The objective of event-based encoding is to create a framework for efficient representation of a continuous-time signal by capturing its values only at important instants (events), rather than registering it at regular time intervals as in classical methods of signal discretization. The event rate depends on the nature of the input signal, growing for example when the input changes substantially, and becoming smaller during periods of low activity. This allows for minimizing the number of events required to accurately represent the signal, reducing unnecessary computations and data transmissions (Miśkowicz, 2003).

The efficient event-based signal representation preserves signal characteristics by retaining its original key features, such as dynamics and frequency content, while avoiding artifacts or noise contribution that can cause generation of the events too frequently. With a flexible definition of events, event-based encoding of continuous-time signals can meet diverse system design objectives and application needs. Most definitions refer to the event as to a change of the state of an object occurring at an instant (Miśkowicz, 2015).

A class of event-based encoding that may be referred literally to the concept of the event as a significant change of the particular signal parameter are threshold-based criteria, known in the context of communication as the send-on-delta encoding (Miśkowicz, 2006). In the send-on-delta scheme, an input signal is encoded as an event when it deviates by a certain threshold (Δ) (Figure 1a). If x(t) is a continuous-time signal to be encoded, the send-on-delta encoding times t_n≥0 for n = 1, 2, …  with the threshold Δ are determined such that the following condition holds:

The size of the threshold Δ defines a trade-off between encoding resolution and the event rate. The threshold can be fixed or modified during system operation depending on the safety and/or performance requirements of the system (Tang et al., 2025), or as a response to variation of a signal slope (Trakimas and Sonkusale, 2011; Wang et al., 2018).

A different integration-based encoding scheme is the integrate-and-fire (IF) encoder that mimics the behavior of biological neurons by describing how a potential of a neuron membrane changes in response to input stimuli (Moser et al., 2025). The IF encoder accumulates an input over time until the total input reaches a threshold V_thr, which causes emission of a spike and a reset of the accumulator to zero:

where τ_int is the integration constant.

In a more biologically realistic neuron model, called leaky integrate-and-fire (LIF) encoder, the content of the accumulator decays exponentially with the time constant τ_leak (Figure 1b) (Thao et al., 2023):

Another generic class of event-based encoding relevant to many applications in event-based signal processing is not related to detection of an explicit change of the input but focused on matching a certain reference. In the reference-crossing encoding, the input is registered when it crosses a prespecified function. The examples are the sine-wave crossing (Selva, 2012) or level-crossing encoding (Mark and Todd, 1981).

In the level-crossing encoding, the reference function can be defined as a single level (Abrahams, 1986), or multiple reference levels (L₁, …, L_m) disposed in the amplitude domain (Mark and Todd, 1981) (Figure 1c).

The level-crossing encoding with the set of levels L₁, …, L_m is defined as follows:

where L_k and L_k+1 are reference levels, L_k+1>L_k, 1 < k<m.

This condition specifies that the next level crossing after the actual crossing of L_k will occur for the same level (L_k) or the higher level (L_k+1) in case of the up-crossing (x′(tn-1)>0) of L_k at t_n−1, or for the same level (L_k) or the lower level (L_k−1) in case of the down-crossing (x′(tn-1)<0) of L_k at t_n−1.

The level-crossing encodings provide not only time instants when the relevant reference levels are crossed but also imply that the signal remains between consecutive levels during the time between the level crossings (Figure 1c). This means that for t∈(t_n−1, t_n):

The extra knowledge defined by the above inequalities, called the implicit information, implies that no event occurs between consecutive encoding instants (Rzepka et al., 2018). The implicit information is relevant not only to the level-crossing encodings but also to any event-based encoding scheme.

The reference levels in the level-crossing encoding are usually uniformly distributed in the amplitude domain although adaptive (Senay et al., 2010) or optimal distributions of levels (Kozat et al., 2013) have been also proposed.

