Delay learning based on temporal coding in Spiking Neural Networks.

Spiking Neural Networks (SNNs) hold great potential for mimicking the brain's efficient processing of information. Although biological evidence suggests that precise spike timing is crucial for effective information encoding, contemporary SNN research mainly concentrates on adjusting connection weights. In this work, we introduce Delay Learning based on Temporal Coding (DLTC), an innovative approach that integrates delay learning with a temporal coding strategy to optimize spike timing in SNNs. DLTC utilizes a learnable delay shift, which assigns varying levels of importance to different informational elements. This is complemented by an adjustable threshold that regulates firing times, allowing for earlier or later neuron activation as needed. We have tested DLTC's effectiveness in various contexts, including vision and auditory classification tasks, where it consistently outperformed traditional weight-only SNNs. The results indicate that DLTC achieves remarkable improvements in accuracy and computational efficiency, marking a step forward in advancing SNNs towards real-world applications. Our codes are accessible at https://github.com/sunpengfei1122/DLTC.

Time cells in the retrosplenial cortex.

The retrosplenial cortex (RSC) is a key component of the brain's memory systems, with anatomical connections to the hippocampus, anterior thalamus, and entorhinal cortex. This circuit has been implicated in episodic memory and many of these structures have been shown to encode temporal information, which is critical for episodic memory. For example, hippocampal time cells reliably fire during specific segments of time during a delay period. Although RSC lesions are known to disrupt temporal memory, time cells have not been observed there. In this study, we reanalyzed archival RSC neuronal firing data during the intertrial delay period from two previous experiments involving different behavioral tasks, a blocked alternation task and a cued T-maze task. For the blocked alternation task, rats were required to approach the east or west arm of a plus maze for reward during different blocks of trials. Because the reward locations were not cued, the rat had to remember the goal location for each trial. In the cued T-maze task, the reward location was explicitly cued with a light and the rats simply had to approach the light for reward, so there was no requirement to hold a memory during the intertrial delay. Time cells were prevalent in the blocked alternation task, and most time cells clearly differentiated the east and west trials. We also found that RSC neurons could exhibit off-response time fields, periods of reliably inhibited firing. Time cells were also observed in the cued T-maze, but they were less prevalent and they did not differentiate left and right trials as well as in the blocked alternation task, suggesting that RSC time cells are sensitive to the memory demands of the task. These results suggest that temporal coding is a prominent feature of RSC firing patterns, consistent with an RSC role in episodic memory.

Time Cells in the Retrosplenial Cortex.

The retrosplenial cortex (RSC) is a key component of the brain's memory systems, with anatomical connections to the hippocampus, anterior thalamus, and entorhinal cortex. This circuit has been implicated in episodic memory and many of these structures have been shown to encode temporal information, which is critical for episodic memory. For example, hippocampal time cells reliably fire during specific segments of time during a delay period. Although RSC lesions are known to disrupt temporal memory, time cells have not been observed there. In the present study, we examined the firing patterns of RSC neurons during the intertrial delay period of two behavioral tasks, a blocked alternation task and a cued T-maze task. For the blocked alternation task, rats were required to approach the east or west arm of a plus maze for reward during different blocks of trials. Because the reward locations were not cued, the rat had to remember the goal location for each trial. In the cued T-maze task, the reward location was explicitly cued with a light and the rats simply had to approach the light for reward, so there was no requirement to hold a memory during the intertrial delay. Time cells were prevalent in the blocked alternation task, and most time cells clearly differentiated the east and west trials. We also found that RSC neurons could exhibit off-response time fields, periods of reliably inhibited firing. Time cells were also observed in the cued T-maze, but they were less prevalent and they did not differentiate left and right trials as well as in the blocked alternation task, suggesting that RSC time cells are sensitive to the memory demands of the task. These results suggest that temporal coding is a prominent feature of RSC firing patterns, consistent with an RSC role in episodic memory.

