Recurrent spiking neural networks (RSNN) in the human brain learn to perform a wide range of perceptual, cognitive and motor tasks very efficiently in terms of energy consumption and requires very few examples. This motivates the search for biologically inspired learning rules for RSNNs to improve our understanding of brain computation and the efficiency of artificial intelligence. Several spiking models and learning rules have been proposed, but it remains a challenge to design RSNNs whose learning relies on biologically plausible mechanisms and are capable of solving complex temporal tasks. In this paper, we derive a learning rule, local to the synapse, from a simple mathematical principle, the maximization of the likelihood for the network to solve a specific task. We propose a novel target-based learning scheme in which the learning rule derived from likelihood maximization is used to mimic a specific spiking pattern that encodes the solution to complex temporal tasks. This method makes the learning extremely rapid and precise, outperforming state of the art algorithms for RSNNs. We demonstrate the capacity of our model to tackle several problems like learning multidimensional trajectories and solving the classical temporal XOR benchmark. Finally, we show that an online approximation of the gradient ascent, in addition to guaranteeing complete locality in time and space, allows learning after very few presentations of the target output. Our model can be applied to different types of biological neurons. The analytically derived plasticity learning rule is specific to each neuron model and can produce a theoretical prediction for experimental validation.
Based upon the membrane currents generated by an action potential in a biologically realistic model of a pyramidal, hippocampal cell within rat CA1, we perform a moment expansion of the extracellular field potential. We decompose the potential into both inverse and classical moments and show that this method is a rapid and efficient way to calculate the extracellular field both near and far from the cell body. The action potential gives rise to a large quadrupole moment that contributes to the extracellular field up to distances of almost 1 cm. This method will serve as a starting point in con…
University of Leeds（利兹大学）；Tsinghua University（清华大学）；Fujian Normal University（福建师范大学）
One stream of reinforcement learning research is exploring biologically plausible models and algorithms to simulate biological intelligence and fit neuromorphic hardware. Among them, reward-modulated spike-timing-dependent plasticity (R-STDP) is a recent branch with good potential in energy efficiency. However, current R-STDP methods rely on heuristic designs of local learning rules, thus requiring task-specific expert knowledge. In this paper, we consider a spiking recurrent winner-take-all network, and propose a new R-STDP method, spiking variational policy gradient (SVPG), whose local learn…
Understanding how the dynamics of neural networks is shaped by the computations they perform is a fundamental question in neuroscience. Recently, the framework of efficient coding proposed a theory of how spiking neural networks can compute low-dimensional stimulus signals with high efficiency. Efficient spiking networks are based on time-dependent minimization of a loss function related to information coding with spikes. To inform the understanding of the function and dynamics of biological networks in the brain, however, the mathematical models have to be informed by biology and obey the sam…
Deep neural networks have surpassed human performance in key visual challenges such as object recognition, but require a large amount of energy, computation, and memory. In contrast, spiking neural networks (SNNs) have the potential to improve both the efficiency and biological plausibility of object recognition systems. Here we present a SNN model that uses spike-latency coding and winner-take-all inhibition (WTA-I) to efficiently represent visual stimuli using multi-scale parallel processing. Mimicking neuronal response properties in early visual cortex, images were preprocessed with three d…
There has been a strong push recently to examine biological scale simulations of neuromorphic algorithms to achieve stronger inference capabilities. This paper presents a set of piecewise linear spiking neuron models, which can reproduce different behaviors, similar to the biological neuron, both for a single neuron as well as a network of neurons. The proposed models are investigated, in terms of digital implementation feasibility and costs, targeting large scale hardware implementation. Hardware synthesis and physical implementations on FPGA show that the proposed models can produce precise …
We introduce a novel, biologically plausible local learning rule that provably increases the robustness of neural dynamics to noise in nonlinear recurrent neural networks with homogeneous nonlinearities. Our learning rule achieves higher noise robustness without sacrificing performance on the task and without requiring any knowledge of the particular task. The plasticity dynamics -- an integrable dynamical system operating on the weights of the network -- maintains a multiplicity of conserved quantities, most notably the network's entire temporal map of input to output trajectories. The outcom…