The mean rate of level-crossing and send-on-delta encodings depends on the average slope of the signal (Miśkowicz, 2006), while the rate of spikes in IF encodings is defined by the average values of the input signal. If the hysteresis is adopted to triggering (multiple) level crossings (i.e., the repeated crossings of the same level are not encoded), then such level-crossing criterion coincides with the threshold-based encoding (send-on-delta scheme).

The general model of threshold-based encoding that provides a unified framework for send-on-delta, leaky integrate-and-fire, and other threshold-based schemes (e.g., leaky send-on-delta) has been introduced in Moser (2017).

The threshold-based event encoding is a fundamental paradigm in event-based control (Heemels et al., 2012; Miśkowicz, 2015) and state estimation (Ge et al., 2020) designed for efficient utilization of computation and communication resources, especially when implemented with wireless connectivity in IIoT (Aranda-Escolástico et al., 2024; Miśkowicz, 2006). The send-on-delta encoding is applied to event sensors that mimic the function of eyes (silicon retina), ears (silicon cochlea), nose (e-nose), or touch (e-skin) and emit events when a signal representing relevant modality (vision, sound, olfaction, touch) changes by a prespecified threshold (Tayarani-Najaran and Schmuker, 2021; Cheng et al., 2019). On the other hand, the level-crossing encoding is an effective signal representation in energy-efficient signal processing applications (e.g., ECG analysis with wearable devices) (Ravanshad et al., 2013).

Integrate-and-fire encoders as simplified models of neuronal activity are foundational in computational neuroscience and extensively used in the development of SNNs (Thao et al., 2023; Moser et al., 2025). The SNNs are particularly well-suited for processing temporal data due to their inherent ability to handle time-dependent information (e.g., speech recognition, real-time sensory processing, and dynamic vision) (Nunes et al., 2022). One of the active research areas focuses on improving the efficiency of encoding techniques to enhance the performance and applicability of SNNs in various domains (Auge et al., 2021).

A recent work (Zanoli et al., 2025) has shown that optimization-based level-crossing encoding parameter selection methodologies achieve better signal reconstruction in ECG signal monitoring. In this paper, we analyze signal-to-event encoding schemes by examining how signal representation affects the performance of a machine learning model that processes event data using an event distance measure within the Bayesian optimization process. The analysis of event-based encoding schemes is conducted using sensor data for vehicle classification in an intelligent transportation system.

Event stream data can be processed by specialized machine learning models such as the spiking neural networks (SNN). These models process data using impulses that propagate asynchronously through the network (Pfeiffer and Pfeil, 2018). This approach allows SNNs to mimic biological networks more closely than traditional neural networks. While the development of the training rules for SNNs is an active area of research, several major training paradigms have been identified: plasticity-aware training (Falez et al., 2019; Mozafari et al., 2019); network conversion, which maps each component of the source network to its spiking equivalent (Rueckauer et al., 2017; Midya et al., 2019; Stöckl and Maass, 2021); and training with backpropagation (Lee et al., 2016; Wu et al., 2018; Rasmussen, 2019). The latter approach leverages existing algorithms and best practices developed for deep learning with nonspiking neural networks.

Backpropagation-based training of SNNs must address the challenge that the spike-generating function is non-differentiable. The methods to overcome this problem are of two types, depending on how much information from the forward pass is needed to compute the surrogate gradient signal. In event-driven learning the error is propagated only through spikes (Zhang and Li, 2020; Wunderlich and Pehle, 2021; Zhu et al., 2022). In contrast, in a learning scheme similar to that used in the Recurrent Neural Networks (RNNs) the error information is propagated also through time steps which did not elicit a spike (Wu et al., 2018; Neftci et al., 2019; Xing et al., 2020; Bauer et al., 2023). Training models with these methods usually requires simulating the state of the entire network over a finite time window with a fixed time step. However, it is possible to design learning rules that do not require such extensive simulation. One example is the time-to-first-spike SNN (Mostafa, 2018; Kheradpisheh and Masquelier, 2020; Zhou et al., 2021). This model is trained using locally exact gradients of the spike-generating function, making both the forward- and backward-pass through the network event-centric. Recently, the time-to-first-spike SNN model has been extended to the scenario where each postsynaptic neuron can generate multiple events in response to observed spike trains (Pabian et al., 2024).

