot target for sample i.
We optimized the learnable KC - MBON synaptic weights WKC-MBON using backpropagation through time (BPTT), unrolling the network over the evaluation window. Because LIF spikes arise from step nonlinearity with zero derivative almost everywhere, we used surrogate gradient during the backward pass. Specifically, we replaced the derivative of the Heaviside with a smooth aretan-based surrogate:
kj
o' (u)
(11)
1 (k2u)²
where k1, h2 O are scaling constants.
Training uses Adam with L2 weight decay (weight regularization) improve generalization. We also employed ReduceL.RnnPlateee scheduler that monitors classification accuracy on a held-out set and reduced the learning rate by factor a 0.2 accuracy did not improve for n = 10 epochs.
Each model was trained for 100 epochs using mini-batches of size 256. After each batch, the loss was computed, gradients were backpropagated through time, and parameters were updated using the optimizer.
3 Experiments
We generated an odor dataset comprising 30,000 training samples and 10,000 test samples, each drawn at random as described above. For most simulations, we evaluated three network configurations: (i) the Baseline model, which includes neither LI nor SFA; (ii) the LI model, which adds LI onto PNs; and (iii) the SFA model, which implements SFA PNs, LNs, and KCs. In also simulated the full model with both LI and SFA.
Dataset and models:
Figure
Experimental settings: Simulations were implemented in Python (snnTorch) and run on an NVIDIA A800 GPU. Network dynamics were simulated with a 1-ms time step; each trial com- prised a 10-ms pre-stimulus baseline followed by 30-ms odor presentation. All neurons shared membrane time constant of 10 ms. Firing thresholds were 0.8 for PNs. LNs, and KCs, and 1.2 for MBONs. Connectivity featured sparse PN + KC projections (cach KC received inputs from 6 PNs; fixed weight 0.3) and fully connected KC -> MBON synapses initialized uniformly in [0, 0.08). LI used a 5-ms LN trace time constant, and SFA used 50-ms adaptation time constant. Models were trained for 100 epochs (batch size 256) with Adam (initial learning rate 1.0 10-4). Performance was evaluated from the time-averaged MBON membrane potentials over the stimulus window.
4 Results
We evaluated our fly olfactory network model on noisy odor discrimination task by incorporat- ing LI and SFA mechanisms. The results show that these two seemingly redundant mechanisms play complementary roles in learning across varying noise conditions, thereby optimizing odor discrimination.
4.1 Odor discrimination in noise-free conditions
Our results show that the fly olfactory circuit model learns odor discrimination effectively (Figure We first examined discrimination in noise-free conditions. In the baseline mitho-tithout LI or SFA-tth discrimination accuracy reaches 91.7% for 1, 000 odor classes. Although accuracy decreases the number of classes increases, remains 74.72% for 10, 000 odor classes. These
2).
5

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Buseline model
LI model
model
100
95
Accuracy (%)
90
85
80
75
70
1000 classes
2000 classes
5000 classes
10000 classes
Figure 2: Odor discrimination accuracy for fly olfactory circuit variants in noise-free setting. Performance is shown for three configurations Baseline, LI, and SFA models as function of the number of odor classes 1,.000-10,000,
findings indicate that the circuit's other features confer strong pattern pattern-classificttion capacity without explicit sparsifying mechanisms in the circuit 46].
Both LI and SFA improve odor discrimination relative to the Baseline model across all tested numbers of classes. By comparison, the LI model achieves significantly higher accuracy than the SFA model under the same conditions.
4.2 Odor discrimination in noisy conditions
Table Pelleppreeenntt a comparative analysis of discrimination performance under varying noise intensities for the Baseline, LI, and SFA models, with odor classes ranging from 1, 000 to 5, 000. At low- and medium-noise eivels-defing
as noise intensity (N.I.) < 0.20 for 0000000 and 2, 000-class odor discrimination, and N.I. < 0.15 for 5. 000-class odor discrimination the results are consistent with the noise-free context (LI model > SEA model > Baseline model), although overall test accuracy decreases. These findings indicate that sparsification of neuronal spikes in KCs via LI more effective than SFA in enhancing odor discrimination under no- and low-noise conditions. However, when odor inputs become noisier (N.I. 2 0.20 for 1, 000- and 2, 000-class discrimination, and N.I. 2 0.15 for 5, 000-class discrimination). the SFA model consistently achieves the highest discrimination accuracy.
Table Comparative performance of the Baseline, SFA, and LI models for 1,000-, 2,000-, and 5,000-class odor discrimination under different noise ntensities. Magenta values indicate the highest performance under each condition, violet values represent the second-best performance, and blue values denote the lowest performance.
1000 classes
2000 classes
5000 classes
N.I.
