Towards Neuromorphic Compression based Neural Sensing for Next-Generation Wireless Implantable Brain Machine Interface

As the number of recording channels increases, traditionally used analog multiplexing schemes (as shown in Fig. 1(b) Scheme-I) become prone to noise and interference, therefore multiplexing digital signals becomes a preferred scalable solution. Newer neural recording arrays such as Neuropixel [11], Neuralink [15], Argo [13] and $59$K in-vitro electrodes [12] attempt to tackle the power and data-rate limitations by either using programmable switch matrix or by implementing on-chip multiplexing for sub-array digitization, which is a hybrid between the Schemes I and II in Fig. 1(b) involving multiplexing of a group of recording electrodes in the analog domain before digitization, thereby making it feasible for only about $3-4\%$ of the electrodes ($2,048$ channels for Argo and $384$ channels for Neuropixel) that can be addressed simultaneously. [12, 10] integrate the ADC under a neuro-pixel while increasing the electrode count. This allows full-frame readout from all electrodes besides ensuring high-SNR, robust digital readout from an arbitrarily selectable subset of electrodes. They however neither address the data deluge post-digitization nor provide compression strategies to realize scalable, low-power, wireless neural implants.

Analog techniques such as spatial compression before digitization and compression via superposition were proposed in [16, 17]. However, they either involve large complexity hardware-intensive algorithms for the front end or are limited by noise summation, which limits the scalability of such neural implants. Compression schemes such as compressive sensing [18] and autoencoder [19] also fall short of the requirements to meet the available wireless data rates with increasing electrode count. On-chip spike sorting [20, 21, 22, 23] and compression [24] have been proposed to reduce the transmitted data (as shown in Fig. 1(b) Scheme-I/II followed by Scheme-C). However, these do not tackle the issue of multiplexing and digitization in the front end of the neural implant sufficiently.

An interesting image sensor inspired technique, presented in [25], exploits the spatio-temporal sparsity of neural signals to simultaneously achieve compression and digital multiplexing with wired-OR interactions. It provides a lossy compression by discarding samples in the baseline region via wired-OR contention among pixels retaining samples potentially corresponding to spikes. When multiple pixels compete for access to the limited wires, collision occurs, and more than one row/column decoders are activated, resulting in no unique decoding solution for recovery of quantized voltages. Such collisions may also occur for spike signals depending on the choice of the baseline, especially when neural firing is correlated– leading to loss of spike data. Reducing the loss of valid samples to collision would require a more complex wiring configuration and address decoding schemes.

Data rate and power-sensitive methods propose transmitting a binary train of spike information indicating the presence or absence of spikes in time bins[26] for real-time clinically viable iBMI. While these methods reduce power consumption and data rate by an order of magnitude, they preclude features such as spike shapes for tasks such as spike sorting. However, the performance of iBMI systems employing such compression with increasing electrode count on the neural interface array is still unknown. Some other works such as [27, 28] advocate the integration of decoders in the implant (as shown in Fig. 1(b) Scheme-I/II followed by Scheme-D). While this addresses the problem convincingly, it also limits the implant to specific tasks, reducing its adaptability in the future [29].

Limitations imposed by power and bandwidth with electrode scaling on neural interfaces could be addressed effectively with the promising low-power neuromorphic approach as demonstrated previously for sensory applications such as event-based vision [30], audio [31], tactile [32], and olfactory [33] sensors. This approach essentially ‘morphs’ the initial sensory information processing stages of biological sensors/receptors into VLSI chips using a combination of efficient analog and digital circuitry to mimic their asynchronous spatio-temporal activity. A neuromorphic event-driven neural recording approach was first proposed in [34] for iBMI and more recently implemented in [35, 36, 37]. The neuromorphic approach can also provide benefits of digital multiplexing due to integration with address event representation (AER) circuits and digitizing/communicating data only during spikes by virtue of in-pixel thresholding. The AER-based handling of events could potentially address the shortcomings of data loss due to collisions in SPDWOR configuration. Works in [20, 35, 37] introduce a pipeline involving spike train generation using an analog-to-spike conversion block on-chip decoding using a spiking neural network, which limits its usability to specific tasks. While [35] uses a round-robin arbitration based AER scheme, [20, 37] does not have a collision handling strategy that could scale with the size of the neural electrode. None of the aforementioned neuromorphic/event-based neural recording schemes investigate the gains from using the neuromorphic compression in terms of reduction in data rate, nor assess its impact on iBMI performance. The fidelity of the compressed signal and the effect of collisions in the AER block of a neuromorphic compressive iBMI on task-specific performance when scaling to large Nx-iBMI systems has hitherto been unexplored.