Optimization of Temporal Coding of Tactile Information in Rat Thalamus by Locus Coeruleus Activation.

The brainstem noradrenergic nucleus, the locus coeruleus (LC), exerts heavy influences on sensory processing, perception, and cognition through its diffuse projections throughout the brain. Previous studies have demonstrated that LC activation modulates the response and feature selectivity of thalamic relay neurons. However, the extent to which LC modulates the temporal coding of sensory information in the thalamus remains mostly unknown. Here, we found that LC stimulation significantly altered the temporal structure of the responses of the thalamic relay neurons to repeated whisker stimulation. A substantial portion of events (i.e., time points where the stimulus reliably evoked spikes as evidenced by dramatic elevations in the firing rate of the spike density function) were removed during LC stimulation, but many new events emerged. Interestingly, spikes within the emerged events have a higher feature selectivity, and therefore transmit more information about a tactile stimulus, than spikes within the removed events. This suggests that LC stimulation optimized the temporal coding of tactile information to improve information transmission. We further reconstructed the original whisker stimulus from a population of thalamic relay neurons' responses and corresponding feature selectivity. As expected, we found that reconstruction from thalamic responses was more accurate using spike trains of thalamic neurons recorded during LC stimulation than without LC stimulation, functionally confirming LC optimization of the thalamic temporal code. Together, our results demonstrated that activation of the LC-NE system optimizes temporal coding of sensory stimulus in the thalamus, presumably allowing for more accurate decoding of the stimulus in the downstream brain structures.

Rethinking skip connections in Spiking Neural Networks with Time-To-First-Spike coding.

Time-To-First-Spike (TTFS) coding in Spiking Neural Networks (SNNs) offers significant advantages in terms of energy efficiency, closely mimicking the behavior of biological neurons. In this work, we delve into the role of skip connections, a widely used concept in Artificial Neural Networks (ANNs), within the domain of SNNs with TTFS coding. Our focus is on two distinct types of skip connection architectures: (1) addition-based skip connections, and (2) concatenation-based skip connections. We find that addition-based skip connections introduce an additional delay in terms of spike timing. On the other hand, concatenation-based skip connections circumvent this delay but produce time gaps between after-convolution and skip connection paths, thereby restricting the effective mixing of information from these two paths. To mitigate these issues, we propose a novel approach involving a learnable delay for skip connections in the concatenation-based skip connection architecture. This approach successfully bridges the time gap between the convolutional and skip branches, facilitating improved information mixing. We conduct experiments on public datasets including MNIST and Fashion-MNIST, illustrating the advantage of the skip connection in TTFS coding architectures. Additionally, we demonstrate the applicability of TTFS coding on beyond image recognition tasks and extend it to scientific machine-learning tasks, broadening the potential uses of SNNs.

Predicting gene-level sensitivity to JAK-STAT signaling perturbation using a mechanistic-to-machine learning framework.

The Janus kinase (JAK)-signal transducer and activator of transcription (STAT) pathway integrates complex cytokine signals via a limited number of molecular components, inspiring numerous efforts to clarify the diversity and specificity of STAT transcription factor function. We developed a computational framework to make global cytokine-induced gene predictions from STAT phosphorylation dynamics, modeling macrophage responses to interleukin (IL)-6 and IL-10, which signal through common STATs, but with distinct temporal dynamics and contrasting functions. Our mechanistic-to-machine learning model identified cytokine-specific genes associated with late pSTAT3 time frames and a preferential pSTAT1 reduction upon JAK2 inhibition. We predicted and validated the impact of JAK2 inhibition on gene expression, identifying genes that were sensitive or insensitive to JAK2 variation. Thus, we successfully linked STAT signaling dynamics to gene expression to support future efforts targeting pathology-associated STAT-driven gene sets. This serves as a first step in developing multi-level prediction models to understand and perturb gene expression outputs from signaling systems. A record of this paper's transparent peer review process is included in the supplemental information.