The goal of Intelligent Transportation Systems (ITS) is to enhance the efficient use of existing transportation infrastructure by leveraging accurate traffic data acquisition technologies to monitor and manage traffic flow. Despite recent advancements in sensor technology, inductive loop (IL) sensors remain the most widely used in modern traffic control systems (Klein et al., 2006). This technology features low installation costs, a long lifespan due to its simple design, robustness to weather conditions such as rain, fog or snow, and a flexible architecture that can be adapted to various applications. Systems based on IL sensors are capable of vehicle classification (Gajda et al., 2001; Oh et al., 2002; Ki and Baik, 2006; Jeng and Ritchie, 2008; Meta and Cinsdikici, 2010), vehicle re-identification and tracking (Kwon, 2005; Ndoye et al., 2011; Guilbert et al., 2013, 2014), speed estimation (Sun and Ritchie, 1999; Coifman et al., 2003; Lu et al., 2012), as well as wheel and axle detection (Gajda et al., 2012; Marszałek et al., 2011, 2015, 2018).

At minimum, an IL detector consists of two components: a wire loop with one or more turns mounted on or embedded in the roadway pavement, and a controller cabinet that houses an electronics unit (Klein et al., 2006). When a ferromagnetic or conducting metallic mass passes over the IL connected to a conditioning circuit, the currents induced in the object alter the magnetic field distribution affecting the loop inductance and resistance (Mocholí-Salcedo et al., 2017). These dynamic interactions between the loop and the vehicle can be monitored and analyzed as impedance changes, generating a waveform signal known as the vehicle magnetic profile (VMP), where R-VMP represents its resistive component and X-VMP its reactive component.

Recently, a quad loop, four-channel VMP measurement system was proposed by Marszałek and Duda (2020). It consists of two standard loops (IL1, IL3) and two slim loops (IL2, IL4) arranged in series. The standard loops are well-suited for general-purpose tasks, while the slim loops are preferable for axle identification and wheel rim detection (Gajda et al., 2012; Marszałek and Sroka, 2016). Using two loops of each type instead of a single one introduces redundancy enhancing the system robustness against signal interference and simplifying the estimation of traffic parameters, such as vehicle speed (Mocholí Belenguer et al., 2019). Additionally, three different excitation frequencies are applied to each channel. The simultaneous multi-frequency measurement increases the system resilience to noise, reducing the risk of poor signal quality affecting downstream processing tasks. Figure 2 presents exemplary VMP profiles acquired by this measurement system. We use the quad loop sensor VMP signals originally discretized at 1 kHz in our event-driven signal analysis. A detailed description of the VMP data used in this study is provided in Section 4.

The main goal of this paper is to identify a set of signal-to-event encoding parameters that preserve information relevant to a multiple event classification task. We operate under the assumption that, for a simple classification model such as the k-NN classifier, the choice of spike encoding parameters has a measurable impact on classification performance and, intuitively, on the pairwise similarity of the generated event data. Consequently, event data that can be accurately classified by the k-NN model are expected to perform well as input to other event-based classifiers, assuming a positive correlation in their outcomes. This makes our method model-agnostic as it does not rely on any assumptions regarding the specific classifier to be used.