National University of Singapore（新加坡国立大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Chulalongkorn University（朱拉隆功大学）；Awecom, Inc（奥威康公司）；University of California, Berkeley（加州大学伯克利分校）
Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the synapse. By exploiting asymmetry in the connections between binary neurons, we show that MPN can be trained to robustly memorize multiple spatiotemporal patterns of binary vectors, generalizing the ability of the symmetric Hopfield…
The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of synaptic delays could help us in developing effective brain-inspired computational models in providing aligned insights with the experimental evidence. In this paper, we propose an unsupervised biologically plausible learning rule for adjusting the synaptic delays in spiking neural networks. Then, we provided some mathematical proofs to show that our learning rule …
Department of Computer Science, Rutgers University（罗格斯大学计算机科学系）
Spiking neural networks (SNN) are delivering energy-efficient, massively parallel, and low-latency solutions to AI problems, facilitated by the emerging neuromorphic chips. To harness these computational benefits, SNN need to be trained by learning algorithms that adhere to brain-inspired neuromorphic principles, namely event-based, local, and online computations. Yet, the state-of-the-art SNN training algorithms are based on backprop that does not follow the above principles. Due to its limited biological plausibility, the application of backprop to SNN requires non-local feedback pathways fo…
We present a method of estimating the gradient of an objective function with respect to the synaptic weights of a spiking neural network. The method works by measuring the fluctuations in the objective function in response to dynamic perturbation of the membrane conductances of the neurons. It is compatible with recurrent networks of conductance-based model neurons with dynamic synapses. The method can be interpreted as a biologically plausible synaptic learning rule, if the dynamic perturbations are generated by a special class of ``empiric'' synapses driven by random spike trains from an ext…
It is widely believed that the perceptual system of an organism is optimized for the properties of the environment to which it is exposed. A specific instance of this principle known as the Infomax principle holds that the purpose of early perceptual processing is to maximize the mutual information between the neural coding and the incoming sensory signal. In this article, we present a method to implement this principle accurately with a local, spike-based, and continuous-time learning rule.
An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; (iii) neuronal outputs are nonnegative. Closest is the work by Pehle…
The backpropagation algorithm is often debated for its biological plausibility. However, various learning methods for neural architecture have been proposed in search of more biologically plausible learning. Most of them have tried to solve the "weight transport problem" and try to propagate errors backward in the architecture via some alternative methods. In this work, we investigated a slightly different approach that uses only the local information which captures spike timing information with no propagation of errors. The proposed learning rule is derived from the concepts of spike timing d…
Spiking Neural Network (SNN) is considered more biologically realistic and power-efficient as it imitates the fundamental mechanism of the human brain. Recently, backpropagation (BP) based SNN learning algorithms that utilize deep learning frameworks have achieved good performance. However, bio-interpretability is partially neglected in those BP-based algorithms. Toward bio-plausible BP-based SNNs, we consider three properties in modeling spike activities: Multiplicity, Adaptability, and Plasticity (MAP). In terms of multiplicity, we propose a Multiple-Spike Pattern (MSP) with multiple spike t…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain unresolved or controversial. In particular, current implementations often involve separate value and error neurons and require symmetric forward and backward weights across different brain regions. These features have not been experimentally confirmed. In this work, we show that the PC framework in the linear regime can be modified to map faithfully onto th…
Flatiron Institute（弗莱德哈钦森研究所）；Columbia University（哥伦比亚大学）；NYU Medical Center（纽约大学医学中心）
Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is c…
University of Washington（华盛顿大学）；Allen Institute for Brain Science（艾伦脑科学研究所）；McGill University（麦吉尔大学）；Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Montreal Neurological Institute（蒙特利尔神经学研究所）；Université de Montréal（蒙特利尔大学）
To unveil how the brain learns, ongoing work seeks biologically-plausible approximations of gradient descent algorithms for training recurrent neural networks (RNNs). Yet, beyond task accuracy, it is unclear if such learning rules converge to solutions that exhibit different levels of generalization than their nonbiologically-plausible counterparts. Leveraging results from deep learning theory based on loss landscape curvature, we ask: how do biologically-plausible gradient approximations affect generalization? We first demonstrate that state-of-the-art biologically-plausible learning rules fo…