In this work, we investigate the architectural trade-offs of neuromorphic compression of neural signals for iBMI inspired by asynchronous event detection image sensors (AEDIS) such as the dynamic vision sensor (DVS) using next-generation large neuromorphic neural recording systems for simulated and realistic neural recordings. We make the following contributions:

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  We explore the use of address event representation (AER) based readout with a pair of handshaking signals (request and acknowledgment) for elegant collision management to prevent loss of detected pulses by delaying them.

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  We assess the extent and effect of neuromorphic compression on spike shape and spike detection performance for two modes of transmission - ‘All pulse mode’ (APM) and ‘Pulse count mode’ (PCM) quantitatively with a set of standard evaluation metrics and compare them with other popular methods of transmitting neural signals.

• •

  We evaluate task-specific fidelity, specifically spike shape preservation and spike detection performance, for APM and PCM pipelines and investigate the performance variation across different synthetic and real datasets (100-channel non-human primate, i.e., NHP and 384-channel Neuropixel recordings).

• •

  We assess the collision handling capability and effect of collision on signal recovery.

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  We discuss the scalability of the proposed method to a higher number of recording channels and the potential to compress the proposed read-out further.

An initial version of this work was presented in [38] where the proposed neuromorphic compression based neural sensing pipeline was analyzed using a single-channel synthetic recording. This work extends the findings for higher channel count recordings including real neural recordings from non-human primates and mice to understand the scalability of the proposed pipeline, besides investigating its collision handling capability and exploring options for further compression. The neuromorphic iBMI event dataset obtained from the simulation of the proposed pipeline is made publicly available at: \urlhttps://sites.google.com/view/brainsyslab/neuromorphic-ibmi-dataset.

A neuromorphic compression based neural sensing system as shown in Fig. 2(a) is proposed to consist of a DVS-pixel-like ON and OFF threshold crossing detection circuit [30] integrated into each cell, similar to the implementation in [34]. Generally, the front end comprises a capacitive low-noise amplifier with gain $A_{1}$ followed by a second programmable gain stage with gain $A_{2}$. The total gain of the amplifier stages is typically $\approx 200-1000$. This is followed by an asynchronous delta modulator to generate an output $\mathrm{V_{mod}}$ and pulses $p$ (+1/ON and -1/OFF). The AER readout strategy is facilitated by arbitration logic, address decoders, and a pair of handshaking signals for event readout. The readout events are then packetized depending on the mode of operation and transmitted wirelessly for further downstream processing of the neural event stream. The following subsections elaborate on the working principle of some of the main blocks of the proposed pipeline.

Each pixel consists of an asynchronous delta modulator typically composed of an input operational transconductance amplifier (OTA) with a capacitive divider gain stage, a pair of comparators, and inverters that generate the pulse train commonly referred to as ‘events’. ON ($\mathrm{+1}$) and OFF ($\mathrm{-1}$) pulses/events, are produced when the change in the amplified version of the input signal ($\mathrm{V_{in}}$) increases above the reference voltage, $\mathrm{V_{ref}}$, by $\mathrm{Th_{ON}}$ or decreases below $\mathrm{V_{ref}}$ by $\mathrm{Th_{OFF}}$ respectively. The pulse generation process can be described as follows:

where $\mathrm{V_{cm}}$ is the common mode voltage of the ADM. An example waveform with a spike reconstruction is shown in Fig. 2(b). Other implementations[39] have also combined this function in one stage, where the signal reconstruction method was different. An enhanced adaptive version of the asynchronous delta modulator, as introduced in [36], could be used to modulate and minimize the event generation rate by following the amplitude and noise characteristics of the input signal. This could effectively suppress event generation due to noise or abnormalities in the baseline region. For the purpose of simplicity, the event generation block in this work is assumed to contain a basic asynchronous delta modulator, as implemented in [34].