Baseline
SFA
Baseline
LI
SFA
Baseline
LI
SFA
0
91.70
98.30
93.50
88.85
96.85
90.90
82.00
92.15
85.06
0.05
78.46
96.35
82.78
68.62
92.47
74.81
52.22
77.47
58.93
Acc.
0.1
74.61
91.85
78.26
61.70
83.07
67.87
38.65
57.83
45.18
(%)
0.15
74.04
83.63
79.94
61.14
71.52
68.54
34.47
42.15
43.89
0.2
72.64
74.78
78.77
58.80
58.87
67.34
32.70
31.91
43.04
0.25
67.32
62.63
74.34
52.26
45.84
61.55
27.74
22.26
36,94
0.3
59.03
53.82
69.34
43.34
37.50
55.78
20.26
16.55
30.38
We systematically analyzed the impact of the strength of each sparsification mechanism- LI and SFA-on discrimination performance (Figure(3). The simulation results indicate that both facilitation effects depend on noise levels, but in distinct ways. For LI, discrimination accuracy initially improves

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as N.I. increases, but then gradually diminishes and can even reverse at higher noise levels. Across of the tested N.I. range, stronger inhibition promotes discrimination accuracy. Compared the Baseline model, strong inhibition improves accuracy by 6.80% when N.I. = 0.0 and 18.52% when N.I. 0.1. Notably, although impairs discrimination at high N.I., (-4.5% when N.I. 0.30), the reduction is still less pronounced for stronger inhibition.
In contrast LI, SFA consistently facilitates odor discrimination across all tested N.I. ranges. As with LI, greater SFA strength generally yields higher accuracy, with improvements of 1.80% when N.I. 0.0, 3.65% when N.I. 0.1, and 11 1.566% when N.I. 0.30.
Ll model
SFA model
25
20
Accuracy Difierence (%)
-10
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Noise Intensity
Noise intensities
Low
Medium
High
Figure 3: Changes in discrimination performance of the SFA and LI models relative to the Baseline model across varying degrees of inhibition and adaptation under different noise intensities. Results are shown for 1,000-class odor discrimination only. The "Low," "Medium," and "High" conditions (distinguished by color) represent increasing strengths of the respective mechanisms, achieved by systematically adjusting the relevant synaptic weights: WIN-PN in Eq. 2 for LI, and WSFAXX Eq. forr SFA. For both mechanisms, "Low," "Medium," and "High" correspond to weight increases in an approximate 1:2:3 ratio.
N-1000
N=2000
N=5000
100
90-
80-
Accuracy (%)
70-
60
50-
40
20
0.05
0.10
0.15
0.20
0.25
0.30
0.55
0.10
0.15 Noise Intensity
0.20
0.25
0.30
0
0.05
0.10
0.15 Noise Intensity
0.00
0.s
0.3
Noise Intensity
Reseline model
LI model
SFA model
Pull model
Figure 4: Discrimination performance of the SFA model, LI model, Full (SFA + LI) model, and Baseline model under different noise intensities. The models tested odor discrimination tasks with 1,000, 2,000, and 5,000 odor classes.
In addition, we investigated whether LI and SFA could be dynamically combined to achieve optimal odor discrimination learning (Figure Our results show that orchestrating these two mechanisms produces higher discrimination accuracy than using either mechanism alone under low- and medium- noise levels. Only under high-noise conditions does the SFA model outperform all other models. The benefits of these two mechanisms additive. These findings suggest that, although each mechanism

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is most effective within specific noise regimes, LI and SFA can work together in complementary manner, combining their individual effects to optimize the learning process.
4.3 Learning speed
1000
N 2000
N - 5000
50
Convergence
40
20
6.0
Perskjoch Increate (1g)
5.0
4.0
3.0
2.0
0.05
0.15
0.25
0.30
0.05
0.25
Noúse Intensity
Noise Intensity
Noise Innensity
Reveline
Llmodd
model
Figure 5: Impacts of III and SFA on model convergence speed. The top (bottom) panel shows the number of training epochs required for convergence (the accuracy gain per epoch) for the Baseline, L.I, and SFA models, plotted against noise intensity for different odor category sizes: 1,000, 2,000, and 5,000 classes. avoid potential misinterpretations from relying solely on maximum accuracy and to objectively assess learning progress, convergence is defined as the point at which model accuracy growth plateaus. Specifically, a model considered converged when the average improvement in accuracy over 10 consecutive epochs falls below predefined threshold (threshold = 0.003).
