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Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…

Probability · Mathematics 2018-11-05 Fuqing Gao , Lingjiong Zhu

Traditional neuron models use analog values for information representation and computation, while all-or-nothing spikes are employed in the spiking ones. With a more brain-like processing paradigm, spiking neurons are more promising for…

Neural and Evolutionary Computing · Computer Science 2021-02-05 Qiang Yu , Shiming Song , Chenxiang Ma , Linqiang Pan , Kay Chen Tan

Bayesian inference provides a principled framework for understanding brain function, while neural activity in the brain is inherently spike-based. This paper bridges these two perspectives by designing spiking neural networks that simulate…

Neurons and Cognition · Quantitative Biology 2026-01-01 Sepideh Adamiat , Wouter M. Kouw , Bert de Vries

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…

Machine Learning · Statistics 2024-02-08 Sobin Joseph , Shashi Jain

Artificial Intelligence has looked into biological systems as a source of inspiration. Although there are many aspects of the brain yet to be discovered, neuroscience has found evidence that the connections between neurons continuously grow…

Neural and Evolutionary Computing · Computer Science 2020-10-29 Javier Lopez Randulfe , Leon Bonde Larsen

Deep learning has recently led to great successes in tasks such as image recognition (e.g Krizhevsky et al., 2012). However, deep networks are still outmatched by the power and versatility of the brain, perhaps in part due to the richer…

Machine Learning · Statistics 2014-03-25 David P. Reichert , Thomas Serre

In this article, we review a class of neuro-mimetic computational models that we place under the label of spiking predictive coding. Specifically, we review the general framework of predictive processing in the context of neurons that emit…

Neurons and Cognition · Quantitative Biology 2024-09-10 Antony W. N'dri , William Gebhardt , Céline Teulière , Fleur Zeldenrust , Rajesh P. N. Rao , Jochen Triesch , Alexander Ororbia

The excitability property of spiking neurons describes their capability to output an action potential as a real-time response to an input synaptic excitation current and is central to the event-based neuromorphic computing paradigm. The…

Statistical Mechanics · Physics 2025-11-18 Léopold Van Brandt , Grégoire Brandsteert , Denis Flandre

Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A…

Neurons and Cognition · Quantitative Biology 2015-06-19 Sadra Sadeh , Stefan Rotter

Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the…

Neural and Evolutionary Computing · Computer Science 2022-10-27 Alexander Henkes , Jason K. Eshraghian , Henning Wessels

The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…

Statistics Theory · Mathematics 2024-08-20 Tsz-Kit Jeffrey Kwan , Feng Chen , William Dunsmuir

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability…

Neurons and Cognition · Quantitative Biology 2013-06-14 Einat Granot-Atedgi , Gašper Tkačik , Ronen Segev , Elad Schneidman

Spiking Neural Networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…

Signal Processing · Electrical Eng. & Systems 2019-10-22 Hyeryung Jang , Osvaldo Simeone , Brian Gardner , André Grüning

The human brain constantly learns and rapidly adapts to new situations by integrating acquired knowledge and experiences into memory. Developing this capability in machine learning models is considered an important goal of AI research since…

Artificial Intelligence · Computer Science 2023-06-08 Arsham Gholamzadeh Khoee , Alireza Javaheri , Saeed Reza Kheradpisheh , Mohammad Ganjtabesh

Understanding cognitive processes in the brain demands sophisticated models capable of replicating neural dynamics at large scales. We present a physiologically inspired speech recognition architecture, compatible and scalable with deep…

Computation and Language · Computer Science 2024-09-26 Alexandre Bittar , Philip N. Garner

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so…

Neural and Evolutionary Computing · Computer Science 2016-09-08 Davide Zambrano , Sander M. Bohte

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

Neurons and Cognition · Quantitative Biology 2018-11-30 Zhi-Qin John Xu , Douglas Zhou , David Cai

Recently, brain-inspired computing models have shown great potential to outperform today's deep learning solutions in terms of robustness and energy efficiency. Particularly, Spiking Neural Networks (SNNs) and HyperDimensional Computing…

Neural and Evolutionary Computing · Computer Science 2021-10-04 Zhuowen Zou , Haleh Alimohamadi , Farhad Imani , Yeseong Kim , Mohsen Imani

Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…

Neurons and Cognition · Quantitative Biology 2017-05-24 Sophie Denève , Alireza Alemi , Ralph Bourdoukan

We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…

Statistical Finance · Quantitative Finance 2021-09-17 Maxime Morariu-Patrichi , Mikko S. Pakkanen