Altered neural encoding of vowels in noise does not affect behavioral vowel discrimination in gerbils with age-related hearing loss.

Introduction: Understanding speech in a noisy environment, as opposed to speech in quiet, becomes increasingly more difficult with increasing age. Using the quiet-aged gerbil, we studied the effects of aging on speech-in-noise processing. Specifically, behavioral vowel discrimination and the encoding of these vowels by single auditory-nerve fibers were compared, to elucidate some of the underlying mechanisms of age-related speech-in-noise perception deficits. Methods: Young-adult and quiet-aged Mongolian gerbils, of either sex, were trained to discriminate a deviant naturally-spoken vowel in a sequence of vowel standards against a speech-like background noise. In addition, we recorded responses from single auditory-nerve fibers of young-adult and quiet-aged gerbils while presenting the same speech stimuli. Results: Behavioral vowel discrimination was not significantly affected by aging. For both young-adult and quiet-aged gerbils, the behavioral discrimination between /eː/ and /iː/ was more difficult to make than /eː/ vs. /aː/ or /iː/ vs. /aː/, as evidenced by longer response times and lower d' values. In young-adults, spike timing-based vowel discrimination agreed with the behavioral vowel discrimination, while in quiet-aged gerbils it did not. Paradoxically, discrimination between vowels based on temporal responses was enhanced in aged gerbils for all vowel comparisons. Representation schemes, based on the spectrum of the inter-spike interval histogram, revealed stronger encoding of both the fundamental and the lower formant frequencies in fibers of quiet-aged gerbils, but no qualitative changes in vowel encoding. Elevated thresholds in combination with a fixed stimulus level, i.e., lower sensation levels of the stimuli for old individuals, can explain the enhanced temporal coding of the vowels in noise. Discussion: These results suggest that the altered auditory-nerve discrimination metrics in old gerbils may mask age-related deterioration in the central (auditory) system to the extent that behavioral vowel discrimination matches that of the young adults.

An exact mapping from ReLU networks to spiking neural networks.

Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an exact mapping from a network with Rectified Linear Units (ReLUs) to an SNN that fires exactly one spike per neuron. For our constructive proof, we assume that an arbitrary multi-layer ReLU network with or without convolutional layers, batch normalization and max pooling layers was trained to high performance on some training set. Furthermore, we assume that we have access to a representative example of input data used during training and to the exact parameters (weights and biases) of the trained ReLU network. The mapping from deep ReLU networks to SNNs causes zero percent drop in accuracy on CIFAR10, CIFAR100 and the ImageNet-like data sets Places365 and PASS. More generally our work shows that an arbitrary deep ReLU network can be replaced by an energy-efficient single-spike neural network without any loss of performance.

Gradients of response latencies and temporal precision of auditory neurons extend across the whole inferior colliculus.

Neural responses to acoustic stimulation have long been studied throughout the auditory system to understand how sound information is coded for perception. Within the inferior colliculus (IC), a majority of the studies have focused predominantly on characterizing neural responses within the central region (ICC), as it is viewed as part of the lemniscal system mainly responsible for auditory perception. In contrast, the responses of outer cortices (ICO) have largely been unexplored, though they also function in auditory perception tasks. Therefore, we sought to expand on previous work by completing a three-dimensional (3-D) functional mapping study of the whole IC. We analyzed responses to different pure tone and broadband noise stimuli across all IC subregions and correlated those responses with over 2,000 recording locations across the IC. Our study revealed there are well-organized trends for temporal response parameters across the full IC that do not show a clear distinction at the ICC and ICO border. These gradients span from slow, imprecise responses in the caudal-medial IC to fast, precise responses in the rostral-lateral IC, regardless of subregion, including the fastest responses located in the ICO. These trends were consistent at various acoustic stimulation levels. Weaker spatial trends could be found for response duration and spontaneous activity. Apart from tonotopic organization, spatial trends were not apparent for spectral response properties. Overall, these detailed acoustic response maps across the whole IC provide new insights into the organization and function of the IC.NEW & NOTEWORTHY Study of the inferior colliculus (IC) has largely focused on the central nucleus, with little exploration of the outer cortices. Here, we systematically assessed the acoustic response properties from over 2,000 locations in different subregions of the IC. The results revealed spatial trends in temporal response patterns that span all subregions. Furthermore, two populations of temporal response types emerged for neurons in the outer cortices that may contribute to their functional roles in auditory tasks.

