These clusters of neurons form large hierarchical modules along the cortex.

Attention is the brain's ability to selectively focus on a few specific aspects while ignoring irrelevant ones. This biological principle inspired the attention mechanism in modern Transformers. Transformers now underpin large language models (LLMs) such as GPT, but at the cost of massive training and inference energy, leading to a large carbon footprint. While brain attention emerges from neural circuits, Transformer attention relies on dot-product similarity to weight elements in the input sequence. Neuromorphic computing, especially spiking neural networks (SNNs), offers a brain-inspired path to energy-efficient intelligence. Despite recent work on attention-based spiking Transformers, the core attention layer remains non-neuromorphic. Current spiking attention (i) relies on dot-product or element-wise similarity suited to floating-point operations, not event-driven spikes; (ii) keeps attention matrices that suffer from the von Neumann bottleneck, limiting in-memory computing; and (iii) still diverges from brain-like computation. To address these issues, we propose the Spiking STDP Transformer (S$^{2}$TDPT), a neuromorphic Transformer that implements self-attention through spike-timing-dependent plasticity (STDP), embedding query--key correlations in synaptic weights. STDP, a core mechanism of memory and learning in the brain and widely studied in neuromorphic devices, naturally enables in-memory computing and supports non-von Neumann hardware. On CIFAR-10 and CIFAR-100, our model achieves 94.35\% and 78.08\% accuracy with only four timesteps and 0.49 mJ on CIFAR-100, an 88.47\% energy reduction compared to a standard ANN Transformer. Grad-CAM shows that the model attends to semantically relevant regions, enhancing interpretability. Overall, S$^{2}$TDPT illustrates how biologically inspired attention can yield energy-efficient, hardware-friendly, and explainable neuromorphic models.

Recent extensions of the Perceptron, as e.g. the Tempotron, suggest that this theoretical concept is highly relevant also for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron and of its variants might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if the respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons are efficiently learned. The proposed mechanism might underly the acquisition of mappings of spatio-temporal activity patterns in one area of the brain onto other spatio-temporal spike patterns in another region and of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

This paper introduces Bio-Inspired Mamba (BIM), a novel online learning framework for selective state space models that integrates biological learning principles with the Mamba architecture. BIM combines Real-Time Recurrent Learning (RTRL) with Spike-Timing-Dependent Plasticity (STDP)-like local learning rules, addressing the challenges of temporal locality and biological plausibility in training spiking neural networks. Our approach leverages the inherent connection between backpropagation through time and STDP, offering a computationally efficient alternative that maintains the ability to capture long-range dependencies. We evaluate BIM on language modeling, speech recognition, and biomedical signal analysis tasks, demonstrating competitive performance against traditional methods while adhering to biological learning principles. Results show improved energy efficiency and potential for neuromorphic hardware implementation. BIM not only advances the field of biologically plausible machine learning but also provides insights into the mechanisms of temporal information processing in biological neural networks.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.

Recent extensions of the Perceptron as the Tempotron and the Chronotron suggest that this theoretical concept is highly relevant for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if these respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons and Chronotrons are learned. The proposed mechanism enables incremental associative learning from a continuous stream of patterns and might therefore underly the acquisition of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

Recent extensions of the Perceptron, as e.g. the Tempotron, suggest that this theoretical concept is highly relevant also for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron and of its variants might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if the respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons are efficiently learned. The proposed mechanism might underly the acquisition of mappings of spatio-temporal activity patterns in one area of the brain onto other spatio-temporal spike patterns in another region and of long term memories in cortex.

Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptation of brain neurons during the learning process. It was introduced by Donald Hebb in his 1949 book The Organization of Behavior.[1] The theory is also called Hebb's rule, Hebb's postulate, and cell assembly theory. Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability.

Recent extensions of the Perceptron, as e.g. the Tempotron, suggest that this theoretical concept is highly relevant also for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron and of its variants might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if the respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons are efficiently learned. The proposed mechanism might underly the acquisition of mappings of spatio-temporal activity patterns in one area of the brain onto other spatio-temporal spike patterns in another region and of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.