In this paper we explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. It consists of feedback controllers that learn to achieve a desired state by selecting the errors that should drive them. This selection happens through a family of differential Hebbian learning rules that, through interaction with the environment, can learn to control systems where the error responds monotonically to the control signal. We next show that in a more general case, neural reinforcement learning can be coupled with a feedback controller to reduce er…
Backpropagation is widely used to train artificial neural networks, but its relationship to synaptic plasticity in the brain is unknown. Some biological models of backpropagation rely on feedback projections that are symmetric with feedforward connections, but experiments do not corroborate the existence of such symmetric backward connectivity. Random feedback alignment offers an alternative model in which errors are propagated backward through fixed, random backward connections. This approach successfully trains shallow models, but learns slowly and does not perform well with deeper models or…
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been used to model spiking neural networks. Using mean-field approximation, the response of the network to a stimulus is computed and we provide a notion of stimulus sensitivity. It appears that the maximal sensitivity is achieved in the sub-critical regime, yet almost critical for a range of biologically relevant parameters.
Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of simplified neuron models, requiring the coupling of the neuronal membrane potential with its delayed value. However, this coupling has no obvious biological correlate. Here we propose a canonical neuronal microcircuit with standard chemical synapses, where the delayed inhibition is provided by an interneuron. In this biologically plausible scenario, a smooth tran…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；CAS Center for Excellence in Brain Science and Intelligence Technology, Chinese Academy of Sciences（中国科学院脑科学与智能技术卓越创新中心）
Spiking neural networks (SNNs) possess energy-efficient potential due to event-based computation. However, supervised training of SNNs remains a challenge as spike activities are non-differentiable. Previous SNNs training methods can be generally categorized into two basic classes, i.e., backpropagation-like training methods and plasticity-based learning methods. The former methods are dependent on energy-inefficient real-valued computation and non-local transmission, as also required in artificial neural networks (ANNs), whereas the latter are either considered to be biologically implausible …
Flatiron Institute（弗莱提伦研究所）；Rutgers University（罗格斯大学）；NYU Medical Center（纽约大学医学中心）
The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer network, we derive an algorithm for training a neural network which avoids this problem by not requiring explicit error computation and backpropagation. Furthermore, our algorithm maps onto a neural network that bears a remarkable resemblance to the connectivity structure and learning rules of the cortex. We find that our algorithm empirically performs comparabl…
The design and analysis of spiking neural network algorithms will be accelerated by the advent of new theoretical approaches. In an attempt at such approach, we provide a principled derivation of a spiking algorithm for unsupervised learning, starting from the nonnegative similarity matching cost function. The resulting network consists of integrate-and-fire units and exhibits local learning rules, making it biologically plausible and also suitable for neuromorphic hardware. We show in simulations that the algorithm can perform sparse feature extraction and manifold learning, two tasks which c…
Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model paramet…
The spectacular successes of recurrent neural network models where key parameters are adjusted via backpropagation-based gradient descent have inspired much thought as to how biological neuronal networks might solve the corresponding synaptic credit assignment problem. There is so far little agreement, however, as to how biological networks could implement the necessary backpropagation through time, given widely recognized constraints of biological synaptic network signaling architectures. Here, we propose that extra-synaptic diffusion of local neuromodulators such as neuropeptides may afford …
Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation Analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multi-channel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and…
Flatiron Institute（弗拉特研究所）；NYU Medical Center（纽约大学医学中心）；Rutgers University（罗格斯大学）
The brain effortlessly solves blind source separation (BSS) problems, but the algorithm it uses remains elusive. In signal processing, linear BSS problems are often solved by Independent Component Analysis (ICA). To serve as a model of a biological circuit, the ICA neural network (NN) must satisfy at least the following requirements: 1. The algorithm must operate in the online setting where data samples are streamed one at a time, and the NN computes the sources on the fly without storing any significant fraction of the data in memory. 2. The synaptic weight update is local, i.e., it depends o…