Enhancement of phase-locking in rodents. II. An axonal recording study in chinchilla.

The trapezoid body (TB) contains axons of neurons residing in the anteroventral cochlear nucleus (AVCN) that provide excitatory and inhibitory inputs to the main monaural and binaural nuclei in the superior olivary complex (SOC). To understand the monaural and binaural response properties of neurons in the medial and lateral superior olive (MSO and LSO), it is important to characterize the temporal firing properties of these inputs. Because of its exceptional low-frequency hearing, the chinchilla (Chinchilla lanigera) is one of the widely used small animal models for studies of hearing. However, the characterization of the output of its ventral cochlear nucleus to the nuclei of the SOC is fragmentary. We obtained responses of TB axons to stimuli typically used in binaural studies and compared these responses to those of auditory nerve (AN) fibers, with a focus on temporal coding. We found enhancement of phase-locking and entrainment, i.e., the ability of a neuron to fire action potentials at a certain stimulus phase for nearly every stimulus period, in TB axons relative to AN fibers. Enhancement in phase-locking and entrainment are quantitatively more modest than in the cat but greater than in the gerbil. As in these species, these phenomena occur not only in low-frequency neurons stimulated at their characteristic frequency but also in neurons tuned to higher frequencies when stimulated with low-frequency tones, to which complex phase-locking behavior with multiple modes of firing per stimulus cycle is frequently observed.NEW & NOTEWORTHY The sensitivity of neurons to small time differences in sustained sounds to both ears is important for binaural hearing, and this sensitivity is critically dependent on phase-locking in the monaural pathways. Although studies in cat showed a marked improvement in phase-locking from the peripheral to the central auditory nervous system, the evidence in rodents is mixed. Here, we recorded from AN and TB of chinchilla and found temporal enhancement, though more limited than in cat.

Online spike-based recognition of digits with ultrafast microlaser neurons.

Classification and recognition tasks performed on photonic hardware-based neural networks often require at least one offline computational step, such as in the increasingly popular reservoir computing paradigm. Removing this offline step can significantly improve the response time and energy efficiency of such systems. We present numerical simulations of different algorithms that utilize ultrafast photonic spiking neurons as receptive fields to allow for image recognition without an offline computing step. In particular, we discuss the merits of event, spike-time and rank-order based algorithms adapted to this system. These techniques have the potential to significantly improve the efficiency and effectiveness of optical classification systems, minimizing the number of spiking nodes required for a given task and leveraging the parallelism offered by photonic hardware.

Adaptive STDP-based on-chip spike pattern detection.

A spiking neural network (SNN) is a bottom-up tool used to describe information processing in brain microcircuits. It is becoming a crucial neuromorphic computational model. Spike-timing-dependent plasticity (STDP) is an unsupervised brain-like learning rule implemented in many SNNs and neuromorphic chips. However, a significant performance gap exists between ideal model simulation and neuromorphic implementation. The performance of STDP learning in neuromorphic chips deteriorates because the resolution of synaptic efficacy in such chips is generally restricted to 6 bits or less, whereas simulations employ the entire 64-bit floating-point precision available on digital computers. Previously, we introduced a bio-inspired learning rule named adaptive STDP and demonstrated via numerical simulation that adaptive STDP (using only 4-bit fixed-point synaptic efficacy) performs similarly to STDP learning (using 64-bit floating-point precision) in a noisy spike pattern detection model. Herein, we present the experimental results demonstrating the performance of adaptive STDP learning. To the best of our knowledge, this is the first study that demonstrates unsupervised noisy spatiotemporal spike pattern detection to perform well and maintain the simulation performance on a mixed-signal CMOS neuromorphic chip with low-resolution synaptic efficacy. The chip was designed in Taiwan Semiconductor Manufacturing Company (TSMC) 250 nm CMOS technology node and comprises a soma circuit and 256 synapse circuits along with their learning circuitry.