Figure 3 illustrates the proposed methodology for selecting signal-to-event encoding parameters. The approach involves performing V-fold cross-validation using a k-NN classifier that leverages an event-based distance metric to classify signals from the validation subsets. Within each data fold, encoding parameters are sampled via a Bayesian optimization process, guided by the classification accuracy observed in prior iterations. The resulting scores are aggregated into ranked lists (one per data fold) along with their corresponding encoding parameters. The final set of encoding parameters is then selected based on these rankings. Detailed descriptions of the proposed methodology are provided in Sections 3.1.1-3.1.3. It is important to note that if the distance metric used by the k-NN classifier is itself parameterized, its impact on the classification accuracy must be marginalized, e.g., by sampling multiple distance parameter values for each fixed set of signal encoding parameters during the Bayesian optimization process.

To assess how the set of encoding parameters selected by our methodology can be reused to train a more sophisticated event classification model, we train a spiking neural network. Specifically, we use the multiple-input, multiple-output (MIMO) time-to-first-spike SNN introduced by Pabian et al. (2024). This model extends the work by Mostafa (2018) by relaxing the implicit assumption of an infinitely-long refractory period τ_ref.

We introduce a neuron response delay factor τ_delay in the first hidden layer of the MIMO SNN. This parameter defines the earliest time at which a given neuron is capable of responding to input events. Functionally, this is equivalent to initializing the neuron in a refractory state lasting τ_delay. We hypothesize that assigning a different τ_delay value to each neuron in the layer enables them to observe slightly different event sequences, thereby mitigating the issue of early events disproportionally influencing the training process. Let us consider the following scenario: assume that all neurons start in a resting state, i.e., τ_delay = 0 for all neurons. Additionally, assume that one neuron becomes specialized through training to detect a pattern occurring relatively late in the input event sequence. In this case, this neuron must either adopt smaller synaptic weights to avoid firing prematurely, or maintain comparable weights to other neurons, while producing spikes that are not informative (i.e., spikes triggered by early, irrelevant events). Such behavior arises when a neuron reacts to parts of the input sequence that are not aligned with its intended function.

Figure 4 presents an example raster plot of a network trained with nonzero τ_delay values assigned to neurons in the first layer, increasing linearly across the layer. We do not apply τ_delay to neurons in deeper layers as the SNN-generated event sequences contain significantly fewer events than the network input, simplifying neuron specialization in those layers.

The MIMO SNN models are trained by minimizing the following risk function

where

is the modified cross-entropy loss for a single example indexed by n with:

The parameter γ is the synaptic regularization parameter for the spike-firing penalty

where Rmh=max(0,1-∑k∈Bmhwkh) with B_mh = {k:t_kh < ∞} being the set of valid inputs for the m-th output of the h-th postsynaptic neuron. Lastly, the parameter λ controls the strength of the L₂ regularization term of the network weights

For completeness R_mh = 0 if {k:t_kh < ∞} = ∅ . Models are trained with the RMSprop optimizer (Tieleman and Hinton, 2012) with a learning rate of 0.001 over 2,500 iterations with a batch size of 50 examples. We set λ = 10⁻⁵ in all experiments. Similarly to Pabian et al. (2024), the regularization parameter γ is initially set to a large value of 10⁵ in order to guide the model toward a solution that is capable of propagating event throughout the entire network. Then, after η iterations, the value of γ is decreased to 10³ in order to increase the relative importance of solving the classification task.

We use Hyperopt (Bergstra et al., 2013) to optimize the hyperparameters that control how the information is processed by the network. Specifically, the following Bayesian optimization search space was defined:

This parameter selection process is executed over 30 optimization iterations on a single data split from the V-fold cross-validation. Subsequently, the five best-performing parameter sets are selected and used to train MIMO SNN models on the remaining data splits. In case of tied performance scores, the top-5 Hyperopt models are chosen according to the following heuristic rule: prioritize lower τ_{max delay}, higher τ_ref, and lower η, in that order of importance. This selection strategy favors models that generate fewer events and exhibit faster response time.

