Abstract

Introduction:

Understanding how artificial neural networks (ANNs) can capture biologically meaningful dynamics is a central challenge in systems neuroscience. In this work, we investigate whether spiking neural networks (SNNs) can function not only as machine-learning tools but also as biologically inspired computational analogs and tractable testbeds for studying pathological neural dynamics.

Methods:

We implemented a spiking autoencoder composed of Leaky Integrate-and-Fire and Synaptic neuron models to create a controlled framework for analyzing how biologically related parametric changes to neuronal and synaptic dynamics influence learning and information transfer. By tuning model parameters to induce persistent overfiring-like behavior, we emulated a hyperexcitability-like regime conceptually analogous to NaV channel dysfunction in hippocampal circuits. Reconstruction performance and network activity were evaluated under both noiseless and noisy conditions.

Results:

The induced hyperexcitability-like regime degraded image reconstruction performance and disrupted stable information propagation, consistent with impaired processing in hyperexcitable neural systems. Layer-wise firing-rate analysis revealed that the altered regime was characterized by unstable activity redistribution rather than sustained global overactivation. Importantly, introducing controlled Gaussian noise into the input stream partially restored reconstruction quality and improved learning performance, suggesting that stochastic perturbations can partially compensate for instability in dysfunctional network regimes.

Discussion:

These findings demonstrate that specific SNN parameter regimes can reproduce key signatures of pathological excitability while also providing a platform for investigating compensatory mechanisms. Overall, this work positions spiking autoencoders as scalable, biologically grounded frameworks for hypothesis-driven studies of neural dysfunction and candidate interventions, supporting the integration of ANN methodologies with mechanistic models in systems neuroscience.

1 Introduction

Artificial intelligence (AI) traces many of its core ideas to brain physiology, inspiring the design of neural-network algorithms that approximate how biological systems process information. Over the past decades, a range of architectures has been developed, including convolutional neural networks (LeCun et al., 1989, 1998), recurrent neural networks (Graves et al., 2013), and graph neural networks (Wu et al., 2020). Beyond software, neuromorphic hardware has emerged to emulate neuronal computation in silicon (Upadhyay et al., 2019; Zhao et al., 2023).

While artificial neural networks (ANNs) are typically optimized as engineering tools, spiking neural networks (SNNs) occupy a distinctive niche: by explicitly modeling spike timing and synaptic dynamics, they provide an intermediate framework that is both computationally scalable and grounded in biologically meaningful parameters (Guo et al., 2023). SNNs capture temporal dynamics and spike-based information processing observed in biological neural systems, and have been applied across tasks such as ECG classification and radar-based action recognition (Chu et al., 2022; Fontanini et al., 2022). Crucially, because SNNs expose parameters that map onto neuronal and synaptic physiology, it seems they have a potential capability to be used not only to solve tasks but also as tractable, hypothesis-driven platforms for studying network dynamics that are relevant to systems neuroscience.

The brain learning process plays a fundamental role in cognitive function and knowledge acquisition (Conway, 2020). Motivated by this, we adopt the perspective that SNNs can serve as biological network analogs to probe how altered neuronal excitability affects network-level computation and learning (Botvinick et al., 2020). In particular, we examine whether parametric changes to neuron and synapse dynamics in an SNN can represent abnormalities analogous to those arising from NaV channel dysfunction in hippocampal circuits (e.g., hyperexcitability implicated in Temporal Lobe Epilepsy), and whether simple interventions can mitigate those effects.

To provide a controlled experimental scaffold, we implement a spiking autoencoder that performs image compression on handwritten digit images. Autoencoders compress high-dimensional inputs into a lower-dimensional latent representation and then reconstruct approximations of the original data (Theis et al., 2017). Here, the autoencoder is used as a diagnostic task: it exposes how changes in neuronal and synaptic parameters (e.g., those that increase spiking rate) might influence information encoding, transport, and decoding across network layers.

Concretely, we design the autoencoder using a combination of Synaptic and modified Leaky Integrate-and-Fire (LIF) neuron models and ask the following question: Can neurons and networks parameterized to overfire sustain learning and processing performance comparable to networks operating under biologically typical excitability? We investigate both noiseless and noisy inputs (Gaussian noise) to test whether stochastic perturbations can stabilize network dynamics under emulated pathological-like regimes. In this work, SNNs are not evaluated as direct competitors to conventional artificial neural networks in terms of performance metrics. Instead, they are employed as computational testbeds to investigate how controlled changes in neuronal and synaptic dynamics influence network-level behavior under different dynamical regimes.