Channelrhodopsin fluorescent tag replacement for clinical translation of optogenetic hearing restoration.

Sensory restoration by optogenetic neurostimulation provides a promising future alternative to current electrical stimulation approaches. So far, channelrhodopsins (ChRs) typically contain a C-terminal fluorescent protein (FP) tag for visualization that potentially poses an additional risk for clinical translation. Previous work indicated a reduction of optogenetic stimulation efficacy upon FP removal. Here, we further optimized the fast-gating, red-light-activated ChR f-Chrimson to achieve efficient optogenetic stimulation in the absence of the C-terminal FP. Upon FP removal, we observed a massive amplitude reduction of photocurrents in transfected cells in vitro and of optogenetically evoked activity of the adeno-associated virus (AAV) vector-transduced auditory nerve in mice in vivo. Increasing the AAV vector dose restored optogenetically evoked auditory nerve activity but was confounded by neural loss. Of various C-terminal modifications, we found the replacement of the FP by the Kir2.1 trafficking sequence (TSKir2.1) to best restore both photocurrents and optogenetically evoked auditory nerve activity with only mild neural loss few months after dosing. In conclusion, we consider f-Chrimson-TSKir2.1 to be a promising candidate for clinical translation of optogenetic neurostimulation such as by future optical cochlear implants.

Spike timing-dependent plasticity alters electrosensory neuron synaptic strength in vitro but does not consistently predict changes in sensory tuning in vivo.

How do sensory systems optimize detection of behaviorally relevant stimuli when the sensory environment is constantly changing? We addressed the role of spike timing-dependent plasticity (STDP) in driving changes in synaptic strength in a sensory pathway and whether those changes in synaptic strength could alter sensory tuning. It is challenging to precisely control temporal patterns of synaptic activity in vivo and replicate those patterns in vitro in behaviorally relevant ways. This makes it difficult to make connections between STDP-induced changes in synaptic physiology and plasticity in sensory systems. Using the mormyrid species Brevimyrus niger and Brienomyrus brachyistius, which produce electric organ discharges for electrolocation and communication, we can precisely control the timing of synaptic input in vivo and replicate these same temporal patterns of synaptic input in vitro. In central electrosensory neurons in the electric communication pathway, using whole cell intracellular recordings in vitro, we paired presynaptic input with postsynaptic spiking at different delays. Using whole cell intracellular recordings in awake, behaving fish, we paired sensory stimulation with postsynaptic spiking using the same delays. We found that Hebbian STDP predictably alters sensory tuning in vitro and is mediated by NMDA receptors. However, the change in synaptic responses induced by sensory stimulation in vivo did not adhere to the direction predicted by the STDP observed in vitro. Further analysis suggests that this difference is influenced by polysynaptic activity, including inhibitory interneurons. Our findings suggest that STDP rules operating at identified synapses may not drive predictable changes in sensory responses at the circuit level.NEW & NOTEWORTHY We replicated behaviorally relevant temporal patterns of synaptic activity in vitro and used the same patterns during sensory stimulation in vivo. There was a Hebbian spike timing-dependent plasticity (STDP) pattern in vitro, but sensory responses in vivo did not shift according to STDP predictions. Analysis suggests that this disparity is influenced by differences in polysynaptic activity, including inhibitory interneurons. These results suggest that STDP rules at synapses in vitro do not necessarily apply to circuits in vivo.

Heterogeneity of network and coding states in mouse CA1 place cells.