Shahid Rajaee Teacher Training University（沙希德·拉贾伊师范大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所（IPM））
Brain can recognize different objects as ones that it has experienced before. The recognition accuracy and its processing time depend on task properties such as viewing condition, level of noise and etc. Recognition accuracy can be well explained by different models. However, less attention has been paid to the processing time and the ones that do, are not biologically plausible. By extracting features temporally as well as utilizing an accumulation to bound decision making model, an object recognition model accounting for both recognition time and accuracy is proposed. To temporally extract i…
Populations of neurons display an extraordinary diversity in the behaviors they affect and display. Machine learning techniques have recently emerged that allow us to create networks of model neurons that display behaviours of similar complexity. Here, we demonstrate the direct applicability of one such technique, the FORCE method, to spiking neural networks. We train these networks to mimic dynamical systems, classify inputs, and store discrete sequences that correspond to the notes of a song. Finally, we use FORCE training to create two biologically motivated model circuits. One is inspired …
Gatsby Computational Neuroscience Unit（盖茨比计算神经科学单位）；University College London（伦敦大学学院）；London, W1T 4JG（伦敦W1T 4JG（地址，非机构））
The state-of-the art machine learning approach to training deep neural networks, backpropagation, is implausible for real neural networks: neurons need to know their outgoing weights; training alternates between a bottom-up forward pass (computation) and a top-down backward pass (learning); and the algorithm often needs precise labels of many data points. Biologically plausible approximations to backpropagation, such as feedback alignment, solve the weight transport problem, but not the other two. Thus, fully biologically plausible learning rules have so far remained elusive. Here we present a…
Victoria University of Wellington（惠灵顿维多利亚大学）；ETH Zurich（苏黎世联邦理工学院）
Error backpropagation is an extremely effective algorithm for assigning credit in artificial neural networks. However, weight updates under Backprop depend on lengthy recursive computations and require separate output and error messages -- features not shared by biological neurons, that are perhaps unnecessary. In this paper, we revisit Backprop and the credit assignment problem. We first decompose Backprop into a collection of interacting learning algorithms; provide regret bounds on the performance of these sub-algorithms; and factorize Backprop's error signals. Using these results, we deriv…
The Backpropagation algorithm relies on the abstraction of using a neural model that gets rid of the notion of time, since the input is mapped instantaneously to the output. In this paper, we claim that this abstraction of ignoring time, along with the abrupt input changes that occur when feeding the training set, are in fact the reasons why, in some papers, Backprop biological plausibility is regarded as an arguable issue. We show that as soon as a deep feedforward network operates with neurons with time-delayed response, the backprop weight update turns out to be the basic equation of a biol…
Spike-timing dependent plasticity (STDP) which observed in the brain has proven to be important in biological learning. On the other hand, artificial neural networks use a different way to learn, such as Back-Propagation or Contrastive Hebbian Learning. In this work, we propose a new framework called mstdp that learn almost the same way biological learning use, it only uses STDP rules for supervised and unsupervised learning and don' t need a global loss or other supervise information. The framework works like an auto-encoder by making each input neuron also an output neuron. It can make predi…
Communication University of China（中国传媒大学）；State Key Laboratory of Mathematical Engineering and Advanced Computing（数学工程与先进计算国家重点实验室）
The problem of catastrophic forgetting has a history of more than 30 years and has not been completely solved yet. Since the human brain has natural ability to perform continual lifelong learning, learning from the brain may provide solutions to this problem. In this paper, we propose a novel biologically plausible audio-visual integration model (AVIM) based on the assumption that the integration of audio and visual perceptual information in the medial temporal lobe during learning is crucial to form concepts and make continual learning possible. Specifically, we use multi-compartment Hodgkin-…
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory rhythms using STDP, and show that scaling is necessary to balance both positive and negative changes in input from potentiation and atrophy. We discuss some of the issues that arise when considering synaptic scaling in such a model, and show that scaling regulates activity whilst allowing learning to remain unaltered.