To further assess the impacts of and SFA on learning efficiency, we provide a quantitative analysis of how these two sparsification mechanisms shape the time course of odor discrimination learning. As shown in Figure 5 (top). similar to the final discrimination accuracy values (Table D the number of training epochs required for convergence depends noise level. In the low-noisc range, the LI model requires more epochs to reach the defined converged state, regardless of odor category size. SFA follows LI, while the Baseline model reaches convergence fastest. The convergence speed can be explained by combining the final discrimination accuracy (Table [ with the accuracy gain per epoch (Figure bottom). In the low-noise range, both LI and SFA require higher final accuracy thresholds to converge, but their per-epoch gains show no advantage over the Baseline model, resulting in slower convergence.
In higher-noise ranges, however, the LI model exhibits the fastest convergence, followed by the Bascline model, with the SEA model consistently the slowest. In this regime, the LI model generally maintains an advantage over the Baseline model in per-epoch accuracy gain, explaining its faster convergence (Figure top). When N.I. 0.3, the per-epoch accuracy gain is similar across models; however, SFA requires a higher final accuracy threshold to reach convergence compared to both the Baseline and LI models (Table I]. Consequently. LI reaches the converged state first, the Baseline model second, and the SFA model last.
These results suggest that, depending on the noise level, learning alongside discrimination accuracy-may be an important factor determining which sparsification mechanism is recruited during noisy odor discrimination learning.

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4.4 Sensitivity analysis
4.4.1 Sensitivity noise types
The previous results were obtained by simulating the odor discrimination task with Gaussian noise. To assess the generalizability of our findings, we evaluated the effects of the sparsification mechanisms under different noise environments. addition to Gaussian noise, we simulated noise generated by an Ornstein- -hheenbechleekkkkkk (OU) process, which captures the temporal correlations often observed in natural odors. Odor samples with OU noise were generated using a procedure analogous to that used for Gaussian noise.
The results, summarized in Table show that the effects of LI and SFA on discrimination performance with OU noise are generally consistent with those observed using Gaussian noise. I.I achieves the highest discrimination accuracy at low- and medium-nois levels, whereas SFA is most effective at higher noise intensities. The main difference is that, within the tested noise range, LI-like SFA- consisnssste improves the discrimination of noisy odors compared to the Baseline model, rather than impairing performance at high noise levels, although its benefit gradually diminishes. Overall, these findings confirm that the complementary effects of and SFA are robust across the tested noise types.
Table 2: Comparative performance the Baseline, LI, and SFA models for 1,000-class odor discrimination under different OU noise intensities.
N.I.
Baseline
LI
SFA
0.1
86.02
97.98
88.66
0.3
78.66
96.43
82.55
Acc.
0.5
76.01
93.10
78.85
(%)
0.9
74.54
87.84
78.50
1.5
67.55
69.72
77.49
4.4.2 Parameter sensitivity analysis
To further verify the reliability of our simulation results, we conducted comprehensive parameter sensitivity analysis. Three key syperparameetes--randeee seed, learning rate, and batch size-were varied while keeping all other experimental conditions fixed to assess their impacts on odor discrimi- nation.
Our tests reveal that:
Varying the random seed typically changed accuracy by less than 1.3%.
Adjusting the learning rate to 0.5-2.0 of its default value resulted in accuracy changes generally under 1.6%.
Scaling the batch size to 0.5-2.0 of its standard value produced accuracy differences typically below 3.0%.
These results demonstrate that, within reasonable variation ranges, model performance is highly robust hyperparameter choices. Importantly, across all parameter variations, our core conclusions remain unchanged: the LI model achieves optimal performance in low- and medium-noiss environments, whereas the SFA model performs best under high-noise conditions. This analysis confirms that our main findings are reliable and independent of specific hyperparameter settings, providing strong foundation for the interpretations presented in this study.
Conclusion
In this paper, we present computational demonstration of how two distinct neural sparsification apechaniss--circit-eee LI and neuronal-level SFo-idovide complementary advantages for noisy odor discrimination. Both mechanisms, well-documented in biological neural systems, actively shape and refine spatiotemporal neuronal responses. Our simulation results reveal a noise-dependent

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recruitment pattern: LI is preferentially engaged under low-noise conditions, whereas SFA dominates in high-noise environments. The fly can orchestrate these two sparsification mechanisms achieve optimal discrimination performance. These findings illustrate how seemingly redundant circuit modules biological systems may, in fact, represent an optimized strategy for maintaining robust learning performance across diverse environmental conditions. This study sits at the interface of computational neuroscience and spiking neural networks, leveraging Al methods to investigate learning processes in the fly olfactory circuit. While this interdisciplinary approach is enriching, also carries several limitations, as discussed below.
6 Limitations
We present a computational model of the fly olfactory circuit and investigate roles of LI and SFA in odor discrimination learning. While our findings offer valuable insights, several limitations point to promising directions for future research.
First, regarding the training and test datasets, our simulations used artificially generated odors Although the odor generation method was experimentally inspired and provided controlled environment, future work should validate odor discrimination performance using more naturalistic and physiologically realistic odor stimuli.