Our contributions are therefore threefold: (1) we demonstrate that tuning SNN parameters to induce overfiring-like reproduces degraded information processing consistent with hyperexcitable biological circuits; (2) we show that adding Gaussian noise has the potential to counteract network instability, or even might act as a stabilizing intervention, that improves learning and reconstruction in otherwise unstable regimes; and (3) we position SNN-based autoencoders as tractable platforms for hypothesis testing at the interface of ANN methodologies and mechanistic models of neuronal dysfunction, thus advancing the goals of the “Unraveling Neural Network Dynamics” Research Topic.

2 Materials and methods

The methodological framework presented below is designed to operationalize the central objective of this study: using spiking neural networks as a controlled computational testbed for investigating neural network dynamics under physiological-like and hyperexcitable-like regimes. Rather than optimizing performance alone, the selected neuron models, parameters, and task are explicitly chosen to emulate learning, information propagation, and instability mechanisms relevant to hippocampus-related hyperexcitability and noise-driven compensation.

SNNs are inspired by natural neural communication processes and use an artificial representation of time-dependent spikes to propagate information (Rathi et al., 2023). In such networks, the information is only transmitted when the neuron membrane potential exceeds a certain threshold instead of on each propagation cycle, like in typical artificial neural networks (Kramer, 1991). Different methods have been explored to model the spike activation in artificial neurons, resulting in several neuronal network architectures that are able to solve machine learning problems, such as data classification and pattern recognition (Guo et al., 2023). Traditionally these applications use SNNs as task-oriented tools; here we emphasize their alternate role as biological-network analogs and tractable testbeds for studying neural dynamics.

Our SNN (see Figure 1) expands the architectures proposed in the literature by combining LIF and Synaptic neuron models, allowing us to control the generation of spikes and observe their effect on the network performance while processing handwritten digit images.

Schematic of autoencoder architecture related to hippocampus neuronal network and their related equivalent electrical circuit to observe the effect of overfiring-like on an image data recognition learning process.

The LIF model is widely used in neural networks due to its lower complexity and higher computational efficiency compared to more complex biophysical models,such as the Hodgkin–Huxley (HH) model (Eshraghian et al., 2023). Although the HH model describes the influence of the ionic channel on the action potentials of a neuron in detail, the LIF model provides a spike pattern, which is useful when investigating time-dependent or spiking behavior of neurons (Börgers, 2017). The LIF model lies between conventional Artificial Neural Networks, an abstract representation that is practical toward AI applications, and the HH model, which is oriented toward biological realism. In other words, the LIF model occupies an intermediate modeling regime: more biologically grounded than typical ANNs yet more scalable than full biophysical models such as Hodgkin–Huxley.

In the LIF model, a neuron is represented by an electronic circuit that includes a capacitor and a resistor in parallel, driven by an input current, as shown in Figure 2. The membrane potential Vout is the activation function for this neuron model and is evaluated considering its input current Iin, the resistance Rmem and capacitance Cmem of the membrane (Gerstner et al., 2014). Therefore,

where τ = RmemCmem and it represents the time taken by the membrane potential to reach a certain percentage of its steady-state value. By solving (Equation 1) when the input current is equal to zero, Iin(t) = 0, and Δt < < τ (Eshraghian et al., 2023), we obtain

where β is the LIF neuron decay rate. Here, we use β to increase/decrease the generation of spikes in the LIF model and observe its relation with the neuron conductivity, g, by assessing (Equation 2) in terms of the initial state of the neuronal network (that is, when Iin(t) = 0 and Vout(t) = V0) as follows (Equation 3):

then we consider Δt = Cmem to obtain

which produces similar values to the ones typically measured in healthy biological neurons (e.g., g = 0.1 mS results in β≈0.9) (Khodashenas et al., 2019; Eshraghian et al., 2023). From (Equation 4), we can conclude that lower β values, results in higher g values which is related to neuronal conductivity; in this work, the term overfiring-like and/or hyperexcitability-like regime is defined as increased neuronal conductivity g, which is now mapped to reduced decay parameter β in the LIF model. This parameterization is inspired by channel/leak conductivity increases in membrane excitability in biological neurons.

LIF Neuron Model as a parallel resistor capacitor (RC) circuit; This model captures the essential dynamics of neuronal spiking by simulating the integration of synaptic inputs (Isyn) and the subsequent generation of action potentials. It also shows how the Gain/Loss of function mutations can be associated with the resistance (conductivity) component, ultimately affecting the membrane potential.