Theta sequences and phase precession shape hippocampal activity and are considered key underpinnings of memory formation. Theta sequences are sweeps of spikes from multiple cells, tracing trajectories from past to future. Phase precession is the correlation between theta firing phase and animal position. Here, we reconsider these temporal processes in CA1 and the computational principles that they are thought to obey. We find stronger heterogeneity than previously described: we identify cells that do not phase precess but reliably express theta sequences. Other cells phase precess only when medium gamma (linked to entorhinal inputs) is strongest. The same cells express more sequences, but not precession, when slow gamma (linked to CA3 inputs) dominates. Moreover, sequences occur independently in distinct cell groups. Our results challenge the view that phase precession is the mechanism underlying the emergence of theta sequences, suggesting a role for CA1 cells in multiplexing diverse computational processes.

A Redundant Cortical Code for Speech Envelope.

Animal communication sounds exhibit complex temporal structure because of the amplitude fluctuations that comprise the sound envelope. In human speech, envelope modulations drive synchronized activity in auditory cortex (AC), which correlates strongly with comprehension (Giraud and Poeppel, 2012; Peelle and Davis, 2012; Haegens and Zion Golumbic, 2018). Studies of envelope coding in single neurons, performed in nonhuman animals, have focused on periodic amplitude modulation (AM) stimuli and use response metrics that are not easy to juxtapose with data from humans. In this study, we sought to bridge these fields. Specifically, we looked directly at the temporal relationship between stimulus envelope and spiking, and we assessed whether the apparent diversity across neurons' AM responses contributes to the population representation of speech-like sound envelopes. We gathered responses from single neurons to vocoded speech stimuli and compared them to sinusoidal AM responses in auditory cortex (AC) of alert, freely moving Mongolian gerbils of both sexes. While AC neurons displayed heterogeneous tuning to AM rate, their temporal dynamics were stereotyped. Preferred response phases accumulated near the onsets of sinusoidal AM periods for slower rates (<8 Hz), and an over-representation of amplitude edges was apparent in population responses to both sinusoidal AM and vocoded speech envelopes. Crucially, this encoding bias imparted a decoding benefit: a classifier could discriminate vocoded speech stimuli using summed population activity, while higher frequency modulations required a more sophisticated decoder that tracked spiking responses from individual cells. Together, our results imply that the envelope structure relevant to parsing an acoustic stream could be read-out from a distributed, redundant population code.SIGNIFICANCE STATEMENT Animal communication sounds have rich temporal structure and are often produced in extended sequences, including the syllabic structure of human speech. Although the auditory cortex (AC) is known to play a crucial role in representing speech syllables, the contribution of individual neurons remains uncertain. Here, we characterized the representations of both simple, amplitude-modulated sounds and complex, speech-like stimuli within a broad population of cortical neurons, and we found an overrepresentation of amplitude edges. Thus, a phasic, redundant code in auditory cortex can provide a mechanistic explanation for segmenting acoustic streams like human speech.

Binaural temporal coding and the middle ear muscle reflex in audiometrically normal young adults.

Noise exposure may damage the synapses that connect inner hair cells with auditory nerve fibers, before outer hair cells are lost. In humans, this cochlear synaptopathy (CS) is thought to decrease the fidelity of peripheral auditory temporal coding. In the current study, the primary hypothesis was that higher middle ear muscle reflex (MEMR) thresholds, as a proxy measure of CS, would be associated with smaller values of the binaural intelligibility level difference (BILD). The BILD, which is a measure of binaural temporal coding, is defined here as the difference in thresholds between the diotic and the antiphasic versions of the digits in noise (DIN) test. This DIN BILD may control for factors unrelated to binaural temporal coding such as linguistic, central auditory, and cognitive factors. Fifty-six audiometrically normal adults (34 females) aged 18 - 30 were tested. The test battery included standard pure tone audiometry, tympanometry, MEMR using a 2 kHz elicitor and 226 Hz and 1 kHz probes, the Noise Exposure Structured Interview, forward digit span test, extended high frequency (EHF) audiometry, and diotic and antiphasic DIN tests. The study protocol was pre-registered prior to data collection. MEMR thresholds did not predict the DIN BILD. Secondary analyses showed no association between MEMR thresholds and the individual diotic and antiphasic DIN thresholds. Greater lifetime noise exposure was non-significantly associated with higher MEMR thresholds, larger DIN BILD values, and lower (better) antiphasic DIN thresholds, but not with diotic DIN thresholds, nor with EHF thresholds. EHF thresholds were associated with neither MEMR thresholds nor any of the DIN outcomes, including the DIN BILD. Results provide no evidence that young, audiometrically normal people incur CS with impacts on binaural temporal processing.