For this study, we used the same VMP dataset as Marszałek et al. (2023). The dataset consists of 3,328 records categorized into six classes as follows: motorcycle (24.32%), bicycle (20.42%), electric scooter (19.52%), car (15.02%), delivery van (14.11%), and truck (6.61%). Each record contains simultaneous multi-frequency measurements of the real and imaginary components of the VMP signal as described in Section 2.3. For our analysis, we select a subset of channels, retaining only four of them for further processing (the R-VMP signals recorded at the lowest excitation frequency). This choice streamlines our analysis while also encouraging future research that explores the full scope of the available data.

In our analysis of the vehicle classification dataset we consider three encoding types introduced in Section 2.1: level-crossing, send-on-delta and leaky integrate-and-fire (LIF). For the proposed encoding parameter selection with Bayesian optimization we constrain the search space to the following set of probability distributions for each encoding type:

These constraints were chosen based on preliminary experiments, which showed that certain parameter values resulted in suboptimal event stream densities (e.g., the send-on-delta encoding with Δ>0.2 produced event streams that were too sparse).

Before the signal-to-event encoding, we upsample the digital VMP signals from 1 kHz to 10 kHz in order to more accurately assign the event occurrence time instants. Furthermore, as shown in Figure 2, the individual signals exhibit either all-positive or all-negative amplitudes with only minor variations near the zero baseline. Hence, we take the absolute value of each signal and apply min-max normalization to scale them to the 0–1 range. This normalization eliminates the need to account for variability in amplitude ranges across different VMP sensors. As a side effect of this signal normalization process, the LIF-negative event type cannot occur in the encoded sequences. Additionally, the spike sequences are time-shifted so that the first event within each sequence (across all event types) occurs at a relative time t = 0. This adjustment serves two purposes. Firstly, the sensors are positioned in a series, making it essential to preserve the relative time shifts between channels as the vehicle moves over the measurement system. Secondly, any sensor data recorded before the vehicle enters the measurement space should be discarded, enforcing a consistent effective signal start time t = 0.

Figure 5 shows an example of event sequences obtained for a VMP time series. Each signal-to-event encoding scheme produces a different number of distinct event types for each VMP sensor: level-crossing encoding produces one event type per amplitude threshold; send-on-delta encoding generates two event types (one for “rising” and one for “falling” signal amplitude); LIF encoding produces one event type due to the amplitude normalization step described earlier.

The results of the Hyperopt optimization runs are summarized in Figure 6, and show a wide range of the obtained classifier accuracy spanning approximately from 0.775 to 0.950. This variation highlights the significant impact of encoding parameter selection on the k-NN classifier performance. It is evident that some data splits are more challenging to classify than others, although none of the classifiers deviates significantly from their respective overall-average performance. Furthermore, the results indicate that suboptimal LIF encoding parameters can lead to significantly worse performance than compared to the level-crossing and send-on-delta encoding schemes. In particular, the van Rossum distance parameters were also optimized, influencing the final classification scores. However, determining whether one encoding scheme is definitely superior to the others is not possible based solely on these raw results, due to the factors discussed earlier in Section 3.1.3.

Additional insights into the encoding schemes were gained by analyzing the classification scores of models trained with Hyperopt in relation to the average number of events produced per VMP sensor³. The total number of events in the spike train was normalized by the number of VMP sensors to account for the fact that signals observed by the sensors tend to generate roughly the same number of events after encoding. As a result, the total number of events generated in the system scales linearly with the number of channels, regardless of the selected coding scheme. Additionally, this normalization allows for an assessment of the computational burden associated with adding an additional VMP sensor to the system. The results presented in Figure 7 indicate that the number of events alone is not the sole determinant of classification performance. Specifically, send-on-delta models maintained similar performance regardless of the number of events produced by the encoding scheme. In contrast, different LIF parameter sets, even when generating event sequences of similar length, led to significantly varied k-NN classifier performance.