Regarding the biological neurons behavior, we inducate hyperexcitability evidence, using direct electrophysiological measurements obtained from the NEURON simulator in Figure 3. This biophysical overfiring condition has been shown using increased NaV voltage-gated sodium channel conductivity (gNa) results in a marked increase in spike rate and reduced temporal stability compared to baseline conductance regimes, confirming a mechanistic hyperexcitability phenotype that supports the hypothesis based on increased neuronal conductivity. This neuronal dynamic has been quantified not only by membrane potential dynamics but also including spike counts/raster and firing rate comparison for different (gNa). Three different status has been shown, gNa = 0.12 mS for condition, gNa = 0.25 mS as intermediate status, and finally gNa = 1.0 mS as overfiring/hyperexcitable regime.

Spike counts, firing rates, and membrane potential dynamics based on three levels of neuronal conductivity gNa = 0.12mS as, gNa = 0.25mS as intermediate, and gNa = 1.0mS as overfiring/hyperexcitable.

For a defined β value, the SNN will then optimize its performance by updating its weights (filter or kernel), using the loss gradient (Eshraghian et al., 2023), while executing the image compression task; critically, we use the compression task as a controlled scaffold to probe how altered excitability impacts network-level computation rather than as an end in itself. This learning process is given by solving (Equation 1), using a forward Euler method, when

Rmem = 1 (reducing the losses that may occur by triggering the SNN), resulting in the following activation function

where W1 = Δt/τ is the learnable weight, X(t) is the network input, and r(reset) = V0(Δt/τ) allows to reset the network behavior whenever a spike is output from the neuron. In other words, to minimize (Equation 5), the network calculates the loss gradient for each learnable parameter by applying the chain rule from the final layer back to each weight, leading to an error reduction on the image compression task.

For the proposed SNN-based autoencoder, we also modulate the spike generation through the synaptic conductance. Natural neurons regulate their communication by activating their AMPA and NMDA receptors facilitating the passage of potassium and sodium ions, which can result in an increased generation of spikes, and are involved in various neurological functions and disorders (Paoletti et al., 2013). In practical terms, the Synaptic neuron model implements temporally extended synaptic currents (parameterized by α and βsyn), enabling us to manipulate synaptic decay and thereby emulate synaptic dynamics linked to pathological hyperexcitability. From a biological perspective, when using the Synaptic neuron model we are gradually releasing neurotransmitters from the pre- to post-synaptic cell, instead of an using the instantaneous jump in the synaptic current. To observe this gradual temporal dynamics of the input current, we modify (Equation 2) to include the synaptic current and solve it using a forward Euler method, which results in Equation 6:

where α is the synaptic current decay, and βsyn is the synaptic decay rate.

2.1 Lossy Image Compression using SNNs

To investigate the behavior of neurons when subjected to an increased spiking rate, we created a SNN-based autoencoder, integrating LIF and Synaptic neuron models, capable of compressing handwritten digits. To this end, we used handwritten digit images from the MNIST dataset (Modified National Institute of Standards and Technology), which is an extensive collection of handwritten digits and is a popular resource for training various image processing systems (LeCun et al., 1998). To compress these image data, we opt to design an autoencoder, which has been applied to compress images (with losses) in unsupervised learning scenarios (Kramer, 1991; Takeishi and Kalousis, 2021). In the proposed architecture, the LIF and Synaptic neuron models are layered in a specific order to encode, transport, decode, and reconstruct handwritten digit images. The proposed architecture is shown in Figure 4, where the encoder performs a series of operations on the handwritten digit image to extract its compressed representation. Through these operations, the encoder progressively reduces the spatial dimensions and increases the number of channels in the data until a flattened representation (i.e., encoded latent space) is obtained. Then, an additional linear layer is used to transform the latent space back to the shape of the encoder's final layer. The decoder then performs inverse operations to reconstruct the original input data from the encoded handwritten digit images, resulting in a compressed version of the original input data (see Table 1 for the autoencoder configuration).

Network architecture of the autoencoder model based on LIF and Synaptic neuron models in encoder and decoder parts.