Upon generation of ON/OFF events, the $\mathrm{Req}$ signal is generated and, an additional logic asserts the $\mathrm{Ack}$ signal once the event is readout, which in turn resets the pixel. The reset state will be held for a ‘refractory period’ determined by the values of the capacitor and the bias voltage in the pixel circuitry. The number of pulses generated by each pixel depends on the amplitude and frequency of the input signal, and also on the parameters of the delta modulator - ON/OFF pulse generate thresholds and refractory period. The pixels across the rows and columns of the electrode array are tied via a wired-OR connection to pass the read request (Req) to the readout block. Row $\mathrm{(Req~{}Y_{i})}$ and column $\mathrm{(Req~{}X_{i})}$ request lines from each of the neural recording pixels are connected to the row (Y) and column (X) arbiter similar to DVS [30]. For realizing an AER-like readout and managing collision efficiently, we use a toggle tree fair X, Y-arbiter [40] to decide the sequence of readout when pulse read requests are generated by multiple electrodes simultaneously. As in any AER system, time represents itself and events are generated asynchronously. The address $\mathrm{(x_{i},y_{i})}$ and polarity ($\mathrm{p_{i}}$) of the generated pulses (ON/$\mathrm{+1}$ or OFF/$\mathrm{-1}$) are communicated to the next stage. Acknowledgment signals ($\mathrm{Ack~{}Y_{i}}$ and $\mathrm{Ack~{}X_{i}}$) are then sent from the X, Y-arbiters to the cell ($\mathrm{x_{i},y_{i}}$) after read out, to reset its amplifier for continuing the delta compression.

The proposed neuromorphic scheme allows the neural data to be encoded as a train of asynchronous binary ON/OFF pulses, instead of producing an n-bit word for each sample at the output of the ADC. Events from the event stream are packetized depending on the mode of transmission before they are transmitted. In this work, we investigate two modes of operation: APM and PCM. In APM, all the generated pulses are transmitted off-chip asynchronously through a wireless link, with the event pulse packetized to contain the address and polarity of the event, $\mathrm{(x_{i},y_{i},p_{i})}$. In contrast, PCM involves electrode-wise accumulation of events with fixed-time bins. If the width of the bin is chosen to be ‘n’-sampling intervals long, then it is denoted as PCM‘n’ (e.g. PCM1, PCM2, and PCM4 have bin-widths equal to 1, 2, and 4 times the traditional sampling interval in neural recording systems respectively). The ON and OFF Events generated by an electrode at $\mathrm{(x_{i},y_{i})}$ location in PCM mode are packetized as the ON and OFF event counts - $\mathrm{n_{ON}}$ and $\mathrm{n_{OFF}}$ as $\mathrm{(x_{i},y_{i},n_{ON},n_{OFF})}$. For a bin width of duration $\mathrm{t_{b}}$, in PCM the ON/OFF events are accumulated as follows:

The number of bits per APM event is, $1+\log_{2}\mathrm{N_{r}}+\log_{2}\mathrm{N_{c}}$ whereas the number of bits per PCM event is, $\mathrm{n_{ON}}+\mathrm{n_{OFF}}+\log_{2}\mathrm{N_{r}}+\log_{2}\mathrm{N_{c}}$ where $\mathrm{N_{r}}\times\mathrm{N_{c}}$ is the size of the electrode array. In both modes, nothing is transmitted when no events are generated. At the receiver end, the electrode signals can be recovered by the accumulation of pulses depending on their polarity by stair-step reconstruction or directly processed using spiking neural networks, for further processing downstream processing such as spike detection, spike sorting, decoding, etc.

