The paper extends the Transmission Neural Network model to include inhibitory connections and neurotransmitter populations. It characterizes neuron firing probabilities under technical assumptions and shows that these can be represented by a neural network with continuous two‑dimensional neuron states. The authors also derive a limit network model as the number of neurotransmitters at all synaptic connections tends to infinity and provide sufficient conditions for its stability and contraction properties.
arXiv:2608. 15335v1 Announce Type: new Abstract: We consider for an arbitrary fixed $\rho$ and for each positive integer $n$ a multilayer feedforward artificial neural network with $\rho$ layers, $n$ neurons in the first layer (the input layer) and only one neuron, the output neuron, in the last layer.
arXiv:2610. 22484v1 Announce Type: cross Abstract: The input space of single-spike neural networks decomposes into causal pieces, and the number of causal pieces has been shown to provide a lower bound on the approximation error for some spiking neural networks.
arXiv:2507.10383v5 Announce Type: replace-cross Abstract: Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neu...
The paper demonstrates that for a broad class of spiking neuron models, including the leaky integrate‑and‑fire with subtractive reset, any approximation bound proven for multi‑spike networks can be translated to an equivalent single‑spike network with only a linear change in neuron count, and vice versa. This establishes that single‑spike and multi‑spike neural networks possess identical approximation capabilities for general machine learning tasks. Consequently, existing approximation results for single‑spike networks automatically extend to the multi‑spike case.
arXiv:2605. 30370v2 Announce Type: replace-cross Abstract: From their inception in the 1950s, artificial neural networks (ANNs) started using the so-called point neuron model then prevalent in neuroscience, hoping that this analogy would allow for a better emulation of brain function.
arXiv:2512.12767v2 Announce Type: replace-cross Abstract: Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation...
arXiv:2607. 11540v1 Announce Type: cross Abstract: We study tropical circuits with scalar multiplication gates, that is, algebraic circuits whose gates implement $\max$, $+$, or multiplication with a positive constant.
The paper introduces a framework for defining and certifying computational sufficiency in neural systems constrained by a connectome. It formalises sufficiency as a cost-indexed family of neuron subsets conditioned on a task and a tolerance pair, and certifies candidate circuits using one-sided bounds over held-out parameter draws. Experiments on a walking simulator demonstrate that the published 148-neuron circuit is uniquely sufficient, while variations in task or tolerance yield different sufficient subsets, highlighting that sufficiency is set-valued and task-dependent.
arXiv:2605. 19178v2 Announce Type: replace-cross Abstract: The great success of neural networks primarily arises from the presence of the large number of weight parameters combined with nonlinearities in the input-output relationship of single neurons.
arXiv:2610.08750v1 Announce Type: new Abstract: Petri nets have been used to describe chemical processes such as reactions.They map well to chemistry: Places are the bonds between atoms and the free...
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.
arXiv:2606. 31700v1 Announce Type: new Abstract: Biological neural circuits obey Dale's principle: each neuron's synapses are uniformly excitatory or inhibitory.