LayersHeightWidthChannelsFilter sizeNeuron modelOriginal/Reconstructed image32321EN-Convolutional 1 (EC1)1616323 × 3LIFEN-Convolutional 2 (EC2)88643 × 3SynapticEN-Convolutional 3 (EC3)441283 × 3SynapticEN-Linear Layer (Flatten)LIFLS-Linear Layer––128 × 4 × 4–LIFDE-Linear Layer (unFlatten)LIFDE-Transposed Convolutional 1 (DC1)441283 × 3SynapticDE-Transposed Convolutional 2 (DC2)88643 × 3SynapticDE-Transposed Convolutional 3 (DC3)1616323 × 3LIF

Configuration of the proposed autoencoder application for the proposed SNN.

Please note that EN is referring to encoder,LS to latent space,and DE to decoder.The inclusion of the Synaptic neuron model in the layers EC2,EC3,DC1 and DC2 aimed to replicate the temporal dynamics of biological neural systems

To compress an image using the SNN-based autoencoder, we first utilize a black and white handwritten digit image without noise (32 by 32 pixels) as the network input X(t), see Figure 4. Please note that noisy images can also be used as input to the proposed SNN-based autoencoder, and in Section 3.1 we add Gaussian noise to handwritten digit images and investigate the SNN's network performance under such conditions. The noise experiments are explicitly framed as interventions to probe noise-driven compensation in pathological parameter regimes. Then, we reduce the spatial dimensions of the input signal X(t) by convolving it with a kernel filter K (a weight 3 by 3 matrix) in the layer EC1 as follows:

where F(i, j) is the output feature map as (X*K)(i, j) represents the value of the convolution at position (i, j), * denotes the convolution operation, m and n are indices that iterate over the dimensions of the kernel. Please note that a similar operation is performed for layers EC2 and EC3. In (Equation 7) we show how each pixel in the output feature map is computed by taking a weighted sum of its neighboring pixels in the input image, with the weights defined by the kernel. Using a 3 × 3 kernel is common practice in convolutional neural networks because it effectively captures local spatial patterns in the input image while keeping computational complexity manageable (Simonyan and Zisserman, 2014). We repeat this process twice using the Synaptic neuron model instead of the LIF. The final layer of the encoder is another SNN based on the LIF model, which flattens the handwritten digit image to be processed and transported to the decoder. Please note that we opted to have the LIF models at the input and output layers of the encoder to observe the impact of the synaptic current on the signal propagation through the encoding network and not on the information acquisition/retrieval. In other words, the focus is on how the signal (information) moves through the network rather than how the network retrieves or acquires information. Therefore, we are interested in investigating the effects of increased spiking rate on the signaling process of our SNN-based autoencoder, which may affect its learning capabilities. Please also note that the decoder does the reverse operations executed by the encoder, therefore, we use the same layer composition of the encoder.

2.1.1 SNN-based autoencoder performance analysis

To achieve a good performance, all the autoencoder's SNNs have to learn how to adapt themselves to the variations the hyperparameters may suffer due to the scenarios that they are subjected to. This learning process occurs by updating the SNNs' weights through backpropagation and adapted gradient descent algorithms (i.e., surrogate gradient); see (Eshraghian et al., 2023; Lee et al., 2016; Neftci et al., 2019). After compressing the handwritten digits, we compute the mean square error to assess the performance of SNN. We define two experimental regimes, a biologically-informed “benchmark" (healthy-like excitability) and an “overfiring-like" (pathological/hyperexcitable) regime, and use metrics to quantify how these regimes affect encoding, latent representations, and reconstruction MSE is used to observe and quantify how much error occurs during the image compression task, and El to measure the level of uncertainty of each autoencoder's layer when performing the same task. It is worth mentioning that, the experimental design focuses on controlled manipulation of spiking dynamics rather than exhaustive benchmarking across architectures or hyperparameter spaces.

Here, we also measure the MSE displacement, MSEd, to observe how much these metrics vary over a set number of SNNs' iterations; and the layer's MSE, MSEl, when comparing the data difference between the scenario with a typical and the excessive spiking rates (hereafter named benchmark and overfiring-like scenarios, respectively). Please note that MSEl is the only metric that applies a direct comparison between the scenarios we devised for this work. The remaining metrics are evaluated for each scenario separately.