Simulations were performed using the data processing pipeline shown in Fig.3. In order to incorporate realistic arbitration delay when simulating for larger electrode count, we simulated a toggle-tree fair arbiter as introduced in [40] in a $65$ nm CMOS process using Cadence Virtuoso to determine the arbitration delay. The arbitration delay ($\mathrm{t_{arb}}$) was estimated to be in the order of a few nanoseconds. This delay was incorporated in the timing of colliding events by delaying transmission of the event by $\mathrm{p_{e}}\times\mathrm{t_{arb}}$ where $\mathrm{p_{e}}$ is the event priority decided by the arbiter. Thus, the estimated arbitration delay was fed to the processing pipeline along with the recorded neural signals and, calibrated thresholds for ON/OFF pulse generation and spike detection ($\mathrm{Th_{ON}}$/ $\mathrm{Th_{OFF}}$ and $\mathrm{Th_{SPD}}$ respectively). To evaluate the correctness of neural signal encoding in the form of neural events using the proposed scheme, we recover the signal by following the steps detailed in Section - IV-C1. The recovered signal which approximates the original channel recording was thus obtained. The drift in the trace of the recovered signal from the baseline owing to the open loop asynchronous behavior of delta modulation was removed using a high-pass filter on the recovered signal. The following subsections elaborate on the neural recording datasets that were used for the simulations in this work, along with the evaluation metrics used and key results.

The simulations in this work have been performed for three diverse datasets, ranging from single-channel synthetic data to 100-channel non-human primate (NHP) motor cortex and 384-channel mice visual cortex neural recordings. The details of the datasets used are as follows:

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  Synthetic dataset provided in [41] with varying noise levels ($\mathrm{\sigma_{noise}}$ = 0.05, 0.1, 0.15 and 0.2) and sampling frequency of $24$ KHz with spike duration of $\approx 1-2$ ms. The dataset also contains ground truth for the spike detection task. For worst-case simulation of large n-channel electrode arrays, the single-channel signal is replicated to all the n-channels.

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  Non-human primate (NHP) motor cortex recordings containing 100 channels sampled at 30 KHz previously used in [27, 42] for decoding motor intention. Since no ground truth is available for this dataset, spike detection was performed on the original recorded signal using the absolute threshold method in [41]. The resultant spike detections were used as a ground truth of potential spike samples for performance analysis of the different compression methods investigated in this work.

• •

  Recordings of mice’s visual cortex to visual stimuli with 384 channels Neuropixel [43] at $30$ KHz and $<7~{}\mu$V RMS noise levels were made available in [44]. Spike detection ground truth containing potential spike times was obtained in the same way as was described for the NHP dataset above. Spike signal duration is $<1~{}\mu$ S in the Neuropixel recording.

In order to analyze the effect of neuromorphic compression on iBMI we evaluate the spike information retention i.e., how well the compressed signal preserves spike shape (used in tasks such as spike sorting). This is measured in terms of signal recovery performance. We also show that better tradeoffs may be obtained by using other metrics, such as task-specific performance analysis. To this end, we use spike detection performance to assess the task-specific usability of signal recovered from the compressed data for downstream iBMI tasks, such as spike-based decoding.