43
Second, our current model assumes that plasticity is confined to synaptic connections between KCs and MBONs. The synaptic update rule follows backpropagation through time, which is generally considered biologically implausible. While we believe this does not alter our conclusions, future stud- ies should explore biologically plausible learning algorithms. Moreover, as in most cerebellum-lik circuit models, the synaptic weights between the input and hidden layers ORRNKKC synapses) are fixed 18 These connections may also undergo other forms of plasticity, such as unsupervised learning via Oja's rule [48] Exploring these possibilities would provide a more comprehensive understanding of how learning unfolds across the entire circuit.
Finally, although our parameter robustness analysis and exploration of different noise types support the generalizability of our findings, the parameter ranges and noise characteristics examined remain limited. Broader investigations into diverse environmental conditions and increased model complexity could further strengthen the conclusions.
Acknowledgement
This work was supported by the National Key Research and Development Program of China (2033YFF1204200), the National Natural Science Foundation of China (6247619) 197, 12372060, 92370103, 62176179), and the Xiaomi Foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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A Discrimination Accuracy over Training Epochs under Different Noise Intensities
The main text primarily presents the final discrimination accuracy values under specific experimental conditions. To better illustrate the learning dynamies. this section includes results showing the time course of recognition accuracy for the three models (Baseline, LI, and SFA models) as they learn to discriminate 1,000 odor classes under varying noise intensities (N.I. 0.1, 0.2, and 0.3), as shown in
Figure 6
(A)
(B)
(C)
80
60
Accumayy
60
80
100
0
20
40
60
80
100
20
100
Epoch
Egach
Epoch
Baseline model
SEA model
model
Figure 6: Evolution of discrimination accuracy over training epochs under different noise intensities. The subfigures show results for: (A) N.I. 0.1, (B) N.I. 0.2, and (C) N.I. 0.3.
B Model Performance with Enhanced Strength of Input Signal
The experiments described signals to better isolate performance differences attributable to the LI and SFA mechanisms. Under conditions with a large number of odor categories and substantial noise interference, this constraint led to relatively low absolute accuracy values across all models. In this section, we demonstrate that a moderate increase in input signal strength can significantly enhance overall discrimination performance.
main text imposed certain limits on the strength of the input odor
Table Comparative performance of the Baseline, SFA, and LI models for 10,000-class odor discrimination under different noise intensities with enhanced strength of input signal.
N.I.
Baseline
LI
SFA
0
99.82
99.99
99.97
0.05
98.46
99.90
99.45
0.1
96.87
98.59
98.14
Acc.
0.15
90.13
86.58
93.27
%%)
0.2
69.80
60.79
81.31
0.25
45,21
34.17
60.07
0.3
25.94
18.40
37.45
Table summarizes the final discrimination accuracy of the Baseline, LI, and SFA models after increasing the input signal strength. Enhancing the input signal strength led to substantial accuracy improvements for all models across the tested conditions. For example, with 10,000 odor classes and noise = 0.1, the accuracy the Baseline model rose from 21.800 880 to 96.87%.
20


Reviews:
[{"review_id": "TaxVGbZutl", "reviewer": "Reviewer_qgpQ", "summary": "This paper explores the role of lateral inhibition (LI) and spike frequency adaptation (SFA) in the olfactory circuitry of fruit flies for various levels of input noise. For this, they simulated a layered network featuring receptor, projection and local neurons, Kenyon cells, and mushroom body output neurons. The neurons were modeled using the leaky-integrate-and-fire model. All synapses were initialized randomly kept fixed except for the Kenyon cells which were trained using Backpropagation through time. Experiments were conducted using a generated dataset of odor signals. The base model was compared to incorporating LI and SFA respectively. The results suggest that LI increases classification accuracy for low noise levels. Moreover, SFA increases accuracy especially for higher noise levels.", "questions": "1. How would the switching between the two modes of inhibition work? How can the circuitry distinguish between low- and high-noise settings?\n2. You say that \"These findings suggest that the fly olfactory circuit is inherently efficient in pattern recognition due to its structural properties, even in the absence of sparsening activity in Kenyon cells.\" How does an unstructured network (LSTM or even MLP) of similar size compare to the architecture used here?\n3. Can minibatch optimization have an influence on the reported results? If so, how could it be implemented in-vivo?", "limitations": "The discussion of limitations is very limited. Please also focus on differences between BPTT and more biologically plausible alternatives.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**:\n1. An interesting premise was explored in the paper: the use of two different inhibition mechanisms in the olfactory circuitry for enhancing learning under different input noise levels.\n2. The paper text ist well written and easy to follow.\n3. Reproducibility is facilitated by including all necessary information in the main manuscript such as all hyperparameter settings, optimizer, and loss function used.\n\n**Weaknesses**:\n1. Overall the scope of the investigation is very limited. More experiments would improve the paper. e.g.:\n- How does the architecture used compare to regular unstructured neural networks?\n- What is the combined effect of LI an SFA?