The selected parameter sets, determined using this strategy, are presented in Table 1, which also includes the stratified 10-fold cross-validated k-NN classifier performance for data splits preprocessed with the chosen encoding schemes. According to these results, level-crossing encoding performs slightly better than the alternatives for the VMP vehicle type classification task. Each signal prior to event encoding contains an average of 1,590 samples. This means that the most data-intensive encoding scheme—send-on-delta—produces a representation that uses approximately 97.8% fewer samples than the original signal.

Next, we analyzed the average number of events produced by the selected encoding schemes for each VMP sensor separately. Together with the classification results, this analysis provides insights into the encoding efficiency. Figure 8 summarizes our findings. To visualize these distributions, we use letter-value plots (Hofmann et al., 2017)—an extension of the classical boxplot that more accurately represents distribution tails for large datasets. The results reveal a clear distinction between the empirical distributions of event sequences produced by the two standard inductive loops (IL1 and IL3) and the two slim loops (IL2 and IL4), regardless of the signal-to-event encoding scheme. Additionally, the level-crossing and send-on-delta encoding schemes produce similar overall number of events, with send-on-delta sequences containing slightly more events on average. In contrast, the LIF encoding generates significantly fewer events with the median number of events being approximately three times lower for IL1–IL3 sensors and about six times lower for IL2–IL4 sensors. Moreover, the LIF encoding is capable of adapting to the original signal variability, as evidenced by the broad range of event counts across all data samples. Given that all three classifiers in Table 1 achieve comparable classification accuracy, the LIF encoding appears to be more efficient in terms of the amount of information encoded per event.

Finally, relating the set of selected encoding parameters summarized in Table 1 with the original optimization search space reveals that the proposed method did not trivially select the parameter sets that would maximize the number of events in the event stream sequences. In fact, only the threshold voltage of the LIF encoding was on the sampling space boundary [selected V_thr = 0.2 for V_thr~U(0.2, 0.4)] with all other parameters being selected away from the boundary. This result suggests that the proposed method is not biased in favor of high event density encodings. However, the method itself does not have any safeguards and relies on carefully choosing the parameter bounds to avoid trivial solutions.

Selecting a parameter value for V_thr that lies on the search space boundary raises a question of whether the parameter space for the LIF encoding has been fully explored. In order to investigate this topic and challenge our initial choice of the search space, we repeated the LIF encoding parameter selection in a post-hoc experiment. In this analysis the LIF threshold voltage parameter sampling space was specified as V_thr~U(0.05, 0.4). Furthermore, due to an increase in the search space scope, we increased the number of iterations for the Bayesian optimization from 150 to 250. The new set of LIF encoding parameters selected by our method, as well as the average number of generated events and the classifier performance metrics, is presented in Table 1. Not only is the new choice of V_thr away from the sampling space boundary, but also the k-NN classifier performance for this encoding is on par with the one achieved by the send-on-delta scheme. Additionally, compared to the original result, this new set of LIF encoding parameters more than doubles the number of generated events (on average). Overall, this shows that the proposed method will achieve suboptimal results when the choice of the parameter sampling space for the Bayesian optimization is too constrained. As this result was obtained in a post-hoc experiment, we did not use this updated set of parameters of the LIF encoding in subsequent analysis.

The set of parameters identified in the previous analysis was used to encode VMP signals into the spiking domain before training the MIMO SNN models for the vehicle type identification task. We applied the same stratified 10-fold data split for cross-validation. The network parameter settings and the hyperparameter optimization grid were described in Section 3.2. In all experiments we used the same C-64-128-128-6 architecture, where the number of input neurons C depends entirely on the encoding scheme. The specific values of C for the encoded VMP data are as follows: C = 48 for level-crossing encoding, C = 8 for send-on-delta encoding, and C = 4 for LIF encoding. This results in a small network with a total of 25, 344+64C parameters. However, it is important to note that the effective capacity of the MIMO SNN model is higher than what the raw parameter count suggests, due to the repeated firing of the IF neurons, which are influenced by the refractory period τ_ref. In total, we optimized the weights of 225 models across the three spike encoding schemes.