For APM and PCM, the ON and OFF thresholds were determined from trade-off curves between threshold and performance metrics mentioned in IV-C. During the calibration stage (a few seconds long), the input-referred pulse generation threshold for each recording channel was determined as a factor of the spike amplitudes $\mathrm{V_{spike-max}}$ and is obtained as follows:

The factor $k$ was obtained from trade-off curves as shown in Fig. 4(b) by sweeping $k$ in the range $(0,1)$ in steps of $0.1$ and determining the value at which $k$ balances off the performance metrics and pulse generation rate. As shown in the left plot of Fig. 4(b), for the synthetic dataset, an input referred threshold obtained with of $k=\pm 0.3$ was found to provide a good tradeoff between data rate and signal recovery. As expected, spike detection required a less stringent threshold, obtained with $k=\pm 0.45$. $\mathrm{Th_{ON/OFF}}$ is a parameter of the asynchronous delta modulator and therefore affects the pulse generation rate. A larger $\mathrm{Th_{ON/OFF}}$ would result in a lower data rate. However, this results in coarser reconstruction of the signal from the pulse data and suppression of samples whose values are below the threshold, resulting in degraded signal recovery (affecting CC and RMSE) and spike detection performance (affecting Acc and S). Similar trade-off curves were obtained for the NHP and Neuropixel datasets, and a $k=\pm 0.3$ yielded better performance without a significant increase in the data rate as shown in Fig. 4(d-e). The more stringent threshold for signal recovery is used to report the results presented in the following subsections.

The theoretical model for the estimation of transmission data rate (TDR) in terms of the firing rate of the biological neuron, for the architecture studied in this work is:

where $\mathrm{R_{p}}$ is the sample/pulse generation rate for an $\mathrm{N_{r}}\times\mathrm{N_{c}}$ array requiring $\mathrm{n_{b}}$ bits to represent the pulse, $\mathrm{f_{neu}}$ is the biological spike firing rate, $\mathrm{N_{AP}}$ is the average number of pulses generated per spike, $\mathrm{n_{b}}$ is the number of bits per pulse/sample, $\mathrm{R_{noise}}$ is the pulse generation rate corresponding to non-spike samples. $\mathrm{R_{bin}}$ is the rate of non-empty event count bins in PCM, which depends on the number of bins per second ($\mathrm{n_{b}}$) and the probability of non-empty bin ($\alpha_{\mathrm{b}}$), and is related as follows:

$\alpha_{\mathrm{b}}$ in Eq. 6 represents the sparsity of PCM event counts. SPDWOR involves transmitting $\mathrm{b_{ADC}}$ bits for $\mathrm{f_{neu}}\times\mathrm{N_{spike}}$ spike samples, where $\mathrm{N_{spike}}$ is the number of samples per spike. The theoretical model was validated by comparing with several seconds of synthetic data and was found to match well with an error of $\pm 5\%$.

The extent of compression for the proposed method is evaluated by computing the compression ratio (CR), which is defined as the ratio of the transmission data rate for full sample transmission ($\mathrm{TDR_{fs}}$) as done in [10, 11, 12] to the transmission data rate of spike-sample transmission ($\mathrm{TDR_{spk}}$) as done in SPDWOR [25] or that of the proposed PCM/APM ($\mathrm{TDR_{APM/PCMn}}$). The CRs for different transmission modes (APM and PCM) were computed using the following equations:

The CR comparison plot shown in Fig 5 (a-d) was obtained for the synthetic dataset by sweeping the firing rate $\mathrm{f_{neu}}$ of the channel and linearly extrapolating the compression ratio for different $\mathrm{f_{neu}}$ for different background noise levels. As expected, the $\mathrm{TDR_{APM/PCMn}}$ increases with increasing noise levels (due to added events generated by background noise) and results in a drop in the CR. Higher the $\mathrm{f_{neu}}$ higher is the APM/PCM event generation rate ($\mathrm{R_{p}}$ in Eq. IV-E), resulting in a drop in the CR as $\mathrm{f_{neu}}$ increases. An ideal SPDWOR-like implementation transmits all the samples (8-12 bits per sample besides the address bits) corresponding to each of the spikes, irrespective of the change in the signal value compared to the previously recorded sample. In contrast, APM transmits 1 bit and PCM transmits $\mathrm{n_{ON}+n_{OFF}}$ (typically $<12$) bits only when the signal exceeds $\mathrm{Th_{ON/OFF}}$, thereby transmitting fewer bits per spike compared to SPDWOR. Therefore, at neural firing rates of $\approx$ $30-60$ Hz, the CR of the proposed method is $\approx 20-50$ and $6-8\times$ SPDWOR [25] as shown in Fig.5(e). Even though CR in proposed methods decreases with increasing electrode numbers (Fig. 5(f)) due to a higher number of bits needed to encode the address, it is still $\approx 3\times$ better than [25] for $10$K channels. For the 100-channel NHP dataset with an average neural firing rate per channel of $\approx 62$ Hz, CR1 = $3.23$, CR2 = $25.2$, CR3 = $15.4$, and CR4 = $850$ were obtained, which is consistent with the estimated CR in Fig. 5(f).