The MSE measures the difference between the original and output data, and is used to trigger the computation of gradients for all the learnable parameters in the network through backpropagation, to update the weights of each SNN. Although this is not the focus of this work, it is important to note that MSE optimization can lead to improved SNN performance. Here, we focus on measuring data loss during the image compression task using MSE as an indicator of the network learning process. Therefore, we compute MSE as follows (Equation 8) (Weng, 2020),

where xi is a handwritten data sample, i = 1, ..., n is the sample index, and the reconstructed handwritten data sample. With a defined number of training and testing iterations of the SNNs, we evaluate the MSEd as the area of the MSE over the number of iterations plot curve, which we obtain using a trapezoidal rule as follows (Equation 9) (Atkinson, 1991)

where MSEj is the MSE value at iteration j, Δj is the difference between consecutive iterations, and j = 1, ...m is the iterations index. In this context, MSEd quantifies the MSE behavior for the autoencoder's training and testing iterations. Then, we evaluate the MSEl by quantifying the difference between corresponding elements of the benchmark and overfiring-like scenarios feature maps as follows (Equation 10):

where H and W represent the height and width of the feature maps, respectively, B and O stand for the benchmark and overfiring-like scenarios, respectively. The MSEl allows us to observe the data loss behavior for each layer of the autoencoder when subjected to a typical or excessive spiking rate.

Spike activity in the SNN was defined as the binary output of spiking neuron modules (0 or 1), corresponding to threshold-crossing events in Leaky Integrate-and-Fire (LIF) and Synaptic neuron models. Mean firing rate for each layer was computed as the average spike probability across all neurons, spatial locations, and time steps in Equation 11:

where denotes the spike output of neuron i in layer ℓ at time t, N is the number of neurons, and T is the number of simulation steps.

3 Results

The results are organized to examine how parametrically induced hyperexcitability alters network learning dynamics and information reconstruction, and how stochastic input perturbations (Gaussian noise) modulate these effects. We first characterize baseline (benchmark) and hyperexcitable-like (overfiring-like) regimes, then assess how noise influences stability, layer-wise information flow, and latent representations. To evaluate the information encoding and reconstruction performance of the proposed SNN-based autoencoder, we first designed our benchmark and overfiring-like scenarios. Then, we compressed noiseless and noisy MNIST-sourced handwritten digit images using our SNN-based autoencoder (considering both scenarios) and computed the data lost in this process using the metrics introduced in Section 2. For the benchmark scenario, we defined hyperparameter values that emulate the network behavior of biological neurons; β = 0.9, α = 0.9 and βsyn = 0.9 for the LIF and Synaptic neuron models (Eshraghian et al., 2023; Khodashenas et al., 2019). We considered a unitary threshold value for all neuron models (τ = 1) and set the number of steps as numstep = 5. We also defined the total number of epochs to 50 and utilized the AdamW optimizer (i.e., the widely used tool in deep learning for optimizing model parameters during training), setting the parameter lr to 0.0001, the values of the parameters betas of (0.9, 0.999) and weightdecay = 0.001 (Loshchilov and Hutter, 2017). We then modified the LIF (β = 0.0001) and Synaptic neuron models' hyperparameters (either βsyn = 0.0001 or αsyn = 0.0001 or both) to systematically induce a hyperexcitability-like regime and evaluate its impact on network dynamics and reconstruction performance. Due to computational constraints associated with full-scale SNN training on the MNIST dataset, the majority of experiments were conducted using a single-run configuration, consistent with the study's objective of providing a mechanistic analysis rather than performance optimization. To assess the robustness of the key finding regarding noise-driven compensation, additional experiments evaluating test MSE across noise levels were repeated using three independent random seeds (123, and 999). Results from this analysis are reported as mean ± standard deviation across runs. Training was performed using surrogate gradient learning with an arctangent surrogate function, surrogate.atan(α = 2.0). All other hyperparameters, including optimizer settings and training configuration, were kept fixed across experiments to isolate the effect of excitability and noise.

We define hyperexcitable-like regimes by parameter configurations corresponding to increased effective conductivity (i.e., reduced β and/or altered synaptic decay), and subsequently evaluate their impact on reconstruction performance. Among the explored parameter configurations, the regime producing the strongest degradation in reconstruction performance is used as a representative hyperexcitable-like condition.