University of Chicago（芝加哥大学）；Department of Statistics（统计系）
We develop biologically plausible training mechanisms for self-supervised learning (SSL) in deep networks. Specifically, by biological plausible training we mean (i) All updates of weights are based on current activities of pre-synaptic units and current, or activity retrieved from short term memory of post synaptic units, including at the top-most error computing layer, (ii) Complex computations such as normalization, inner products and division are avoided (iii) Asymmetric connections between units, (iv) Most learning is carried out in an unsupervised manner. SSL with a contrastive loss sati…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Universite de Montreal（蒙特利尔大学）；Institute of Neuroinformatics（神经信息学研究所）；University of Zurich（苏黎世大学）；ETH Zurich（苏黎世联邦理工学院）；University of Bern（伯尔尼大学）
In the past few years, deep learning has transformed artificial intelligence research and led to impressive performance in various difficult tasks. However, it is still unclear how the brain can perform credit assignment across many areas as efficiently as backpropagation does in deep neural networks. In this paper, we introduce a model that relies on a new role for a neuronal inhibitory machinery, referred to as ghost units. By cancelling the feedback coming from the upper layer when no target signal is provided to the top layer, the ghost units enables the network to backpropagate errors and…
The estimation of causal network architectures in the brain is fundamental for understanding cognitive information processes. However, access to the dynamic processes underlying cognition is limited to indirect measurements of the hidden neuronal activity, for instance through fMRI data. Thus, estimating the network structure of the underlying process is challenging. In this article, we embed an adaptive importance sampler called Adaptive Path Integral Smoother (APIS) into the Expectation-Maximization algorithm to obtain point estimates of causal connectivity. We demonstrate on synthetic data …
Robotic vision introduces requirements for real-time processing of fast-varying, noisy information in a continuously changing environment. In a real-world environment, convenient assumptions, such as static camera systems and deep learning algorithms devouring high volumes of ideally slightly-varying data are hard to survive. Leveraging on recent studies on the neural connectome associated with eye movements, we designed a neuromorphic oculomotor controller and placed it at the heart of our in-house biomimetic robotic head prototype. The controller is unique in the sense that (1) all data are …
In this work we study biological neural networks from an algorithmic perspective, focusing on understanding tradeoffs between computation time and network complexity. Our goal is to abstract real neural networks in a way that, while not capturing all interesting features, preserves high-level behavior and allows us to make biologically relevant conclusions. Towards this goal, we consider the implementation of algorithmic primitives in a simple yet biologically plausible model of $stochastic\ spiking\ neural\ networks$. In particular, we show how the stochastic behavior of neurons in this model…
Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of dis…
The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivati…
Gatsby Unit, UCL（伦敦大学学院盖茨比单元）；DeepMind；CoMPLEX, UCL（伦敦大学学院CoMPLEX）
Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously problematic, since they require weight sharing - something real neurons simply cannot do. Consequently, while neurons in the brain can be locally connected (one of the features of convolutional networks), they cannot be convolutional. Locally connected but non-convolutional networks, however, significantly underperform convolutional ones. This is troublesome for …