As discussed in Section IV-C, signal recovery and spike detection metrics are used to understand the effect of compression. Table I summarizes the effect of neuromorphic compression on large iBMI for the two modes of pulse transmission- APM and PCM for bin widths that are 1,2 and 4 times (PCM1, PCM2, and PCM3) the sampling interval used in conventional neural signal transmission for all the three datasets introduced earlier. Over 90% of the spike shape can be fully recovered on average, from APM, whereas the recovered signal is relatively degraded with increasing levels of compression in PCM, as seen in the RMSE and CC columns of Table I. While PCM4 ensures lower TDR compared to APM, it comes at the cost of spike shape recovery. The higher the level of PCM, the coarser the event generation and recovery of the signal.

Spike detection is a typical but significant task in firing-rate based iBMI systems. Therefore, it is necessary to assess whether the proposed APM/PCM effectively captures the spike-time information. We do this by performing spike detection on the signal recovered from the APM/PCM events, comparing the detection from the recovered signal with the ground truth, and quantitatively computing the metrics (A, S and FDR) described in Section IV-C2, it can also be observed that the sensitivity of spike detection is not significantly affected by the poor spike shape recovery. A higher sensitivity ensures that spikes are not missed, especially those closer to the noise level, and this factor is all the more significant in noisy channels. It can be seen that spike detection on signals recovered from APM, PCM1, and PCM2 results in very high sensitivity. As expected, spike detection performance, particularly FDR and accuracy, degrades with increasing noise ($0.05$ to $2.0$) and compression (APM to PCM4).

For the NHP and Neuropixel datasets, the evaluation of performance metrics relied on how ‘potential spikes’ were defined in the absence of the ground truth. We determined the absolute threshold for spike detection, which is a few factors higher than the noise margin as typically done in AT-SPD, and recorded the time of the positive and negative spike-detection threshold ($\mathrm{Th_{SPD}}$) crossing as potential spike times. Despite the constraint, the sensitivity of SPD and CC are decent for the NHP and Neuropixel datasets. We found that the spike information (spike time and shape) is well-preserved in the proposed APM/PCM. We leave spike detection directly using the generated APM/PCM events as future work.

Simulations performed in this work using the synthetic datasets inherently test the robustness of the neuromorphic compression pipeline, owing to the replication of single-channel signal to $\mathrm{10K}$ channels. This results in creating a worst-case scenario where events are simultaneously generated by each of the $\mathrm{10K}$ channels, requiring arbitration without loss of events. Thanks to the sparsity of spikes and the sampling interval, the arbiter has sufficient time to complete the AER handshaking and reading out of events in time without dropping any event, which is evident from the high CC and S recorded in Table I. The AER-based read-out process however introduces a small delay owing to the arbitration time in case of collision as shown in Fig. 6(a). For the NHP dataset, it was determined that an average of $10.0748\pm 3.5741$ channels collide in the recording, with $0-74$ collisions at any instance. Similarly, for the Neuropixel dataset, $29.5113\pm 33.51$ channels collide, with $\approx 5$ of them carrying spike samples. There are $0-321$ collisions at any instance in the Neuropixel recording. For the NHP and Neuropixel datasets, $\approx 25\%$ of events correspond to spike samples undergoing collision. If spike-sample only transmission scheme akin to SPDWOR-like read-out were to be used in scenarios like this, it would result in the loss of the spike samples that undergo collision. While SPDWOR uses collisions to an advantage to suppress samples corresponding to the background activity, it also loses some samples corresponding to the spike. The reference [25] reports $80-90\%$ spike recovery measure in terms of spike sorting performance, which indicates over a tenth of spike information is lost. The spike sample loss using the SPDWOR scheme might be more prominent in high-density neural probes that exhibit a high spatiotemporal correlation among the neighboring recording sites/channels [47]. Owing to the inherent noise sample suppression of the ADM and collision handling mechanism of the AER-arbiter, the loss of spike samples is negligible for the proposed APM/PCM pipeline. This can be inferred from the change in RMSE due to collision is negligible and mainly due to delay in the sample as shown in Fig. 6(b).