\n- What about different types of noise?\n3. The learning algorithm makes use of BPTT which is not deemed biologically plausible. It would add a lot to the paper if biologically plausible alternatives to BPTT (i.e. STDP) were used.", "was_revised": true, "final_justification": "The paper has a solid experimental validation, but the signficance of this research seems to be minor.", "rebuttal": "Thank you for constructive comments. We have revised the manuscript as follows：\n\n**1.Fly olfactory network VS unstructured network**\n\nWe 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.\n\n(1) Fly neural network vs. fully connected feedforward network\nWe 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.\n\n(2) Fly neural network vs. sparse connectivity of feedforward network \nTo 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%.\nThese results strongly support that sparse connectivity of fly olfactory circuit architecture is crucial for learning in the fly neural network.\n\n**2.The combined effect and noise-induced switching of LI and SFA**\n\nWe 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.\n\n(1) Combined effect\nTo 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.\n| N.I. | LI+SFA | Base  | LI    | SFA   |\n| :-: | :-: | :-: | :-: | :-: |\n| 0    | 99.10  | 91.70 | 98.30 | 93.50 |\n| 0.1  | 95.58  | 74.61 | 91.85 | 78.26 |\n| 0.2  | 85.28  | 72.64 | 74.78 | 78.77 |\n| 0.3  | 68.48  | 59.03 | 53.82 | 69.34 |\n\n(2) Noise-induced switching\nThe 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. \n\n**3.Different types of noise**\n\nConsidering 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.\n 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.\n| OU  | Base  | LI    | SFA   |\n| :-: | :-: | :-: | :-: |\n| 0.1 | 86.02 | 97.98 | 88.66 |\n| 0.3 | 78.66 | 96.43 | 82.55 |\n| 0.5 | 76.01 | 93.10 | 78.85 |\n| 0.9 | 74.54 | 87.84 | 78.50 |\n| 1.5 | 67.55 | 69.72 | 77.49 |\n\nThe 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.\n\n\n**4.Biologically plausible algorithm for learning**\n\nWe 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).\nWhile 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:\n\n(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.\n\n(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.\n\nWe 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.\n\n**5.Minibatch optimization**\n\n(1)\tThe influence of minibatch optimization on the reported results\n\nWe 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.\n\n(2)\tThe implementation in-vivo\n\nNotably, 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.\n\nIn 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."}, {"review_id": "DgvSuqKPZq", "reviewer": "Reviewer_pcFb", "summary": "The paper did spiking RNN simulations of fruit fly olfactory circuits. The main scientific question is whether inhibition through self-adaptation (LI model) or another group of inhibitory neurons (SFA model) helps random pattern classification performance and robustness. The authors claim that LI is more effective when the input noise is low and SFA is more effective when the input noise is high.", "questions": "The authors did not include line numbers, which makes commenting on all the issues difficult. Below, I pointed out some of them.\n\n### Formulation and typos:\n\nSome formulations and notations are not consistent\n\nPage 2, Input Data, $X_{i_j}$, double subscription is confusing, and not consistent with later usage of commas to separate i and j.\n\nPage 2, Input Data, Xki = max(0, Xki). This is a confusing formulation. It looks like a self-consistent equation, but it is not.\n\nm in subscription of $\\bar{V}$ in eq (4) is not explained. Does it mean MBONs?\n\nPage 3, 2nd paragraph, “…reduced by the value of the value of the threshold.”\n\nPage 3, bottom, “the synaptic weights wLN→PN, representing the connection from LNs to PNs, are often negative” Why it is not “always negative”?\n\n### Questions on simulations:\n\nThe output neuron, MBON, is time-averaged (Learning Algorithm, page 4, middle), so why the temporal difference/separate is important (5.1 page 5 bottom, 3 page 4 bottom)? \n\nPage 5 bottom “The LI mechanism results in larger spatio-temporal differences in spike trains and firing rates, facilitating better separation of odor input patterns.” It is not obvious. The blue and red look always overlap with some fluctuation noise.\n\nQuestions on 5.2, table 1, and figure 4. In Figure 4, the authors show the base model performance as gray curves. However, the curve trend doesn’t match the number in Table 1 (0.3 noise level, 53.82% in the table, but ~ 52% in the plot). In the table, the LI model is always better than the base models, but in the plot when the noise level is high, LI is worse than the base model. Another question on the “inhibition level”, it looks like in both LI and SFA the best performance is always the largest inhibition level. Does this mean an even higher inhibition can even lead to better performance?\n\nFigure 5 (B) is redundant as the curves already appear in Figure 4. \n\nThe metrics $S_\\phi$ and $S_\\theta$ are confusing. They are the product of the intra-class dissimilarity and inter-class dissimilarity. However, intra-class dissimilarity and inter-class dissimilarity have opposite effects on the embedding quality as the authors said, why the product of the two is a meaningful measure?\n\nThe authors claim LI is more effective in low-noise situations, and SFA is more effective in high-noise situations. A straightforward expectation is that combining the two will lead to better performance in both cases. However, the author did not explore it.