Analyzing time-to-first-spike coding schemes: A theoretical approach.

Spiking neural networks (SNNs) using time-to-first-spike (TTFS) codes, in which neurons fire at most once, are appealing for rapid and low power processing. In this theoretical paper, we focus on information coding and decoding in those networks, and introduce a new unifying mathematical framework that allows the comparison of various coding schemes. In an early proposal, called rank-order coding (ROC), neurons are maximally activated when inputs arrive in the order of their synaptic weights, thanks to a shunting inhibition mechanism that progressively desensitizes the neurons as spikes arrive. In another proposal, called NoM coding, only the first N spikes of M input neurons are propagated, and these "first spike patterns" can be readout by downstream neurons with homogeneous weights and no desensitization: as a result, the exact order between the first spikes does not matter. This paper also introduces a third option-"Ranked-NoM" (R-NoM), which combines features from both ROC and NoM coding schemes: only the first N input spikes are propagated, but their order is readout by downstream neurons thanks to inhomogeneous weights and linear desensitization. The unifying mathematical framework allows the three codes to be compared in terms of discriminability, which measures to what extent a neuron responds more strongly to its preferred input spike pattern than to random patterns. This discriminability turns out to be much higher for R-NoM than for the other codes, especially in the early phase of the responses. We also argue that R-NoM is much more hardware-friendly than the original ROC proposal, although NoM remains the easiest to implement in hardware because it only requires binary synapses.

Training Spiking Neural Networks for Reinforcement Learning Tasks With Temporal Coding Method.

Recent years witness an increasing demand for using spiking neural networks (SNNs) to implement artificial intelligent systems. There is a demand of combining SNNs with reinforcement learning architectures to find an effective training method. Recently, temporal coding method has been proposed to train spiking neural networks while preserving the asynchronous nature of spiking neurons to preserve the asynchronous nature of SNNs. We propose a training method that enables temporal coding method in RL tasks. To tackle the problem of high sparsity of spikes, we introduce a self-incremental variable to push each spiking neuron to fire, which makes SNNs fully differentiable. In addition, an encoding method is proposed to solve the problem of information loss of temporal-coded inputs. The experimental results show that the SNNs trained by our proposed method can achieve comparable performance of the state-of-the-art artificial neural networks in benchmark tasks of reinforcement learning.

A simple neuronal model with intrinsic saturation of the firing frequency.

We present a comparison of the intrinsic saturation of firing frequency in four simple neural models: leaky integrate-and-fire model, leaky integrate-and-fire model with reversal potentials, two-point leaky integrate-and-fire model, and a two-point leaky integrate-and-fire model with reversal potentials. "Two-point" means that the equivalent circuit has two nodes (dendritic and somatic) instead of one (somatic only). The results suggest that the reversal potential increases the slope of the "firing rate vs input" curve due to a smaller effective membrane time constant, but does not necessarily induce saturation of the firing rate. The two-point model without the reversal potential does not limit the voltage or the firing rate. In contrast to the previous models, the two-point model with the reversal potential limits the asymptotic voltage and the firing rate, which is the main result of this paper. The case of excitatory inputs is considered first and followed by the case of both excitatory and inhibitory inputs.