In the simulations for the APM/PCM pipeline using the synthetic dataset, it is to be noted that the CRs reported are for the worst-case scenario where events are simultaneously generated in each of the $\mathrm{10K}$ channels and the AER-arbiter handles the collisions. The worst-case analysis is a by-product of simulations with single-channel synthetic data of varying noise levels copied to $\mathrm{10K}$ channels. We noticed there is only a small difference in the signal recovery performance due to the arbitration delay in the proposed pipeline. Since we did not implement the SPDWOR, we estimate the data rate based on the assumption that under ideal conditions, SPDWOR captures all the samples corresponding to the spike. Work in [25] demonstrates the scalability of the wired-OR readout for up to 512-channel electrode array with about $80\%$ spike recovery, however, the increase in complexity of wiring and the effect of collision on the quality of spike information captured for higher electrode counts is still unknown.

In order to analyze the scalability of the proposed neuromorphic compression scheme for the real recordings, we take a subset of $100$ channels with the highest firing-rate channels from the 384-channel Neuropixel dataset. As seen in the last few rows of Table I, TDR for APM/PCM drops when the number of channels is limited to 100 high firing-rate channels. We notice that TDR increases significantly for APM and PCM1 when scaled from 100 to 384 channels of the Neuropixel dataset while the increase is not as high for PCM2 and PCM4. The probability of non-empty bins (studied further in Section V-B) is higher for PCM2 and PCM4, as a result, the TDR does not change dramatically with scaling. On examining the cause for higher TDR in APM/PCM1 with scaling, we identified that a significant number of events generated by an ADM in APM/PCM with a single fixed threshold ($\mathrm{Th_{ON/OFF}}$ with $k=0.3$), correspond to background activity, resulting in higher TDR (as shown in green in Fig. 8(a)). In order to reduce TDR and improve CR, it is necessary to choose ($\mathrm{Th_{ON/OFF}}$) such that the ADM generates events only for the spike and suppresses background activity in the channel. In Section V-C we explore some schemes to reduce TDR and improve CR by suppressing event generation due to background activity.

While transmitting in PCM, as opposed to APM seems to have a better CR for lower noise and thresholds as seen from the results in the previous sections, the improvement in compression does not change dramatically at higher noise levels. To understand this effect, Table II presents the sparsity of PCM events, in other words, the probability of non-zero event counts in PCM bins ($\alpha_{b}$ in Eq. 6). It can be seen that there is a higher probability of non-empty bins in PCM at higher noise and for lower pulse generation thresholds, which results in higher TDR and therefore lower CR. Owing to the design of the asynchronous delta modulator ADC (ADM-based pulse generator) used in this work, a fast-rising or falling input signal such as spikes results in dense pulse generation which translates to higher APM event rate and higher PCM event counts per bin, whereas a smooth/flat input signal results in few or no event pulses. Thus, the sparsity of APM events or non-zero event counts depends on the choice of the ON/OFF pulse generation threshold.