\n\n### Sparsity\n\nThe current analysis of the representation is simple and not sufficient to reveal the underlying mechanism. The authors talked about sparsity but did not analyze it. A simple hypothesis is that the effectiveness of LI and SFA can be fully explained by the coding sparsity they induced. Such analysis will give a better picture of the underlying mechanics.", "limitations": "As I noted in the weaknesses and questions section, I believe the simulations in the manuscript are not thorough or sufficient to support the conclusions.", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strength:\n\nThe question is framed clearly. The view of the role of self-adaptation and lateral inhibition regarding different levels of input noise is novel.\n\n### Weakness:\n\nSee my questions on the simulation, which makes me suspect the experiments are not sufficient to support conclusions. The manuscript does not include any theoretical or more rigorous analysis. The combined effect of both LI and SFA is not shown. \n\nSince the simulation results could be due to the choice of the parameters, and most of the curves in the result figures look noisy and sometimes complex non-monotonic trends, I do not think the experiments conducted are sufficient to fully understand the behavior of this RNN model. The analysis of the representation geometry is somehow simple. Thus the conclusions are weakly supported.", "was_revised": true, "final_justification": "The authors provided extra analysis in the rebutal, which could improve the quality of the manuscript.", "rebuttal": "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.\n\n**1. The combined effect and noise adaptability of LI and SFA**\n\nWe 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.\n| N.I. | LI+SFA | Base  | LI    | SFA   |\n| :---: | :----: | :---: | :---: | :---: |\n| 0    | 99.10  | 91.70 | 98.30 | 93.50 |\n| 0.1  | 95.58  | 74.61 | 91.85 | 78.26 |\n| 0.2  | 85.28  | 72.64 | 74.78 | 78.77 |\n| 0.3  | 68.48  | 59.03 | 53.82 | 69.34 |\n\n**2. The potential for higher inhibition**\n\nWe 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:\n\n(1) Resolving the apparent discrepancy between the table and high-noise plots\n\n(2) the potential for higher inhibition\n\nTo 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:\n\n1) 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%.\n\n2) 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. \n\nThese 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.  \n\nIn 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.\n\n**3.Robustness analysis of parameters**\n\nWe 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.\n\nWe 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:\n\n(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.\n\n(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.\n\n(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.\n\nCrucially, 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.\n\nTherefore, 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.\n\n**4.time-averaged MBON**\n\nWe 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.\n\nFrom 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.\n\nBeyond 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.\n\nIn 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.\n\n**5.Sparsity**\n\nTo 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:\n\n(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.\n\n(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.\n\nBy 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.\n\n**6.Inconsistency and inadequate explanation of notations**\n\nWe are sorry for the inconsistency and inadequate explanation of notations. We have clarified more details and have added more discussions to improve the readability.\n\n1.  Input Data $X_{i,j}$ represents the $j_{th}$ element of $i_{th}$ class odor, we revise it as $X_{i,j}$.\n\n2.  we revise $X_i^k = \\max(X_i^k, 0)$ as $\\tilde{X}_i^k = \\max(X_i^k, 0)$.\n\n3.  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.”\n\n4.  Page 3, bottom, “the synaptic weights $w_{LN \\rightarrow PN}$, representing the connection from LNs to PNs, are always negative”."}, {"review_id": "9lAI1Eiy64", "reviewer": "Reviewer_R1XK", "summary": "In this work, the Authors investigate two parts of the fruit fly's olfactory circuit. These parts, performing lateral inhibition and spike frequency adaptation, were both previously attributed to pattern separation in odor learning, although their mechanisms are different. To see if there are differences in the function of these parts of the olfactory circuit, the Authors have built a spiking neural network model grounded in the architecture of the fruit fly's olfactory circuit. Through the modifications of the model and ablation studies, they found the differences in the pattern separation performance of lateral inhibition vs. spike frequency adaptation under different levels of noise, suggesting different roles of these subcircuits in the fruit fly's olfaction.", "questions": "Please see the Weaknesses section above.", "limitations": "Please see the Weaknesses section above.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n\nI really liked this work. It deals with the fruit fly's olfactory system, which is a system of interest to the olfactory community and has made notable appearances in top machine-learning conferences due to its fine neuronal mapping that has led to the emergence of local-sensitive hashing algorithms.\n\nAs the Authors have pointed out, this system has further potential to inform the field of machine learning and help the development of noise-tolerant classifiers based on an architecture successfully deployed in the real world.\n\nThe results on the different functions of LI and SFA are, to my knowledge, novel, and useful for the fields of neuroscience and machine learning alike.\n\nThe text is well-written and easy to follow: the steps are explained and the concepts / variables are introduced. Overall, it's a nice, principled, well-documented work.