Figure 9a summarizes the classification accuracy of models trained during the Bayesian optimization procedure on a single data split from the stratified 10-fold cross-validation. On average, the LIF encoding performed worse than the alternatives. Recall that all three encoding schemes when parameterized using the weighted median selection strategy achieved similar k-NN classifier accuracy of approximately 0.908 (Table 1). This indicates that the Bayesian optimization procedure failed to find a LIF model that outperformed its own baseline. In contrast, the level-crossing and send-on-delta models performed better than their respective k-NN classifiers, with both achieving similar median accuracy. However, the presence of outliers in the lower accuracy range suggests that poor hyperparameter selection during training can significantly degrade the final model performance. Nonetheless, these results confirm that running the optimization procedure over multiple iterations can lead to a high-performing model, provided that the signal-to-event encoding is chosen correctly.

Figure 9b presents the classification accuracy for models trained with the top-5 best-performing parameter sets selected by Hyperopt, separately for each encoding type and each cross-validation data split. This analysis evaluated the robustness of classifiers trained with these hyperparameters when applied to different input data. Several differences emerge between models operating on differently encoded data. Once again, LIF models exhibited significantly lower absolute performance compared to the other encoding schemes. Additionally, both level-crossing and LIF models evaluated on data splits #2–10 demonstrated worse classification accuracy than the reference split #1, which was used to determine the top-5 hyperparameter sets. In contrast, send-on-delta model evaluated on data splits #3, #7, #8, and #10 achieved performance levels comparable to scenario #1. This suggests that the hyperparameters selected for send-on-delta encoding are more robust across different training datasets. However, this encoding scheme also exhibited an extreme performance outlier in data split #9, deviating from all other trained models. Overall, these findings indicate that send-on-delta encoding is less sensitive to variations in training data, whereas level-crossing and the LIF encoding require more precise tuning to achieve optimal performance.

Lastly, Table 2 presents the top-5 parameter sets for the three encoding types along with the stratified 10-fold cross-validated performance metrics for models trained with these hyperparameters. Notably, the top-5 parameter sets selected for the send-of-delta and LIF models are significantly more similar to each other than those chosen for the level-crossing encoding. This may suggest that, for this specific task, 30 steps of the Bayesian optimization process are sufficient to converge to a good-enough (local minimum) solution for these two model types, but not enough for the level-crossing scheme. Interestingly, the selected values of τ_{max delay} were smaller for the send-on-delta and LIF models when compared to level-crossing scheme. This suggests that a nonzero τ_{max delay} is more beneficial when the number of neurons in the input layer is large (as in level-crossing encoder) rather than when they generate a large number of events (as in send-on-delta encoder). Finally, recall that the prior on the number of training iterations with a larger spike-firing penalty η was U{300,800}. Almost all of the selected values of η ended up at the higher end of this range. This indicates that training the model for longer with a relatively smaller weight assigned to the task-specific loss leads to better final model performance.

When compared to the performance of the baseline k-NN classifiers (Table 1), training the SNN results in lower error rates for the vehicle type classification task, provided that the signal-to-event encoding scheme is properly selected. While processing an example through the SNN is undoubtedly more computationally demanding than computing the multi-neuron van Rossum distance between a pair of examples, a k-NN-based system prediction time scales poorly with the size of the reference database, making it less efficient as the number of training examples increases.

Considering these factors, the send-on-delta model emerged as the most effective event-based encoding scheme for the VMP-based vehicle classification. This model achieved the highest stratified 10-fold cross-validation performance, demonstrated greater robustness across different data splits, and allowed the Bayesian optimization procedure to converge to a locally optimal solution within the given number of optimization steps. In particular, this cannot be solely attributed to the large average number of events generated by the encoding, as it is comparable to that for the level-crossing event sequences (as shown in Figure 8).