A good threshold for ADM is critical in ensuring higher compression. Higher thresholds i.e., increasing the factor $k$ can ensure that background activity causes no pulse/event generation and improves overall compression, however, the spike shape captured might be coarser resulting in poor recovery. An adaptive delta modulator as introduced in [36] or a delta modulator with a two-level threshold - one for detecting the spike and the other for finer asynchronous sampling of the spike, may be implemented.

Fig. 7(a) presents a logical block diagram for a simple dual threshold ADM with two sets of thresholds - $\mathrm{Th_{High}}$ and $\mathrm{Th_{Low}}$. In this approach, the ADM initially operates with the higher threshold, until the input signal level exceeds $\mathrm{Th_{High}}$ and then switches to a lower threshold $\mathrm{Th_{Low}}$ for a fixed time $T_{timer}$ determined by the timer (typically, spike duration $\approx 1-3$ ms) to capture the spike shape with finer step size. When the timer elapses, the ADM switches back to asynchronous sampling with $\mathrm{Th_{High}}$. Following the notation used in Eq. 4, $\mathrm{Th_{High}}$ and $\mathrm{Th_{Low}}$ are adjusted by varying the factors $k_{1}$ and $k_{2}$ respectively. Table IV summarizes the observation for two different values of $k_{2}$ ($k_{2}=0.1~{}\text{and}~{}0.3$), fixed value of $T_{timer}=1$ ms and a fixed higher $k_{1}=2\times$$k=0.6$ ($k=0.3$ as discussed in Section IV-D). $k_{2}=0.3$ results in higher CR ($\approx 2\times$ more than single-threshold ADM) and $16-18\times$ higher compression than SPDWOR. As shown in Fig. 8(a), a dual-threshold ADM captures the spike shape well depending on the chosen $k_{2}$ and prevents spurious events from background activity that are captured by single-threshold ADM.

Another approach for increasing compression and suppressing background activity events is presented in Fig. 7(b), where event-based temporal filters may be employed following a single-ADM neuromorphic compression based readout to limit the transmission of APM/PCM events corresponding to spikes only. Leveraging on the sparsity of events and pulse generation pattern discussed in Section V-B, the event filters may track the event rate (for APM) or event counts (for PCM) within a temporal neighborhood to determine whether the current event corresponds to a spike or not. An event from a channel may be said to result from a spike if it is preceded by a dense spike train in the near past from the same channel. A low-complexity event-based spike detector may thus be realized as a byproduct of the event filters. However, implementation of this approach is left for future work. With an average of $4-8$ events per spike, the filtered event stream is estimated to result in up to $8\times$ more compression per channel. Thus, with future improvements to the proposed pipeline to transmit events corresponding to detected spikes only, a CR of about $50-100$ can be achieved for a mean neural firing rate of $\mathrm{f_{AP}=60}$ Hz.

We do not present circuit simulation of the Asynchronous Delta Modulator since such schemes have been published in several papers such as [34] or even the recent [36, 35]. Unlike SPDWOR, no expensive wiring is needed to handle collision scenarios, which are inherently handled by the AER-based readout strategy in our proposed pipeline. Neuromorphic circuits are known for low power consumption, and thus a neuromorphic compression based iBMI system is expected to consume far less power than conventional neural recording systems with full-sample transmission. Relying on the hardware measurements from [35] which implements an ADM-based pulse transmission in $40$ nm CMOS technology, the ADM configured consumes $\approx 7~{}\mu$W per channel. A neuromorphic compression based readout as proposed in this work, operating in low-power mode can be estimated to result in a surface power density of $\approx 4.36$ mW/cm², which lies well within the power dissipation budget of $\approx 80$ mW/cm² for iBMI[14].

A summary of the high-level comparison of the proposed neuromorphic compression based neural sensing with prior works is presented in Table III. The proposed pipeline is a low-complexity, scalable, and high-compression neural recording system that preserves spike shape by handling collision scenarios effectively without the need for additional wiring. High compression may be obtained by recording systems that capture spike times only or perform on-chip decoding, however, this limits their adaptability to a limited set of iBMI tasks.