We computed the lossy information encoding and reconstruction performance (MSE and MSEd) for five scenarios, including the benchmark and overfiring-like cases; see Table 2. For this analysis, we split the MNIST dataset into 60, 000 digits for training and 10, 000 for testing, all images were resized to have 32 × 32 pixels, converted to grayscale, and normalized to ensure uniform data formatting (aligning well with the proposed SNNs). We also set the threshold value τ = 1 and set a time step of 5 ms for each simulation run; split the data set into batches of equal size (250, in this case) and used 50 epochs, resulting in 12, 000 and 2, 000 iterations for training and testing, respectively. Neuron models were imported from the installed PyTorch and snntorch libraries and the required neuron models were called using “snn.leaky()” and “snn.synaptic()” commands. For the benchmark case (scenario 1), the obtained MSE shows a high similarity between the input and output data processed by the autoencoder (when using natural-based hyperparameter values), while the MSEd demonstrate a fast convergence to a constant error performance (that is, low MSE with a low number of iterations). In Scenario 2, it seems that there is not a huge difference in loss values compared to Scenario 1, which could be associated with the network topology and architecture, as the synaptic neuron models perform without a change in their hyperparameters, as we had in Scenario 1. By modifying βsyn, we can excite neurons to excessively fire action potentials and to be less sensitive to input changes, impairing the ability of the network to process information properly (instability and loss of information). This issue can be seen in Scenario 3, where we obtained the worst performance (highest MSE and MSEd values), thus becoming our overfiring-like scenario. In contrast, we obtained the best performance in Scenario 4, where we only modified αsyn. By keeping βsyn unchanged while modifying αsyn, neurons remained sensitive to input data, maintaining a balance between excitatory and inhibitory signals, and improving overall system performance. When modifying both αsyn and βsyn (Scenario 5), we obtained MSE and MSEd performances similar to Scenario 3, which showed that reducing αsyn did not counteract the effect of a slow decay rate for the synaptic neuron model.

ScenarioSub-scenarioMSEMSEd1 - BenchmarkNo changes0.099635.322 - LIFβ = 0.00010.076473.963 - Synapticβsyn = 0.00010.2771396.84 - Synapticαsyn = 0.00010.064504.545 - Synapticαsyn = 0.0001, βsyn = 0.00010.101098.64

Sample results of different scenarios based on the MSE loss value of the model.

The overfiringlike scenario is highlighted in bold.

Figure 5A,C shows the final-epoch mean firing rates across encoder and decoder layers.

Average firing rate of (A) Noiseless (top) vs. (C) Noisy (bottom) data across SNN layers in the final epoch, and (B,D) across iterations for both benchmark (black) and overfiring-like (red) regimes.

In the noiseless condition (Figure 5A), encoder layers consistently exhibit reduced firing rates under the hyperexcitability-like regime (e.g., EC_Syn1: 0.2288 → 0.1577; EC_Syn2: 0.2339 → 0.1913), indicating impaired temporal integration due to faster membrane decay (reduced membrane decay rate). In contrast, decoder layers exhibit heterogeneous behavior: the first decoder leaky layer shows increased activity (DC_Lk1: 0.4242 → 0.5525), while downstream synaptic layers display reduced firing (DC_Syn1: 0.2591 → 0.1824; DC_Syn2: 0.2800 → 0.1811). This non-uniform pattern demonstrates that the hyperexcitability-like regime does not correspond to a global increase in firing activity, but rather induces a redistribution of activity across layers.

Under the noisy condition (Figure 5C), the interaction between input perturbations and reduced temporal integration further reshapes this activity distribution. Certain encoder layers exhibit increased firing rates under the hyperexcitability-like regime (e.g., EC_Syn1: 0.1846 → 0.2431), suggesting partial restoration of responsiveness. However, deeper encoder and decoder layers show reduced activity (e.g., EC_Lk2: 0.7619 → 0.5341), indicating impaired propagation of information.

These results suggest that noise does not uniformly amplify activity, but instead redistributes firing in a manner that partially compensates for instability induced by reduced temporal integration.

Figure 5B shows the temporal evolution of network-wide firing rates. The hyperexcitability-like regime exhibits a non-monotonic profile, characterized by elevated activity during early training epochs followed by a progressive decline below the benchmark condition. This contrasts with the relatively stable firing profile observed in the benchmark regime and indicates reduced temporal stability.

Under the noisy condition (Figure 5D), the hyperexcitability-like regime exhibits consistently lower average firing rates compared to the benchmark, suggesting that noise further limits effective temporal integration at the network level.

Figure 6 provides a detailed layer-wise comparison of firing rates across all conditions. Consistent with the aggregate analysis, the hyperexcitability-like regime is characterized by a redistribution of activity rather than a uniform increase in firing. Specifically, encoder synaptic layers show reduced activity, while decoder leaky layers exhibit increased activation, indicating an imbalance in signal propagation across the network. Importantly, the introduction of noise partially mitigates this imbalance by restoring activity in previously suppressed layers (e.g., EC_Syn1) while reducing excessive activation in dominant layers (e.g., EC_Lk2), supporting the interpretation that noise can stabilize spike-based information flow under reduced temporal integration.