\n\nWeaknesses:\n\nThe PN-to-KC connections are fixed and not trained in the model here. Meanwhile, there's growing empirical and theoretical evidence suggesting that there may be structure: Modelling work suggests that training that sparse matrix via backpropagation improves the model's performance (works by Dmitry Krotov and colleagues), while experimental work suggests that there may be a shared low-dimensional structure in that matrix (works by Alex Koulakov and colleagues). Theoretical works (the models of olfaction) also suggest that there may be a coupling between the statistics of olfactory inputs and the statistics of the PN-to-KC connections. Whether that turns out to be true or not, it would be interesting to test these ideas in the modeling work here and see how these factors would affect the obtained results.\n\nCould you please discuss the need for the use of spiking neural networks here as opposed to the usual, non-spiking models? Spikes seem to require significant computational resources, so it is important to know what additional benefits they provide compared to simpler models.\n\nIt would also be interesting to hear the Authors' thoughts / further Discussion on possible differences in the ethological roles of the two investigated subcircuits based on the new results of this paper.", "was_revised": true, "final_justification": "After the discussion with the authors and communication with other reviewers, I am convinced that my original rating still best reflects my take on this work.", "rebuttal": "Thank you for your constructive comments. We have reflected on the content as follows:\n\n**1. Consideration of Flexible PN-to-KC connections**\n\nWe thank the reviewer for highlighting this important point and appreciate the insights drawn from relevant empirical and theoretical work.\n\nWe 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.\n\nWe 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.\n\nWe believe these experiments will add significant depth to our analysis, and we thank the reviewer for encouraging this important direction.\n\n**2. The necessity of using spiking neural network**\n\nWe 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:\n\n(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.\n\n(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.\n\nModeling 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.\n\nIn 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.\n\n**3. the ethological roles of LI and SFA**\n\nThank 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.\n\nWe 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.\n\nWe 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.\n\nThank you again for pushing us to explore this important dimension."}, {"review_id": "puJYM4bG9t", "reviewer": "Reviewer_rDRe", "summary": "This paper studies the seemingly redundant computational mechanisms of lateral inhibition (LI) and spike frequency adaptation (SFA) in olfactory identification. The authors utilize models that do or do not include LI and SFA, and find that LI enables better learning of odor identity than SFA, when the amount of noise present in the olfactory input is low. In contrast, the authors find that SFA leads to better learning when the noise present is high. The authors argue that this demonstrates that the seeming redundancy enables complementary benefits in learning across different noise scenarios.", "questions": "As noted in the weakness section, I have a few questions about the results: \n\n1. What $t_{jk}^X$ and $t{kl}^{LN}$ are (Eqs. 2 and 3)? \n\n2. Why was the spiking threshold of the readout layer neurons \"slightly higher\"? What does slightly mean? \n\n3. And why are only one set of weights plastic? \n\n4. How does Fig. 3 shows that the LI mechanism leads to larger differences in population firing rates and patterns? l\n \n5. What are the different lines in Fig. 4?", "limitations": "The authors need to add more discussion on the limitations as the two sentences do not adequately provide context. The authors should discuss the limitations of having only 1 layer of weights being plastic, using the assumption of Gaussian noise, and training with a gradient based optimizer.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**STRENGTHS**\n\n1. This paper is well motivated and I found the introduction well written. In addition, I believe the introduction provides a good coverage of past work and situates the authors' work nicely in the existing literature. \n\n2. The results are interesting and provide a nice demonstration of the growing understanding that seeming redundancy in neural computations can actually be playing distinct roles. The results are also demonstrated across a number of noise conditions and odor sizes, which was helpful for understanding the extent to which these conclusions hold. \n\n3. The results are clearly explained and Figure 1 was very helpful at understanding the authors' model.\n\n**WEAKNESSES**\n\n1. I think the biggest weakness of this work is that clarity could be improved. In particular: \n    a. I found the description of the model somewhat confusing, in part because of the notation. For instance, $X$ is used both to denote layer and input. Also, what $t_{jk}^X$ and $t{kl}^{LN}$ are (Eqs. 2 and 3) were not ever defined. I additionally felt like a few of the modeling choices were also not explained in great detail. For instance, why was the spiking threshold of the readout layer neurons \"slightly higher\"? What does slightly mean? And why were only one set of weights plastic? \n   b. The author's mention that Fig. 3 shows that the LI mechanism leads to larger differences in population firing rates and patters. But that was not clear to me from the figure. The authors should provide more commentary on this and some quantitative analysis to show that this is clear, or they should remove this point from the text. \n    c. Fig. 4 seems to be a very interesting one, but it was not clear to me what \"base, low, medium, and high\" were (each of the lines). I assume this was achieved by changing the relative strength of the different mechanisms, but how was that actually implemented? \n\n2. The paper ends on a slightly lower note, as the conclusion and limitations are very short and do not leave the reader feeling the significance of the work. The authors' have the space (almost a whole additional page) and they should use it to provide more discussion on what the implications of their work are, what this work inspires next (e.g., looking at the learning dynamics associated with having LI and SFA) and how their work could be improved upon. The author's wrote a really great introduction, and having a similar quality discussion would elevate the quality and impact of this work. \n\n3. I really liked the authors' approach in studying the different mechanisms by including only SFA or only LI. However, both exist in the fly. I think it would be good to include some results from a \"full\" model, which includes LI ***and*** SFA. This could help illustrate that the combination of both computational elements allows for good learning in any noise condition. I don't think the authors have to do a full analysis of this, but even one table or figure would be good. \n\n**MINOR POINTS**\n\n1. The authors mention LI improves discrimination in their abstract. But their results seem to point to LI improving the ***learning*** for discriminating odors (which the authors say throughout their paper). I think making it clear in the abstract that the results are about learning would be good. \n\n2. It was not clear to why assuming a normal distribution in odor noise was reasonable. Is there any evidence of this? Or is this just for keeping it simple and in-line with previous work? \n\n3. \\tau_{trace_ln} and \\tau_{trace_LN}are used. \n\n4.  I assume the bold dot in Eqs. 3 and 8 are just inner product, but this should be noted. \n\n5. Figure 2 was never referenced in the main text. \n\n6. In Table 1, the first row, left column, the Base model is incorrectly labeled as having the second highest accuracy. Table 1 should also have a note on what the colors mean.", "was_revised": true, "final_justification": "The authors have sufficiently addressed all my concerns. I am increasingly confident in my general belief that this is an interesting, impactful, and correct paper.", "rebuttal": "Thank you for constructive comments. We have revised the manuscript as follows：\n\n**1. Dual use of the symbol and explanations of $t_{jk}^X$ and $t_{kl}^{LN}$**\n\nWe 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.\n\nWe fully acknowledge that the dual use of the symbol X (to denote both layer and input) has introduced confusion. To address this, we will:\n\n(1) Revise notation for clarity:\n\nIntroduce a distinct symbol for input (e.g., I) to replace X in the context of input data description.\n\n (2) Add notation table for readability:\n\nExplicitly 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.\n\n**2.More precise description of spiking threshold**\n\nThank you for the question, which helps us clarify the rationale behind key modeling choices and enhance the precision of our description.\nWe 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:\n\n(1) The highly convergent architecture from KCs to MBONs (KCs: MBONs $\\approx$ 2000:1).\n\n(2) Fully connected between KCs and MBONs.\n\nA 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.\n\n**3. Consideration of the learning site**\n\nThe 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:\n\n(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.\n\n(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.\n\nWe 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).\n\nThese 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.\n\n**4. Explanation of Figure 3**\n\nWe 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:\n\n(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).\n\n(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.\n\n**5. Explanation of Figure 4**\n\nWe 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.\n\nWe 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.\n\n**7.Corrections to minor points**\n\n(1) improves discrimination/ learning for discriminating odors\n\nWe 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.\n\n(2) Noise types\n\nWe 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.\nWe 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.\n\n(3) Inconsistency and explanation in notation\n\nWe 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.\nThe 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.\n\nWe appreciate your attention to this detail, which enhances the clarity and rigor of our notation.\n\n(4) References to the Figure 2\n\nWe 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.\n\nWe appreciate your attention to this detail, which helps strengthen the clarity of our presentation.\n\n(5) Color in the Table 1\n\nWe sincerely apologize for the errors and omissions.\n\n1) 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.\n\n2) 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.\nThese revisions enhance the accuracy and clarity of Table 1. We appreciate your careful review, which helps improve the rigor of our presentation."}]

Author rebuttal:

Meta-review: This paper is a borderline submission that was aided by a robust discussion period that led to new results and cleaner explanations, which mostly satisfied the reviewers. While there was still discussion about whether the results would prove impactful enough, I believe this is a solid addition to NeurIPS, where the rigorous computational work here could inspire future Neuroscience experiments.
Decision: Accept (poster)